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Full text of "Heat for engineers : a treatise on heat with special regard to its practical applications"

jfmsfcurg edmical manuals 




EDITOR OF THE SERIES 



PROFESSOR SILVANUS P. THOMPSON 



D.Sc. B.A. F.R.S. M.I.F..E. ETC. 



BY THE SAME AUTHOR 



PYROMETRY 

A Practical Treatise on the Measurement 
of High Temperature 

60 illustrations, 200 pp. cr. 8vo., cloth, 
5/- net. 



E. & F. N. SPON, Ltd. 



HEAT FOR ENGINEERS 



3V featts* on 



WITH SPECIAL REGARD TO ITS PRACTICAL 
APPLICATIONS 



BY 



CHAS. R. DARLING 

Associate of the Royal College of Seienoe, Dublin ; Whitworth Exhibitioner ; 

Fellow of the Institute of Chemistry, eta. ; Demonstrator in the 

Department of Applied Physios and Electrical Engineering, 

and Lecturer on Heat at the City and Quilds 

Technical College, Finsbury, E.C. 



SECOND EDITION, REVISED 



110 ILL'JSTPAYIONS 




Xonfcon : 

E. & F. N. SPON, LTD., 57 HAYMARKET 



Iftew 
SPON & CHAMBERLAIN, 123 LIBERTY STREET 

1912 



(Ti <J 



J 



CONTENTS. 



CHAPTER I. 

HEAT AS A FORM OF ENERGY. UNITS. 

Nature of heat Rumford's experiments Joule's experiments Connection 
between heat and other forms of energy Conservation of energy 
Heat units Connection between heat units and other energy units 
Useful constants and miscellaneous data ... 1 



CHAPTER II. 

METHODS OF PRODUCING HEAT. THE PROPERTIES, USES 
AND EVALUATION OF FUELS. 

Heat produced by chemical action, electricity, friction, impact, compression 
of gases, molecular rearrangement, and radium Fuels : solid, liquid and 
gaseous Fuel calorimeters Calorific values and evaporative powers 
of various solid fuels Air required for combustion Prevention of 
smoke Liquid fuels Gaseous fuels Methods of producing high tem- 
peratures Siemens' regenerative furnace Electric furnaces Thermit 



CHAPTER III. 

SPECIFIC HEAT. 

Thermal capacity Specific heat Method of mixtures Method of fusion 
Bunsen's ice calorimeter Condensation method Joly's steam calori- 
meter Cooling method Two specific heats of gases, at constant 
pressure and constant volume Table of specific heats Effect of 
temperature on specific heat Dulong and Petit's law. 



CHAPTER IV. 

EXPANSION. 

Expansion of bodies on heating Exceptional cases Recalescence of iron 
and steel Force exerted during expansion Coefficient of expansion ; 



300475 



vi Heat for Engineers. 

PAGE 

methods of determination for solids, liquids and gases Relative and 
absolute expansion Tables of coefficients of expansion Special cases 
of nickel-steel non-expansive alloy and vitrified silica Anomalous 
expansion of water ; maximum density Uniform expansion of gases ; 
Charles' law 50 



CHAPTER V. 

PRACTICAL APPLICATIONS OF THE PROPERTY 
OF EXPANSION. 

Expansion of rails, girders, boilers, and working parts of engines Steam- 
pipe joints Shrinking of tires, etc. Contraction of metal castings 
Allowance for contraction in making patterns Breakage due to sudden 
expansion and contraction Correction of measures Scales of constant 
length Correction for expansion of liquids Thermo-regulators Com- 
pound strips Fire-alarms Compensated balance-wheel of watch 
Thermostats Steam-traps, or water-ejectors Compensated pendulums 73 



CHAPTER VI. 

ATMOSPHERIC PRESSURE. GENERAL PROPERTIES OF GASES. 

The atmosphere Atmospheric pressure The mercury barometer For tin's 
barometer Correction of readings "Normal" barometric pressure 
Aneroid barometer Kinetic theory of matter Distinctive properties of 
gases Gaseous pressure Boyle's law Definition of a " perfect "gas 
Isothermals Work done in isothermal compression Charles' law 
Absolute zero Combination of the laws of Boyle and Charles Heat 
produced by the compression of gases Joule's experiments Porous 
plug experiment Adiabatic compression and expansion Ratio of the 
two specific heats of gases Calculation of rise in temperature due to 
adiabatic compression Mayer's calculation Pressure caused by explo- 
sives Absorption of gases by porous solids ; application to gas-lighters 
and production of vacua. ........ 



CHAPTER VII. 

THE MEASUREMENT OF TEMPERATURE. LIQUID AND 
GAS THERMOMETERS. 

Definition of temperature Standards Available methods of measuring 
temperatures The mercury, gas, and thermodynamic scales Making 
and graduation of liquid-in-bulb thermometers Defects Conversion 
of Centigrade, Fahrenheit, and Reaumur scales Special range thermo- 



Contents. vii 



PAGE 



meters Registering thermometers High temperature thermometers 
Constant pressure and constant volume gas thermometers : use in 
establishing standards of temperature . . . . . .119 



CHAPTER VIII. 

THE MEASUREMENT OF HIGH TEMPERATURES. 
PYROMETRY. 

Available methods for measuring high temperatures Fixed points Wedg- 
wood's pyrometer Calorimetric method Gas pyrometers Electrical 
resistance pyrometers Siemens' and Callendar's platinum resistance 
pyrometers Comparison of platinum and air scales Indicators 
Callendar's recorder Thermo-electric pyrometers Le Chatelier's 
pyrometer Use of rhodium and iridium alloys Suitable galvano- 
meters Method of use Standardising The Roberts- Austen and 
Thread recorders Special forms of thermo-electric pyrometer Practical 
details of an installation Heat-radiation pyrometers Stefan-Boltzmann 
radiation law "Black body" radiations Fery's pyrometers Optical 
methods The Le Chatelier, Wanner, Holborn, and Mesure and Novel 
optical pyrometers Linear expansion pyrometers Fusion method ; 
alloys, salts and fusible clays Miscellaneous forms of pyrometers- 
High temperature data . . . . . . . .136 



CHAPTER IX. 

CHANGE OF STATE. FUSION. 

Physical changes in solids produced by heat Critical points of steel 
Change of state from solid to liquid Determination of melting and 
freezing points " Partial " melting points Eutectics Structure of 
alloys Melting points of mixtures Fusible alloys Change of volume 
on melting Effect of pressure on melting point Regelation of ice 
Table of melting points Surfusion Latent heat of fusion Table- 
Effect of dissolved solids on freezing-point of water . 182 



CHAPTER X. 

PRACTICAL APPLICATIONS OF FUSION AND ALLIED 
PHENOMENA. 

Soldering Automatic water-sprinklers Other uses of fusible alloys- 
Fusible plugs Use of materials of high melting points Furnace 
linings Electric furnace refractory products Utilisation of latent heat 
of fusion Railway foot-warmers Freezing mixtures Limit of low 
temperature obtainable with freezing mixtures 200 



vl11 Heat for Engineers. 

CHAPTER XL 

VAPOURS. 

PACK 

Molecular changes in liquids due to heat Change of state from liquid to 
vapour Saturated and unsaturated vapours Vapour pressure Defini- 
tion of boiling point Determination of saturation pressure of vapours 
Table for water vapour Rise of steam pressure compared with gas 
pressure Mixed gases and vapours Dalton's laws Pressure exerted 
by volatile liquids stored in vessels Safe storage of petrol, ether, etc. 
Test for storage pressure Pressure of vapour in communication with a 
cold space Watt's separate condenser for steam engines Differences 
between gases and vapours Vapour density Flash point of inflam- 
mable liquids 211 



CHAPTER XII. 

EBULLITION, 

Determination of boiling points Table Effect of pressure on boiling point 
Boiling under diminished pressure Vacuum pans Altitudes from 
boiling point observations Hypsometer Effect of dissolved solids on 
boiling point Boiling under increased pressure Digesters Normal 
and abnormal boiling Bumping Spheroidal state Boiler explosions 229 



CHAPTER XITT. 

LATENT HEAT OF VAPORISATION. PROPERTIES OF STEAM. 

Determination of latent heat of vaporisation Table for various liquids 
Effect of temperature of boiling on latent heat Total heat of saturated 
vapours Total heat of steam Table of properties of saturated steam 
Superheated steam Priming water Determination of moisture in 
steam "Throttling" and "separating" calorimeters Use of steam 
for heating purposes Distillation Patent stills Evaporators Con- 
densers Cooling jets 



CHAPTER XIV. 

ATMOSPHERIC MOISTURE. HYGROMETRY. 

Existence of moisture in the atmosphere Effect of temperature Deposition 
of moisture ; dew point Hygrometric state or relative humidity 
The chemical hygrometer Dines', Daniell's, and Regnault's hygro- 
meters The wet and dry bulb hygrometer Hygroscopes Lambrecht's 
polymetev Uses of hygrometric observations Mists and fogs Clouds 
and rain ........... 247 



Contents ix 



CHAPTER XV. 

THE PRODUCTION OF LOW TEMPERATURES. 
LIQUEFACTION OF GASES. 

Lowering of temperature caused by the evaporation of liquids Liquefaction 
of gases ; effect of pressure and temperature Critical temperature 
Critical pressure Pictet's liquefaction of oxygen Cailletet's apparatus 
Siemens' regenerative process Linde's apparatus for liquefying air- 
Liquefaction of hydrogen Dewar's vacuum vessel Low temperature 
data Properties of matter at very low temperatures Use of liquefied 
gases . 262 



CHAPTER XVI. 

REFRIGERATING MACHINERY, ICE MANUFACTURE, AND 
COLD STORAGE 

Objects of commercial refrigeration Early forms of refrigerating machines 
Principles of modern machines Air-expansion machines The com- 
pression system Choice of medium Properties of ammonia, carbon 
dioxide, and sulphur dioxide Types of compression machines Descrip- 
of parts The absorption system Modern absorption machines 
"Capacity" of refrigerating machines Energy ratio Working data 
Ice manufacture Can, cell, and plate systems Ccst Cold storage 
Suitable storage temperatures Cooling by circulation of brine, air, or 
the medium Insulation of cold stores ...... 276 



CHAPTER XVII. 

THE TRANSFER OF HEAT. CONDUCTION. 

Methods by which heat may pass from one place to another Good and bad 
conductors Coefficient of conductivity Tables of conductivities- 
Uses of good conductors Uses of bad conductors, or heat insulators 
Insulating materials for hot surfaces Tests for thermal efficiencies of 
laggings Heat escaping through different materials at various tempera- 
tures Effect of surface Lagging materials in common use Lagging 
of cold stores Diffusivity . . . . . . 3 r 



CHAPTER XVIII. 

THE TRANSFER OF HEAT. CONVECTION. 

Nature of convection Circulation of water in boilers Heating by hot-water 
circulation Dimensions of pipes required Fire-grate area Radiators 
Convection in air; winds Draught of a chimney Heights of 



Heat for Engineers. 



chimneys Weight of gases delivered by chimney Ventilation, prin- 
ciples "Natural" systems of ventilation "Artificial" ventilation 
Size and arrangements of inlets Electric heaters . 337 



CHAPTER XIX. 

THE TRANSFER OF HEAT. RADIATION. 

Heat waves Radiation and absorption Effect of surface The absolute 
"black body" Connection between heat radiated and temperature 
The Stefan-Boltzmnnn fourth-power law Rate of cooling Detection 
of radiant heat by various instruments Melloni's experiments Actual 
quantity of energy radiated under different conditions Experiments of 
Lummer, Kurlbaum, and Pringsheim "Scattering" Distribution of 
energy in the spectrum ; Wein's laws Effect of temperature on 
luminosity Diathermancy Selective emission and absorption . . 358 



CHAPTER XX. 

THE CONVERSION OF HEAT INTO WORK. LAWS 
OF THERMODYNAMICS. 

First law of thermodynamics Experiments of Joule, Him, Rowland, 
Griffiths, Callendar, and others Value of J in different units The 
second law of thermodynamics Carnot's ideal engine Cycle of opera- 
tions Efficiency Reversibility Efficiency in relation to temperatures 
Energy ratio of refrigerating machine Entropy Temperature- 
entropy diagrams .......... 379 



CHAPTER XXI. 

THE CONVERSION OF HEAT INTO WORK. PRACTICAL 
HEAT ENGINES. 

Disposal of heat in a steam engine Radiation losses Flue losses Con- 
denser losses Frictional losses Availability of heat Steam compared 
with other media Cycle of operations in steam engine Disposal of 
heat in internal combustion engines Losses by radiation, cooling 
water, and escape gases Working temperatures Cycle of operations 
in internal combustion engines Comparison with steam engine Losses 
in refrigerating machines Cycle of operations in refrigerating machine 399 



INDEX 417 

INDEX TO TABLES 429 



PREFACE 



TO 

THE SECOND EDITION 



THE author desires to express his thanks for the reception accorded 
to the first edition of this book, the disposal of which, in a com- 
paratively short time, confirms his view that a treatise embodying 
the principles and practical applications of Heat would commend 
itself to engineers and to students of applied science. It has 
been a source of much satisfaction to learn that the contents have 
been found useful in many industrial establishments, in which the 
economic aspects of the subject are of great importance. The 
adoption of the treatise as a text-book in a number of educational 
institutions of high standing has been further gratifying to the 
author, who has long been of opinion that a presentation of the facts 
concerning Heat from a practical point of view would in all cases 
be preferable to the mere academic treatment of the subject. 

In the present edition a number of errors which escaped de- 
tection in the first issue have been corrected, and paragraphs added 
where necessary summarizing the results of recent investigations 
bearing upon different branches of the subject. It is hoped that 
these alterations will be found to add to the value of the book. 

CHAS. R. DARLING. 
WOOLWICH : 1911. 



PREFACE. 



THE writing of this book was suggested to the author by DR. 
SILVANUS P. THOMPSON, F.R.S., Principal of the City and Guilds 
Technical College, Finsbury, at which Institution the author has for 
some years discharged the duties of Lecturer in Heat, and has also 
conducted laboratory studies in this subject. The practical applica- 
tions of heat in the various branches of engineering are now so 
numerous and important that adequate treatment cannot be given 
to them in books devoted mainly to theory. Such subjects, for 
example, as Refrigerating Machinery, Ice Manufacture, Cold Storage, 
Fuels, and Pyrometry, although of great commercial importance, 
seldom receive more than the briefest mention in ordinary treatises 
on heat, and the engineer or student seeking information on these 
matters, frequently finds it difficult to obtain. The object of the 
present volume is to deal with the numerous applications of heat in 
modern industrial processes, and to furnish the information and data 
requisite for a correct understanding of the thermal phenomena 
involved. 

The author has endeavoured throughout to explain thoroughly 
the principles underlying the matters dealt with, as mere technical 
descriptions, unaccompanied by such explanations, do not result in 
an intelligent grasp of the subject being obtained. The connection 
between heat and work has been kept prominent throughout ; and 
the use of the various formulae given has been illustrated by examples 
embodied in the text. Every care has been taken to include the 
most recent and reliable data in the numerous tables, and the recent 
advances in the science have, as far as possible, been given mention. 
A number of original experimental methods and commercial tests 
will be found in the book, based on the author's laboratory experience. 

In order to keep the volume within the limits contemplated, the 
author has been compelled to exclude matter which, in the opinion 
of some, might, with advantage, have been included. The growth o 



xiv Heat for Engineers. 

scientific knowledge in recent years is such as to make it possible to 
compile a treatise on almost every section of the subjects embraced 
in the present volume ; and in selecting the matter for inclusion, the 
author has been largely guided by his own experience of the require- 
ments of engineers and engineering students. In the chapters dealing 
with the conversion of heat into work, for example, the author has 
restricted himself to an explanation of the two fundamental laws of 
thermodynamics, and the consideration of the disposal of heat in 
actual engines in conjunction with these laws. In this, and other 
cases in which restriction has been necessary, the author has 
endeavoured to include sufficient to give the reader a grasp of the 
points of fundamental importance. 

With regard to the question of units, the author has recognised 
the fact that British engineers whether rightly or wrongly do not 
favour the metric system of weights and measures, or the Centigrade 
scale of temperature ; and accordingly the pound, foot, and Fahren- 
heit scale, figure frequently in the book. The term "calorie" is 
retained for the gram-degree Centigrade unit of heat, as the attempt 
to use this term to express a kilogram- degree Centigrade unit, with a 
view to replacement of the British Thermal Unit, has resulted in 
confusion only, and has not achieved the desired end. 

The special thanks of the author are due to Dr. SILVANUS P. 
THOMPSON, F.R.S., for invaluable assistance in collecting materials 
for the various chapters, and for most useful advice during the writing 
of the book. To Mr. J. HUSBAND, of Sheffield University, the 
author also tenders his sincerest thanks for a number of excellent 
illustrations of practical appliances, and for many valuable suggestions. 
The author also wishes to acknowledge the kindness of numerous 
firms who have placed information and illustrations at his disposal. 

CHAS. R. DARLING. 
WOOLWICH : 1908. 



HEAT FOR ENGINEERS 



CHAPTER I. 

HEAT AS A FORM OF ENERGY. UNITS. 

Heat as Energy. Previous to the commencement of the nine- 
teenth century, heat was generally regarded as being due to the 
action of a fluid which pervaded matter, to which the name " caloric " 
was given. This fluid was regarded as indestructible, and was 
further supposed to be self-repellent, although strongly attracted by 
the particles of matter. When a substance became warmer, it was 
held that " caloric " was added to it ; and conversely was believed to 
grow colder owing to " caloric " leaving it. This theory, modified as 
occasion demanded, served to explain most of the known phenomena 
connected with heat. 

The first experimental observations which resulted in establishing 
the modern view of the nature of heat were made by Count Rumford 
in 1798. Whilst engaged in the boring of brass cannon at Munich, 
Rumford was impressed by the great amount of heat developed in 
the operation. In order to investigate the matter quantitatively, he 
surrounded one end of the cannon by a wooden box, in which water 
was placed, and employed a blunt boring-tool, in order to remove as 
little brass as possible, and thus permit of the continuation of the 
experiment. By causing the cannon to revolve between the centres 
of a lathe, Rumford found that it was possible to boil the water ; 
and moreover found that heat was produced in undiminished 
quantity so long as the friction between the tool and the revolv- 
ing cannon was maintained. According to the caloric theory, the 
quantity of heat produced by such a method should be limited by 
the amount present in the bodies concerned ; but Rumford's 
experiments showed that the supply was inexhaustible, and could 
only be rationally explained on the basis that work was convertible 



2 Heat for Engineers. 

into heat continuously by the agency of friction. Rumford therefore 
expressed the view that " heat is motion'' 

The supporters of the caloric theory, however, endeavoured to 
harmonise the results of Rumford's experiments with their own 
views, and some years elapsed before heat was generally recognised 
as a form of energy. The work of Dr. Joule, of Manchester, com- 
menced in 1840, placed the issue beyond doubt. Joule showed that 
when heat is produced by friction, or other means, the amount of 
work done always bears a definite ratio to the amount of heat 
produced. The numerical connection, as determined by Joule (and 
signified by the letter " J "), was 772 foot-pounds per British 
Thermal Unit; or that 772 foot-pounds of work, if converted into 
heat, would raise the temperature of i pound of water by i Fahren- 
heit. More recent determinations, with better appliances, indicate 
the figure 778 foot-pounds as being the true mechanical equivalent 
of a British Thermal Unit. 

The view that heat is merely a form of energy has received ample 
confirmation in later times. The doctrine of the Conservation of 
Energy, which states that all the different forms of energy, such as 
electricity, mechanical energy, heat, etc., are only modifications of 
one another, and may be converted into each other without the 
destruction of energy, is well exemplified in the transformations that 
heat may be made to undergo. Thus the heat from fuel burnt in 
the boiler of an engine is converted into work by the agency of 
steam ; the work may be expended in driving a dynamo and pro- 
ducing electricity ; and, by passing the electricity through a 
resistance, heat is again reproduced. Heat may be converted 
directly into electricity by means of a junction of two different 
metals, which, when heated, give rise to an electric current in a 
closed circuit. Hammering a substance, or rubbing one substance 
on another, gives rise to heat, and represents the conversion of work 
into heat. Moreover, whenever it is possible to measure the 
amounts of energy involved, it is invariably found that a given 
quantity of one kind of energy, when converted into another kind, 
always gives rise to the same quantity of the latter, no matter 
under what circumstances the change has been effected. Hence, it 
is possible to predict the maximum amount of heat that can be 
produced by a given amount of work, or the maximum number 
of units of electricity obtainable from a given quantity of heat or 
work. 

Heat, as a form of energy, bears many resemblances to light, and 
in the form of radiant heat possesses the properties of light. All 



Heat as a form of Energy. Units. 3 

bodies send off heat in the form of waves, and such heat waves 
possess not only the same velocity as light, but are capable of 
refraction, dispersion, reflection, and polarisation. The heat of the 
sun reaches the earth in the form of waves, and the sense of 
warmth experienced near a fire or hot substance arises from the 
same cause. It is due to this process of radiation (assisted by 
conduction and convection) that bodies at different temperatures in 
a room tend to attain the same temperature. The hotter bodies 
radiate more heat energy than they receive from the colder ones, 
and equilibrium is established when the heat radiated is balanced by 
the heat received. 

The dissipation of all other forms of energy results in the pro- 
duction of heat. When the electricity disappears from a charged 
body, such as a rod of glass which has been rubbed, the dis- 
appearance is due to the conversion of the electricity into heat. 
Similarly, the result of stopping the motion of a projectile, in 
which mechanical energy disappears, is to produce an equivalent 
amount of heat. The general tendency of all kinds of energy, under 
the conditions obtaining on this planet, is to become heat. It is 
possible that under other conditions a converse tendency might be 
manifested, and speculations that all the energy in the universe will 
finally become " degraded " into heat should be received with caution. 

Measurement of Heat and other forms of Energy : Units and 
Constants. It is highly desirable, from the standpoint of the con- 
vertibility of the different forms of energy, that all units should be 
expressed in terms of common standards. Although this is carried 
out generally for scientific purposes, many of the units in everyday 
use have no accurate relation to each other. The British standards 
of weights and measures are wholly unsuited for the purpose of the 
calculations which enter daily into the duties of the engineer, and 
will no doubt ultimately be superseded or placed on a more scien- 
tific basis. For scientific work energy in all its forms is measured 
in terms of the centimetre, gram, and second or, as abbreviated, 
C.G.S. units. 

One centimetre = y^ part of the standard of length in the 

metric system, viz. the metre. 

One gram = the mass of i cubic centimetre of water at a 
temperature of 4 C. 

The C.G.S. unit of fora is i dyne, and is denned as "that force 
which, acting upon a mass of i gram for i second, generates a velo- 
city of i centimetre per second. 

B 2 



4 Heat for Engineers. 

The C.G.S. unit of work is i erg, and represents the amount of 
work done by i dyne acting through a distance of i centimetre. 

The C.G.S. unit of activity or rate of doing work is i erg per 
second. 

The above units are all "absolute" units, involving only the 
mass of i gram as distinct from a weight of i gram. The weight of 
i gram varies from place to place, whereas the quantity of matter 
it contains is constant. The weight of a substance depends upon 
the force with which gravitation acts upon it. For example, a lump 
of lead, if suspended on a delicate spring balance, would indicate a 
less weight at the equator than when near the poles, owing to the 
variation of the force of gravitation on the earth's surface. Any unit 
based upon the weight of a substance will therefore only have a fixed 
value in a given latitude, whereas " absolute " units are not subject 
to any such variation. Units in which " weight " is employed are 
termed " gravitation " units. 

The C.G.S. " gravitation " unit of force is the weight of i gram, 
and at London is equal to 981 dynes, as a body falling in vacua for 
i second has a velocity of 981 centimetres per second generated in 
it by gravitation. At other parts of the earth the acceleration pro- 
duced by gravitation (g) differs from 981, and accordingly the unit 
of force expressed in terms of it would differ also. The same remarks 
apply to the other gravitation units, viz. the centimetre-gram, which 
is equal to 981 ergs in London, and the activity unit, which is 981 ergs 
per second, or i cm.-grm. per second. 

The disadvantage of the C.G.S. units given above is that they 
involve very small quantities, and lead to large figures when em- 
ployed for calculations on the large scale. It is therefore customary 
to employ larger units, consisting of multiples of the smaller units, 
when necessary. Thus the metre-gram = 100 cm.-grms. is some- 
times employed ; and also the metre-kilogram, which is equal to 
T 00,000 cm.-grms. The activity unit, on the large scale, is \heforce- 
de-cheval, and is equal to 75 metre-kilos per sec. = 7,500,000 cm.- 
grms. per sec. = 7,360,000,000 or 7*36 x io 9 ergs per second. 

The practical unit of electrical work is the "joule," and repre- 
sents i volt x i ampere for i second. The choosing of the volt 
and ampere is such that i joule = 10,000,000 or io 7 ergs. The 
rate of doing electrical work, or electrical activity unit, is the " watt," 
and is defined as i joule per second = io 7 ergs per second. A 
larger unit, the kilowatt = 1000 watts, is frequently employed ; and the 
Board of Trade unit, by which electricity is sold for consumption, 
is i kilowatt hour, or 1000 watts foi i hour. 



Heat as a form of Energy. Units. ^ 

In British units the foot and pound take the place of the 
centimetre and gram in the C.G.S. units. The " absolute " unit of 
force is the poundal, and represents the force which, acting on a 
mass of i Ib. for i second, generates a velocity of i foot per second. 
The unit corresponding to the erg is the foot-poundal, and is denned 
as the work done by a poundal working through a foot. The work- 
rate or activity unit is i foot-poundal per second. In practice the 
gravitation units are almost invariably employed. The foot-pound 
= 32-2 foot-poundals, as the value of g in the terms of the foot and 
second = 32*2 at London. A force of one pound = 32-2 poundals. 
The work-rate unit is i foot-pound per second. The larger work-rate 
unit = 550 ft.-lb. per second, or 33,000 ft.-lb. per minute, and is 
termed i horse-power. The numerical connection between the 
British and C.G.S. units will be found in the following table. Where 
the equivalent unit is represented by an excessively small fraction, 
it has been omitted. 



Name of 
Unit 


Equivalent in other Units 


Centimetre- 
grams 


Foot-lb. 


Horse- 
power 


Force-de- 

cheval 


Watts 


Ergs 


Centimetre- 
gram 


} " 


I 


.. 





.. 


981 (London) 


13,823 


Foot-lb. . 


13,823 







" 


("1-356 x io 7 
\ (London) 


Horse- } ( 7 '6 x io 6 j 
power j \ per sec. J 


/ 33,ooo } 
\ per min. j 





1-01385 


746 (7-46 x io 9 
\ per sec. 


Force-de- ) 
cheval / 


/ 7'5 X IO 6 | 
\ per sec. / 


/ 32,549 } 
\ per min. / 


0-9863 





736 (7-36 X io 
\ per sec. 


Watt . . 


JI'OIQX I0 4 | 
\ per sec. J 


( 44-22 | 
\ per min. / 


I 
"746 


I 
736" 





io 7 per sec. 


Erg . . 




i 


- 










g x (London) 


I '356 x io 7 



Heat Units. Although heat, as a form of energy, may be ex- 
pressed in terms of energy units, such a mode of expression must be 
derived from some effect produced by heat on a standard substance. 
In terms of the centimetre and gram, the unit quantity of heat, 
or " calorie" is denned as the amount of heat required to raise the 
temperature of i gram of water by i degree Centigrade. In this 
definition no particular degree is specified, such as from 4 to 5, 
or 40 to 41, it being assumed that the amount of heat involved is 
the same whatever degree is selected. This is not the case, how- 



6 Heat for Engineers. 

ever, as less heat is required to raise the temperature of i gram of 
water i when the degree is chosen between 30 and 40 than at 
any other temperatures. The quantity involved at any temperature 
between 30 and 40 (e.g. 35 to 36) is less than that required 
between o and i in the ratio 4173 to 4219, a difference which 
falls within the scope of many heat determinations. No special 
degree has yet been adopted, but the temperature rise of 17 C. to 
1 8 C. is probably the best, and may finally come into general use. 
The heat required to raise i gram of water from 17 C. to 18 C. 
represents the average of that required for every degree between o 
and 100; or T ^ part of the heat required to raise i gram of 
water from o to roo C. In most ordinary heat calculations it is 
assumed that the gram-degree of heat is the same at all tempera- 
tures, and by choosing the degree 17 to 18 the least discrepancy 
would, in general, result from the assumption made. The variation 
of the calorie with temperature will only be taken into account in 
special cases in the examples given in succeeding chapters, in order 
to avoid confusion. It is highly desirable, however, that a standard 
degree should be adopted in connection with the unit, as a correction 
table could then easily be prepared and applied to a given result. 

The disadvantage of the calorie as a practical unit is its smallness, 
large figures being involved when the heat values have reference to 
operations on the commercial scale. To overcome this drawback 
the kilogram-degree Cent, unit is sometimes employed. One of these 
units is equal to 1000 calories. 

In engineering circles in Britain the unit generally adopted is 
the British Thermal Unit (B.Th.U.), which is defined as the amount 
of heat required to raise i Ib. of water by i degree Fahrenheit. The 
interval represented by i F. is equal to f of i C., and i Ib. = 453 * 6 
grams. The number of calories represented by i B.Th.U. will there- 
fore be 453-6 x f = 252. 

In many cases, however, a heat unit involving the pound and 
degree Centigrade is used, and is known as the " pound-degree 
Centigrade" unit. It is evidently equal to 453*6 calories, and to 
f or 1*8 British Thermal Units. Both these units are employed 
without reference to any specified degree of temperature. Adopting 
the temperature range recommended in the case of the calorie 
i7C. to 1 8 C. the corresponding interval on the Fahrenheit 
scale would be from 63 F. to 64 F. In practice the variation of 
the unit with temperature is seldom taken into account. 

Energy Equivalents of Heat Units. Expressed in ergs, the 
value of the gram-degree or calorie is represented by the round 



Heat as a form of Energy. Units. 



7 



number 42,000,000, or 4*2 x io 7 . The energy equivalent of the 
average calorie, represented by i gram of water raised from i7C. 
to 18 C, is 41,860,000, or 4-186 x io 7 ergs. If the calorie be 
denned with respect to the range o C. to i C., the equivalent is 
42,180,000 or 4*218 x io 7 ergs. It will suffice for general pur- 
poses to use the round number 42,000,000 ergs as the equiva- 
lent of i calorie. This figure, multiplied by 252 and 453*6 re- 
spectively, will give the number of ergs represented by a B.Th.U. 

and a lb-C. unit. If expressed in centimetre-grams ( = 5- ) the 

\ 9817 

value of the calorie is 42,650. 

When the foot-pound is adopted as the work-unit, i calorie is 
represented by 3*087 ft -Ib. ; i B.Th.U. by 778 ft.-lb. ; and i pound- 
degree Centigrade unit by 1400 ft.-lb. The kilogram-degree Centigrade 
unit = 1000 calories, is equal to 3087 ft.-lb. One horse-power is 
equal to 23*57 lb-C. units, or 42*42 B.Th.U. per minute. A table 
showing the connections between the various heat units and the 
work values of each is appended for convenience of reference. 





Equivalent in other Heat Units 


Work 


Equivalent 


Unit 


Kilogram- 












Calories 


degree 
Centigrade 


Thermal 


Units 


Foot-lb. 


Ergs 




Units 










Calorie . 


tt 


I 


I 


I 


3-087 


4-2 x io 7 


I COO 


252 


453-6 


Kilogram- 
degree 


1000 


.. 


3'97 


2*205 


3087 


4-2 x io iy 


Centigrade 










British thermal 


252 


252 





r 

9 


77 8 


1-058 X I0 1U 


Pound-degree 'I 
Centigrade / 


453'6 l *453 6 


1-8 





1400 


1-905 x io 10 



The following data will be found useful for reference in calcula- 
tions concerning heat : 

METRIC UNITS IN COMMON USE. 
Length. 

i metre =39*37 inches, 

i centimetre = 'oi metre = '3937 in( ' h - 

i millimetre ooi metre '03937 ,, 

i kilometre = 1000 metres = 3280*8 feet 



Heat for Engineers. 



Volume. 
i litre 

i cubic centi- 1 
metre f 

Weight. 

i gram 

i milligram 

i kilogram 



= 1*762 pints = 61*02 cubic inches. 
= *ooi litre = * 06102 cubic inch. 



= 15*432 grams. 

= *OOT gram. 

= 1000 grams = 2*2046 Ib. 



METRIC EQUIVALENTS OF BRITISH UNITS. 
Length. 

i inch 



i foot 
i yard 
i mile 

Volume. 

i cubic inch 
i ,, foot 
i pint 
i gallon 

Weight. 

i grain 

i ounce avoir. 

i Ib. 

Stress. 

i Ib. per sq. inch 
i inch of mercury 
at o C. 



2 *54 centimetres. 



o* 



91*4404 
160,935 



= 16*388 cubic centimetres. 

= 28,317 

=567-63 

= 454i'o2 



0648 gram. 
28 "3495 grams. 
453-59 

= 70*31 grams per sq. centimetre. 
34-534 



30 inches of mercury ) 

ato'C. '[=1036 

i centimetre of mer- ^ 

cury at o C. \ = I 3'59 6 

76 centimetres of ) 

mercury at o C. \ ~ I0 33 3 



Work and Energy. 
i foot-pound 

i foot-ton 



13,823 centimetre-grams = 1*3560 

x io 7 ergs. 

3*096 x io~ centimetre-grams 
= 3'374 x to 10 ergs. 



Heat as a form of Energy. Units. 9 

Work-rate. 

i horse-power J - 7 ' 64 x io cm.-grms. per sec. 

( = 7 -46 x io 9 ergs per sec. 

MISCELLANEOUS DATA. 
Specific gravity of mercury = 13 '596 at o C. 

Weight of i cubic inch of) = . 
mercury 

Standard height of barometer = 7 6 centimetres = 29 "92 inches. 

Normal atmospheric pres- } = 1033*3 grams per sq. centi- 
sure metre = 14/7 Ib. per sq. in. 

Weight of i litre of air at ) 

oC. and 76 cm. pressure f " ' ' ^ rams - 

Value of"," at London 

Weight of i cub. ft. of air at ) = . ogo Jb 
o" C. and 7 60 mm. press, j 

Weight of i litre of | 

hydrogen at C. and > = '0896 gram. 
760 mm. press. 



io Heat for Engineers. 



CHAPTER II. 

METHODS OF PRODUCING HEAT. THE PROPERTIES, USES, AND 
EVALUATION OF FUELS. 

Methods of Producing Heat. Heat energy may be produced in 
the following ways : 

i. Chemical action, such as the burning of coal or other matter in 
air or oxygen; the decomposition of an explosive; or the com- 
bination of quicklime with water. 

2. By passing a current of electricity through a resistance, as in 
the case of incandescent, Nernst, or arc lamps. The dissipation of a 
charge of static electricity also gives rise to heat. 

3. By friction. Bearings, when insufficiently lubricated, become 
hot owing to the production of heat by friction. 

4. By percussion. The hammering of a piece of metal causes a 
rise of temperature ; and a leaden bullet, on being brought to rest by 
striking a target, may be melted by the heat produced. 

5. By the compression of a gas. A mixture of a combustible gas 
and air may be raised to the temperature of ignition by compres- 
sion, as in certain forms of engines. 

6. By the absorption of a gas by a porous solid. Freshly-made 
charcoal, if powdered, may become so hot from this cause as to 
ignite in air ; and the heating of platinum caused by the absorption 
of hydrogen or coal gas is sufficient to ignite a jet of these gases. 

7. By molecular re-arrangement. A bar of iron, cooling from a 
high temperature, suddenly becomes hotter again at certain stages, 
owing to molecular changes taking place which liberate energy in 
the form of heat. 

8. By atomic decomposition, as illustrated in the case of radium 
compounds. The breaking up of the atoms sets free a considerable 
amount of energy in the form of heat. 

Only the first two methods are of general importance in con- 
nection with the generation of heat on the large scale. 

In producing heat for practical purposes, such as for lurnaces or 
steam-raising, bodies known as fuels are employed. In general, the 



Methods of Producing Heat. 1 1 

heat is produced by the chemical union of carbon and hydrogen, 
which are contained in the fuel, with the oxygen of the air. Coal, 
coke and wood represent solid fuels ; petroleum and its extracts, 
and also alcohol and certain hydrocarbons, such as benzol and 
naphthalene, are used as liquid fuels ; whilst coal gas, natural gas 
and producer gas are employed as gaseous fuels. The selection of 
a fuel for a given purpose is guided by considerations of economy, 
suitability, and convenience. 

In recent years great progress has been made in the utilisation 
of electricity for producing heat. Wherever fuel can be obtained at 
a reasonable price the cost of electrical heating will be the greater ; 
but, on the other hand, a much higher temperature may be obtained 
by the aid of electricity. A number of electric furnace products, 
which are now in everyday use, cannot be obtained in furnaces 
employing fuel. Examples of these products are calcium carbide, 
used for making acetylene, and highly refractory substances such as 
carborundum, siloxicon, etc., used as furnace linings. Electric fur- 
naces have the further advantages of easy control and localisation of 
heat, and will no doubt be extensively used in the future, particularly 
where cheap water-power is available. 

Heating Power of Fuels. The combustible portions of all fuels 
consist of one or more of the following : 

1. Free carbon. 

2. Free hydrogen. 

3. Carbon combined with one or more of the elements hydrogen, 
oxygen and nitrogen. 

Experiments show that i gram of carbon, burning in air or 
oxygen, gives out 8080 calories. One Ib. would therefore produce 
8080 lb-C. units, or 14,544 B.Th.U. These figures represent the 
heat units given out when the carbon is completely converted into 
carbon dioxide (CO 2 ). If burnt so as to produce carbon monoxide 
{CO), the heat produced is much less, being 2420 calories per 
gram = 2420 lb-C. units per Ib. = 4356 B.Th.U. per Ib. When 
fuel is burnt in an insufficient supply of air, considerable quantities 
of carbon monoxide are formed, with the result that only a portion 
of the full heating power of the fuel is utilised. Hence the necessity 
for a sufficient amount of air if the best results are to be obtained. 

The heat produced by the burning of i gram of hydrogen is 
34,000 calories. One Ib. will yield 34,000 lb-C. units, or 61,200 
B.Th.U. Expressed as volume, i litre of hydrogen yields 3,046 
calories (since i litre of hydrogen weighs '0896 gram), and i cubic 
foot will produce 191 lb-C. units, or 344 B.Th.U. 



1 2 Heat for Engineers. 

Compounds of carbon and hydrogen, when completely burnt in 
oxygen, produce carbon dioxide and water. The hydrocarbons 
commonly present in gaseous fuels are marsh gas or methane (CH 4 ) 
and olefiant gas or ethylene (C 2 H 4 ). Liquid fuels consist of a 
mixture of many hydrocarbons, and in the burning of many kinds 
of coal numerous hydrocarbons are present in the flame. All these 
compounds, when burnt in excess of air, give rise to carbon dioxide 
and water. Alcohol contains oxygen, and has the formula C 2 H 6 O ; 
the products of burning in this case also are carbon dioxide and 
water. The nitrogen present in fuels usually appears uncombined 
in the products; in some instances, however, it undergoes partial 
oxidation. This gas is never present to any great extent in solid 
or liquid fuels, but may form a large proportion of gaseous fuels, in 
which case it acts as an inert constituent. 

The heating power of carbon compounds cannot be calculated 
from that of the constituents, but must be made the subject of direct 
experiment. Marsh gas, for example, contains 12 grams of carbon 
and 4 grams of hydrogen in 16 grams of the gas. Considered as 
free carbon and free hydrogen the heating power would be as 
under : 

12 x 8080 = 96,960 calories produced by 12 grams of carbon 
34,000 x 4 = 136,000 4 hydrogen 

Total = 232,960 calories 

But experiment shows that 12 grams of carbon when combined with 
4 grams of hydrogen form marsh gas : that is, 1 6 grams of marsh 
gas yield on burning only 209,600 calories. The difference between 
the two figures, viz. 23,360 calories, represents heat already evolved 
from4he carbon and hydrogen in the act of combination. 

Acetylene (C 2 H 2 ) furnishes a further example of the thermal 
difference between a compound and its components in the free state, 
as the following figures show : 

26 grams of acetylene contain 24 grams of carbon and 

2 grams of hydrogen. 

Calories. 

24 grams of carbon on burning in oxygen give 193,920 
2 , hydrogen 68,000 

Total ..... 261,920 

But 26 grams of acetylene on burning in oxygen give 
294,000 calories, or 32,080 calories more than the free 
constituents. 



Methods oj Producing Heat. 



In this case the chemical union of carbon and hydrogen to form 
acetylene is attended by the absorption of extraneous heat, which 
is liberated when the acetylene is burnt in oxygen or otherwise 
decomposed. Bodies which, like acetylene, absorb extraneous heat 
when forming are said to be " endothermic? whilst those which evolve 
heat during formation, such as water, carbon dioxide, and marsh 
gas, are termed " exothermic" The enormous energy developed by 
explosive compounds of the type of guncotton and nitro-glycerine is 
due to the liberation of heat absorbed during the formation of these 
substances, which are therefore, like acetylene, endothermic com- 
pounds. 

The experimental determinations of the heating values of several 
compounds containing carbon and hydrogen is given in the follow- 
ing table : 



Substance 


Calories 
per gram 


Calories 
per litre 


use- 


B.Th.U. 




( Marsh gas, CH 4 


13,100 


9.395 


23,560 1052 


Gases 


. < Ethylene, C 2 H 4 


11,900 


14,910 


21,420 


1677 




'.Ethane, C 2 H, . 


12,350 


16,610 22,230 1865 




[Benzene, C 6 H 6 . 


10,100 9,090,000 


18,180 


Liquids 


. < Alcohol, C 2 H 6 O 


6,900 


5,457,900 


12,420 




Petroleum (average) . 


11,000 


9,900,000 


19,800 


.. 


Solid 


. Naphthalene, Cj H 8 . 


9,690 





17,442 


' 



When the proportions of the mixture of combustible gases in 
a gaseous fuel are known by chemical analysis, it is possible to 
calculate the heating value of the fuel by assigning to each con- 
stituent its calorific value. In general, however, it is much simpler 
to find the heating value by direct experiment, as an exact chemical 
analysis of a mixture of gases is a somewhat tedious operation. In 
the case of solid and liquid fuels, analysis does not reveal the manner 
in which the hydrogen and oxygen are combined with the carbon, 
and consequently the heating value cannot be calculated with any 
degree of accuracy from analytical data, which merely furnish the 
percentage of each element present. In the case of coal, various 
formulae have been proposed by means of which the calorific value 
may be approximately calculated from the constituents. Mahler's 
formula takes the form 

Q = T*O [8140 C + 34,5oo H - 3000 (O + N)] 



1 4 Heat for Engineers. 

where Q = calorific value in calories per gram, and C, H, O and N 
represent the percentages of carbon, hydrogen, oxygen and nitrogen 
respectively. The use of this formula in certain cases gives results 
not varying greatly from those found by direct experiment. Instances 
are known, however, in which specimens of coal, whilst possess- 
ing the same percentage composition, differ considerably in calorific 
value, and consequently no formula of this type can have any general 
application. An experimental determination is not only the simplest, 
but also the only reliable method of arriving at the heating value of 
a solid or liquid fuel. Instruments for this purpose are known as 
fuel calorimeters, and consist of three chief types, examples of which 
will now be described. 

Fuel Calorimeters. In all fuel calorimeters the method adopted 
is to burn a weighed quantity ot the fuel in oxygen, so as to impart 
the heat produced to a known quantity of water. The number of 
heat units evolved is obtained by noting the rise of temperature 
produced in the water. The many varieties of instruments in use 
differ in the method ot carrying out the combustion of the fuel, and 
also in the arrangements for imparting the heat to the water. All 
may be referred to one or other of the three following types : 

1. Calorimeters in which the fuel is burnt in oxygen under 
pressure. (Berthelot, modified by Mahler, Kroeker, Donkin, and 
others.) 

2. Calorimeters designed for burning the fuel in a stream of air 
or oxygen. (W. Thomson, Junker, Wedmore, Darling, and others.) 

3. Calorimeters in which a solid, such as potassium chlorate, 
sodium peroxide, or potassium nitrate, is mixed with the fuel to 
furnish oxygen for the combustion. (Lewis Thompson and others.) 

Examples of each class of calorimeter will now be described, the 
instruments chosen in each case being suitable for commercial 
purposes. 

Mahler's Calorimeter. This instrument is a modification of the 
original " bomb " calorimeter of Berthelot, which was composed 
largely of platinum, and therefore very costly. The combustion of 
the fuel is carried out in a steel chamber (B, Fig. i), enamelled on 
the interior to prevent oxidation or corrosion. A weighed quantity 
of the fuel is placed in a capsule C, preferably made of platinum, 
and may be ignited by passing a current of electricity through the 
fine iron or platinum wire F, which is embedded in the sample. 
The circuit through F is made by means of the rod E, which is 
insulated from the lid of the vessel B, and the corresponding rod 
which sustains the capsule. The chamber B is furnished with a 



Fuel Calorimeters. 




1 6 Heat for Engineers. 

screwed top, and a valve for admitting oxygen from a cylinder. 
During the combustion the chamber B is surrounded by a known 
quantity of water in the vessel D, which stands on wooden supports 
in the double-walled shield A. The vessel A is encased in felt, and 
serves to protect D and its contents from external heat disturbances. 
The water in D is stirred by the arrangement S, which is caused to 
move up and down and also to rotate by means of the lever L, and 
the steep-pitched screw K. The rise in temperature is registered 
by the thermometer T. 

In experiments with solid or liquid fuels i gram is placed in the 
capsule, and oxygen admitted to the combustion chamber until the pres- 
sure rises to 25 atmospheres. The capacity of the vessel D is such that 
2200 grams of water are required in order that the combustion chamber 
may be completely immersed. The temperature of the water in D 
is noted, and the combustion started by passing a current of elec- 
tricity through the wire F. As the combustion proceeds, the 
thermometer will show a gradual rise in temperature, and the experi- 
ment must be continued, with constant stirring, until the reading of 
the thermometer is stationary. The number of heat units developed 
is obtained by multiplying the weight of water taken in D by the 
rise in temperature, and adding to the result the number of heat 
units absorbed by the combustion chamber B, the vessel D, and the 
stirrer S, which also participate in the rise of temperature. 

The capacity for heat possessed by the various parts of the 
apparatus is determined by a special experiment, and is recorded, 
for convenience of calculation, in terms of the amount of water which 
would absorb an identical quantity of heat ; that is, the " water 
equivalent" To obtain this value a substance of known calorific 
power is burnt in the apparatus under experimental conditions, 
and the water equivalent calculated from the observed rise of tem- 
perature. 

Example. To find the water equivalent of a Mahler calorimeter, 
i gram of naphthalene was burnt under experimental conditions. 
Weight of water in vessel = 2200 grams; observed rise in tempera- 
ture = 3 62 C. ; calorific value of naphthalene = 9690 calories per 
gram. 

Calories absorbed by water = (2200 x 3*62) = 7964 
apparatus = (9690 - 7964) = 1726 

Weight of water which would absorb 1726 calories on being 
raised through 3 62 C. = =476-8 grams. 



Fuel Calorimeters. 17 

The water equivalent was therefore 476-8 grams; that is, the 
heat taken up by the apparatus i* equal to the quantity absorbed by 
47 6 8 grams of water. 

When the water equivalent has been accurately determined, it may 
be used in subsequent calculations by adding the figure to the actual 
.amount of water taken, and multiplying the sum by the rise in 
temperature. The total number of heat units given out by the 
weighed sample of fuel is then obtained. Thus, if i gram of coal 
were burnt, and caused a rise of temperature of 3 2 C. in 2200 grams 
of water, the water equivalent of the apparatus being 480 grams, then 
the calorific value of the fuel would be (2200 + 480) x 3-2 = 8576 
calories per gram. 

The heat developed by a gaseous fuel is obtained by exploding 
a known volume of the gas with an excess of oxygen in the combus- 
tion chamber. In this case the pressure before explosion should not 
exceed 5 atmospheres, as otherwise the force of the explosion might 
cause some of the joints to burst, and thus allow the hot gases to 
escape. The calculation is made as in the case of solid or liquid 
fuels. 

In order to secure very exact results, the thermometer used is 
graduated so as to read to 3^ or y-^ C. ; and a correction for loss 
or gain of heat by radiation must be made. Results of extreme 
accuracy, however, are of more importance from the scientific rather 
than the commercial standpoint, for reasons that will be given later. 

Other Varieties of " Bomb " Calorimeters. Bryan Donkin's calori- 
meter resembles Mahler's in general arrangement and method of 
working, but the combustion chamber is gilt instead of enamelled. 
There are also slight differences in some of the minor details. In 
the form due to Kroeker, the lid of the combustion chamber is fitted 
with an arrangement whereby, on opening a valve, the remaining 
gases may be allowed to escape through a series of drying-tubes, be 
means of which the amount of water formed by the combustion may 
be determined. Other modified forms have been introduced by 
Hempel, Atwater, and others. 

Carpenter's calorimeter occupies a position intermediate between 
the " bomb " type and those in which a stream of oxygen is used. 
In this calorimeter the combustion chamber is connected to a spiral 
of copper tubing, which is also surrounded by water. The oxygen 
is fed continuously into the chamber, and passes, together with the 
products of combustion, through the copper spiral, which terminatey 
in a pin-hole outlet outside the combustion vessel. The excess of 
pressure over atmospheric is 2 to 5 Ib. per square inch in the combus- 

c 



1 8 Heat for Engineers. 

tion chamber. A feature of Carpenter's calorimeter is that the water 
in the vessel is completely closed in, and by expanding on heating 
rises up a graduated glass tube which passes into the vessel. The 
amount of the expansion observed furnishes the calorific power, the 
instrument having previously been standardised by burning sub 
stances of known calorific value. This apparatus does not furnish 
results as accurate as those of the bomb calorimeters ; nor is complete 
combustion always obtained. 

Commercial Uses of Bomb Calorimeters. For ordinary commer- 
cial purposes, bomb calorimeters possess several drawbacks, notably 
the high cost, and the great care and skill necessary to work the 
apparatus. In Mahler's calorimeter, and others of the same type, 
there is no means of telling whether the ignition has been successful, 
other than the rise of temperature. A further drawback is the 
quantity of oxygen wasted with each combustion. On the other 
hand, combustion is complete with all fuels under the conditions 
existing in the combustion chamber, and consequently very reliable 
results may be obtained. In practice, however, it is much more im- 
portant to know which of a given set of samples has the highest 
heating power, than to obtain very accurate figures; or, in other 
words, comparative values are of more importance than absolute 
values. Coal, in particular, varies in calorific value considerably 
according to the time and conditions under which it has been kept, 
and consequently a figure obtained for the calorific power applies 
only to a particular set of conditions, and can only be regarded as 
approximate for the varied circumstances under which the coal is 
used. Kroeker has also pointed out that all calorimeters of this type 
give higher results for a fuel containing hydrogen, than that which 
represents the actual heat developed under working conditions ; as 
the water formed by the combustion in the calorimeter condenses, 
and gives out latent heat to the extent of 537 calories per gram, 
whereas no such condensation occurs in a furnace. If i gram of a 
fuel containing 5 per cent, of hydrogen were experimented with, the 
weight of water produced would be 45 gram, which, on condensing, 
would give out 242 calories. Kroeker' s calorimeter enables the 
amount of water formed to be estimated, and the correction from this 
source is deducted from the result of the combustion. The chief 
value of the accurate results of a bomb calorimeter is that the figures 
serve as standards of comparison, and may be used to check the 
results obtained by simpler and more expeditious methods. 

Darlings Calorimeter. The principle adopted in this instrument 
is to burn the fuel in a stream of oxygen, and to allow the hot gases. 



Fuel Calorimeters. 



to bubble through the water surrounding the combustion chamber. 
In early forms of calorimeters of this type, the gases were allowed to 
escape through a few large holes into the water, in which case the 
total extraction of heat from the bubbles is doubtful. Wedmore in- 
troduced an improvement by causing the hot gases to escape through 
a series of fine perforations, which is the principle adopted in the 
calorimeter designed for fuels in general by the author. Fig. 2 
shows the apparatus as fitted for gaseous fuels ; Fig. 3 for solid fuels. 





FIG. 2. DARLING'S CALORIMETER, 
FITTED FOR GASEOUS FUELS. 



FIG. 3. DARLING'S CALORI- 
METER, AS USED FOR SOLID 
FUELS (Gas fittings detached). 



the fittings used for gases having been detached ; and Fig. 4 shows 
the special arrangement adopted for liquid fuels. When used for 
solid fuels, i gram or thereabouts is carefully weighed into the 
crucible C (Fig. 3), which is held in position by three clips springing 
from the brass tube A. The author has found that nickel crucibles 
are quite as good as platinum for this purpose ; and, in addition to 
being very durable, are extremely cheap. If porcelain crucibles be 
used, some of the fuel may escape ignition. The crucible is sur- 
rounded by a glass bell-jar, B, which has a flange on its lower rim 

c 2 



20 



Heat for Engineers* 



and is supported by a brass plate which rests on three legs, L. An 
air-tight joint is secured by allowing the flange of B to stand on a 
rubber ring, and clamping it down firmly by means of a brass cover- 
ing ring and three nuts, which screw on to extensions of the legs L. 
The combustion is started by passing a current of electricity through 
a piece of platinum or iron wire embedded in the fuel, which is con- 
nected to thick copper wires passing through a rubber cork in the 
neck of the bell-jar to the leads P and Q. Oxygen is led into the 
combustion chamber from a cylinder or gas-holder by the tube O, 




FIG. 4. DARLING'S CALORIMETER AS USED FOR LIQUID FUELS. 

which may be made of glass, and preferably furnished with a brass 
cone at the lower extremity. The hot products of combustion, mixed 
with excess of oxygen, pass through the tube A into a chamber made 
by fitting together two recessed brass plates, through the upper of 
which are drilled numerous fine holes, H, through which the gases 
escape. During the combustion the whole apparatus is immersed in 
water, to which the heat carried by the gases from the combustion 
chamber is imparted. The vessel containing the water may be made 
of glass or metal, and may be shielded from radiation by standing i 



Fuel Calorimeters. 21 

on cork or wooden supports in a larger vessel. The rise of tem- 
perature is observed by the thermometer T, which should be capable 
of reading to $ C, or T V F. 

Instead of the device for electrical ignition, a small quantity of 
sulphur ^-Q of a gram is sufficient, or even less may be used to 
start the ignition. In this case the sulphur is placed in a small heap 
on the top of the fuel, and touched with a hot rod, after which the 
cork is inserted in the bell-jar, a gentle stream of oxygen turned on, 
and the apparatus transferred rapidly to the vessel containing the 
water. This method of ignition is in many ways preferable to 
electrical ignition, and the heat produced by the sulphur may be 
deducted from the result. One gram of sulphur on burning in oxygen 
gives out 2200 calories; hence if -^ of a gram has been used, no 
calories must be deducted from the result obtained. 

The water equivalent of the apparatus is determined experi- 
mentally, and radiation readings may be taken if it be desired to 
apply a correction for this possible source of error. In practice, 
radiation errors may be largely eliminated by commencing with the 
water at a temperature as much below atmospheric temperature as 
the final reading is above the latter. 

An example is given to illustrate the data required and method 
of calculation. 

Sample taken : i gram of Welsh steam coal. 

Initial temperature of water = i6'2C. 
Final = 2i'3C. 

Weight of water taken = 1400 grams 

Water equivalent of apparatus = 252 
Ignited by ^ of a gram of sulphur. 

Calorific power 

(weight of water + water equivalent) x rise in temp. 

weight of fuel used 
(1400 + 252) x 5'i 

i 
= 8425 calories per gram. 

Deducting no calories for sulphur used, the corrected value 
is 8315 calories per gram. 

When liquid fuels are to be tested, the calorimeter is arranged as 
in Fig. 4. A quantity of the liquid is placed in a small brass lamp, 
A, furnished with an asbestos wick, and the lamp and its contents 



2 2 Heat for Engineers. 

weighed before placing in the clips used to hold the crucible when 
solid fuels are burnt. The brass tube from which the clips spring is 
closed by a rubber cork, through which passes a glass tube C, bent 
as shown, through which the hot products of combustion escape. 
This enables the lamp to be surrounded by water during the com- 
bustion, and so ensures tranquil burning. In the absence of such a 
cooling arrangement, the heat of combustion would boil the residual 
liquid in the lamp, and give rise to an explosion. The oxygen 
delivery-tube is bent, so that it may not come into contact with the 
flame of the burning fuel, and the direction of the escaping gases is 
as indicated by the arrows. Ignition may be commenced by lower- 
ing a lighted match into the combustion chamber, or by passing an 
electric spark across the wick. After burning has entirely ceased 
the lamp is removed, carefully dried, and re-weighed, the loss in 
weight representing the fuel burnt. The calculation is then made as 
for solid fuels. The most volatile liquid fuels may be safely tested 
in this way, it being necessary, however, to use a very narrow wick 
(about ^ inch diameter) for light petrols, whilst for alcohol and 
ordinary petroleum the diameter may be T 3 F inch. 

When used for combustible gases, two brass tubes are passed 
through the plate on which the glass cover rests, and are connected 
by unions with an arrangement similar to a blowpipe (Fig. 2). The 
gas under test is burnt at a fine jet, oxygen being passed into the 
tube which surrounds the jet. Ignition is commenced by an electric 
spark, and the supply of gas is measured by mercury displacement or 
a suitable meter. The calculation is made as before, the calorific 
value being referred to i litre of the gas. The evaluation of a 
gaseous fuel by this calorimeter requires considerable experimental 
skill ; the apparatus being better adapted for solid and liquid fuels 
than for gaseous. 

In this calorimeter the combustion is visible and under the control 
of the operator, and no special skill is requisite to conduct an ex- 
periment. Results may be obtained which do not differ from those 
of a bomb calorimeter by more than i or 2 per cent. ; which falls 
well within the possible alterations of a solid fuel on keeping. It is 
customary to perform the routine tests with one of these calorimeters, 
reserving cases where special accuracy is required for a bomb 
calorimeter. 

Junker's Calorimeter for Gaseous Fuels. In this instrument the 
gas to be tested is burnt in a Bunsen or Argand burner, the heated 
products of combustion passing over a series of metal pipes through 
which water is flowing, and which serve to absorb the heat generated 



Fuel Calorimeters. 23 

by the flame. In working the instrument, the burner is first ignited, 
and a steady stream of water passed through the pipes, until stationary 
temperatures are registered on two thermometers, one of which is 
placed in the water at the point of entrance, and the other at the 
exit. The reading of a gas-meter attached to the supply pipe is now 
taken, and a 2000 c.c. measure placed so as to collect the escaping 
water. When the measure is filled to the mark, the gas-meter is 
again read, and the volume of gas burnt is thus obtained. The cal- 
culation is illustrated by the following example : 

In testing a sample of coal gas the entering water was at 16 C., 
and the escaping water at 21 C. During the collection of 2000 c.c. 
of water, '058 cubic foot of gas was burnt. Hence 2000 x (21 16) 
= 10,000 calories were produced by the combustion of -058 cub. ft. 
of the gas, or 17,240 calories per cubic foot. Dividing calories by 
252 to convert into B.Th.U., the result obtained is 684 B.Th.U. per 
cubic foot. 

The Junker gas calorimeter, which has been modified by Sim- 
mance-Abady and Boys, is now the recognised apparatus for the 
commercial evaluation of gaseous fuels. In testing producer gas a 
difficulty sometimes arises owing to the choking of the meter by 
tarry matter carried by the gas. This trouble is best overcome by 
passing electric sparks continuously through the gas in front of the 
entrance to the meter, which effect the deposition of the particles of 
tarry liquid. The rate of flow of the water should be such that about 
5 minutes are occupied in the collection of 2 litres. 

Calorimeters in which the Fuel is mixed with a Solid Oxygen Pro- 
vider. In calorimeters of this type the fuel is mixed with a solid or 
solids which furnish oxygen, the mixture forming a kind of fireworks, 
which is caused to ignite in a diving-bell under water. A weli-known 
instrument is that of Lewis Thompson, illustrated in Fig. 5. Two 
grams of finely-divided fuel are mixed with 26 grams of "combustion 
mixture " (potassium chlorate, 3 parts ; potassium nitrate, i part). 
The mixture is introduced into a copper cylinder, C, which is then 
fixed into position on the base of B. A fuse, made of wick, soaked 
in a solution of saltpetre, and dried, is placed with its lower end em- 
bedded in the mixture. The upper end of the fuse is ignited, and 
the cover, D (which, when the tap is closed, forms a diving-bell), 
is rapidly placed over the combustion cylinder, where it is held in 
position by flexible tongues of metal placed on the base B. The 
whole arrangement is now rapidly transferred to the vessel V, which 
contains a known quantity of water at a known temperature. When 
the fuse burns down to the contents of the copper cylinder, vigorous 



24 Heat for Engineers. 

combustion takes place, the gases produced passing through the 
holes at the lower part of D, and rising to the surface of the water 
In rising, the bubbles are deprived of the excess temperature they 
possess by the water, and should fall to the temperature of the latter 
before escaping into the air. When no more bubbles escape, the tap 
is opened, allowing the water to rise in D and submerge the com- 
bustion cylinder. The water is then mixed and the temperature 
taken. The calorific power is found, as in the previous cases, from 
the expression 

(weight of water + water equivalent) x rise of temp, 
weight of fuel burnt 

The drawbacks of this instrument are (i) complete combustion 
is seldom secured, particularly in the case of anthracite, coke, and 




FIG. 5. LEW T S THOMPSON'S CALORIMETER. 

fuels containing a high percentage of fixed carbon ; (2) a certain 
amount of chemical heat is disengaged by the breaking-up of the 
potassium chlorate, which is an endothermic substance ; (3) the fuse 
sometimes fails to act, or ignites the mixture before the apparatus 
has been immersed in the water; and (4) the bubbles of gas are 
large and escape rapidly, leaving the water before being entirely 
deprived of the surplus heat they possess. Consequently, the results 
obtained are in general lower than the figures furnished by other 
types of calorimeter. 

Parr's calorimeter differs from Lewis Thompson's in several 
details. The fuel is mixed with barium peroxide or sodium peroxide, 
and placed in a cartridge sealed by a valve, through which a piece 
of hot copper wire is dropped to commence the ignition. The 



Fuel Calorimeters. 25 

carbon dioxide and water produced are absorbed by the peroxide ; 
no gases therefore escape. The heat produced is due partly to the 
combustion of the fuel, and partly to the chemical union of the 
products with the sodium or barium compound. In the case of an 
average coal, 73 per cent, of the total heat is found to be due to the 
combustion proper, and consequently 73 per cent, of the total heat 
units evolved by i gram of coal, when burnt in the calorimeter, is 
taken as the calorific power. During the experiment the combustion 
chamber, which is furnished with projecting arms, is caused to rotate 
by means of a small motor, thus acting as a stirrer to the water. 

Commercial Uses. Calorimeters of the Lewis Thompson and Parr 
type are useful in places where a supply of oxygen gas cannot readily 
be obtained. The results are not so reliable as those obtained by 
direct combustion in oxygen, nor are these calorimeters so expeditious 
as those employing free oxygen, owing to the time taken in mixing - 
the fuel with the chemical ingredients, and the subsequent cleaning 
of the cartridge or combustion chamber. 

Methods of Expressing Results. The figure obtained for the 
calorific value of a fuel by any of the foregoing methods expresses 
the number of calories evolved on burning i gram of the fuel. 
The conversion into units involving the pound or degree Fahrenheit 
may be readily made. Thus, if 

i gram of fuel evolves 8000 calories, 
then x grams evolve (8000 x x) calories, 
or x grams will raise (8000 x x) grams of water i C. 

Itx = 453*6 (number of grams in i lb.), it follows that i Ib. of 
fuel will raise 8000 lb. of water i C. That is, the figure expressing 
calories per gram also expresses lb-C. units per lb. 

To convert into B.Th.U., the figure must be multiplied by f or 
1*8, as an interval of temperature of 1 C. = i ' 8 F. 

8oco calories per gram therefore equal 8000 lb-C. units per lb. 
= 8000 x 1-8 = 14,400 B.Th.U. per lb. 

It is customary also to express the results in terms of evaporative 
power, that is, the number of grams (or lb.) of water at 100" C., 
which would be converted into steam at 100 C. by the heat 
furnished by i gram (or lb.) of fuel. This figure is obtained by 
dividing the calorific power by the number expressing the latent heat 
of steam at 100 C., which in Centigrade units is 537 calories per 
eram, or 537 lb-C. units per lb. ; or 967 B.Th.U. per lb. Hence 



26 



Heat for Engineers. 



the evaporative power of a fuel of calorific value 8000 calories per 

gram will be 

8000 or 14,400 

537 967 

This is only the theoretical figure, as in any practical boiler 
a considerable portion of the heat escapes with the hot gases up the 
flue, besides losses by radiation, etc. 

Interpretation of Results. The values obtained with samples of 
coal vary considerably, according to the composition. A good 
Welsh steam coal will be found to possess a calorific power exceeding 
8000 calories per gram ; specimens from other localities falling 
between 7000 and 8000. A result less than 7000 calories per gram 
= 12,600 B.Th.U. per lb., indicates an inferior specimen. Average 
samples of coke should yield about 6000 calories per gram = 10,800 
B.Th.U. per lb. Calorific power alone, however, is not sufficient 
to determine the choice of a fuel. Other considerations, such as the 
rate of burning; the tendency to produce smoke and thus burn 
wastefully ; the amount of ash present, which forms clinkers and thus 
tends to choke the firebars ; and the amount of sulphur, which causes 
corrosion of the furnace, must also be taken into account. The cost 
is also of great importance, and it is generally necessary to resort to 
practical trials before the most suitable fuel for a given purpose can 
be discovered. 

Liquid fuels, in the form of petroleum or petroleum extracts, 
should possess a calorific value approximating to 11,000 calories per 
gram, or 19,800 B.Th.U. per lb. The volatile portions are specially 
suitable for the internal combustion engines now so common in 
motor vehicles, whilst heavy varieties or residues may be used for 
steam raising or small furnaces. 

The calorific value of gaseous fuels varies widely, according to the 
nature of the gas. This is indicated by the figures appended foi 
four varieties : 





Name 


Calorific Power 




Lb.-C. 
units per cubic foot 


B.Th.U. 
per cubic foot 


Pittsburg natural gas 


495 


8 9 I 


Producer gas (Siemens) . 


in 


200 




Coal gas (average) 


378 


680 




Water gas (best) . 


193 


347 





British Coals. 



27 



The difference in the values is due to difference in composition. 

British Coals : Varieties, Properties and Uses. The composition, 
and consequently the properties, of coal differ considerably, and a 
classification of the chief varieties may be made accordingly, as shown 
in the following table : 



Percentage of 



Name of Coal 


Carbon 


Hydrogen 


Oxygen Ash > Sulphur, 
etc. 


Anthracite 


1 9i'5 


3'5 


2-6 


2-4 


Dry bituminous 


87 


5 


4 


4 


Caking . 


! 8 5 


5 


6 


4 


Cannel . 


. ; 8 4 


6 


8 


2 


Dry long flaming 


. I 77 


5 


15 


3 


Lignite . 


. j 70 


5 


20 5 



The first two varieties occur largely in South Wales, and possess 
a higher calorific power than the remainder. The amount of gaseous 
constituents is lowest in anthracite, which for this reason is more 
difficult to burn than other classes of coal. Coal rich in gaseous in- 
gredients generally burns easily and rapidly, giving a considerable 
amount of flame, but is usually inferior in calorific value to a coal 
rich in carbon, which does not produce much flame. Gaseous coals 
also tend to produce smoke, which is due to the imperfect combus- 
tion of gaseous hydrocarbons which distil from the coal. Anthracite 
and dry bituminous coal, on the other hand, are practically smoke- 
less. The coalfields of Britain, other than South Wales, yield coal of 
a gaseous character. 

The table on next page, compiled from the figures obtained in the 
Admiralty Coal Investigation, shows the differences between the coal 
derived from different localities. 

It will be seen from the table that the Welsh samples are superior 
in respect to evaporative power, and in addition occupy less space, 
weight for weight, than the remainder. The slow burning of Welsh 
coal is also indicated in the table, as the number of pounds of water 
evaporated per hour is practically the same as that of the Lancashire 
coal, which is much inferior in evaporative power, but burns more 
rapidly, entailing more frequent stoking. The general superiority of 
Welsh coal, whenever sufficient draught is available, has been well 



28 



Heat for Engineers. 



Locality 


Practical 
Evaporative 
Power 
(in boiler 
furnace) 


No of Ibs. 
Evaporated 
per hour 


Percentage 
of Ash 


Specific 
Gravity 


Space 
Occupied 
by i ton 
in 
cubic feet 


Average of : 












37 samples from Wales 


9*05 


448-2 


4-91 


I'3I5 


42-71 


17 ,, ,, Newcastle. 


8-37 


4II-I 


3'77 


1-256 


45'3 


28 ,, ,, Lancashire. 


7"94 


447-6 


4-88 


1-273 


45^5 


8 ,, ,, Scotland . 


7-70 


431 '4 


4-03 


1-259 


49*99 


8 ,, ,, Derbyshire. 


7-58 


432-7 


2-65 


1-292 


47'45 



established by repeated trials. Amongst the many varieties of Welsh 
coal the best known are Nixon's Navigation, Powell Duffryn, Hill's 
Plymouth, and Wayne's Merthyr. In a good form of boiler any of 
these kinds show a practical evaporative power of about 10, and differ 
from each other very slightly. Welsh steam coals in general are in 
great demand for steam-raising purposes, particularly on steamships. 
The comparatively high cost is balanced by the steady burning, high 
evaporative power, comparatively small amount of ash, and the 
absence of smoke. 

Coal from other localities, being in general easier of combustion 
than Welsh coal, is adapted for uses in which a strong draught is not 
available, as in the case of domestic fires, locomotives, and small 
stationary boilers. The highly gaseous varieties are used for the 
manufacture of gas ; the residue, or coke, being employed in metal- 
lurgical and other operations. Gaseous coals are also used in obtain- 
ing the high temperatures requisite in various furnaces used in the 
treatment of metals. Owing to the cost of transit, ordinary coal is 
frequently used in cases where Welsh coal would be more suitable, 
but less economical. 

Amount of Air required to burn Coal. The oxygen present in the 
air only constitutes ^ of the total volume, the remaining J not taking 
part in the combustion of fuel. When the composition of a fuel is 
known, the amount of air requisite for combustion may be calculated 
from chemical data. One gram of carbon requires i'86 litre of 
oxygen (measured at o C. and 760 mm. pressure) for complete com- 
bustion ; and i gram of hydrogen combines with 5*58 litres of 
oxygen. Hence if the proportion of carbon and hydrogen in a fuel 
be known, the volume of oxygen required for combustion may be 
calculated. The result, multiplied by 5, will give the requisite volume 
of air necessary exactly to burn the fuel. In practice, however, a 



Smoke Prevention Liquid Fiiels. 29 

greater quantity must be admitted to a furnace, as the air is not in 
contact with the fuel for a sufficient time to enable all the oxygen to 
be consumed. An excess of , or 33 per cent, above the theoretical 
quantity, is found most economical in practice, and the spacing of 
firebars and draught of the chimney should be such as to admit this 
quantity to the fuel. A larger excess is wasteful, as it merely serves to 
carry heat away into the flue. An average coal requires, theoretically, 
about 12 Ib. of air (which at 60 F. occupies a volume of 157 cubic 
feet) to burn i Ib. completely. Adding , the volume of air admitted 
to a furnace to ensure good combustion should be 210 cubic feet for 
every pound of coal burnt. 

Smoke Prevention. The smoke produced on burning fuels rich in 
volatile matter is due to the distillation of heavy hydrocarbons from 
the fuel, which are decomposed by the heat yielding free carbon. If 
the hydrocarbons escape suddenly, the soot produced is carried by 
the draught into the flue before the particles have attained the tem- 
perature of ignition, thereby giving rise to smoke. Many appliances 
have been devised with a view to preventing smoke, but none have 
proved completely successful. The aim in smoke-prevention apparatus 
is either to admit an additional quantity of air to the furnace, so as 
to consume the carbon or soot ; or to stoke the furnace gradually 
from the forward end, so that no large generation of soot takes place 
suddenly. The extra quantity of air is brought into the furnace either 
by an induced draught created by a fan placed in the flue, or by 
aspirating air through or over the fuel by the aid of steam-jets. 
Gradual stoking is accomplished by mechanisms which feed the fuel 
forward at any desired rate ; many mechanical stokers having been 
devised for this purpose. Smoke prevention arrangements can only 
be applied to comparatively large plant, and no practicable scheme 
has yet been devised to prevent the smoke arising from domestic 
fires, locomotives, and small stationary plant. Liquid fuels are liable 
to give rise to smoke, unless care is taken in the control of the 
furnace ; and the experience of many years' trial of various smoke- 
prevention apparatus points to the conclusion that careful stoking, 
combined with a judicious selection of fuel, is the best means of 
reducing smoke to a minimum. The introduction of cheap gaseous 
fuel, such as Mond's gas, is very desirable from the standpoint of 
smoke abatement. 

Liquid Fuels. The use of liquid fuels has greatly extended in 
recent years, not only for internal combustion engines, but also for 
steam raising and small furnaces. The various petroleum distillates 
and residues represent the chief source of liquid fuel ; alcohol being 



30 Heat for Engineers. 

used to a small extent only. The lighter petroleum extracts, known 
as petrol, etc., are suited to high speed internal combustion engines, 
such as are used to propel motor vehicles. The heavier portions 
and residues have been successfully employed in producing heat for 
various purposes. 

The petroleum obtained from various sources (Russia, America, 
etc.) possesses approximately the same calorific power, which 
averages 11,000 calories per gram or 19,800 B.Th.U. per Ib. The 
specific gravity of crude petroleum ranges from 0*938 to 0*884; the 
lighter distillates having a specific gravity of 0*7 and upwards. 
Weight for weight, the heating power of petroleum is about \ greater 
than that of good coal. In oil engines the vapour of the oil is ex- 
ploded with air in the cylinder, the heat generated by the action 
furnishing the motive power. When used for producing heat, the 
petroleum is injected into the furnace in the form of a spray, sufficient 
air being also admitted to secure proper combustion. The chief 
advantages of liquid fuels are : (i) Greater calorific power than coal, 
resulting in a reduction in weight of fuel of over 30 per cent, for a 
given heating effect ; (2) Occupies less space than solid fuel ; (3) 
More convenient to store and load ; (4) Greater speed in getting up 
steam; (5) Complete control over the combustion, which may be 
stopped instantaneously, or reduced as required. The chief draw- 
backs are : (i) Danger of explosion of the stored oil; (2) Loss by 
evaporation ; (3) Cost, which is largely a question of locality. 

Experiments conducted on the South-Eastern Railway of Russia 
showed that in that locality, under the prices prevailing for coal and 
petroleum, a saving of 70 per cent, was effected by using petroleum 
instead of coal for the locomotives. On many steamships, and also 
on the locomotives of the Great Eastern Railway of England, 
petroleum has been used to feed coal fires, with economical results. 
Mr. Holden, of the Great Eastern Railway, employed petroleum 
residue, known as " astatki," with a resultant saving of 2 14 per cent, 
on the cost of coal, but has recently abandoned the use of liquid fuel 
for other reasons. The use of petroleum fuel, either alone or as an 
auxiliary to coal, is extending in many directions, notably to steam- 
ships and small furnace operations. The time and labour saved in 
coaling is an important factor in the case of steamships ; and in small 
furnaces the extra cleanliness and easy control are considerations 
which frequently outweigh the extra cost of the petroleum. 

Gaseous Fuels. Many important metallurgical processes are con- 
ducted with the aid of gaseous fuel, notably the Siemens- Martin 
steel process, which has now largely supplanted other methods. 



Gaseous Fuels. 



Re-heating and other furnaces also employ gaseous fuel ; and, in ad- 
dition, gas is extensively used as a prime motor in the various types 
of gas engine. In the United States of America, Russia, China, and 
other places, large stores of combustible gases are obtained from the 
earth, and are known as " natural " gas. Manufactured gas is ob- 
tained by one of three chief processes, viz. : (i) By the distillation 
of coal in closed resorts, producing coal gas ; (2) By burning fuel in a 
limited supply of air, to which steam is added, forming producer gas ; 
(3) By passing steam over red-hot coke or anthracite, giving water 
gas. Coal gas is used for illuminating purposes and gas engines ; 
producer gas is chiefly used for the production of heat in furnaces. 
The gases escaping from blast furnaces are used for heating purposes, 
and have been shown by Bryan Donkin to be sufficiently combustible 
for use in gas engines of special construction, and a number of instal- 
lations are already in use in which the motive power is furnished by 
these gases. 

The combustible constituents of gaseous fuels are chiefly hydrogen, 
marsh gas (CH 4 ), carbon monoxide (CO), and small quantities of 
other hydrocarbons. The proportions of the constituents vary with 
the origin of the gas, and a quantity of non-combustible gases are 
also present. The calorific value is highest in the case of gases rich 
in marsh gas and other hydrocarbons. A table is appended, 
showing the composition and calorific value of gases from different 
sources. 





Percentage of 










Calorific 
















Value in 


Name 


Carbon 
Mon- 
oxide 


Carbon 
Dioxide 


Hydro- 
gen 


Marsh 
Gas 


i Other 

^r.. Gases, 
Nltr - chiefly 
S en Hydro- 


B.Th.U. 
per cubic 
foot 












carbons 




Pittsburg natural ) 


I'O 


0'8 


22" O2 


72-I8 


nil 


6-0 


891 


gas J 










Siemens' producer)' 92 . 27 

gas (best quality)/ ' 


6-1 


28-7 


I'O 41'9 


nil 


20O 


Coal gas (average) 


6-64 


3^7 


45^8 


34-90 ; 2-46 


6-75 680 


Water gas (best) . 


35-88 


2-05 


52-76 


4'ii 4'43 


0-77 


347 


Mond's producer | 

gas J 


13-2 


12*9 


24-8 


2'3 46-8 nil 


155 



Mond's gas is an extremely cheap form of producer gas, made 
from a cheap bituminous coal slack. Arrangements exist in the 



32 Heat for Engineers. 

process for the recovery ol ammonia, which in other producers is 
wasted. The value of the recovered ammonia is equal to the cost 
of the fuel used, the only charges being labour and upkeep of the 
plant. The gas may be used for metallurgical processes and gas 
engines, and its cheapness renders it an economic source of heat 
and power. The distribution of the gas for manufacturing purposes 
from a large central station is being tried in Staffordshire, and should 
the result prove economical and successful the use of Mond's gas 
will extend largely. One beneficial result of such an extension 
would be the mitigation of the smoke nuisance. 

During the last few years, gas generators working on the " suction " 
system have been introduced for the direct working of gas engines. 
The charge of gas is drawn into the engine directly from the producer, 
in which a mixture of air and steam is drawn over red-hot anthracite 
by the action of the engine. After discharging the exhaust gases, 
the cylinder is in direct communication with the producer, and the 
back stroke of the piston causes a fresh quantity of air and steam to 
pass over the anthracite. A cheap form of gaseous fuel is thus 
generated as required, the result being to furnish an extremely cheap 
source of power, as well as a self-contained plant. The use of 
suction plant is in consequence extending rapidly. 

The low heating power of producer gas is due to the large amount 
of nitrogen present, derived from the air used in the manufacture. 
A considerable quantity of carbon dioxide, also an inert constituent, 
is also present. The calorific values of the three chief combustible 
constituents, expressed in B.Th.U. per cubic foot, are as follows : 
marsh gas, 1050; hydrogen, 344; carbon monoxide, 342. 

Methods of producing High Temperatures ; Electric Furnaces. In 
using fuel for steam boilers an extremely high temperature is not 
desirable, and, if obtained, would result in the loss of a considerable 
quantity of heat owing to the high temperature of the waste gases. 
In metallurgical operations, however, a very high temperature is 
frequently requisite for the success - of the process. Where coal 
or coke is employed, the required temperature is obtained by the 
use of a blast or forced draught of air, which renders the combustion 
more rapid than if burnt under normal conditions. The rapid 
combustion gives rise to a high temperature, which in the case 
of coal or coke may be made to approximate 1800 C., or 3240 F., 
a temperature which will melt all ordinary metals. 

When gas is used as a fuel for furnaces in which a very high 
temperature is desired, the method in general use is known as the 
" regenerative " system, and is due to Sir W. Siemens. In this 



Production of High Temperatures. 33 

system, which is now almost universal in steel-making processes, the 
products of combustion are caused to pass through a network of 
firebricks, which are heated thereby. Two pairs of firebrick chambers 
are provided, and by an arrangement of valves the air and gas may 
be admitted through either pair to the bed of the furnace, where they 
mix and burn. At the commencement air and gas are admitted 
through one pair of chambers, the products passing through the other 
pair. On reversing the valves the air and gas are each heated by 
passing over the hot firebricks, and enter the furnace at a compara- 
tively high temperature, which augments the temperature produced 
by burning the gases under ordinary conditions. Thus, if 1000 C. 
were obtained by burning the gas and air when used at atmospheric 
temperature, and if in the process the gas and air were heated 
to 200 C. before entering the furnace, the temperature produced 
would be nearly 1200 C. In consequence of the increased tempera- 
ture, the firebricks through which the products escape will be hotter 
than before, and may attain, say, 400 C. On again reversing, the 
temperature in the furnace would be nearly 1400 C. ; and conse- 
quently, any desired high temperature may be obtained by reversing 
periodically. Hie practical limit is the melting point of the furnace 
lining, and the theoretical limit is the temperature at which the 
chemical actions giving rise to the heat cease to be realised, or are 
so weak as to be practically inoperative. 

The advances made in the cheap production of electricity on the 
large scale have led to the introduction of the electric furnace, which 
is capable of yielding a temperature higher than that obtainable by 
any other known method. Electric furnaces are being largely used 
in smelting operations, particularly in places where water power is 
available for generating current. The heating effect is obtained by 
the current passing through a resistance, and the temperature obtain- 
able is at least 3700 C., or 6660 F. In some electric furnaces the 
material to be operated on is fed through an electric arc ; in other 
cases the material is placed on a carbon grid, which is heated to the 
desired temperature by regulating the current. In another form a 
refractory chamber is heated externally by surrounding it with pow 
dered carbon, or a mixture of graphite and fireclay, through which 
the current is passed. In certain small operations graphite tubes are 
heated by the current, the material being placed in a carbon vessel 
inside the tube. Fresh forms of electric furnaces are continuously 
being devised, and will doubtless play an important part commercially 
in the future. The cost of producing a given quantity of heat by 
electricity is much greater than in the case of fuel; but in many 

D 



34 Heat J or Engineers. 

processes other advantages more than compensate this item. Further, 
owing to the extremely high temperature attainable, an entirely new 
field has been opened for the production of materials which cannot 
be otherwise obtained. An example is calcium carbide, which when 
acted on with water yields acetylene, and is now of much commercial 
importance. 

A method of producing high temperatures has recently been in- 
troduced by Goldschmidt, who employs a mixture of powdered 
aluminium and oxide of iron, the mixture being known as " thermit." 
When this mixture is ignited by a special fuse, an exceedingly high 
temperature, approximating to that of the electric arc, is obtained. 
The action results in the production of oxide of aluminium and 
metallic iron. The process has been applied to welding pipes, rails, 
etc. ; the operation consisting in igniting " thermit " placed round the 
junction of the separate pieces, when the heat produced melts the 
metals at the junction and causes complete fusion. 

On the small scale high temperatures, exceeding 2oooC., may be 
obtained by burning hydrogen, or better still, acetylene in a blowpipe 
fed with oxygen. The oxy-acetylene flame is now used to a con- 
siderable extent for small welding operations, the temperature pro- 
duced being sufficient to melt iron readily, and to cause it to flow 
freely. 



35 



CHAPTER III. 

SPECIFIC HEAT. 

Thermal Capacity. The addition of equal amounts of heat energy 
to equal weights of different substances does not cause the same rise 
in temperature. Thus i calorie, if imparted to i gram of water, 
causes a rise of i C. ; but if imparted to i gram of mercury the tem- 
perature rises by about 33 C. For i gram of iron the rise in tem- 
perature would be 9 C. ; for i gram of aluminium 5 C., and so on. 
If deprived of i calorie, a fall in temperature, equal to the rise on 
adding i calorie would be observed in each case. It is evident, 
therefore, that temperature alone does not indicate the amount of 
heat energy possessed by a substance, which must depend upon its 
capacity for storing heat, or thermal capacity. 

Water possesses a greater thermal capacity than any other or- 
dinary substance, being only exceeded in this respect by hydrogen, 
liquid ammonia, and certain mixtures of alcohol and water. From 
the above figures it will be seen that, compared weight for weight, the 
thermal capacity of water is 33 times as great as that of mercury, and 
9 and 5 times as great as that of iron and aluminium respectively. 
For this reason water is a suitable substance with which to form a 
standard of thermal capacity, to which all other bodies are referred. 
Water possesses other advantages, however, which add to its suit- 
ability for this purpose, viz. the comparative equality of its thermal 
capacity at temperatures between o C. and 100 C. ; the fact that it 
is always available for experimental purposes ; its use involves no 
cost \ it is not a corrosive liquid to any great extent, and does not 
evaporate readily at ordinary temperatures. For these reasons the 
thermal capacities of all substances are expressed in terms of that of 
water, which is taken as unity. 

Specific Heat. The ratio of the thermal capacity of a substance 
to that of water is termed its " specific heat," which may be denned 
as the ratio of the amount of heat required to raise a given weight of 
the substance through a given temperature, to that required to raise 
an equal weight of water through the same temperature. By taking 

D 2 



36 Heat Jor Engineers. 

i gram as unit weight, and i C. as the rise of temperature, the 
definition becomes : 

Heat units required to raise i gram of substance i C. 
Heat units required to raise i gram of water i C. 

Taking the calorie as heat unit in each case, the denominator 
becomes equal to unity, as i calorie will raise i gram of water i C. 
by definition. Hence the specific heat of a substance is equal to the 
number of calories required to raise the temperature of i gram i C. 
It should be observed that the same figure is given by the number of 
lb-C. units required to raise i Ib. of the substance i C. ; or by the 
number of B.Th.U.'s required to raise i Ib. of the substance i F. 
The specific heat of water is unity. 

Example i. A substance of specific heat 'ii would require 'u 
calorie to cause arise of temperature of i C. for each gram of sub- 
stance. 

Hence 

453-6 grams (= i Ib.) require 453*6 x 'u calories per C. 

But 453 -6 calories = i lb-C. unit. 
Therefore 

i Ib. requires 'n lb-C. units for i C. rise of temp. 
Similarly 

i Ib. would require 453-6 x n x f calories per F., 
as a rise of i F. only represents | C. 

But 453-6 x | = 252 calories = i B.Th.U. 
Hence 

i Ib. raised i F. requires n B.Th.U. 

Example 2. Twenty grams of a substance of specific heat -21, 
when cooled from 60 C. to 40 C., would give out 20 x 2 1 x (60-40) 
calories = 84 calories. 

Experimental determination of Specific Heats. Four chief methods 
exist for determining the specific heat of a substance, and are 
known as 

1. The method of mixtures 

2. Method of fusion. 

3. Condensation method. 

4. Cooling method. 

Each of these will now be described. 



Specific Heat. 



37 



Method of Mixtures. This method was employed by Regnault in 
his experiments on specific heats, and is a simple and accurate 
means of obtaining the value in the case of solids and liquids, and 
also for gases at constant pressure. When the specific heat of a solid 
is to be found, it is heated to nearly iooC. 
in a vessel surrounded by steam, and then 
allowed to fall into a known quantity of 
cold water. After permitting the solid 
and water to attain the same temperature, 
the rise in degrees is noted, and the specific 
heat calculated from the data obtained. 
Fig. 6 shows the apparatus, which con- 
sists of the double vessel A, in the inner 
of which the solid is placed. Steam from 
a boiler circulates in the space between 
the vessels, and after a few minutes the 
solid will have attained a steady tempera- 
ture (never quite equal to that of the 
steam), which is recorded on the thermo- 
meter placed in contact with the solid. 
The water is weighed out in a vessel or 
calorimeter, B, made of thin copper or 
silver, and suspended in a larger vessel or 
shield, which is intended to protect the 
inner vessel from loss or gain of heat due 
to the surroundings. The temperature 
of the cold water is taken with a delicate 
thermometer, and the hot solid rapidly 

dropped in. The water is then stirred until a steady temperature 
is obtained, and the result calculated as under : 

Heat units lost by solid 
Heat units lost by solid 
Heat units gained by water 




but 
and 



A.CALLEtlKimr & Co 



FIG. 6. APPARATUS FOR 

SPECIFIC HEATS BY METHOD 

OF MIXTURES. 



= Heat units gained by water 

and calorimeter. 
== Weight x specific heat 

x fall in temp. 
= Weight x rise in temp 



also 



Heat units gained by calorimeter = Weight x specific heat of 

material x rise in temp. 
The equation therefore becomes 

(Weight of solid x specific heat x fall in temp.) 

= (Weight of water x rise in temp.) + (weight of calorimeter 

x specific heat of its material x rise in temp.) 



3 8 Heat for Engineers. 

It is presumed that the specific heat of the material of which the 
calorimeter is made is known, and consequently in the above 
equation the only unknown quantity is the specific heat of the solid, 
which is calculated from the data furnished by the experiment. 

Example. 250 grams of copper are immersed in 150 grams of 
water at 20 C., contained in a calorimeter weighing 100 grams, 
made of material of specific heat ' i. The temperature of the mixture 
is 30*3 C. Find the specific heat of the copper. 

Inserting values in the equation given above 

250 x specific heat x (100 - 30-3) = (150 x 10*3) 
+ (TOO x * i x 10*3) 

From which the value of the specific heat is * 0946. 

It is evident that the product " (weight of calorimeter x specific 
heat of its material) " has a constant value, and is equal to the 
weight of water which would take up an equal amount of heat. 
Thus if the calorimeter weigh 50 grams, and the material have a 
specific heat of i, then a rise of i C. would require (50 x i) = 
5 calories. The weight of water which would be raised i C. by 5 
calories = 5 grams ; or, in general, x calories will raise x grams of 
water i C. Hence the product " wt. of calorimeter x sp. heat of 
material " gives a figure which represents the number of grams of 
water equal in thermal capacity to the calorimeter. Hence this 
product represents the " water equivalent" which may be added to the 
actual water taken in order to simplify the calculation, which then 
becomes 

(wt. of solid x sp. ht. x fall in temp.) = (wt. of water -f water equiv.) 

x rise in temp. 

Calorimeters for determinations of this kind are made of copper 
or silver, both of which are good conductors of heat; and con- 
sequently the portions of the vessel above the water will nearly 
attain the temperature of the parts in contact with the water. This 
would not be the case if glass, or other bad conductor, were used ; 
and the quantity of heat absorbed by the calorimeter would then be 
uncertain, and would require a special experiment to determine. It 
should be noted that the outer vessel, or shield, does not participate 
in the gain of heat due to the hot solid, and therefore does not enter 
into the calculation. It will avoid confusion if it be remembered 
that the term " calorimeter " applies only to the parts which are 



Specific Heat. 39 

affected by the rise in temperature. Expressed in symbols, the equa- 
tion giving the specific heat is 

s _ (W, + w) x (/ 2 - /,) 
W x (t - / 2 ) 

where S = specific heat of solid. 
W = weight of solid. 

t = temperature of solid before immersion. 
Wj = weight of water. 
w = water equivalent of calorimeter. 
/! = initial temperature of water and calorimeter. 
/ 2 = final 

In refined experiments the water equivalent of the thermometer 
should be added to w t but is usually a small quantity, falling within 
the limits of other experimental errors. 

The method of mixtures may be applied to liquids also, by em- 
ploying a solid of known specific heat, which is dropped into a 
calorimeter containing the liquid under experiment. The procedure 
is the same as for solids, but the calculation differs slightly as shown. 

Heat given out by solid = heat taken up by liquid. 

(wt. of solid x sp. ht. x fall in temp.) 
= (wt. of liquid x sp. ht. x rise in temp.) 
+ (water equiv. x rise in temp.) 

Or, in symbols, 

g = {(W x x) x (/ - / 2 )} - {w x J/gj^/i)} 

where S is the specific heat of the liquid 

x known heat of the solid 
W T weight of liquid taken 

the remaining symbols having the same significance as before. 

Example. To determine the specific heat of turpentine a piece 
of copper (specific heat = '093), weighing TOO grams, was heated tft 
98'2C. and dropped into 125 grams of the turpentine, initially at 
1 8 7 C. The temperature after mixing was 28 2 C, and the water 
equivalent of the vessel 12 grams. This gives the specific heat of 
turpentine as *45 2 - 

When a solid is soluble in water, the specific heat may be ob- 
tained by allowing it to fall into a liquid of known specific heat, in 



40 Heat for Engineers. 

which the solid is insoluble. The calculation is made, as usual, by 
balancing the loss of heat to the gain. It should be observed that 
when a liquid other than water is used in the calorimeter, the water 
equivalent must not be added to the weight of the liquid, but the 
calculation performed in detail. 

The values obtained by the method of mixtures represent only 
the mean or average specific heat of the substance between the tem- 
peratures employed, as the calculation presumes that an equal amount 
of heat is given out for each degree during the fall in temperature. 
This is seldom the case, as at higher temperatures most substances 
give out a greater amount of heat on falling through i than at lower 
temperatures. Or, in general, the specific heat increases with the 
temperature, which it is therefore necessary to specify in connection 
with any given value. 

The specific heat of gases will be reserved for special con- 
sideration. 

Method of Fusion. This method is based on the principle that a 
fixed number of heat units are required to melt i gram of ice at o C, 
producing water at o C. The heat is expended in producing the 
physical change, and is spoken of as " latent " heat. The latent 
heat of fusion of i gram of ice is 80 calories. 

Black, who first used this method, used a block of ice in which 
a cavity had been made, which could be covered by another slab of 
ice, After carefully drying out the cavity with blotting paper, the 
weighed substance, at a known temperature, was dropped in, and 
covered over by the slab of ice. After remaining in the cavity until 
it had fallen to the temperature of the ice, the body was removed, 
and the amount of water collected in the cavity found by absorbing 
it in dry blotting paper (previously weighed) and weighing. The 
increase represented the weight of ice melted, and the specific heat 
was calculated from the equation 

Heat units lost by substance = Heat units gained by ice, 
that is, 

Wt. of substance X S X fall in temp. = Wt. of ice melted X L, 
where S = specific heat, 

L = latent heat of fusion of ice. 

Example. On placing 150 grams of iron at 25 C. into a cavity 
in a block of ice, it was found that 5 i grams of ice were melted. 
The specific heat of iron is therefore, 
c _ 5 ' i X 80 



150 X (25-0) 



= 109 nearly. 



Specific Heat. 41 

Lavoisier and Laplace improved the method, using a vessel con- 
taining broken ice, and furnished with a tap from which the water 
resulting from the fusion could be collected. This vessel was sur- 
rounded by a larger protecting vessel, also containing ice, which 
served to shield the inner one from external heat influences. In 
using the apparatus, the tap of the inner vessel was opened, and any 
water present allowed to drain out. The tap was then closed, and 
the substance inserted, the whole arrangement being covered by a 
lid. The water resulting from the melting ice was then run out at 




7. BUNSEN'S ICE CALORIMETER. 



the tap and weighed, the result being calculated as in Black's ex- 
periment. The results were liable to error owing to the difficulty of 
preventing the water formed from clinging to the ice. 

Bunsen's calorimeter is an arrangement in which the contraction 
produced by ice on melting is measured, the specific heat of the sub- 
stance being deduced from the contraction observed. It consists of 
a large test-tube (T, Fig. 7) sealed into a wider tube, B, with which 
is connected a narrow tube, C, bent into a parallel branch, and ter- 
minating in a wider part, D. Into the upper part of D is passed a 



42 Heat for Engineers. 

fine, graduated tube, E, by means of a cork. By pushing the cork 
into D, mercury may be made to pass to any desired mark along E. 
The test-tube T is surrounded by air-free water, the remainder of B 
and the connecting tube C being filled with mercury. In using the 
apparatus it is completely surrounded by ice or snow in a large 
vessel, the temperature being thus reduced to o C. By bubbling air 
through ether placed in T, the water in contact with the tube is frozen. 
The ice produced will at first be below o C., but on standing will 
attain the common temperature. The mercury is now made to reach 
a fixed point near the end of E, and the weighed substance dropped 
into T, which is then corked up. A certain amount of ice is melted, 
causing a contraction, which is measured by the altered position of 
the mercury in E. The result may be obtained by taking i c.c. of 
contraction to represent 1 2 grams of ice melted, a figure obtained by 
other experiments. If then the tube E be graduated in fractions of 
a cubic centimetre, the amount of contraction may be read off and 
translated into the corresponding weight. Thus a contraction of 
25 c.c. would represent 3 grams of ice melted, requiring 3 x 80 = 
240 calories, which are received from the substance dropped into T. 
The calculation is now identical with that used in Black's method. 
If, however, the tube E be graduated arbitrarily, the value in calories 
of a given contraction is obtained by pouring into T a weighed 
quantity of water at a known temperature, which on cooling to o C. 
would give out a known number of calories. Thus 5 grams of water 
at 20 C. would furnish 100 calories, from which the scale of E can 
be made to indicate calories evolved. 

Example. On placing 5 grams of water at 20 C. in a Bun sen 
calorimeter, the observed contraction was 30-8 scale divisions. On 
placing 20 grams of tin, also at 20 C., in the instrument, a con- 
traction of 6 '95 divisions was observed. 

5 x 20 = 100 calories given out by water, 

therefore 

30*8 scale divisions = 100 calories, 
and 

6-95 scale divisions = 22-5 calories. 

The specific heat of tin that is, the number of calories given out 

by i gram falling i C. in temperature = ^ = '0562. 

20 x 20 

Bunsen's calorimeter may be made to yield very accurate results, 
but owing to the necessity of keeping the apparatus continuously sur- 



Specific Heat. 43 

rounded by ice, is somewhat troublesome to use. The actual ex- 
periment, when the apparatus is ready, may be rapidly performed, 
and the specific heat of solids or liquids obtained with equal facility. 
The instrument, as will be shown later, may also be used to determine 
the latent heat of fusion of ice. 

Condensation Method. When steam at a given temperature 
condenses to form water at the same temperature, a definite quantity 
of heat is given out. Each gram of steam at 100 C., on condensing 
to water at 100 C., evolves 537 calories. Below 100 C. the number 
of calories given out is greater than 537, above, the number is less; 
being definite, however, at a given temperature. The condensation 
method, due to Dr. Joly, is based on this property of steam. 

The apparatus consists of a sensitive balance, from one of the 
pans of which is hung a fine platinum wire, which is attached to the 
substance under experiment. The substance is surrounded by a 
jacket through which steam can be passed, the platinum wire by 
which the substance is held passing through a plaster of Paris stopper 
to the pan of the balance. The hole in the stopper must be large 
enough to allow the wire to hang freely, so that an accurate weighing 
is possible. The suspended substance is first weighed in air, and its 
temperature taken ; after which steam is passed through the jacket 
for a short time, and the weight again taken. The increase in weight 
is due to water condensed on the surface of the solid, the amount 
condensed being that requisite to raise the temperature of the 
substance to that of the steam. The calculation is made from the 
equation 

Weight of substance x specific heat x rise in temp. 
= (weight of steam condensed x L) 

where L is the latent heat of steam at the temperature at which it is 
supplied to the jacket. 

Example. A piece of brass, weighing 50 grams in air, and at a 
temperature of 20 C., was found to weigh 50-707 grams when 
surrounded by steam at 100 C. 

The specific heat of brass is therefore 

537 = . 095 nearly, 



__ 

50 x (100 - 20) 

since the weight of water condensed is 707 gram, and the latent 
heat of steam at 100 C. = 537 calories per gram. 

If a large quantity of the substance be taken, 'more water may be 
condensed than is able to cling to the surface, and an error would 



44 Heat for Engineers 

ensue from drops of water falling off. This difficulty is overcome 
by placing the specimen in a thin copper pan which is hung in the 
jacket from the platinum wire, and serves to collect any drops of 
water which may thus fall off. A blank experiment must be made 
to determine the weight of steam condensed by the copper pan and 
suspending wire, this weight being deducted from the total increase 
observed when the specimen is placed in the pan. 

By using a metallic sphere, in which a quantity of gas could be 
compressed, Dr. Joly was able to obtain the specific heats of gases 
at constant volume. A blank experiment, with the sphere exhausted, 
gave the weight of steam condensed by the sphere itself, and on 
deducting this amount from the total obtained when the sphere was 
filled with compressed gas, the amount of condensation due to the 
gas was found, and the specific heat calculated in the usual way. 

The condensation method furnishes an accurate means of deter- 
mining the specific heat of a solid, and may also be used for liquids, 
which may be sealed up in a glass vessel of known thermal capacity 
and placed on the copper pan. In performing the experiment, the 
steam should be turned on rapidly, as otherwise there is a danger of 
drops condensing on the top of the jacket and falling on to the 
specimen or the copper pan. 

Cooling Method. If two substances, of equal dimensions and pos- 
sessing the same kind of surface, be allowed to cool from the same 
temperature, the rate of cooling will be nearly proportional to the 
specific heats. Thus if two bars of metal of the same size be covered 
with lamp black, and allowed to cool in air from a temperature of 
200 C., the time taken to fall through a given small range of tem- 
perature will be different in each case. Each bar, in the interval, 
loses an equal number of calories by radiation ; but the loss of these 
calories will cause a different alteration in temperature owing to the 
bars possessing different specific heats. This may be used to compare 
the specific heat of two metals, but as the two bars will not be of 
equal weight, it is necessary also to take the specific gravity into 
account, as specific heats refer to equal weights. The procedure 
will be made clear from the following example : 

Example. Two bars of equal dimensions, one of copper and the 
other of aluminium, were coated with lamp black and heated to 
200 C. It was observed that the fall of temperature at the end 
of i minute on the copper bar was attained in 42 seconds by the 
aluminium bar. The relative specific heats, compared by volume, are 

therefore as = . The copper bar, however, was heavier than 
42 7 



Specific Heat. 45 

the aluminium bar in the ratio of their specific gravities, viz. 
?;j = . Hence an aluminium bar equal in weight to the 

copper bar would have required (42 x 3-37) seconds to cool through 
the given interval. Hence 

Specific heat of copper 60 i 

Specific heat of aluminum 42 x 3 -37 ~~ 2 '36'* 

or the specific heat of aluminium is 2*36 times that of copper. 

The cooling method may also be applied to liquids, which are 
compared with water by observing the time required for equal 
volumes to cool through a given range of temperature. The liquid 
is placed in a small copper vessel coated with lamp black, and placed 
in a larger vessel furnished with an ice-jacket, to secure uniform con- 
ditions of cooling. Readings of temperature are taken by a ther- 
mometer placed in the liquid, and time observations are also made. 
The specific heats, for equal volumes, are proportional to the rate of 
cooling \ and the specific heat of equal weight is obtained by 
dividing the volume result by the specific gravity of the liquid. Thus 
if the time taken by 100 c.c. of water to cool through a given interval 
is i minute, and for 100 c.c. of turpentine, through the same interval, 
is 24 seconds, the specific heat of the turpentine is to that of water as 

> = " 4 by volume, and by weight - = 46, the specific gravity 

DO ' 87 

being '87. 

The method of cooling may be made to yield fairly close results, 
but is not of such importance as the other methods. 

Specific Heat of Gases. The quantity of heat required to raise i 
gram of a gas by i C. depends upon the conditions existing during the 
application of the heat. If the gas be allowed to expand freely when 
heated, its pressure will remain constant, and the specific heat will 
have a certain value. If, on the other hand, the gas is contained in 
a closed vessel, and cannot expand, the pressure will increase when 
heat is applied, but the volume will remain constant, and the specific 
heat will be less than that obtained for the gas at constant pressure 
These conditions would be fulfilled if the gas were contained in a 
cylinder fitted with a piston, which is allowed to move in the first 
case, allowing free expansion and maintaining constant pressure ; but 
prevented from moving in the second case, thus maintaining con- 
stant volume. In the first case (constant pressure) the piston is forced 
along against the resistance offered by the atmosphere, and a certain 
amount of heat is converted into work to overcome the atmospheric 



46 Heat for Engineers. 

pressure, over and above that required to heat the gas. This extra 
amount of heat is not requisite in the second case (constant volume), 
consequently the heat expended is greater at constant pressure than 
at constant volume. 

The specific heat of gases at constant pressure may be found by 
the method devised by Regnault, which is a modification of the 
method of mixtures. A known quantity of the gas is passed through 
a copper worm surrounded by boiling water, being thus heated to a 
known temperature. Immediately connected is a copper spiral sur- 
rounded by cold water in a calorimeter, through which the hot gas 
passes, escaping at the temperature of the water surrounding the 
spiral into the atmosphere. By this arrangement the gas is free to 
expand on heating, and consequently the experiment gives results at 
constant pressure. In calculating the result it must be observed that 
the temperature of the gas at the moment of escape into the atmo- 
sphere is not constant throughout, but rises as the temperature of the 
water in the calorimeter rises. In an experiment conducted uniformly, 
the average temperature of escape would lie midway between the 
initial and final, and this is assumed to be the case in the calculation. 

Example. When 60 grams of dry air, heated to 100 C., are 
passed through a spiral surrounded by 200 grams of water at 20 C., 
the final temperature of the water is observed to be 25 C. The 
water equivalent of the apparatus (calorimeter and spiral) is 20 grams. 

The average fall of temperature = ioo-f- ^J = 77 -5. Cal- 
culating as usual, 

60 x S x 77*5 = (200 + 20) (25 20, 
whence 4650 S = uoo 

and S = "236. 

The specific heat of a gas at constant volume may be obtained 
by Joly's steam calorimeter, as previously explained. As the air is 
not allowed to expand, owing to being enclosed in a sphere, the value 
obtained is the specific heat at constant volume. 

For diatomic gases difficult to liquefy, the ratio of the two 

spec, heat at C.P. 

specific heats : that is, 5 r 7-7^ Ar > approximates to i 4 in each 
spec, neat at \j. v. 

case. For gases easily liquefied the ratio varies according to the 
gas, being, in general, less than i 4. The ratio may be obtained 
by calculations on the velocity of sound, and by other means ; and 
hence when the specific heat at constant pressure and the ratio are 



Specific Heat. 



47 



known, the specific heat at constant volume may be calculated. 
It may be added that for monatomic gases (i.e. gases containing 
i atom in the molecule), such as argon and helium, the ratio of the 
specific heats is i 6 to i. The subject will be referred to again in 
Chapter VI. 

Table of Specific Heats. The specific heats of various substances, 
obtained by the methods described, are appended, the experimental 
temperatures also being given. 



Name 


Mean Specific 
Heat 


Range of Tem- 
perature, C. 


Energy required to 
raise i gram i C. 
(ergs X io e ) 


Chemical Elements : 




Between 




Aluminium . 


2122 


15 and 97 


8-91 


Antimony 


0486 


13 1 06 


2'O4 


Bismuth 


'0298 


9 IO2 


1-25 


Cadmium 


0548 


100 


2-30 


Copper 


0933 


15 ,, loo 


3-92 


Gold . 


'0316 


100 


i'33 


Iron .... 


1124 


O ,, IOO 


4-72 


Lead .... 


0315 


19 48 


1-32 


Mercury (liquid) 


0335 


17 48 


1-41 


(solid) . 


0319 


-70 ,, -40 


i'34 


Nickel 


1092 


14 >, 97 


4'59 


Platinum 


0323 


IOO 


i-36 


Silver .... 


0559 


,, IOO 


2'35 


Tin (cast) . 


0559 


IOO 


2'35 


Zinc .... 


0935 


IOO 


3*93 


Other Solids : 








Glass .... 


188 to -198 


15 97 


7-90 to 8-32 


Brass .... 


094 


15 loo 


3'95 


German silver 


094 


2OO ,, IOO 


3'95 


Ice .... 


5^4 


-20 


21 ' 17 


Liquids : 








Alcohol (ethyl) 


615 


at 30 


25^3 


Chloroform . 


235 


,,30 


9-87 


Ether . 


'5 2 9 


,, o 


22*22 


Benzene 


416 


19 and 30 


I7'47 


Sulphuric acid (cone.) 
(+5H 2 0) 


332 
576 


16 ,, 20 
16 ,, 20 


i3'94 
24-19 


Turpentine . 


'454 


at 40 


19-07 


Gases : 








Air (const, press.) 


237 


10 and 100 


9'95 


Oxygen ,, 


217 


ditto 


9-11 


Nitrogen . , 
Carbon dioxide ,, 


244 
216 


" 


10*25 
9*07 


Ammonia , , 


508 


> 


21*34 


Hydrogen , , 


3-410 


" 


143*22 



Heat for Engineers. 



Name 


Mean 
Specific 
Heat 


Range of Temperature, 


Energy required to 
raise i gram i C. 
(ergs X io 6 ) 


Gases : 




Between 




Byjoly's ( Air (const, vol.) 


172 


( 10 and 100 
(from i to 20 ats. press. 


7-22 


steam -< Carbon dioxide 
calorimeter ( const - vo1 ') 


168 


( 10 and loo 
( at 7 ats. press. 
( 10 and 100 


7'06 


V " " 


174 


\ at 22 ats. press. 


7 3i 


Vapours : 








Steam (const, press.) 


480 


100 and 120 


2O' l6 


Chloroform ,, 


157 


100 ,, 200 


6-59 


Ether 


487 


70 ,, 200 


20 -45 



Effect of Temperature on Specific Heat. In general, the specific 
heat of a substance increases with the temperature. Thus, at o C. 
the specific heat of copper is '0901 ; at 100 C. the value is '0965. 
Taking the mean, the specific heat at 50 C. is '0933, the increase 
with temperature being assumed to be uniform. The effect of 
temperature in the case of several substances is given by the following 
formulae : 

Copper . . -0901 + 

Platinum . . '0317 + 

Silver . . . '0547 + 

Iron . . . *io6o + 

Zinc . . . '0901 + 



0000648 t 
'000012 / 
' 000044 / 

00014 / 
'000075 / 



where / is the temperature in degrees Centigrade. 

The specific heat of water has a minimum value at about 40 C., 
being greater at either higher or lower temperatures. If the value 
at 40 C. be called i, the specific heat at o C. is i-oiio, and at 
100 C., 1*0077. The value at 17-5 C. is i '00263, which repre- 
sents the mean specific heat deduced from the results obtained at 
different temperatures between o C. and 100 C. For this reason 
it is advisable to define the calorie as the amount of heat required 
to raise i gram of water from 17 C. to 18 C., as the extreme varia- 
tions in value are less than if it be defined with respect to any other 
given degree. If the specific heat between 17 C. and 18 C. be 
called unity, the value at o C. is 1-0084, and at iooC., 1-0050. 
The same figures represent the number of average calories (17 - 18) 
required to raise i gram of water from o to i, and from 99 to 100 C. 
respectively. 



Specific Heat. 49 

Tilden has shown that at very low temperatures the specific heat 
of certain metals diminishes considerably. Thus nickel, which has 
a specific heat of 1092 between 20 C. and 100 C., shows the value 
0838 between - 180 C. and 15 C. 

Dulong and Petit s Law. This law, as expressed by its dis- 
coverers, states that "the atoms of all elements have the same 
capacity for heat." Or, in other words, if the specific heat of an 
element be multiplied by its atomic weight, the product will be the 
same for each element. 

This law is not universally true if the specific heats are taken 
between the same range of temperature in each instance. In a large 
number of cases, however, the product (specific heat by atomic 
weight) is nearly constant, and approximates to 6-4. For example, 
the atomic weight of mercury is 200, and the specific heat of the 
solid '0319, hence the product is 6-38. Similarly, in the case of tin, 
atomic weight 118, specific heat '0559, the product is 6 '6. On the 
other hand, the product is only 5 * 4 for sulphur, and i 8 for carbon ; 
elements in general having an atomic weight of less than 30 showing 
a less product than 6 4. The law is obeyed by most of the elements 
of atomic weight higher than 30, and is sufficiently general to be of 
assistance in deciding the atomic weight of a new element. 

Effects of High and Low Specific Heats. The fact that water 
possesses a higher specific heat than other liquids renders it the most 
efficient liquid to employ as a cooling agent in the condensers of 
steam-engines and in stills, and also in keeping down the temperature 
of the cylinders of internal combustion engines, and the barrels of 
machine-guns. Any other liquid would have to be used in greater 
quantity to produce the same cooling effect ; and further advantages 
in favour of water are cheapness and non-inflammability. Hence, 
water is universally employed in all cases where a liquid cooling 
agent is required. The high specific heat of water is also responsible 
for the temperate character of insular climates, the surrounding water 
in the summer being for this reason at a lower temperature than the 
land, and in winter at a higher temperature ; hence, winds from the 
ocean are relatively cool in summer and warm in winter, and ex 
tremes of heat and cold are prevented. 

An example of the advantage of a low specific heat is furnished 
by steam-pipe coverings, as in this case, when starting from the cold, 
a low specific heat means a less absorption of heat by the covering in 
rising to its steady temperature. 



50 Heat for Engineers. 



CHAPTER IV. 

EXPANSION. 

Expansion of Bodies on Heating. The general effect of a rise in 
temperature is to produce an increase in the dimensions of the heated 
body ; and conversely, a decrease in temperature usually causes a 
shrinkage in size. There are, however, well-defined exceptions to 
the general rule. Water, on heating from o to 4 C. contracts ; but 
above 4 C. expands. Water, in the liquid state, has therefore a 
minimum volume and consequently a maximum density, at 4 C. 
Indiarubber and silver iodide also contract on heating, and expand 
on cooling. A bar of iron or steel, on cooling from a high tem- 
perature, contracts uniformly to about 740 C., at which temperature 
it suddenly expands, the change, however, being accompanied by a 
rise in temperature. This phenomenon, discovered by Prof. Barrett, 
has been termed the " recalescence " or re-heating of iron or steel, 
and is due to a molecular re-arrangement which causes heat energy 
to be disengaged. It is interesting to note that iron, which before 
recalescence is non-magnetic, is powerfully attracted by a magnet 
immediately recalescence has occurred, which is likewise true of steel. 
In the case of steel more than one recalescence point may be noted, 
and a careful study of the phenomenon has led to important results 
in the treatment of steel when hardening and tempering. Recalescence 
may be retarded by the presence of other metals in steel ; and by 
alloying manganese with steel Hadfield has obtained manganese 
steels almost entirely non-magnetic. Barrett's discovery was the 
starting-point of a series of most valuable researches on steel and its 
alloys, which have been carried out in recent years by M. Osmond, 
the late Sir W. Roberts- Austen, Hadfield, Arnold, and other workers. 
A number of the results obtained are recorded in the reports of 
the Alloys Research Committee of the Institution of Mechanical 
Engineers. 

The amount by which most substances expand for a rise of i is 
very minute ; but in spite of this fact due allowance for expansion or 
contraction is necessary in many engineering structures, and in 



Expansion. 5 j 

mechanisms. The force exerted by the substance, on expanding, is 
considerable ; and if resisted might easily distort the expanding body, 
or any support to which it was rigidly attached. The actual force 
brought into play on expanding is equal to that required to extend 
the substance, mechanically, by the same amount. If, for example, 
an iron bar were heated from o C. to 100 C., the increase in 
length is found to be 'oon cm. per centimetre of length. The 
force necessary to stretch a piece of iron i cm. long, and i sq. cen- 
timetre section, by 'oon cm., is equal to the weight of 2,000,000 
grams. This figure therefore represents the expansive force exerted, 
and also the contractive force when the bar is cooled through the 
same range. The equivalent of this force in British units is a weight 
of nearly 2 tons ; hence the obvious necessity of due allowance for 
free expansion in large girders, etc., which are subject to consider- 
able variations in temperature. 

Coefficient of Expansion. In many cases, such as rules, measuring 
chains, rails, or bridges, the increase in length is the important factor, 
the expansion in other directions not being necessary to take into 
account. In measures of volume, such as a litre flask, and in the 
case of liquids, the increase in all directions must be considered. In- 
crease in length is referred to as " linear " expansion, and increase in 
volume is termed " cubical " expansion. The amount by which a 
given substance expands is expressed in the form of a coefficient, which 
represents the increase in unit length (or volume) for a rise in tem- 
perature of i C. Hence 

coefficient of linear expansion = increase in unit length for 
a rise of i C. 

increase in length on being raised / 
original length x t 

In dealing with cubical expansion, the word " volume " is sub- 
stituted for " length." Occasionally it is necessary to know the in- 
crease in area only, as in the case of a thin plate, in which instance 
the word " area " may be inserted. Problems involving superficial 
expansion only, however, seldom occur in practice. 

The coefficient of linear expansion of solids is always a small 
figure; that of iron being '0000117, an d of aluminium, '0000222. 
Owing to the small value, the coefficient of cubical expansion is ap- 
proximately equal to 3 times the linear. For if a cube of i cm. side 
be taken, and raised in temperature by i C., each side will increase 
in length by a small amount, a, which represents the coefficient of 

E 2 



Heat for Engineers. 



linear expansion. Hence the volume of the cube would become 
(i + a) 3 = i + 3 a + 3 a 2 + a 3 . As a is a minute fraction, its square 
and cube will be excessively small, and terms involving them may 
be ignored. Hence the new volume = i + 3 a, as nearly as pos- 
sible. But the original volume = i c.c. ; hence the cubical expan- 
sion of unit volume for i = coefficient of cubical expansion = 30 
or linear coefficient. 

Determination of the Linear Expansion of Solids. In determining 
the coefficient of linear expansion of solids, a rod of the substance is 
taken and its length measured accurately at a known temperature, t. 
It is then heated to a known higher temperature, /j , and the increase 
in length measured by a micrometer, sphero- 
meter, vernier microscope, a train of levers, 
or optical means. If K = the increase in 
length, and / the length at t, the coefficient 
a, is determined by the equation 

K 




/Xft- /) 

Example. If the length of a bar = 60 cm. 
at 10 C., and increases in length by * 108 cm. 
when heated to 100 C, the coefficient of 

. *io8 

expansion = 



v 
linear 



60 x (100 - 10) 
00002. For each centimetre increases in 
length by -^ of the total increase for 90 
rise in temperature ; hence i cm. increases 
in length by -^^ of the total for a rise of 



Instruments based on each of the above 

FIG. 8. DETERMINATION methods of measuring the exact elongation 
OF THE COEFFICIENT , . . . 

OF EXPANSION OF 01 a bar are muse. A simple form, involving 

SOLIDS. the use of a spherometer, is illustrated in 

Fig. 8. The rod is enclosed in a brass 

tube, T, which is fastened vertically to a stand. The lower ex- 
tremity of the rod passes through a cork in the end of the tube, 
and rests on a glass plate sunk into the base of the apparatus. 
The upper end of the rod is passed through a cork at the top of the 
tube, and is free to move vertically. The spherometer stands on a 
piece of plate glass held on the shelf, S, a hole being drilled in the 
glass to admit of the central support of the spherometer being 



Expansion. 53 

screwed down so as to touch the rod. In commencing the ex- 
periment cold water is run through the tube until the temperature is 
steady, when the screw is rotated until the central support of the 
spherometer just touches the bar. The temperature and reading of 
the spherometer are now taken, and steam allowed to pass through 
the tube for a few minutes. The spherometer screw is now raised 
until it again just touches the top of the rod, when the reading is 
again taken. The difference between this and the previous reading 
gives the elongation of the rod between the starting temperature and 
that of the steam. The length of the rod when cold is measured 
with a metre rule ; a suitable length for the experiment being 70 cm. 
If the spherometer screw possesses 20 threads per cm., and the 
graduated plate be divided into 100 equal parts, the elongation may 
be measured to ^innr P art f a centimetre, or * 005 cm. 

In another form of apparatus a horizontal bar of the substance is 
clamped at one end, the other end being free to move in a groove. 
A micrometer screw is made to touch the free end when cold, and 
afterwards when hot, the elongation of the bar being the difference 
between the readings. The bar is heated by steam circulating in a 
metal tube enclosing the bar. 

A third method consists in making two fine marks on a rod or 
bar of the substance, and measuring the distance between them when 
cold. The bar is then placed in a water-bath, and a vernier micro- 
scope focused over each mark. The water in the bath is then 
boiled, and after a few minutes the microscopes are moved horizon- 
tally by means of a screw until the cross-wire of each microscope is 
again over the mark on either end of the bar. The distance moved 
by each microscope is read off on the scale ; the two distances added 
together give the total increase in length. Roy and Ramsden's 
method is a refinement of this mode of procedure. 

The plan adopted by Laplace and Lavoisier is illustrated in 
Fig. 9. A rod of the material rests on rollers in a trough, and may 
be heated by boiling water in the trough. One end of the bar is in 
contact with the side of the trough, whilst the other end presses 
against a lever. A telescope is pivoted at O so as to be capable of 
moving in a vertical plane. At the commencement of the experiment 
the telescope is horizontal, and is focused on a scale, S, placed at a 
known distance, the division on the scale covered by the cross-wire 
on the telescope being noted. The water in the trough is now boiled 
causing the bar to expand. The lever L, and the attached telescope 
are thereby made to take up a new position, indicated by the dotted 
lines. On looking through the telescope the cross-wire will now 



54 



Heat for Engineers 



appear over another mark B on the scale. The amount C D, by 
which the bar has elongated, is obtained from the ratio = = , 

as O C D and O A B are similar triangles, in which the lengths of 
the sides O A, A B, and O C are known. The coefficient is ob- 
tained, as usual, by dividing the observed elongation by the original 
length and rise of temperature. It is evident that the distance 
between A and B will depend upon the distance of the scale from the 
centre of the telescope ; and by placing the scale a number of feet 
away a very small increase in length may be observed. 



B 




Y////////. 



y///////////////////////////////////////, 



FIG. 9. LAPLACE AND LAVOISIER'S APPARATUS FOR DETERMINING 
THE LINEAR EXPANSION OF SOLIDS. 



Many forms of apparatus exist in which the elongation is mea- 
sured by a suitable train of levers for multiplying the movement of 
the bar or rod experimented on, the effect being increased in some 
cases by attaching a mirror to the end lever, and observing the move- 
ment of a spot of light reflected from the mirror on to a scale placed 
at a known distance. 

The results obtained by one or other of the above methods are 
appended. The amount of expansion for i F. is f of that occurring 
for a rise of i C. The figures in column 3 are therefore f of the 
corresponding figure in column 2. 

The values given in the following table represent the average co- 
efficient between o and 100 C. At higher or lower temperatures 
the value may vary considerably. The mean coefficient for iron, as 
shown in the table, is -0000117 '> but between o and TOOOC. the 
mean value rises to "000015. When values at high or veiy low tem- 
peratures are required, special experiments must be made. 

Of the substances enumerated, ebonite possesses the highest co- 



Expansion. 



55 



COEFFICIENTS OF LINEAR EXPANSION OF SOLIDS 
BETWEEN C. AND IOO C. 



Substance 


Coefficient of 
Expansion per Degree 
Centigrade 


Coefficient of 
Expansion per Degree 
Fahrenheit 


Zinc 


* OOOO2Q2 




Aluminium ..... 


'0000222 


'OOOOI62 
0000123 


Silver 


0000194 


0000108 




'0000180 






*~_fvAjioy 


OOOOIO5 




OOOOI68 








OOOOO93 


Gold 


*fwv\T A A 




Iron ...... 


VA-MJvJ 1 44 

0000117 


"OOOOOoO 
0000065 


Steel (mild) .... 


ooooiio 


0000061 


Platinum ..... 


0000089 


00000494 


Glass (average) .... 


0000087 


00000483 


Nickel-steel alloy (36 per cent, nickel) 


00000087 


000000483 


Platinum-iridium alloy (10 per cent. j 
iridium) / 


00000884 


00000491 




00000868 


oooor* 8 


Sandstone ..... 


0000117 


0000065 


Sulphur ..... 


0000641 


0000356 


Slate 


"0000104 


*ooooo^ 78 


Marble (white) .... 


0000107 


00000594 


Porcelain 


0000045 


0000025 


Brick 


0000055 


00000306 


Deal (white) 


'0000046 


00000255 


Ebonite 


0000770 


0000428 


Lead 


0000280 


00001555 


Pure vitrified silica (up to 1000 C.) . 


00000059 


00000033 


Jena thermometer glass . 


0000080 


0000044 


Ice (between - 27 C. and - i C). 


0000524 


0000291 



efficient, which is 7 times that of steel. Sulphur has also a high value, 
and amongst metals zinc and lead have the highest values. The 
figure for platinum is very low, and almost corresponds with that of 
glass. The various kinds of glass, however, differ considerably in 
respect to amount of expansion, but it is possible to produce glass 
possessing a coefficient practically identical with that of platinum. 
In such glass platinum wire may be sealed so as to form a vacuum-tight 



56 Heat for Engineers. 

joint, and without danger of cracking owing to unequal expansion. 
This property is taken advantage of in the manufacture of electric 
lamps, the interiors of which are exhausted of air, and the current 
furnished to the carbon or metal filament through platinum wires sealed 
through the glass. Platinum is similarly used for the electrodes of 
vacuum tubes, and for all cases where it is desired to obtain an 
electric discharge between two points in the interior of a sealed glass 
vessel. Ordinary soda or lead glass do not always possess a coefficient 
identical with platinum, and often crack on cooling after sealing-in a 
platinum wire. A special enamel of correct coefficient may be pur- 
chased, however, which on heating will incorporate with the glass. 
In sealing a platinum wire into ordinary glass, therefore, it is best to 
blow a small hole at the desired spot and place a collar of enamel 
round the hole, so as nearly to close it. The wire is then pushed 
through, and heat applied until the enamel has thoroughly melted 
round the wire and into the glass in the vicinity. The joint should 
then be gently blown so as to prevent any undue thickness of 
material at any part, and will then be found durable. The sealing of 
platinum into glass hermetically is probably due not only to identity 
of expansion, but also, in part, to the absence of oxidation on the 
surface of the platinum. It is possible to prepare alloys of nickel 
and steel possessing a coefficient of expansion identical with that of 
glass, and there appears to be no good reason, other than possible 
oxidation, why such an alloy could not be obtained which would 
replace platinum in electric lamps, etc., resulting in a great saving in 
the cost of manufacture. 

The extremely low coefficient of nickel-steel, containing 36 per 
cent, of nickel, is of considerable interest and importance. The value 
is only ^ that of glass, and is so small that i mile of wire or rod 
made of this material would only increase in length by a little more 
than \ an inch on being raised by 10 C. The low expansion of this 
and other nickel-steel alloys was discovered by M. Guillame, who 
found that the value given in the table is not attained immediately, 
as is the case with ordinary metals. If the temperature were raised 
by some small amount say from 10 to 30 C. the material would 
have to be retained at the latter temperature for two months before 
expanding by the amount indicated by the coefficient. During this 
period a gradual increase in length would take place, finally attaining 
a maximum represented by the figure in the table. It therefore 
follows that a bar of the alloy, subjected to ordinary fluctuations of 
temperature in the atmosphere, would remain as nearly as possible 
constant in length. This alloy, which does not easily rust, is now 



Expansion. 57 

being applied to the manufacture of standard measures of length and 
volume, for the pendulums of clocks, and other uses. 

Use of Coefficients of Linear Expansion. A few examples are 
given showing the method of employing the coefficient of expansion 
in calculations. It is not necessary, in general, to change British 
units into metric, or vice versa and if temperatures are expressed in 
Fahrenheit degrees the coefficient per degree Fahrenheit is used. It 
must be remembered that the coefficient expresses the increase of 
unit length for i in terms of that unit, thus 

i cm. of brass increases by '0000189 cm. for a rise of i C., 
or 

i foot of brass increases by '0000189 ft. for a rise of i C., 
or 

i mile of brass increases by '0000189 mile for a rise of i C. 

The increase is therefore always expressed in the same unit as that 
chosen for the original length. 

Example. (a) A brass scale, exactly i metre long at 15" C., is 
at a temperature of 35 C. At this temperature the length will be 
i + ('0000189 x 20 ) metre 1*00038 metre (approx.) or 100-038 
centimetres. 

A nickel-steel scale, under the same conditions, would have a 
length of i + ('00000087 x 20) metre = 1*0000174 metre or 
100*00174 centimetres, if it had been kept at 35 C. for two months. 
Or, if i yard long at 15 C, the length at 35 C. would only increase 
by * 00063 f an inch. 

Example. (b) A steel chain, 66 feet long, as used for surveying, 
if correct at 60 F., would have a length at 32 F. of 

66 - (-0000061 x 28 x 66) feet = 65-989 feet (approx). 

(Note that as i foot contracts by '0000061 foot for a fall of i F., 
the total contraction per F. will be 66 x '0000061 foot.) 

The contraction is about -J- of an inch, and the error in measuring 
i mile under the conditions would be 10 inches. 

Example. (c) A glass measure, of capacity 1000 cubic centi- 
metres at 15 C., would at 45 C. possess a capacity of 1000 + 
(1000 x '0000087 x 3 x 30) c.c. = 1000-783 c.c. 

(The cubical expansion is 3 times the linear, and as the vessel 
expands in every direction it will possess the same external dimen- 
sions as if it were a solid piece of glass.) 



58 Heat for Engineers. 

A brass gallon measure, under the same conditions, would in- 
crease in capacity by 

(0000189 x 3 x 30) gallon = "0017 gallon, or about 
of a gallon. 



Expansion of Liquids and Gases. A measured volume of a liquid 
or gas must be contained in a vessel or envelope, and on raising the 
temperature the vessel, as well as its contents, will expand. Liquids, 
in general, have a higher coefficient of expansion than solids ; hence 
if a vessel be filled with a liquid, and heated, a quantity of the liquid 
will overflow. If vessel and liquid expanded by the same amount, 
no overflow would take place. Any measurement of the expansion 
of liquids from the amount expelled from a vessel on raising the 
temperature by a given amount, is therefore only relative, and dif- 
ferent values would be obtained with vessels of different materials. 
The value is always less than the true expansion, as owing to the in- 
crease in size of the vessel some of the liquid is retained, which 
would be expelled if the vessel could be prevented from expanding. 
The true expansion is evidently the sum of the amount expelled and 
the amount by which the vessel has expanded. The same argument 
holds true for gases ; but as gases have a very high coefficient of ex- 
pansion, the increase in size of the vessel is very small by com- 
parison. 

It is customary, in the cases of gases and liquids, to express the 
coefficient of expansion in terms of the volume occupied at o C. or 
32 F. Hence the coefficient of expansion of a liquid or gas may be 
denned as " that fraction of its volume at o C. by which it increases 
on being raised in temperature by i C." Or, when Fahrenheit 
degrees are used, " that fraction of its volume at 32 F. by which it 
increases for a rise in temperature of i F." Many advantages are 
gained, particularly in the case of gases, by defining the coefficient 
with respect to this special temperature. 

Determination of the Coefficients of Expansion of Liquids. The 
methods which may be adopted for obtaining the coefficients of ex- 
pansion of liquids are : (i) The weight thermometer method, in which 
the weight expelled from a full vessel, containing a weighed quantity 
of the liquid, is observed for a given rise of temperature. (2) By 
measuring the increase in volume in a graduated tube of a known 
volume of the liquid. (3) By observing the specific gravity of the 
liquid at different temperatures. (4) By Dulong and Petit's hydro- 
static method, which gives the real expansion directly, without in- 



Expansion. 59 

volving any correction for the expansion of the containing vessel. A 
description of each will now be given. 

Weight Thermometer Method. A vessel furnished with a capillary 
outlet such as a 25 c.c. specific gravity bottle with a bored stopper 
is filled with the liquid at o C. by surrounding with ice, and, when 
cold, inserting the stopper. The bottle is now weighed, and placed 
in a bath of water at a known, constant temperature. When no 
further outflow of liquid through the bore of the stopper is observed 
the bottle is removed, dried on the exterior, and again weighed. The 
decrease in weight gives the amount of liquid expelled, and this re- 
presents the expansion due not to the quantity of liquid originally 
present, but to the liquid remaining in the bottle. For, if the residual 
liquid be heated from o to the higher temperature, it will expand so 
as just to fill the bottle. Hence the expelled liquid, which would fill 
the vacant space in the bottle, measures the expansion of the liquid 
left in. Taking weights as proportional to volumes, the relative ex- 
pansion of the liquid is given by the equation 

W-W, 



where 

W = original weight of the liquid present, 
Wj = weight of remaining liquid, 
t l = temperature to which liquid is heated, 
/ = initial temperature = o C. 

The figure obtained, however, will only be the relative or apparent 
coefficient ; that is, the amount by which i cubic centimetre or i unit 
volume expands for i C., minus the amount by which a glass vessel 
of i cubic centimetre capacity expands for i C. If the latter be 
known, and be added to the apparent expansion of the liquid, the 
real or absolute coefficient is obtained. Or, 

Coefficient of real expansion = (coefficient of apparent or relative 

expansion + coefficient of cubical 
expansion of material of vessel). 

Example. A glass vessel weighs 50 grams when empty, and 
710 grams when full of mercury at o C. On heating to 100 C, 10 
grams are expelled. Hence the coefficient of apparent expansion = 

weight expelled = I0 _ = -000154. 

residual weight x rise of temp. 650 x 100 



6o 



Heat for Engineers. 



Since the cubical coefficient for glass is "000026, the real expan- 
sion coefficient = ("000154 + '000026) = '00018. 

(Note that the total residual weight is 700 grams, of which 50 are 
due to the vessel.) 

The value obtained by the weight thermometer is, of course, the 
average coefficient between the temperatures employed. 

Coefficients of Expansion of Liquids from Measurement of In- 
creased Volume. In this method, due 
to Pierre, the liquid is placed in a 
bulb of known capacity, to which 
is attached a graduated tube. The 
volume of the bulb must be known 
m terms of the graduations on the 
tube. The volume of the liquid is 
read when the bulb is placed in 
ice, and again when immersed in 
a bath at temperature t v The co- 
efficient of apparent expansion will 
then be given by the equation 



\\ - V 
V (A - / 



where 




B 



V = original volume, at C., 
Vj = increased at / 1 C. 

t = original temperature = oC. 

/! = temperature to which liquid 
is heated. 

If a glass bulb be used, the real 
expansion is obtained by adding 
'000026 to the apparent coefficient. 
An improved form of apparatus 
for this purpose has been devised 
by J. Young and the author, and is 
illustrated in Fig. 10. A bulb of 
about 25 c.c. capacity, B, is con- 
nected to a piece of capillary 

tubing furnished with a tap, T, at the lower end, and to a graduated 
tube, A, about 50 cm. long at the top. A thermometer, C, passes 
through a tight joint into the centre of the bulb ; and the instrument 



^^ 

FIG. 10. YOUNG AND DARLING'S 
APPARATUS FOR DETERMINING 
THE COEFFICIENT OF EXPAN- 
SION OF LIQUIDS. 



Expansion. 6 1 

is fixed in a bath, which may be heated by passing steam through 
the pipe, P. The liquid is drawn up into the bulb by placing the 
end of the tube below the tap in a beaker containing the liquid, and 
applying suction at the end of the tube A, to which a piece of india- 
rubber tubing is attached for the purpose. When bulb and graduated 
tube are full, the tap is closed, and the bath filled with ice. When a 
temperature of o C. has been attained, the tap is carefully opened 
so as to allow the column of liquid in A to fall to the zero mark. 
The ice is now removed, and the bath filled with water, which is then 
raised to any desired temperature by passing steam through the pipe, 
P. The thermometer and position of the liquid in A are read when, 
on constant stirring, both readings are steady. Readings may be 
taken every 10, and the expansion at different temperatures thus 
measured. The apparent coefficient may be calculated as before, the 
volume, V, of the bulb up to the zero mark being ascertained by 
filling with mercury at o C., which is then run out and weighed ; the 
capacity of the tube being similarly found. When this has been 
carefully done, a constant may be found from which the coefficient 
can be obtained from the number of divisions through which the 
liquid expands for a given rise of temperature. 

Example. In an apparatus made as described, the capacity of 
the bulb up to the zero mark was 25*2 cubic centimetres ; and each 
division of the graduated tube corresponded to '0305 of a cubic 
centimetre. When turpentine was allowed to expand from o to 
50 C., the column of liquid in the graduated tube reached the 
position indicated by 40 i divisions. Hence the increase in volume 
(apparent) is 40 'i x "0305 cubic centimetres, and the coefficient 

= 40- 1 :_x__' 0305 = . Q0097> Adding the cubical coefficient of glass, 

25-2 x 50 

000026, the real coefficient for turpentine is -000996, or practically 
ooi. 

The values '0305 and 25^2 are constant, and if a number of 
liquids be compared over the same range, / will also be constant in 

the expression a _ x g 

b x / 

where n is the number of divisions through which the liquid expands ; 
g the capacity of i division of the tube ; b the capacity of the bulb ; 
and / the temperature when the starting temperature is zero or o C. 

The value of -% can be calculated, and the figure obtained will, 

b x / 
on multiplying by , give the coefficient for any liquid between o 



62 Heat for Engineers. 

and f C. Taking / = 50 C., as in the previous example, the value 

of ^ is - 3 y 5 = -0000242. If a liquid expanded through 
b x t 25-2 x 50 

20 divisions for a rise of temperature from o to 50 C., a would 
equal 20 x '0000242 = '000484. Or for this range, a = n x 
0000242. 

The advantage of the apparatus described is that the liquid may 
be run out and replaced by another, which is practically impossible 
with a closed bulb. The labour involved in calibrating and filling 
a fresh bulb for each liquid is thus saved. The simplicity of the 
calculation, and the ease with which the expansions may be tested 
over different ranges of temperature, are further advantages. 

Coefficient of Expansion of Liquids from Specfiic Gravity. When 
a liquid expands its density diminishes. If 10 cubic centimetres of 
a liquid expanded to io'5 cubic centimetres, the density would only 
be \^ or f of its former value ; or, in general, the density varies 
inversely as the volume occupied. By determining the specific 
gravity of a liquid at different temperatures it is therefore possible to 
infer the increase in volume, and hence to calculate the coefficient 
of expansion. The specific gravity may be determined by weighing 
a glass stopper in the liquid at o C. and at some higher temperature, 
the volume of the glass stopper at o C. having been previously 
found. The calculation of the result is obtained as in the following 
example. 

Example. A glass stopper has a volume of 4 cubic centimetres 
at o, and weighs 10 grams in air. When suspended in a liquid at 
o C., it weighs 6 8 grams. Hence the weight of the displaced liquid 
is (10 - 6-8) = 3- 2 grams; and as the volume displaced is 4 c.c., 

the specific gravity of the liquid is ? - = 8 at o C. At 80 C. the 

4 
stopper, when immersed in the liquid, weighs 7*033 grams. The 

weight of liquid displaced = (10 - 7*033) = 2*967 grams. The 
volume of the displaced liquid is equal to that of the stopper at 
80 C., that is, 4 + (4 x '000026 x 80) c.c., = 4^0083 c.c. 

Hence the specific gravity of the liquid at 80 = = 2 - J^ ? = -74. 

4-0083 

But volume at 80 80 e 

volume at o -74' 

* ' T c.c. at o C. will occupy - = i 08 1 c.c. 

74 

Hence increase for i c.c. at o C. '081 

d = r = = ' OOIO2t; 

rise of temperature 80 



Expansion. 



The result will be the absolute coefficient, as the expansion of 
the glass stopper was allowed for. The method possesses the two 
drawbacks of difficulty of maintaining a constant temperature during 
weighing, and the necessity of a complicated calculation to obtain 
the result. 

Dulong and Petifs Hydrostatic Method. This method was devised 
by Dulong and Petit for the purpose of obtaining accurately the 
coefficient of real expansion of mercury, a knowledge of which is 
necessary for many purposes, such as correcting the height of the 
barometer for temperature, and also the height of mercury columns 
in general. The result obtained is independent of the size or material 
of the vessels used, and therefore 
gives the real or absolute expansion. 
The method is based on the principle 
that when two liquids, of different 
densities, are in equilibrium in a 
U-tube, the heights above the com- 
mon level vary inversely as the 
densities, and are the same what- 
ever the diameter of either tube. 
Thus if mercury be present in one 
limb, and water in the other, the 
vertical heights, measured from the 
line of contact, will be as i to 13 ' 6, 
or inversely as the densities. If 
a single liquid be present in the 
U-tube, and one limb be heated 
whilst the other is kept cold, the 
hot portion of the liquid will expand 
and fall off in density. When in 
equilibrium, however, the heights 
must be inversely as the densities, 

irrespective of the expansion of the tube ; and if these two heights be 
accurately measured, the alteration in density, and from it the co- 
efficient of real expansion, may be determined. 

Example. The water in the gauge-glass of a boiler is at the same 
level as the water in the boiler, when both are at the same tempera- 
ture. When steam is being produced, the level in the gauge-glass 
is slightly lower than that in the boiler, as the water it contains is 
colder and therefore denser. The water in the boiler may have 
an area many thousand times that of the gauge-glass, but this makes 
no difference to the respective levels. 




FIG. ii. APPARATUS FOR DETER- 
MINING THE ABSOLUTE EXPAN- 
SION OF LIQUIDS. 



64 Heat for Engineers. 

The apparatus depicted in Fig. 1 1 illustrates the manner in which 
Dulong and Petit's method may be carried out experimentally. It 
consists of a U-tube C D, of which the separate limbs are connected 
by a capillary tube, B, which, whilst allowing a free transference 
of pressure between the two limbs, prevents any appreciable transfer 
of heat by conduction or convection from one limb to the other. 
Each limb of the U-tube is surrounded by a jacket, that surrounding 
C containing ice or cold water, whilst that surrounding D is fitted, so 
that steam from a boiler may be passed through. The heights of 
the separate columns of liquid may be measured from the metre scale 
by means of sliders, S, moving over the scale. The zero of the 
metre scale is placed opposite the centre of the capillary connection, 
which represents the common level, and the heights are read off 
when, on passing steam freely, the levels are observed to be constant. 
The heights may be measured more accurately, if desired, by the aid 
of a cathetometer. The result is calculated as under : 

Let /t Q = height of column surrounded by ice ; d its density; 
h t = steam; d l 

Then from the hydrostatic principle that heights vary inversely as 
the densities, 

/* x d = h t x d l . . . . (i) 

or 

(lesser height x greater density) = (greater height 
x lesser density). 

The density, d^ depends on the amount by which the liquid has 
expanded. Let a = the coefficient of real expansion ; then i c.c. on 
heating from o to / would possess a volume of i + a / c.c., and its 

density will be less in the ratio -- 

I + u / 

Hence 

Density at o i + a / 

Density at f ~~ i ' 
or 

d = d l (i + a /). 

Substituting in (i), we have, 

h Q x d (i + a /) == h t x d l 




// (i + a/) = h 



Expansion. 65 

and 



*,-* 



This value is independent of the expansion of the hot limb, 
which, although causing an increase in diameter, does not affect the 
results obtained from the final measurements. During the ex- 
periment, while the hot limb is rising in temperature, the expansion 
increases the diameter and tends to make the hot liquid fall below 
its correct level. A slight flow of liquid from the cold tube, how- 
ever, causes the columns to maintain equilibrium, and thus com- 
pensates for the expansion. Hence the height of the cold column 
falls slightly until the hot column attains the temperature of the 
steam, and its height must be measured at the end of the ex- 
periment. 

Example. The following values were obtained with mercury : 
Height of column surrounded by ice = 91-2 centimetres; of hot 
column at 100 C. = 92-85 cm. Hence 

02 '8^ - 01 '2 

a = y - = * 000181 nearly. 

91 '2 x 100 

When cold water is used instead of ice, the expression (^ - t 2 ) 
must be used in the formula instead of t\ ^ representing the tem- 
perature of the steam, and / 2 that of the cold water. 

In Regnault's modification of the apparatus, the capillary con- 
nection is near the top of the U tube, being sealed across. Con- 
vection currents of the hot liquid, if existing, would merely float on 
the top of the cold column, and not penetrate its mass. The tubes 
are brought into parallel branches at the lower end, and connected 
by a T piece into which air is forced to maintain the weight of the 
columns. The difference of level is read off from the parallel 
branches, and the lengths measured from the centre of the capillary 
tube to the top of the respective columns. This inverted arrange- 
ment ensures the absence of errors due to convection. 

The coefficients of expansion of several liquids are given in the 
accompanying table, the figures representing the mean values 
between the stated temperatures. The mean value for water between 
15 C. and 100 C. is included, but owing to the exceptional character 
of the expansion at different temperatures, special mention will be 
made of the volume changes observed with this liquid. 

Mercury, which possesses the lowest coefficient, expands by almost 

F 



66 



Heat for Engineers. 
COEFFICIENTS OF EXPANSION OF LIQUIDS. 



Substance and Range 


Apparent or Relative 
Expansion in Glass 


Real Expansion = 
(Relative + -000026) perC. 


Per Degree C. 


Per Degree F. 


Per Degree C. 


Per Degree F. 


Mercury o 


and 100 C. 


000155 


0000855 


OOOlSl 


OOOIOO5 


Alcohol o 


40 


OOIII 


000617 


"001136 


000630 


o 


,, i 


'OOIO2 


00057 


001046 


000581 


Ether o 


33 


'OO2IO 


OOII7 


OO2I26 


'OOIlSl 


Benzene 1 1 


80 


00138 


000766 


'001406 


000781 


Turpentine o 


,, IOO 


OOIO24 


00057 


001050 


000583 


Water 15 


IOO 


00045 


00025 


000476 


000264 



exactly the same amount at any range of temperature between o and 
1 00 C. ; and this is one reason why mercury is selected for use in 
thermometers. Alcohol, and other liquids generally, have a higher 
coefficient at higher ranges. Turpentine probably stands next to 
mercury in respect to the uniformity of its expansion. The special 
case of water will now be considered. 

Expansion of Water. In order to observe the peculiarities con- 
nected with the expansion of water, the apparatus of Young and the 
author, illustrated in Fig. 10, is well suited. Commencing at o C., 
by surrounding the bulb with ice, it will be observed that on 
warming the water at first contracts slightly, until the temperature 
indicated is between 5 and 6 C. On further heating expansion 
takes place, and if the amount of expansion be taken at equal 
intervals say every 5 it will be observed to increase progres- 
sively. Between 90 and 95 C. the amount of expansion will be 
observed to be several times greater than that noted between 10 
and 15. In order better to observe the change of volume near the 
freezing point, the graduated tube should possess a very fine bore, 
and the observation started at about 15 C., the graduated tube being 
nearly filled. The temperature is then gradually lowered by adding 
ice to the water in the bath, and the stationary readings of the column 
and thermometer taken. A progressive contraction will be noticed 
until the temperature is about 5-5 C., and below this temperature 
the column will be observed gradually to rise until o is reached. 

It must not be assumed from this experiment that the minimum 
volume of the water is attained at 5 5 C., for the glass vessel is also 
contracting. The shrinkage of the vessel, however, is uniform, and 



Expansion. 



07 



the experiment indicates that at 5 -5 C. the water and glass contract 
by equal amounts, and hence the column is stationary. Below this 
temperature the glass contracts more than the water, until 4 C. is 
reached, hence the liquid is slightly squeezed up the column. After 
4 C. down to o, the water expands and rises in the column, the 
effect being increased by the continued shrinking of the glass bulb. 
In order to prove that the volume is a minimum at 4 C., it is 
obviously necessary to have some means of eliminating the effects 
clue to the contraction of the vessel. This may be done, experi- 
mentally, by placing in the bulb \ of its volume of mercury. When 



64 



56 



48 



I 32 

55' 









O 2 46 8 10 12 14 Dey.C 

FIG. 12. CURVE SHOWING THE VOLUME CHANGES OF WATER 
BETWEEN o C. and 12 C. 

the glass shrinks, thus tending to raise the column, the mercury will 
shrink by an equal amount, and thus prevent the column from rising 
from any cause other than the expansion of the water. The true 
variations in the volume of the water will then be observed, and ttr 
minimum will be found to occur at 4 C. The reason why ^ of the 
volume of the bulb is filled with mercury, is that the coefficients of 
expansion of glass (cubical) and mercury are in the ratio of i to 7. 
Hence } of a c.c. of mercury will compensate for the expansion of 
i c.c. of the glass vessel. 

The results of an experiment with this apparatus, containing -f of 
its volume of mercury, are shown graphically in Fig. 12, in which 

F 2 



68 



Heat for Engineers. 



scale divisions on the tube are plotted against temperatures. The 
lowest position of the column is called zero, and the following are 
the observations from which the curve is drawn : 





Temperature, C. 


Height of Column 









1 6 divisions 






2 


6 






4 


o ,, 






6 


3'5 ,. 






8 


H 






10 


3i'5 






12 


56 





The curve is not symmetrical on either side of the 4 ordinate, 
as the volume at 2 is equal to that at 6 '6, and at o equal to that 
at 8-3. 

The temperature of minimum volume is also that of maximum 
density, and has been chosen as the standard temperature for the 
unit of mass the gram which is the mass of i cubic centimetre 
of water at 4 C. 

The temperature of maximum density is lowered by the presence 
of dissolved salts in water. Thus an 8 per cent, solution of common 
salt has a maximum density at - 16* 6 C. 
Moreover, the expansion of the solution 
at higher temperatures is much more 
uniform than that of pure water. The 
author has found that strong saline solu- 
tions in general have a slightly higher 
average coefficient of expansion than water 
between ioand 85 C., and expand more 
regularly. 

The temperature of maximum density 
of water may be found by Hope's appara- 
tus, Fig. 13. A cylinder containing water 
is surrounded by a gallery in which a 
freezing mixture is placed. Two thermo- 
meters are inserted in the water, one near the surface, and the 
other near the bottom of the cylinder. Soon after the freezing 
mixture is placed in the gallery, the lower thermometer will indicate 




FIG. 13. 
HOPE'S APPARATUS. 



Expansion. 69 

a fall of temperature, whilst the upper one will be unaffected for 
some time. Finally, the lower thermometer will remain stationary 
at 4 C., whilst the temperature indicated at the top may fall to zero, 
and the upper water may finally freeze. The explanation of these 
observations is that the water opposite the freezing mixture, on 
being slightly cooled, sinks owing to the attainment of a greater 
density by contraction. The warmer water below is displaced 
upwards and also cooled, and this circulation continues until the 
main mass of the liquid attains a temperature of 4 C. A further 
cooling causes expansion, and therefore loss of density ; hence the 
water below 4 C. will rise, and the upper portion will be frozen if 
the freezing mixture be sufficiently powerful. The temperature at 
which the convection currents cease to sink is obviously that at which 
the density is a maximum. 

The freezing of a pond of water on the surface only is due to 
the maximum density occurring above the freezing point. The cold, 
upper layers sink until the whole of the water has fallen in tempera- 
ture to 4 C., after which the colder layers, being lighter, will float 
on the surface and finally freeze. The ice becomes thicker by the 
freezing of the layer of water in contact with it, which falls below 
freezing point owing to the low temperature of the ice above. 

Expansion of Gases. The expansion of gases differs from that 
of solids and liquids not only in extent and in uniformity, but also 
in the fact that all gases, under proper conditions, expand by 
practically the same fraction for a given rise of temperature. The 
reason for this identity is to be found in the molecular similarity 
of gases. 

Owing to the ease with which gases may be compressed, it is 
necessary to avoid fluctuations of pressure when measuring the 
coefficients of expansion. It is possible entirely to prevent the 
expansion of a gas on heating by applying moderate pressures, which 
is not the case with solids or liquids. 

The coefficient of expansion of a gas at constant pressure may 
be determined by means of the apparatus illustrated in Fig. 14, 
which is a simplified form of Regnault's apparatus designed by the 
author for laboratory use. It consists of a bulb, B, of about 25 
cubic centimetres capacity, placed at the end of one limb of a U-tube, 
the other end being open. The limb to which the bulb is attached 
is graduated so as to enable readings of the volume of the bulb and 
tube to be accurately taken. At the bend of the U-tube a T-piece, 
furnished with a tap, is sealed on, and the whole arrangement 
surrounded by a water-bath, the tube containing the tap being passed 



70 Heat for Engineers. 

through the cork. The temperature of the bath may be raised by 
means of a steam-coil, the ends of which also pass through the cork. 
In performing the experiment, mercury or strong sulphuric acid is 
made to occupy the bend of the U-tube to a point on the scale near 
the bulb, the gas being confined above the liquid. The columns of 




* steam. 



FIG 14. APPARATUS FOR DETERMINING THE COEFFICIENT OF EXPANSION 
OF GASES AT CONSTANT PRESSURE. 



liquid in the limbs are brought to the same level by means of the 
tap, when the pressure of the enclosed gas will be equal to that of 
he atmosphere. This must always be done before taking a reading, 
in order to ensure constant pressure. The volume is then read, and 
the temperature of the bath noted. Steam is now passed through 



Expansion. 7 1 

the coil, and the bath stirred; a second reading of volume and 
temperature being taken when both are steady. The result is then 
calculated as follows : 

Let V = the volume the gas would occupy at o C. (This may, 
if required, be observed directly by filling the bath 
with ice at the commencement.) 
Vj = volume at temperature t-^ 
V 2 = volume at temperature t 2 
a = coefficient of expansion. 
Then 

Vi = V + (V x a x /J = V (i + a /J, 

and similarly, 

V 2 = V (l + a / 2 ). 
Hence 

Vi = V (l + a /j) = I +a/! 

V 2 V (l + a / 2 ) I + a / 2 ' 

In the above equations it is presumed that the coefficient a is the 
same between o and ^ as between o and / 2 . That this is actually 
the case may be proved by taking readings every 5 from o, when it 
will be found that the increase in volume at 10 is twice that at 5, 
and so on. If a curve be plotted connecting volume with tem- 
perature, it will be found to be a straight line. All the increases in 
volume must be taken with respect to that occupied at o ; or, in 
general, the expansion = .V/ V , where V* is the volume at f and 



V the volume at o. 



From the general expression l = T ^ the value of a may 

V 2 I ~l~ Ct ' 2 

be calculated, as all the other quantities are known. The value 
should be corrected by adding the cubical coefficient of glass. 

Example. In the above apparatus, using air, the volume at ioC. 
was 26-4 cubic centimetres. At 80 C. the volume was 32*9 cubic 
centimetres. 

Hence 26-4 _ (i + 10 a) 

32 9 ~ (i + 80 a)' 
from which 

a = '00364. 

Adding the cubical coefficient for glass, viz. '000026, 

a = '00366. 
The coefficient of expansion of gases at constant pressure may 



72 Heat for Engineers. 

also be obtained by heating a bulb and tube containing the gas to a 
known temperature, the tube being kept horizontal, and containing a 
pellet of mercury to indicate the increase in volume. The internal 
capacity of the bulb, relative to that of a given length of tube, must 
be known, and the calculation made as above. 

The contraction of a gas below o C. shows the same uniformity as 
that observed when cooling from higher temperatures to o. The 
value of the coefficient for gases is '00366, or T ^ s , and the expansion 
of gases may therefore be generalised in the form of a law, known as 
Charles's Law, which states that at constant pressure all gases expand 
by 2^3- of their volume at o C. for a rise in temperature of T C. 
That is, if a gas occupied 273 cubic centimetres at o C., its volume 
would become 274 c.c. at i ; 283 c.c. at 10 ; and so on, increasing 
by i c.c. per degree. It should be particularly noted that the in- 
crease is expressed as a fraction of the volume at o C., and not a 
fraction of the volume at any other temperature. 

If the value of the coefficient of expansion held indefinitely on 
lowering the temperature, the volume of a gas would finally become 
nil. Thus 273 c.c. at o C. become 263 at -10; 173 at - 100 ; 
and at - 273 C. should become o. This cannot be imagined, and 
with every gas physical changes would occur which would cause an 
alteration in properties, so that the law would no longer hold. The 
conception of a perfect gas, however, which would continuously obey 
Charles's law, is useful as a standard of reference. The temperature 
of -273C., at which a perfect gas would possess zero volume, is 
called the absolute zero of temperature. It may be added here that 
different gases do not possess exactly the same coefficient of expan- 
sion, although for gases well above the temperature at which they 
liquefy the variation from the figure ^3- is very small. When a gas 
is near its temperature of liquefaction, the divergence from Charles's 
law is quite appreciable. 

The expansion of gases, and problems arising therefrom, will be 
further referred to in the chapter dealing with the general properties 
of gases. 



73 



CHAPTER V. 

PRACTICAL APPLICATIONS OF THE PROPERTY OF EXPANSION. 

IN all cases where bodies are subjected to alterations of temperature, 
expansion and contraction must be constantly taking place. Although 
in many instances this effect may be ignored, it is of the highest im- 
portance in other cases to make due allowance for free expansion, or to 
take such steps as will reduce the effect of the expansion to a minimum. 
In addition, a number of useful mechanisms depend for their action 
on the expansion of one or more of the parts of which they are 
composed. It is proposed to deal with a number of the various 
applications of this property in the present chapter ; leaving, however, 
the utilisation of expansion for the purpose of measuring temperature 
to a subsequent chapter. 

Expansion of Rails. A line of railway, with the rails bolted 
together, forms a practically continuous bar of metal, and is subject 
to all the fluctuations of atmospheric temperature. Unless due 
allowance were made, the rails on a hot day would tend to arch 
upwards, and in doing so would disturb the sleepers on which they 
are laid and thus make the line uneven. This is prevented by the 
use of slotted or elongated bolt-holes in the rails themselves, and in 
the fish-plates joining two consecutive rails. When bolted together, 
a small space is left between the ends of the rails, which may there- 
fore expand freely over the bolts. The space to be allowed between 
the ends may be calculated in the manner indicated in the following 
example. 

Example. If steel rails, 20 feet long, are laid at a temperature 
of 10 C., allowance should be made sufficient to take the increased 
length at 55 C., which may be attained on a hot day in summer. 
As the coefficient of expansion of steel is -ooooii per C, the 
length at 55 would be 

20 + ('ooooi i x 20 x 45) feet = 20 '01 feet (nearly). 

The space allowance must therefore be 01 of a foot, or nearly \ 
of an inch. 



74 Heat for Engineers. 

As the rails expand freely in both directions, the movement at 
either end is equal to one-half of the total expansion. Hence the 
space will be rilled by two consecutive rails expanding through half 
the interval allowed, the same occurring at the other end of each rail. 

Some engineers have questioned the utility of making an expan- 
sion space, and it is possible that the results ensuing from the absence 
of the space have been exaggerated. It is customary, in some cases, 
to lay tram-lines without spaces, and even to weld the ends together 
in position by means of thermit ; and it is claimed that no serious 
consequences ensue. In any case, the space should be left as small 
as possible, in order to reduce the jolting of the vehicle at the joints 
to a minimum. 

Expansion of Boilers. The difficulty to be contended with in 
boilers is the unequal expansion of the different portions, owing 
to one part being at a higher temperature than another. The 
tendency is to cause buckling, owing to the expansive force, leaving 
the boiler distorted and weakened. This tendency is manifested at 
the ends, which are pushed outwards by the longitudinal expansion, 
and owing to difference of temperature in different parts, a greater 
expansive force is exerted on some sections of the end than on others, 
producing local strains. Permanent distortion may largely be pre- 
vented by the use of tie-rods, which pass through the length of the 
boiler and are fastened at each end. These serve largely to dis- 
tribute the strain, and, on contracting, tend to pull the expanded 
portion back to its original position. 

Another effect of unequal expansion is the tendency to shear the 
rivets in the region of the parts which expand most. Wherever pos- 
sible, such parts should be strengthened by tie-rods or other means. In 
the flue of a stationary boiler the temperature on the surface in con- 
tact with the fire is much greater than that possessed by the other 
surface, which is at the temperature of the water in the boiler. The 
result is a tendency to arch outwards, as the outer surface expands 
more than the inner, the effect being to weaken the riveted joints. 
The flues are strengthened by the presence of cross-tubes, riveted to 
the flue at both ends, and which also serve as heating surfaces and to 
promote circulation. 

Reference may be made here to the statement, common in text- 
books, that boiler-plates are fastened together with hot rivets because 
the plates are drawn close together by the contraction of the hot 
rivet. The real reason why hot rivets are used is that it would be a 
practical impossibility to form the head if the rivet were cold. 
Although the rivet, if rapidly finished off, may tend by its longitudinal 



Allowance for Expansion. 75 

contraction to draw the plates together, a lateral contraction occurs 
also, with the result that a space is formed between the rivet and the 
hole, and leakages of steam frequently occur on this account. To 
avoid this the leaky rivet is caulked to ensure a good contact of the 
rivet head with the plate, and thus close all channels through which 
steam might escape. 

Steam-pipe Joints. Owing to the expansion of pipes conveying 
steam, there is a tendency for the joints to break and cause a leakage 
of the steam. This is avoided by making telescopic joints, so that, 
on expansion, the pipes may slide over each other, tightness being 
secured by a stuffing gland. The difficulty may also be overcome by 
inserting elbows or loops in the length of the pipes, which possess 
sufficient flexibility to take up the expansion. A third method is to 
join the ends of two consecutive pipes to a flexible copper chamber, 
which gives to the expansion. 

Expansion of Pistons. In steam-engines, and also in internal 
combustion engines, the temperature of the piston is higher than the 
average temperature of the cylinder, and hence will expand more. A 
tight joint is secured by the use of piston rings, which spring out- 
wards and make contact with the cylinder. The expansion is taken 
up by the piston ring, the ends of which are left a small distance 
apart to allow for the extension, and thus prevent the piston from 
jamming. 

In some forms of petrol engines, used for automobiles, the piston 
ring is continuous, and made of such a size as exactly to fit the 
cylinder when the engine is working ; the piston and ring having in- 
creased in diameter. This method prevents leakage through the 
piston, which is always liable to occur through the space between the 
ends of the piston ring when not continuous. On the other hand, 
much more exact fitting is required to ensure a good contact between 
the ring and cylinder. 

Shrinking of Tires and Angle-iron Rings. The iron tires of wheels 
are made to fit tightly on the wooden rim by placing them in position 
whilst red-hot. The contraction on cooling ensures a tight grip on 
the rim. The diminution in diameter may be calculated as follows : 

Example. An iron ring having a mean diameter of 2 feet at 
850 C., will, on cooling to 10 C., possess a mean diameter of 

24 (24 x "000014 x 840 inches) = 23*718 inches. 

Hence the diameter contracts by '282 of an inch, or more than \ of 
an inch. 

It should be noted in the calculation that the ring shrinks to the 



76 Heat for Engineers. 

same extent as would a hot iron rod or spoke placed across it ; for 
since the ring diminishes in circumference by (TT d x a x /), where / 
is the fall in temperature, the diameter will be lessened by 

"***' = d X a x t. 



The mean coefficient of expansion of iron (linear) between 10 
and 850 C. a full cherry-red heat is -000014. 

It will be seen from the foregoing example that the increase in 
size of an iron ring, when heated to a full cherry-red, is rather more 
than \ of an inch per foot of diameter. This permits of the ring 
being easily slipped over a rim which has a diameter equal to, or 
slightly more than that of the ring when cold. 

Angle-iron rings are placed on the ends of the barrels of boilers, 
etc., in the same way. The ring must be placed exactly in its correct 
position before cooling, as afterwards it would be difficult to move. 
Strengthening bands round cylinders of various kinds are often 
shrunk into position in a like manner. The sections of a gun are 
similarly shrunk together. 

Permanent Decrease in Size by Rapid Cooling. A bar of wrought 
iron, if heated to a full red heat and suddenly quenched in cold 
water, undergoes a permanent decrease in length; and if again 
heated and quenched will undergo a further contraction. Box found 
that a bar of iron 40 inches long, and -J of an inch diameter, con- 
tracted by TgVfr part of its length on the first quenching, and continued 
to contract by diminishing amounts up to 20 quenchings, at the end 
of which the total contraction was y-J-g- part of the original length, or 
4 of an inch. This property is sometimes utilised in reducing the 
size of a hole in wrought iron which has accidentally been bored too 
large. Experiments were also made by Box on the permanent con- 
traction of a tire originally 7 feet in diameter, with the result that 
after n heatings and quenchings the diameter was diminished by 
if inch. 

Contraction of Metal Castings on Cooling. The size of a casting 
when cold is, in general, less than that possessed when in the liquid 
state. In most cases, the contraction takes place in two stages, viz. 
a contraction during solidification, and a further shrinkage of the hot 
solid. Cast iron, bismuth, and antimony, possess the exceptional 
property of expanding in the act of solidification ; and in the case of 
bismuth this expansion is so great as to exceed the subsequent con- 
traction of the hot solid. Hence cold bismuth possesses a greater 
volume than the liquid metal. In the case of cast iron, the con- 



Contraction oj Metal Castings. 



77 



traction on cooling is greater than the expansion on solidification ; 
hence the cold casting is smaller than the mould in which the molten 
metal is poured. With brass, lead, tin, zinc, aluminium, and other 
metals and alloys, a shrinkage occurs both on setting and in the 
subsequent cooling. The relation between the volumes when cold 
and molten respectively is of importance in the making of patterns. 
By making due allowance for the volume changes, the size of the 
pattern may be regulated so as to produce a casting of a given size 
when cold. 

The following table gives the results of Robeits- Austen's ex- 
periments on the relation between the cold and mo, ten volumes of 
different metals : 





Name 


Percentage of Increase or De- 
crease in Volume on Changing 
from Cold Solid to Liquid 






Copper ...... 


Increase of 7 I 






Lead 


9'93 






Tin 


6-76 






Zinc 


,, ii'i 






Silver 


,, II-2 






Iron (Cleveland Foundry) 


1-02 






Bismuth ..... 


Decrease of 2*3 





In considering a casting of any given shape, it is correct to assume 
that the shrinkage along any side is proportional to its length. Thus 
in casting a rectangular block, i foot by 6 inches by 3 inches, the con- 
traction in each direction would be as 12 : 6 : 3. Hence if the con- 
traction per foot be known, the pattern may be made proportionately 
longer in each direction. The contraction per foot of length for 
several metals and alloys is appended : 





Name 


Contraction per foot of 
Pattern or Mould 






Cast iron 


T ^y of an inch 






Brass 


to T 3 5 of an inch 






Gun metal 


to*k 






Zinc 


J of an inch 






Aluminium 


i .. 





7 8 Heat for Engineers. 

The above figures represent the allowance made in practice for 
the metals enumerated, and are only approximate, as the total con- 
traction depends on the temperature at which the metal is poured, 
and the expansion of the mould. The addition of the value to each 
foot of length ensures a close approximation to the desired size in 
the cold casting; and the pattern is therefore made by adding to each 
finished dimension the amount indicated in the table. Thus the size 
of a pattern for a gun-metal casting, of finished dimensions 2 feet x 
i foot x 6 inches, will be 2 feet f inch x i foot T 3 g- inch x 6^- inches. 
To save the labour involved in calculating the allowance to be made 
for a given dimension, special rules are made, on which the markings 
are longer than those of a standard rule by the proportionate amount 
of contraction of the metal. For gun metal, a 2 feet contraction rule 
is in reality 24! inches long, and is divided into 24 equal parts, these 
being sub-divided into quarters, eighths, and sixteenths. Contraction 
rules to suit various metals and alloys are in use for the purposes of 
pattern making, and ensure correct size in the finished casting. 

Allowance for Expansion in Girders. If long iron or steel 
girders, as used for bridges, roofs, etc., were rigidly fastened to their 
masonry supports, the effect of expansion would be either to distort 
the shape of the girder, or break down the supports. In the case of 
large steel bridges, the difference between the minimum and maximum 
length is considerable, and free allowance for expansion is absolutely 
necessary. 

Example. The total length of the Forth Bridge is 8100 feet. 
Taking the difference between the lowest winter temperature and the 
hottest summer temperature as 45 C., the difference in length between 
the two extremes is (8100 x -0000117 x 45) feet = 4*265 feet. 

The expansion is taken up by allowing the ends of the girders free 
movement over rollers, upon which they are mounted ; or by attach- 
ing the free end of the girder to a knuckle which permits of sufficient 
movement in either direction. A third method is to insert lattice- 
work with free joints in the girder, which is capable of movement 
outwards or inwards. The steel rails laid over a bridge of the same 
material will, of course, expand or contract by the same amount as 
the bridge itself. 

The distortion due to expansion is strikingly shown when a fire 
occurs in a building constructed with a steel framework. The walls 
of the building are pushed outward, and the girders themselves 
become twisted and bent out of shape. 

Breakage Due to Sudden Expansion or Contraction. A tumbler, 
or other thick glass vessel, when suddenly heated by pouring in hot 



Breakage due to Expansion and Contraction. 79 

water, is liable to break or crack. This arises from the fact that 
glass is a bad conductor of heat, and is brittle ; hence when heated 
suddenly the superficial layer expands before the heat has penetrated 
to the rest of the material. A strain sufficient to crack the glass is 
thus produced ; and for a like reason the sudden contraction of the 
surface produced by the rapid cooling of hot glass in water causes 
breakage. Molten glass, however, may be dropped into water with- 
out breaking, as the molten interior gives way to the contraction of 
the outer layer. Glass thus treated, however, is peculiarly unstable, 
and will break into fragments on penetrating the outer layer. The 
well-known Rupert's drops and Bologna phials are examples of glass 
which has been quenched in this manner. 

Thin glass vessels are not so liable to break as thick ones on 
sudden heating or cooling, owing to the short time required for the 
outer and inner layers to attain the same temperature, and to the pos- 
session of greater flexibility. Hence beakers and flasks intended for 
boiling liquids are made as thin as possible, consistent with strength. 
Some kinds of glass are specially flexible, and may be safely heated 
or cooled suddenly over a larger range of temperature than ordinary 
glass. Jena glass is superior to others in this respect, although other 
special " resistance " glasses are nearly as good. 

Quartz vessels, which may now be obtained, show a remarkable 
resistance to breakage on sudden heating or cooling, and may be 
plunged at a red heat into water without damage. This property is 
probably due to the very low coefficient of expansion of the material, 
combined with a high degree of flexibility. It may be added that 
metal vessels will endure a sudden expansion or contraction safely 
owing to the rapid attainment of the same temperature throughout, 
and to the possession of the properties of malleability and ductility, 
owing to which metals readily alter in shape. 

Correction of Measures of Length. The standards of length in 
different countries are usually bars of bronze on which fine marks 
are engraved at certain distances. The British standard yard is the 
distance between two fine lines drawn on pieces of platinum inserted 
in a bronze bar. It is obviously necessary to specify a temperature 
at which the true yard is defined, and 62 F. = i6 2 C., has been 
selected as the standard temperature. The advantage gained by 
defining the yard with respect to this temperature is t at the average 
temperature of a room in Britain is approximately 62 F., and fairly 
exact comparisons may be made without special temperature pre- 
cautions. The standard metre is defined with respect to the tern- 



& Heat for Engineers. 

perature of melting ice, or o C., which is a definite temperature 
easily obtained experimentally. 

Many accurate copies of the true standards are in existence, from 
which the various workshop gauges are made. It is necessary, when 
making accurate measurements of length as in establishing a base 
line for an accurate survey to make due allowance for the alteration 
in length of the measuring arrangements caused by expansion or con- 
traction. This may be accomplished by calculation from the known 
coefficient of expansion of the material, or by using a standard of 
length which is so constructed as to be of constant length at all 
atmospheric temperatures. The principle upon which such stan- 
dards are made will now be described. 

Measures of Constant Length. The fact that metals on heating 
expand by different amounts has been applied to constructing a 
measure of constant length, the principle of which will be understood 
from Fig. 15. The constant length is the space between two lines 



FIG. 15. PRINCIPLE OF MEASURE OF CONSTANT LENGTH. 

engraved on the ends G and H of the bars G D A, HFC, which are 
fastened at the lower end to a rod of brass, ABC. At the points 
D and F, distant by f of the length of A G or H C, is fastened a bar 
of iron D F. As the coefficient of expansion of iron is to that of 
brass nearly as 3 : 5 (exactly, as 13 : 21), it follows that a rise of 
temperature will cause the extremities G and H to be moved as much 
outwards by the iron bar as the brass bar tends to pull them inwards, 
the net result being that the distance between G and H is constant. 
On cooling, the contraction of the brass bar tends to move G and H 
outwards, but this is again neutralised by the contraction of the iron 
bar. Constancy of length is therefore secured when the cross-bars 
are distant from the ends G and H in the ratio of the respective co- 
efficients of-expansion. Zinc is sometimes used instead of brass, in 

which case the ratio = 00002 9 2 = 2_j>^ Instruments based 

0000117 i 

on this principle are of great service in the accurate measurement of 
base lines for surveys, as the necessity of taking temperature read- 
ings, and thereby correcting for expansion, is avoided. 

It is highly probable that for all but the most exact work, nickel- 



Correction of Measures for Expansion. Si 

steel measures will supersede other forms. The extremely low co. 
efficient of expansion of this alloy has previously been referred to. 

Correction of Measures of Volume, Measures of volume, like 
measures of length, are subject to fluctuations owing to alterations of 
temperature. The British standards of volume are constructed of 
brass, and defined with respect to 62 F. A standard litre, or 1000 
cubic centimetres, should hold exactly IOOD grams of water at 4 C. 
When standardised to read correct volume at another temperature - 
such as i5C. a litre measure should possess the same volume at 
15 C. as that occupied by 1000 grams of water at 4 C. It is more 
convenient, in practice, to use a vessel of standard size when at an 
average temperature, e.g. 15 C., than one standarised at 4 C., as in 
all ordinary measurements the discrepancy caused by expansion or 
contraction may be neglected. 

Example. A litre flask, correct at i5C., would increase in 
volume at 20 C. by (i x '000026 x 5) = '00013 litre, or '13 of a 
cubic centimetre ; and at 10 C. would diminish in volume by a like 
amount. The variations of temperature in a room in which the 
vessel would be used would not greatly exceed 5 C. on either side 
of i5C., and the alteration in volume is for ordinary purposes 
negligible. If made correct at 4 C., the error at 20 C. would be 
416 of a cubic centimetre, or more than 3 times as great as before. 

The glass measures usually sold, such as flasks, pipettes, burettes, 
and measuring cylinders, are only approximately correct, and. 
wherever great accuracy is required, should be tested at the National 
Physical Laboratory, and a table of corrections obtained. The same 
applies to the metal vessels used for the measurement of volume 
commercially in Britain. When the exact volume at a given tem- 
perature is known, the capacity at any other temperature may be 
calculated from the coefficient of expansion. 

Correction for Expansion of Liquids. The comparatively high 
coefficient of expansion of liquids causes a considerable alteration in 
volume for a moderate rise of temperature. When liquids such as 
petroleum and its extracts, or alcohol, are purchased in bulk, an ap- 
preciable error might arise unless the temperature be taken into 
account. Thus 100 gallons of alcohol at 10 C. expand to ioi'i 
gallons at 20 C., or more than i per cent, for a rise of 10 C. The 
increase in the case of petroleum is slightly larger; and hence it is 
necessary, in order to secure the correct quantity, to allow a greater 
volume according to the temperature. This can be accomplished 
readily by specifying a definite weight to represent i gallon, and cal- 
culating the extra volume from the observed specific gravity. 



82 Heat for Engineers. 

Example. i gallon of a liquid, of specific gravity = '80 at 
62 F., would weigh 8 Ib. If the coefficient of expansion = 'ooi 
per i C., then at 80 F. the volume would increase by i per cent., 
and the specific gravity would fall to -792. If the gallon of 8 Ib. 
were specified as the standard, it would be necessary to provide an 

increased volume at 80 F. in the ratio of - , or an extra gallon 

792 

for every hundred. Or, in general, r- - - = volume in 

observed sp. gr. 

gallons which weigh 8 Ib. 

The specific gravity of a liquid frequently furnishes a clue as to 
its purity, as in the cases of milk, spirits, oils, etc. In other instances 
e.g. acids and alkaline solutions the specific gravity is an indi- 
cation of the chemical strength. In all thcs3 cases temperature pre- 
cautions are necessary. The specific gravity at any temperature is 
the ratio of the weight of i cubic centimetre of the substance com- 
pared with that of i cubic centimetre of water at 4 C. It would be 
very inconvenient in practice to reduce the temperature of a liquid 
to 4 C. to obtain the weight of i c.c., and hence it is customary to 
determine the figure for the liquid at the more convenient tem- 
perature of 15 C. If T c.c. of a liquid at 15 C. weighs i '45 grams, 
its specific gravity at 15 C. is i "45, as i c.c. of water at 4 C. weighs 
i gram. It should be noted that if both liquid and water are weighed 
at 15 C. a slightly different result is obtained, as i c.c. of water at 
15 C. weighs -999 gram. In recording a result, it is customary 



to insert the temperatures; thus "specific gravity = 1*45 

means that the substance at 15 C. is i -45 times as heavy as an equal 
bulk of water at 15 C. The true specific gravity at t would be ex- 

pressed thus : " Specific gravity = ( Y" signifying that the weight 

\4 / 

of i c.c. at t had been compared with that of i c.c. of water at 4 C. 
Much confusion may arise unless this method of recording the result 
is observed. 

Another instance in which an appreciable error may arise owing 
to the expansion of liquids is round in the use of standard solutions 
for chemical analysis. This source of error is too frequently ignored, 
and volumes oi" the solution are often recorded to -^ of a cubic cen- 
timetre when tnc expansion error may be as much as y 1 ^ of a c.c. 
When a standard solution is made up, the temperature should be 
noted, and in using afterwards the temperature should not vary by 
more than 5 C. on either side of the standard temperature. In 



Thermo- Regulators. 



" normal " solutions, a difference of 5 C. alters the volume by 2 of a 
c.c. per 100, or '2 per cent. a quite appreciable error in exact 
analysis. An example will make this clear. 

Example. Normal sulphuric acid (49 grams per litre, or neail/ 
5 per cent, acid), has a mean coefficient of expansion, between 15 C. 
and 25" C., of '0004. If correct at 15 C., and used (on a hot day) 
at 25 J C., the increase in volume per 100 c.c. would be (100 x 
0004 x 10) = -4 c.c. If only 25 c.c. were used in the deter- 
mination, the error would still be i of a c.c., an amount which is 
often of importance. It is therefore evident that refinements in 
reading the volume are useless unless 
the temperature be allowed for. 

Thermo- Regulators. The property 
of expansion is utilised in the instru- 
ments known as therm o-regulators, the 
object of which is to secure a constant 
temperature automatically. A simple 
form is illustrated in Fig. 16, intended 
for use in conjunction with a gas supply, 
which is regulated so as to maintain a 
constant temperature in a hot-air oven. 
It consists of a large bulb of mercury 
connected to a tube of fine bore T, 
widened at the upper end so as to re- 
ceive the gas inlet G, which is inserted 
so as nearly to touch the top of the 
mercury column. The gas escapes 
through the side-tube S, which is con- 
nected to a burner beneath the oven. 
On placing the bulb in the oven, the 
mercury will expand until the opening 
of the inlet-tube G is covered, and the 
gas supply cut off. The temperature 

then falls, and the mercury contracts, again admitting gas to the 
burner, which is never entirely extinguished owing to the small con 
stant supply of gas which passes through a fine hole H, in the inlet- 
tube. The temperature at which the main supply is cut off may be 
regulated by the screw D, which enables the column of mercury in 
T to be brought to any desired distance from the end of the gas 
inlet-tube. The adjustment may be carried out so as to maintain a 
temperature in the oven not varying by more than i or 2 degrees 
from that required. 

G 2 




FIG. 16. 
THERMO- REGULATOR. 



84 Heat for Engineers. 

More sensitive thermo-regulators may be made by using a liquid 
of high coefficient of expansion to push up the mercury column. 
Thus alcohol, for a given rise of temperature, expands 6 times as 
much as mercury, and is therefore more sensitive when used in a 
thermostat. It cannot be used above 79 C., at which it boils; but 
for higher temperatures, up to about 140" C., turpentine may be used. 
A very close approach to a constant temperature can be obtained 
with these liquids. In some forms air is employed, which by expand- 
ing raises the mercury column. 

Many forms of thermo-regulator are in use, of which mention 
may be made of a specially sensitive type used in the electrical testing- 
department of the National Physical Laboratory. In this case the 
compound formed by absorbing ammonia gas in silver chloride is 
used in a tube connected to a mercury column, which, on rising, 
closes the gas inlet. This compound possesses a high vapour pres- 
sure, which increases considerably for a small rise of temperature, 
and hence causes the mercury column to close the inlet, either 
wholly or in part, whenever a very slight increase of temperature 
occurs. This arrangement forms a very sensitive thermo-regulator. 

Fire Alarms. Many devices are in use for raising an alarm when 
the temperature of a room rises to such an extent as to indicate the 
existence of a fire. One form of fire-alarm consists of a mercury 
thermometer made with a large bulb and wide-bore tube. Into the 
bulb is sealed a platinum wire, to which is connected one terminal 
of an electric bell. Another piece of platinum wire passes through 
the open end of the tube, and may be raised or lowered so that its 
end is opposite any temperature on the scale. This wire is con- 
nected with the other terminal of the bell, and when the mercury 
rises so as to touch its extremity, the circuit is completed and the 
bell rings. In an ordinary room, on a hot summer day, the tempera- 
ture seldom rises above 80 F. = 26'5C., and hence if the in- 
strument weie adjusted to ring at 100 F., and the bell rang, a fire 
in the room itself or the vicinity would be indicated. In stores for 
inflammable liquids, etc., the instrument would be set to ring at a 
lower temperature, and thus would indicate the existence of dan- 
gerous conditions. 

In another form of fire-alarm a flexible metallic drum, filled with 
air, is used. When the air inside the drum is heated, the expansion 
causes the flexible end of the drum to make contact with a metallic 
stop, and thus to complete an electric bell circuit. The distance of 
the stop from the end of the drum may be regulated by a screw, and 
hence the temperature at which the bell rings may be regulated. 



Applications of Compound Strips. 85 

The advantage of this form is its portability, and the absence of any 
glass parts liable to breakage. Many serious fires have undoubtedly 
been prevented by the use of fire-alarms, owing to the early warning 
obtained. 

Principle, of the Compound Strip. If two pieces of different metals 
be fastened together, either by soldering or riveting, the compound 
piece thus formed will, in general, undergo a change in shape on heat- 
ing or cooling. If, for example, a strip of brass is fastened to one 
of iron, the effect of heating will be to make the compound strip 
assume a curved shape, the brass part occupying the outer portion of 
the curve. Cooling will also cause arching, but in this case the 
brass will occupy the inner portion of the curve. The alteration in 
shape is due to the different amounts by which brass and iron 
expand on heating, or contract on cooling; hence if each com- 
ponent has the same length at ordinary temperatures, the brass, 
which possesses the greater coefficient of expansion, will be longer 
than the iron on heating, and shorter on cooling. The outer portion 
of the curve is longer than the inner portion, and hence will always 
be occupied by the metal which, under the circumstances, is the 
longer. This alteration in shape has been utilised in the construc- 
tion of numerous instruments, some of which will be described in 
the succeeding paragraphs. 

Compensated Balance }V heel for WatcJies. The principle of this 
wheel may be understood by reference to Fig. 17, A. The rim is a 




A B 

FIG. 17. COMPENSATED BALANCE-WHEEL OF WATCH. 

compound strip of brass and steel, the brass being on the outer side. 
In the form illustrated the rim is made in three segments^ each of 
which is attached at one end to a spoke, the other end being free. 
Each segment is provided with an adjustable weight, and the object 
is to arrange that the centre of gravity of the rim and weights shall 
remain at a constant distance from the pivot at all temperatures, in 
which case the period of oscillation will be uniform. The effect of 



86 Heat for Engineers. 

a rise in temperature is to cause the spokes to increase in length, 
thereby tending to move the ccrTre of gravity of the rim and weights 
further from the pivot, in which rase the period of oscillation would 
be slower. Simultaneously, however, the rim increases its curvature, 
or forms a more acute arch, thus causing the weights to move nearer 
the pivot, and consequently bringing the centre of gravity inwards. 
If these opposite tendencies be exactly equal, the result is to obtain 
a constant distance between the centre of gravity and the pivot, and 
this result may be attained by adjusting the position of the weights 
on the segments, as it is evident that the displacement of the centre 
of gravity is greatest when the weights are at the free end, and 
diminishes as the weights are moved along the segment. The correct 
position is found by trial of the watch at different temperatures. 

Fig. 17, B, represents a common form of compensated balance 
wheel. The centre of gravity of the rim may be altered in position 
by screwing the studs outwards or inwards, and the adjustment is 
finer than that obtained by the use of sliding weights. The rim 
consists of two segments, er.ch attached at one end to a single bar 
or spoke. The correct adjustment for temperature is a tedious 
process, involving frequent alterations and trials at different tempera- 
tures. Many cheap watches are provided with a wheel of this type 
for the sake of appearance, but have never undergone a correct 
adjustment. It is quite possible for such a watch to keep worse time 
than one furnished with an ordinary wheel, as the centre of gravity 
may undergo a greater displacement than that produced by expan- 
sion in a simple wheel. 

The Pearson Pire- Alarm. In this device the increased arching 
of a compound strip is made to complete an electric circuit and thus 
cause a bell to ring. A thin, bi-metallic strip, about 6 inches in 
length, is made into the form of an arch and fastened at both ends. 
On? wire of the bell circuit is connected to the compound strip, and 
the other to a screw, the point of which may be brought to any 
desired distance from the centre of the arched strip. When the 
temperature rises, the strip forms a more acute arch, and touches 
the screw, thus completing the circuit and giving the alarm. The 
arrangement permits of adjustment for any desired temperature, by 
altering trn distance of the point of the screw from the strip. By 
employing very thin metals for the compound strip, the sensitiveness 
of the instrument is greatly increased, as the temperature of the sur- 
rounding air is then rapidly attained. By placing an instrument in 
each room of a building, and connecting indicators in the circuits, 
it is possible to locate the room in which a dangerous temperature 



Steam- Traps. 




exists, as the fire-alarm bears the same relation to the electric circuit 
as an ordinary push. This form of fire-alarm is much used, bein" 
more sensitive, and less liable to breakage, than other forms in which 
an expanding liquid is used. Compound strip fire-alarms are much 
used in cold stores, to give warning o f either too high or too 
low temperatures, and are called in this connection " thermostats." 

Jjreguet's Metallic Thermomtter. This instrument consists of a 
thin, triple strip of platinum, gold, and silver, the gold strip being in 
the centre. The strip is made into a 
spiral, with the silver face innermost ; 
one end of the spiral being fixed, and 
the other end, to which a light pointer 
is attached, being free to move. When 
the temperature rises, the silver expands 
more than the gold or platinum, causing 
the spiral to unwind, the reverse effect 
being produced on cooling. The pointer 
at the free end of the spiral moves over 
a scale, graduated in degrees by com- 
parison with an ordinary thermometer. 
The arrangement is very sensitive, but 
has little practical utility. 

Steam-Traps , or }Vatcr Ejfdors. In 
steam pipes and the cylinders of steam- 
engines, condensation takes place owing 
to cooling, and various devices are in use 
for removing the condensed water auto- 
matically. These mechanisms are known 
as steam-traps, and work on the common 
principle of causing an outlet to open 
when cooling occurs, through which the 
water is ejected by steam pressure ; the 
outlet closing when the temperature rises. 
Typical examples will now be described. 

Vaughan and Stubbs' steam-trap (Fig. 
1 8) consists of a brass tube B, which 

communicates with the steam-pipe P, and is surrounded by an iron 
tube A. The lower end of the brass tube is made conical so as 
to fit on the valve V, and is open to the outlet O, when not in 
contact with V. When the tube B is full of steam, its length is such 
as to cause it to press firmly on V, and consequently no steam 
escapes. When, however, a quantity of condensed water has en- 




FIG. 18. VAUGHAN AND 
STUBBS' STEAM-TRAP. 



88 



Heat for Engineers. 



tered B from the steam-pipe, the temperature falls, and consequently 
the tube contracts in length and breaks the joint made with V. The 
condensed water is then driven by the steam pressure through the 
outlet, after which the opening again closes owing to the expansion 
of B occasioned by the rise of temperature. The valve V may be 
adjusted for any pressure of steam by means of the handle H, so 
that when the tube is full of steam the outlet is closed. At high 
pressures the valve V is lower than in the case of lesser pressures, 
as the temperature is higher, and consequently the expansion of 
the tube greater. Incidentally, the tube A participates to some 
extent in the alterations of length, but owing to contact with the 
atmosphere the changes are small ; and, in addition, the tube B, 
being made of brass, expands more than A, which is made of iron, 
for a given rise of temperature. The drawback of the arrangement 
is that the tube B, if overheated, will press so hard on the valve V 
as to cause the tube to distort, and thus make an imperfect junction 
with V. 

A more modern form of steam-trap, known as the " Midget," is 
illustrated in Fig. 19, and depends for its action on the varying ex- 




FJG. 19. "MIDGET" STEAM-TRAP. 



pansive force exerted by a saturated vapour at different tem- 
peratures. The valve V is held on its seat by the lower part of a 
corrugated chamber C, which contains a highly volatile liquid, such 
as light petroleum spirit, and is hermetically sealed. The pressure 
of a saturated vapour (i.e. one in contact with its own liquid) varies 
considerably with the temperature, particularly when the liquid is 
above its normal boiling point ; the variations greatly exceeding 
those experienced by a gas under the same conditions. Hence a 



Steam- Traps. 



small alteration of temperature will make a considerable difference in 
the force with which the valve V is held on its seat. The lower 
diaphragm of the chamber C must be adjusted so that the pressure 
exerted on V is just greater than the steam pressure when the valve 
is full of steam. This adjustment is made by raising or lowering 
the chamber C, a lock-nut N serving to hold it fast in any given 
position. When no water is present, the steam, which enters from 
the steam-pipe in the direction of the arrow, bathes the under side 
of the corrugated chamber, and the valve V is prevented from lift- 
ing by the elastic force of the contained vapour. When water 
accumulates in the trap, the temperature falls, causing a considerable 
reduction of the pressure of the vapour in C ; consequently the valve 
is lifted and the water ejected by the steam pressure. After the 
removal of the water the temperature will again rise, and the valve 
close. This steam-trap is extremely sensitive, and is capable of 
ejecting a teaspoonful of water without any escape of steam. The 
'' Imp" steam-trap is an improved form of the " Midget." 

A third form of steam-trap, suitable for high pressures, is shown 
in Fig, 20, which represents a recent production of Holden and 





3CZE 



FlG. 20. HOLDEX AND BROOKES' STEAM-TRAP. 

Brooke, of Manchester. In this, as in the " Midget" trap, the joint 
with the outlet is not made directly with the expanding tube. Instead 
of this, a valve V, held in position by a spring S, operating on the 
bell-crank lever L, closes the outlet. Two rods R R run parallel 
with the tube T, the right-hand end of these rods bearing against the 
piece P, which is independent of the tube, and capable of rocking 
on the knife-edge K, which is a prolongation of the piece F. As- 
suming the trap to be cold, and the valve pressed on its seat, the ad- 
justment is made by turning the stud N, thereby pressing the upper 



9O Heat for Engineers. 

rod against the bell-crank lever, and causing the valve to lift against 
the pressure of the spring. The motion of the rod is magnified 
about five times by the lever ; and the adjustment must be such as to 
cause the outlet to open when water accumulates, but to close when 
the trap is full of steam. The closing of the valve is effected in- 
directly by the expansion of the tube, which carries the lever at- 
tached to it away from the rods, and permits the spring to close the 
valve. When a quantity of water settles in the tube T, and the 
temperature falls in consequence, the tube contracts, and presses 
the lever on the upper rod, thereby causing the spring to lift and the 
valve to open. The arrangements of the two rods R R, and the rock- 
ing-piece P, obviate any bending strain in the tube T. This steam- 
trap will open when the temperature falls by 5 per cent., and can be 
used directly on a cylinder or steam-pipe. 

Of the numerous other forms of steam-traps, mention may be 
made of those in which the principle of the compound strip is em- 
ployed. In these the arching of a semicircular compound strip of 
two metals is utilised to lift the valve, whilst the straightening of the 
strip causes it to close the outlet. Such steam-traps suffer from the 
defect that overheating will produce distortion, and cause the valve 
to make a defective joint with its seat. 

Compensated Pendulums. The period of vibration of a pendulum 
varies directly as the square root of the length, and consequently a pen- 
dulum subjected to changes of temperature will show a variation in 
the time of vibration, as the length alters with the temperature. 
Any mechanism, such as a clock, controlled by a pendulum, will 
therefore be subject to alterations in the time of movement ; thus 
in warm weather, when the pendulum is longer, a clock will lose 
time, and conversely will gain time in cold weather. The object of 
compensated pendulums is to maintain the effective length that is, 
the distance between the point of suspension and centre of oscilla- 
tion constant at all temperatures. This may be effected by utilis- 
ing the different expansion of two substances in such a manner 
that the vertical motion of the centre of oscillation, due to one 
^instance expanding or contracting, is exactly balanced by a move- 
ment in the opposite direction due to the other material. 

Two simple forms of compensated pendulums are shown in Fig. 
21, where A represents a wooden pendulum with a zinc bob, which 
fits loosely round the wood. The wooden rod, on expanding, tends 
to lower the centre of gravity and thus increase the effective length 
of the pendulum ; the zinc bob, however, expands simultaneously in 
an upward direction, thereby tending to raise the centre of gravity. 



Compensated Pendulums. 



If the two opposing tendencies are equal, the period of oscillation 
will remain constant ; and as the zinc has a much higher coefficient of 
expansion than the wood, the smaller length of zinc may be made to 
compensate the expansion of the greater length of wood. In the 
same figure, B represents Graham's mercurial pendulum, which is 
similar in principle. The bob consists of a vessel containing mercury, 
the rod being made of iron or other metal. The quantity of mercury 
in the vessel is adjusted so that its expansion in an upward direction 
counteracts that of the rod downwards. When both rod and vessel 





FIG. 21. COMPENSATED 
PENDULUMS. 



FIG. 22. HARRISON'S GRIDIRON 
PENDULUM. 



are made of iron, the height of the mercury should be about -/. of the 
total length of the pendulum to secure compensation. 

Harrison's gridiron pendulum consists of a heavy bob suspended 
from a framework composed of alternate rods of iron and brass, as 
shown in Fig. 22, where the black rods are of iron and the others 
of brass. These rods are able to move freely upwards or down- 
wards between cross-pieces, and it will be observed that, whilst the 
expansion of the iron rods tends to lower the bob, the expansion of 



92 Heat for Engineers. 

the brass rods tends to raise it. If the total length of the iron rods 
is about ijj- times that of the brass rods, these movements will 
counteract one another, as the coefficient of expansion of brass is about 
i times as great as that of iron. Considered from the standpoint 
of the expansion produced, the symmetrical rods of iron and brass 
respectively may be regarded as a single rod ; and consequently 
compensation will be secured when the two iron rods on either side 
of the centre, together with the rod carrying the bob, have a combined 
length of ijj- times or more accurately 1-^.y times that of the joint 
length of the two brass rods on either side. The object in duplicat- 
ing the rods is to secure an evenly balanced pendulum. 

The use of the non-expansive nickel-steel alloy would largely 
obviate the necessity for compensated pendulums, and it is highly 
probable that this alloy will be largely employed for this and other 
purposes in the future. 



CHAPTER VI. 

ATMOSPHERIC PRESSURE. GENERAL PROPERTIES OF GASES. 

The Atmosphere. AtmospJieric Pressure. The atmosphere, or 
gaseous envelope surrounding the earth, extends to a height of at 
least 100 miles, and probably, in a very attenuated state, to a much 
greater distance. The density is greatest at the surface of the earth, 
and continuously diminishes as the distance from the surface in- 
creases. In the higher portions the air is extremely rarefied, the 
condition being similar to that obtaining in a vacuum-tube. The 
" aurora borealis " is believed to be due to electric discharges in the 
higher attenuated portions of the atmosphere. 

The gaseous envelope, which is held to the earth by gravitation,, 
exerts a distinct pressure on all objects beneath it. We are not 
conscious of this pressure on our bodies, owing to the fact that 
the pressure acts inside the body as well as externally, and the two 
effects counterbalance. Similarly, a flat surface, such as a table, 
does not show any sign of the presence of this pressure, as, owing to 
the property possessed by fluids of pressing equally in all directions, 
the upward pressure beneath the table balances that on the upper 
surface. To demonstrate the existence of this pressure, it is necessary 
to remove the balancing pressure, which may be done in many ways. 
If a rubber disk be stretched tightly over the mouth of a jar, and the 
air be removed from the jar, the rubber will be forced into the 
interior, and may even burst owing to the pressure upon it, which is 
now unbalanced. A thin glass vessel will break when exhausted of 
air, and a thin metal vessel will be crushed inwards. As this pressure 
is always present, and plays an important part in many phenomena, 
a knowledge of its numerical amount is of great importance, and is 
measured by the instrument known as the barometer. 

The Mercury Barometer. The first 'mercury barometer was con- 
structed by Torricelli, who took a tube about i yard long and J of 
an inch in diameter and closed at one end. This was completely 
filled with mercury and closed with the finger, and then inverted and 
the open end immersed in a cistern of mercury before removing the 



94 



Heat for Engineers. 



finger. The column of mercury which remained in the tube, was 
found to have a vertical height of about 30 inches, the height being 
measured above the mercury surface in the cistern. This column is 
sustained by the pressure of the atmosphere, which is transmitted 
through the mercury in the cistern ; and if the whole arrangement be 
placed in an air-pump receiver, and the air be exhausted completely, 
the mercury in the tube will fall until it stands level with that in the 
cistern. On again admitting air to the receiver, the column will rise 
to its former height. 

A simple barometer of this kind is shown in Fig. 23 ; and it 
should be carefully remembered that the atmospheric pressure 
balances the column of mercury above the cistern level, and not the 
entire length, for if the top of the barometer were 
broken, the pressure of the atmosphere would cause 
the column to fall until the level was the same in both 
tube and cistern, and no further. In making a good 
barometer both the tube and the mercury should be 
scrupulously clean, and every trace of air removed 
from the mercury and tube by boiling, either at ordin- 
ary pressure or when attached to an air-pump. Any 
tangible quantity of air left in the tube causes a 
noticeable depression of the column, and therefore an 
erroneous reading. When inclined, the mercury should 
completely fill the tube, and on sudden tilting, should 
strike the glass with a metallic sound. If well made, 
the space at the top of the column, known as the 
Torricellian vacuum, should contain only mercury 
vapour. 

On ascending, the weight of the overlying column 
of air becomes continuously less, and consequently the 
length of the column of mercury in the barometer falls. 
At an elevation of 1000 feet, for example, the height of 
the barometer is about i inch less than it would be 
if at sea-level. The height of the column of mercury, 
like the density of the atmosphere, falls in a diminish- 
ing ratio as the distance from the surface of the earth increases ; and 
would become zero at the upper limit of the atmosphere. If the 
atmosphere were of the same density throughout as that existing at 
the surface, a height of 5 miles would suffice to hold up the mercury 
in the barometer, and uniform decrease would be observed on ascend- 
ing. It is customary to speak of the atmosphere, on the supposition 
of uniform density, as the "homogeneous atmosphere"; but it 




FIG. 23. 

SIMPLE 

BAROMETER. 



Ba romefers. 9 

should be remembered that in reality the density decreases with the 
height. 

The average height of the barometer at sea-level is approximately 
76 centimetres or 29-92 inches. The height is constantly fluctuating 
owing to alterations in the amount of moisture present in the atmo- 
sphere, winds, etc. A low barometer (i.e., when the reading is much 
below 29 inches 01-73-5 centimetres) is usually accompanied by rain 
and atmospheric disturbances, whilst a high barometer (30 inches and 
over) is generally associated with dry weather and calm conditions. 
In Britain the barometer seldom falls below 28 -5 inches, or 72 '4 
centimetres ; or rises above 30-8 inches or 78*2 centimetres. As it 
is desirable for meteorological and other purposes, to obtain exact 
readings of the height of the barometer, special instruments, fitted 
with verniers for fine readings, are employed. The form in common 
-use, known as Fortin's barometer, will now be described. 

Forth? s Barometer. In any mercury barometer the level in the 
cistern will, of necessity, alter when the column of mercury rises or 
falls. In the one case, mercury from the cistern enters the tube, and 
in the other case mercury leaves the tube and enters the cistern. As 
the height to be measured is the distance between the top of the 
column and the mercury surface in the cistern, it is evident that a 
fixed scale would give erroneous readings unless provision were made 
for the varying level in the cistern. This is accomplished in Fortin's 
barometer by making the lower portion of the cistern of leather ; and 
by means of a screw this can be raised or lowered until the mercury 
.surface just touches a fixed ivory peg, which has a sharp point. 
Exact contact is insured when the point of the peg appears just to 
meet its own reflection in the mercury. The scale is fixed so that 
the heights indicated represent the distance from the point of the 
ivory peg. The mercury in the cistern is adjusted to this point before 
a reading is taken, and thus any error due to altering level is elimi- 
nated. A sliding vernier, reading to 3 -J- ff of an inch, or to 2 ^ of a 
centimetre, is adjusted to the top of the column, and an exact reading 
is thus obtained. 

Corrections of Barometer Readings.- In order that barometer read- 
ings, taken under different circumstances, may be strictly comparable, 
it is necessary to define standard conditions under which the height 
is recorded. The chief causes which affect the reading are temperature 
.and elevation above sea-level, and to secure uniformity the observed 
height is corrected so as to represent what the reading would be if 
the temperature were o C. and the barometer at sea-level. The correc- 
tion for temperature is obtained from the known coefficients of 



96 Heat for Engineers. 

expansion of mercury and the material of the scale. With a brass 
scale, the correction is made from the expression 

Height at o C. = height at t" C. x (i - -000162 /), 

where '000162 is the difference between the coefficient of absolute 
expansion of mercury ( 000181), and the linear coefficient of 
brass ('000019). For accurate observation of the temperature, a 
thermometer is fastened to the barometer. 

Example. J^^Q observed height of the barometer is 765 mm., 
the temperature being 20 C. The corrected height is therefore 

H = H at 20" x { i - (20 x -000162)} 
= 765 x '99676 
= 762^6 mm. 

The correction for elevation may be made by referring to tables 
prepared for the purpose, in which the alteration of barometric 
pressure due to altitude, under given conditions of temperature, 
moisture, etc. is recorded. For rough purposes, -^ of an inch may 
be added for every 100 feet of elevation, up to 1000 feet. Other 
corrections, though of less general importance, are for capillarity and 
latitude, the latter being necessary when the barometer is transferred 
to a locality in which the value of " ( f" differs sensibly, as this would 
cause an alteration in the downward pressure exerted by a given 
column of mercury. 

" Standard" or "Normal" Barometric Pressure. The standard 
pressure to which the volumes of gases and also their densities are 
referred is 760 millimetres of mercury at o C. This is equal to 29 92 
inches; and such a column of mercury is said to represent i "atmo- 
sphere" of pressure. The equivalent of i atmosphere is 1033-3 
grams per square centimetre, or 14*7 Ib. per square inch. 

Example. A tube of i square centimetre section, in which the 
mercury stands at a height of 76 centimetres, will contain 76 c.c. 
of mercury. As i c.c. of mercury at o C. weighs 13*596 grams, the 
pressure per square centimetre = weight of mercury in tube = 76 x 
T 3'59^ = I0 33'3 gra ms ' Similarly, 29*92 cubic inches of mercury 
weigh 14*7 Ib., and the pressure per square inch = 14-7 Ib. A 
column of mercury i inch high represents a pressure of '4913 Ib. 
per square inch, as T cubic inch of mercury weighs "4913 Ib. A 
pressure of i Ib. per square inch is represented by a column of 

mercury - = 2 038 inches high. 

'49*3 



Aneroid Barometers. 97 

Aneroid Barometers. -The chief drawback to the general use of 
the mercury barometer is its lack of portability. Apart from the 
length, which must be about i yard at a minimum, there is always a 
danger of the mercury spilling, or the tube being broken except when 
the greatest care is exercised in transit. These disadvantages are 
not shared by the aneroid barometer, which depends for its action 
on the upward or downward movement of the surface of an ex- 
hausted metallic drum under fluctuations of atmospheric pressure. 
This drum has a corrugated surface, and in the usual form is kept in 
a state of extension by a steel spring ; the low r er end of the drum 
being fastened to a plate, whilst the upper end is free to move. The 
movements of the upper surface are communicated by means of 
multiplying levers to a chain which passes round the spindle carry- 
ing the index. An increase in the barometric pressure causes the 
upper end of the drum to collapse by a definite amount, with the 
result that the index hand moves over the scale. A decrease in 
barometric pressure enables the spring to extend the drum, and the 
movement being conveyed to the index, causes a converse motion 
to that which results from increased pressure. The chain is pre- 
vented from becoming slack by means of a hair-spring. The correct 
markings on the scale over which the index moves are obtained by 
comparison with a mercury barometer. 

A well-made aneroid barometer, which has been carefully graduated, 
and the various parts compensated for temperature, is susceptible of 
very great accuracy. In size aneroid barometers vary from that of 
an ordinary watch to a diameter of 9 or 10 inches, the former being 
intended for carrying in the pocket, and the latter for a fixed position, 
to replace an ordinary barometer. The smaller sizes are usually 
provided with a scale of heights on the face of the instrument, so 
that elevations may be read off at a glance. For rough surveys and 
contouring this form of barometer is greatly superior to the mercury 
barometer, as it is no trouble to carry, and cannot get out cf order 
with ordinary usage. 

The aneroid principle is also adopted in certain forms of 
" barographs," or recording barometers. Several drums are mounted 
on the same spindle, so as to give an increased effect, and the ter- 
minal lever carries a pen, which is in contact with a paper moved by 
clockwork. The pen is set at the correct height on the paper by 
comparison with a mercury barometer ; and as the clockwork revolves 
at a known rate it is possible to obtain a continuous record of atmo- 
spheric pressure. 

States of Matter Kinetic Theory Special Properties of Matter in 

ii 



98 Heat for Engineers, 

the Gaseous State. It is customary to refer to matter as existing in 
three well-defined states the solid, the liquid, and the gaseous. It 
is possible, however, for matter to exist in a transitional state between 
solid and liquid, or between liquid and gas, as will be shown later in 
connection with the phenomena attending change of state. A fourth, 
or ultra-gaseous state of matter, is realised in vacuum tubes, in which 
the residual matter possesses properties entirely different from those 
of a gas under ordinary pressures. 

According to the Kinetic theory, the molecules of which all kinds 
of matter are composed are in a constant state of motion. In a solid, 
the motion is restricted to the space betw r een a given molecule and 
those which surround it, so that each molecule is confined to a small 
area out of which it cannot escape. A much greater freedom of 
motion obtains in a liquid, as in this case the molecules are able to 
wander amongst neighbouring molecules. Finally, in the gaseous 
state, the molecules are free to move in all directions, practically un- 
hindered by the presence of adjacent molecules. This view of the 
condition of matter in its various forms is not only in harmony with 
experimental results in general, but is supported by direct evidence. 
The phenomenon of diffusion, in particular, lends confirmation to 
the theory of molecular motion. If a light liquid be allowed to float 
on a heavy one, it will generally be found that after the lapse of some 
hours a quantity of the heavy liquid has mingled with the lighter one, 
and vice versa. Similarly, a light gas, such as hydrogen, if contained 
in a cylinder and placed upon a cylinder containing a heavy gas, 
such as sulphur dioxide, will penetrate the lower cylinder almost 
immediately, the heavier gas similarly rising into the hydrogen 
cylinder. This mixing in opposition to gravitation is explained satis- 
factorily by the Kinetic theory ; the comparatively slow diffusion of 
the liquids being due to the difficulty expeiienced by the molecules 
in moving between other molecules, and the rapid mixing of gases by 
the practically complete freedom of motion. Roberts-Austen has 
shown that diffusion may occur with solids, though extremely slowly. 
A block of lead was allowed to stand for some months on a block of 
gold, after which it was found that some of the gold had passed up- 
wards into the lead, and conversely. It would appear, therefore, that 
even in solids a molecule is not absolutely hemmed in by its neigh- 
bours, but may though with extreme difficulty move between 
them. 

Gases differ from liquids and solids by possessing the property of 
indefinite expansion. No matter what proportion of a gas is with- 
drawn from a vessel, the residue, however small, distributes itself 



Gaseous Pressure Boyle's Law. 99 

evenly through the vessel, and in this sense fills it. A liquid, on the 
other hand, possesses a boundary surface, which defines its volume. 
A gas has no boundaries save the walls of the containing vessel, and 
the smallest quantity of gas appears to be capable of filling (in the 
sense of even distribution) any vessel, however large. 

Gaseous Pressure. Gases exert a pressure on all the parts of the 
containing vessel, which is equally distributed over the whole surface. 
The existence of this pressure may be shown by taking a jar covered 
with a rubber disk, and removing the surrounding air by placing the 
jar under the receiver of an air-pump, when the rubber disk will be 
observed to stretch into a hemisphere under the pressure of the en- 
closed air. This pressure, according to the Kinetic theory, is due to 
the continuous impact of the molecules of the gas on the walls of the 
vessel. After striking the vessel the molecules rebound, and may 
collide with each other, but as all the molecules are constantly in a 
state of rapid motion a continuous series of impacts on the walls of 
the vessel will occur. The pressure to which these impacts give rise 
will evidently depend upon the mass, velocity, and number of mole- 
cules striking in a given time. If the number of molecules be doubled 
(by forcing into the vessel a further quantity of gas equal to its original 
contents) the pressure will be doubled ; and conversely, removing 
one-half of the gas, or increasing two-fold the area of the vessel, 
will cause the pressure to be halved. An increase in velocity, such as 
is caused by a rise of temperature, will cause an increase of pressure. 
All these conclusions may be verified by experiment. 

Adopting this view of gaseous pressure, it will be seen that a gas 
confined beneath a piston on which weights aie placed will accom- 
modate its volume until the pressure beneath the piston is equal to 
that caused by the weights above. As the gas diminishes in volume, 
the area over which impacts are delivered by the molecules also 
diminishes, and the piston is struck by a greater number of molecules 
in a given time. Finally, the combined force of the impacts is just 
sufficient to counterbalance the weight, and the volume of the gas re- 
mains stationary. This explanation leads to the conclusion that the 
pressure exerted by a given mass of gas (at constant temperature^ 
should vary inversely as the volume occupied which is equivalent 
to Boyle's law. 

Connection between Gaseous Vomme and Pressure. Boyle's Law. 
The effect of varying the pressure on a given mass of air was first 
investigated by Robert Boyle, in 1660. Boyle found that the volume 
of the air varied in the inverse ratio of the pressure within the limit 
of four atmospheres. Later experiments showed that the law could 

H 2 



i oo Heat for Engineers. 

be extended to other gases, within certain limits ; and in the case of 
hydrogen, nitrogen, air and oxygen, the law was found to be closely 
followed, even at considerably higher pressures than were employed 
by Boyle. The useful law deduced from these experiments, is known 
as Boyle's law, and may be stated thus : " The volume occupied by 
a given mass of gas, at constant temperature, varies inversely as the 
pressure to which it is subjected." If the pressure be doubled, the 
volume is halved, or, in general, the product of pressure and volume 
is constant for a given mass of gas. Expressed in symbols, P V = 
a constant ; or P V = P l V\ where P and V are original and P x and 
V x the altered pressure and volume. 

More exact experiments by Regnault, Amagat, and others have 
shown that no known gas obeys Boyle's law exactly. In general, 
the product P V at first diminishes with increase of pressure until 
a minimum value is attained ; after which the value of P V increases. 
The variations of P V depend also upon the temperature at which the 
experiment is conducted. If the temperature be near that at which 
the gas liquefies, the product P V is far less than is demanded by the 
law as the pressure increases. Easily liquefied gases, such as sulphur- 
dioxide and ammonia, therefore show a marked departure from 
Boyle's law, even when subjected to moderate pressures at ordinary 
temperatures. At high temperatures these gases approximate closely 
to the law, and in general the value of P V only approaches a con- 
stant value when the gas is considerably above the temperature at 
which it would liquefy at atmospheric pressure. These discrepancies 
are explained by the facts that the size of the molecules is not 
negligible compared with the spaces between them, and that the 
tendency of molecules to adhere to one another becomes marked as 
liquefaction approaches. At very low pressures, when the molecules 
are widely separated, gases might be expected to obey the law almost 
exactly, and this has been confirmed experimentally by Lord Rayleigh. 

Isothermals. Work done in Compressing a Gas Is oi formally. If 
a substance, kept at a constant temperature throughout, be subjected 
to a continuous pressure, the volume will undergo a continuous dimi- 
nution, and a curve drawn connecting pressures with the corre- 
sponding volumes is known as the isothermal for the substance. 
Isothermals may have various shapes, depending upon the substance 
operated on, but in the case of a gas which is assumed to obey Boyle's 
law accurately, the curve takes the form of a rectangular hyperbola. 
This is shown in Fig. 24, in which a gas originally occupying a volume 
represented by ON, is compressed to a volume O L, the continuous 
change of pressure being exhibited by the curve K F B M. From 



Isothermal Changes. 



101 



Boyle's law it follows that the product of pressure and corresponding 
volume is constant, thus OCxCB = OGxGF, and, in general, 
P V = a constant. The curve possessing this property is an equi- 
lateral hyperbola. 

The isothermal s of a solid, liquid, or vapour may differ widely in 
shape from those of a gas, and it should be remembered that in all 
isothermals the temperature is presumed to be constant throughout. 
This might be realised experimentally by surrounding the substance 
with ice or a large bath, and increasing the pressure gradually. 




FIG. 24. ISOTHERMAL OF A PERFECT GAS. 

The work done during an isothermal compression is represented 
by the area of the figure enclosed by the curve, the perpendiculars 
from the extremities of the curve, and the axis of volume. In Fig. 
24, in which the gas is assumed to be compressed isothermally from 
a volume O N to a volume O L, the starting pressure being repre- 
sented by N M and the final by L K, the work done is expressed by 
the area K L N M. This may be proved by considering the work 



i o 2 Heat for l Engineers. 

done during a very small part of the compression, as from C to D. 
Since the work done is the total force applied x distance moved, and 
since the total force is equal to the area of the piston x pressure per 
unit area, it follows that the work done equals 

(area of piston x pressure per unit area x distance moved) 

But (area of piston x distance moved) = diminution in volume, hence 
work done = (pressure per unit area x decrease in volume) 

= P x CD = 



In the figure the work done in compressing from C to D is the 
area of the rectangle A B C D + the small triangle bounded by A B 
and the curve. If C and D be separated only by an indefinitely 
small distance, di^ the triangle vanishes, leaving the rectangle P d T. 
The area K L N M may be imagined to be composed of an indefinite 
number of such rectangles, and if the areas of all these be added 
together, the result will be the area K L N M. Or, 

Work done - 2 P d :-, or JP d v, 

between the limits O N and O L. Calling O N 7' 15 and O L ?'., the 
total area is found by integration to be 

A *i x h yp- log - ; 

2 

or, in ordinary logarithms 

p l v l x 2-302585 x logy 1 ; 

where p l and T{ are the original pressure and volume respectively. 

Example i. If 2 5 cubic feet of air, at a pressure of 14 7 Ib. per 
square inch, be compressed under isothermal conditions to a volume 
of o 5 cubic foot, the work done will be 

2-5 x (144 x 14-7) x 2-302585 x log ^ = 8526 foot-pounds. 

'5 

Note that when the answer is in terms of the foot and pound, 
the original pressure p l must be expressed in pounds per square foot 
- (14-7 x 144). 

Example 2. On compressing i litre of air, originally at a pressure 
of 1000 grams per square centimetre, to a volume of 100 c.c., under 
isothermal conditions, the work done would be 

TOOO x 1000 x 2*302585 x log >0 ; 

100 

= 2,302,585 gram-centimetres; since i litre - 1000 cubic centimetres. 



CJiarles Law. 103 

Connection between Gascons Volume and Temperature. Charles' 
Law. Absolut: Zero. It has been pointed out previously that the 
increase in volume observed when a quantity of gas is heated at con- 

stant pressure, is uniform; the increase per degree C. being of 

the volume occupied by the gas at o C. Experiment has shown that 
this value holds nearly true for all gases, within certain limits. As in 
the case of Boyle's law, however, gases near the temperature of lique- 
faction show a marked deviation from the above figure. For all 
ordinary calculations involving the volume changes of gases at con- 

stant pressure, it is sufficiently accurate to assume the figure .- , or 

o ' 003663, as representing the coefficient of expansion of a gas. This 
connection between volume and temperature is known as Charles' 
law, and may be expressed in symbols as follows : 

V^V,, (i +*/!> (i) 

where Vj = volume at // ; V = volume at o C, ; and a = the co- 

efficient of expansion = . From this expression the ratio of the 

2 73 
volumes at any two temperatures may be obtained, as it follows that 



Dividing (i) by (2), the relation becomes 

V, = !_+_/! 
V., I + a /o* 

If a gas be cooled below o c C., the contraction is still found to be 

- of the volume at o C. for every degree through which it is 
2 73 
cooled, and, consequently, if a gas could be cooled to a temperature 

of -273C, its volume, on the assumption that the law held true, 
should become zero. Thus 273 volumes of gas at o C. would become 
272 at -i ; 173 at - 100, and nothing at -273. It cannot oe 
imagined that any form of matter could occupy no volume, and con- 
sequently some deviation from the law would occur as the temperature 
of -273' C. was approached, even with a gas that showed no signs 
of liquefaction. There is, however, another method of regarding the 
properties of gases at this temperature. If a gas be heated without 
being allowed to expand, the pressure rises by of the pressure 

** i 3 



1 04 Heat for Engineers. 

at o C. for each degree rise of temperature, and similarly decreases 
on contracting without change of volume. Thus, if the pressure at o C. 
were 760 mm., at 273 itw r ould become 1520 mm., and would vanish 
at - 273. At this temperature, therefore, a gas could not exert pres- 
sure, and, consequently, its molecules would be at rest. In other 
words, the distinctive gaseous properties would have disappeared, and 
consequently, the laws of Boyle and Charles could no longer be 
applied to it. So long as the gas possesses heat energy the molecules 
will be in a state of motion, and therefore it follows that at - 273 C., 
at which temperature the molecules are at rest, the gas has been de- 
prived of all its heat. For this reason, the temperature -273 U C. 
(or -459*4 F.), is called the absolute zero of temperature. Abso- 
lute temperatures, on the Centigrade scale, are therefore 273 higher 
than the ordinary degrees; thus 10 C. = 283 absolute, and so on. 

The law of Charles may be simply expressed in terms of absolute 
degrees as follows : The volume occupied by a gas at constant 
pressure is proportional to its absolute temperature. Or, in symbols, 



T "" T/ 

V and T representing original, and V x and r l\ final, volume and 
absolute temperature respectively. This method of expressing the 
law is more convenient for the purposes of calculation. 

Combination oj Boyle ' s and Charles' Laws. Boyle's law 7 assumes 
that a gas remains at constant temperature whilst altering its pressure, 
and Charles' law assumes constant pressure. If both the temperature 
and pressure alter, a combination of the two laws is necessary to 
calculate the volume. This may be obtained as follows : 

Let V, P, and T represent the initial, and Vj, P 1? and T 15 the final 
volume, pressure, and absolute temperature of a gas. Then, con- 
sidering temperatures only, 

Vj would equal V x r \ 9 
but as the pressure alters also, the final value will be 



from which 

PV 

T? 



Application of Gascons Laws. 105 

which expression may be used in all cases concerning the alteration 
in volume of a gas. If T - r i\, the expression is identical with 
Boyle's law; if P = P 15 Charles' law is expressed as given above. 
The equation may be written in the form 

P V = R T, 

where R is a constant. A few examples to illustrate the application 
of the laws will now be given. 

Examples. (i) 500 cubic feet of gas at 7 C. and 750 mm. 
pressure, are heated to 127 C., and the pressure allowed to rise 
to 800 mm. Find the volume of the gas under the new con- 
ditions. 

Applying in the formula 

PV JP/V^ 
T 1\ ' 

750 x 500 _ 800 x Vj 
280 400 

from which V x = 669-6 cubic feet. (Note that 273 is added to the 
given temperatures to give absolute degrees.) 

(2) A mass of gas, originally at 15 C., is heated in a closed vessel 
to 500 C. Assuming the original pressure to have been i atmo- 
sphere, find the final pressure. 

In this case V = V 1? and the expression becomes 



=__ -- 

T T; s88 773' 

from which Pj = 2 68 atmospheres. 

(3) A closed glass bulb contains air at o C., and 750 mm. pres- 
sure. On placing in a bath the additional pressure exerted is 
1000 mm. Find the temperature of the bath. 

Since V - V v 

P P T 

T = T; 

therefore 

75P = (io + 75) 
273 T i 

and T! = 637 absolute, or 364 C. 



1 06 Heat for Engineers. 

Heat Produced by the Compression cf Gases. The compression 
of a gas causes a rise in temperature, due to the conversion of work 
into heat. The fire-syringe depends for its action on the heat pro- 
duced by the compression of air, and consists of a cylinder fitted with 
a tight piston, on the under side of which is fastened a piece of 
tinder. On suddenly plunging down the piston, a rise in tem- 
perature takes place sufficient to ignite the tinder. More recently 
the heat of compression of a gas has been utilised to ignite the charge 
in certain forms of oil engines ; an operation which involves, how- 
ever, a very high compression of the charge. In a perfect gas, the 
molecules of which are supposed to be quite independent of each 
other, the heat produced would be the exact equivalent of the work 
done in compression, every 1400 ft. Ib. of work producing- i lb- C. 
unit of heat. Conversely, if a compressed gas be allowed to expand, 
so as to do work, a lowering of temperature is produced, the gas 
being deprived of i lb- C. unit of heat for every 1400 ft. Ib. of 
work done by the expanding gas. If the gas expanded into a 
vacuum, no work would be done, and no fall of temperature would 
be produced. On expanding into the atmosphere, however, work is 
done in overcoming the pressure of the overlying air, and a lowering 
of temperature occurs. If the expanding gas be allowed to perform 
a greater quantity of work, such as in driving a machine, a greater 
fall in temperature is caused, this being the principle of refrigerating 
machines of the air-expansion type. It should be remembered, how- 
ever, that the work done on the gas during compression, or by the 
gas during expansion, is the equivalent of the heat produced or ex- 
tracted provided the molecules of the gas are independent of one 
another. No ordinary gas, however, is perfect in this sense, and a 
certain amount of work must be involved in causing the molecules to 
approach each other, or in dragging them apart according to whether 
the molecules repel or attract each other. The work quantity in- 
volved on this account, however, is extremely small, as was shown 
experimentally by Joule. 

Joules Experiments on Expanding Gases. In investigating this 
question Joule took two cylinders, connected by a pipe and stopcock. 
One of the cylinders contained air at 2.1 atmospheres pressure, and 
the other was exhausted. Both were immersed in a calorimeter con- 
taining water, and the stopcock opened. After stirring the water no 
alteration of temperature was observed, and consequently no mea- 
surable amount of heat was converted into work in causing the mole- 
cules of the air to move a greater distance apart from one another, 
as would be the car^e if they tended to adhere to each other. In a 



Joule and Kelvins Experiments on Gases. 107 

second experiment Joule placed the cylinders in separate calorimeters, 
and opened the stopcock. The expanding gas, by doing work in 
overcoming the pressure of the gas accumulating in the other 
cylinder, fell in temperature, whilst a rise in temperature occurred in 
the case of the gas undergoing compression. It was found that the 
amount of heat lost by the expansion was balanced by that gained in 
the compression, showing that in either process the tendency of the 
molecules to adhere or repel one another was too small to be 
detected by the experiment. The conclusion to draw from the ex- 
periments is that the internal work expended during the changes in 
volume of a gas is, at most, a quantity too small to be noticed by the 
methods adopted, and which may be neglected in all ordinary cal- 
culations. That mutual attractions between molecules do exist, how- 
ever, is shown by other experiments, and a method of investigating 
the matter in question was devised by Joule and Kelvin, which will 
now be described. 

Joule and Kelvin's " Porous Ping" Experiment. In this experi- 
ment a compressed gas was allowed to pass through a spiral sur- 
rounded by water at a constant temperature, and afterwards to escape 
through a glass tube in which a plug of cotton wool was placed. By 
this means it is possible to maintain a considerable difference of 
pressure between the sides of the plug, just as in the case of a gas 
escaping through a fine jet into the air; and the molecules of the 
gas, after leaving the plug, would separate to a greater distance. A 
thermometer was placed in the glass tube just beyond the porous 
plug, and in the case of air and carbon dioxide the escaping gas was 
found to have a lower temperature than that of the bath, whilst with 
hydrogen a rise of temperature was observed. In the experiment 
the cooling due to the expansion of the main mass of the gas was 
eliminated by the surrounding bath of water, and any cooling on the 
part of the emerging gas must have been due to the conversion of 
heat into internal work. The external work is performed by the 
main mass of the gas (which is prevented by the bath from cooling), 
and not by the es: aping gas. Hence, if the escaping gas were 
perfect, in the sense that the molecules were independent, and the. 
it obeyed Boyle's law accurately, its temperature should undergo no 
alteration. The greater the departure from perfect conditions, the 
greater should be the thermal effect, and this is what is actually 
observed. 

Joule and Kelvin found that the alteration in temperature was 
proportional to the difference of pressure on the two sides of the 
plug. In the case of air at o C. the fall in temperature observed 



1 08 Heat for Engineers. 

waso'29 3 C. for each atmosphere difference of pressure; for carbon 
dioxide, 1*25" C. ; and for hydrogen a rise of 0*039 C. If the ex- 
periment be carried out below - 90 C., however, hydrogen shows a 
cooling effect like other gases. 

In the above explanation it has been assumed that the whole of 
the thermal effect is due to the separation of the molecules. In 
reality, however, deviation from Boyle's law, and consequent altera- 
tions in the value of the product, P V, at the different pressures, also 
exercise a thermal effect, winch, in the case of hydrogen, tends to 
cause a rise in temperature, and suffices to overcome the cooling due 
to the separation of its molecules. In other cases the alterations in 
P V are such as to assist the cooling action. 

The cooling of gases occasioned by passing through a plug or jet 
is now utilised in the liquefaction of air, hydrogen, and other gases, 
as will subsequently be described. 

Adiabatic Compression and Expansion. Boyle's law applies only 
to gases compressed or expanded at constant temperature, or iso- 
thermally. Such a condition would be realised by slowly altering 
the volume of a gas in a copper cylinder surrounded by a bath kept 
at a constant temperature. If, however, the gas were contained in a 
cylinder made of non-conducting material, and suddenly compressed, 
the heat produced by the compression would not escape, but, by 
raising the temperature of the gas, would tend to cause expansion 
and so oppose the pressure. If the alteration in volume takes place 
in such a manner that heat neither leaves nor enters the gas, the 
change is called " adiabatic." If a curve be drawn connecting 
pressure and volume during an adiabatic compression, it will be 
steeper than the isothermal commencing at the same point, as shown 
in Fig. 25. For, in the case of the adiabatic, a greater pressure 
must be applied to produce a given diminution in volume, as the 
heat generated remains in the gas and increases its pressure. Perfect 
adiabatic conditions cannot be obtained in practice, but fairly close 
approximations occur in the operations of heat engines. It may be 
added that the term " adiabatic " may be applied equally to solids or 
liquids. 

The equation to an adiabatic curve is 

P V> = a constant, 

or 

P Vx = PiV/, 

where P and V are the original and Pj and V l the final pressures and 
volumes, and y the ratio of the specific heat at constant pressure to 



that at constant volume, or 



Adiabatic Changes. 
C J 



109 



For gases difficult to liquefy the 



value of y is about 1-4. The proof of this equation may be found 
in theoretical treatises. 

The value of y for a given gas may be found in several ways. One 
method, by which the figure may be deduced from considerations of 




^-.->. ____> 

FIG. 25. ISOTHERMAL AND ADIABATIC OF A GA 



the velocity of sound, will not be gone into here. The introduction 
of the steam calorimeter by Joly has enabled the specific heat of a 
gas at constant volume to be obtained experimentally, which was no*- 
possible by any previous method. As the specific heat at constant 
pressure may also be determined, the ratio y can be found by 
direct experiments on the individual specific heats. Before Joly's 
method was known, however, an experimental method was devised 
by Clement and Uesorme for obtaining the value of y, and from this 
value calculating the specific heat at constant volume. A large glass 
globe, furnished with a tap of wide bore, and also with a gauge-tube 



1 1 o Heat for Engineers. 

containing a light liquid for noting small alterations in the internal 
pressure, is filled with air at a slightly reduced pressure. On open- 
ing the tap air rushes in, and the pressure rises to that of the atmo- 
sphere. The air originally in the globe thereby undergoes com- 
pression, and its temperature therefore rises. If the tap be closed 
rapidly, the air in the globe will cool, and the pressure will fall below 
atmospheric, but not so much below as initially, as more air is now 
in the globe. If the compression of the gas be performed rapidly by 
the sudden opening of the wide-bore tap, it may be regarded as an 
adiabatic compression, and the value of y may be calculated from the 
three observed pressures as under : 

Let P == the atmospheric pressure ; 

P! = pressure inside the globe before opening the tap ( = P 
- height of liquid in gauge reduced to mercury 
equivalent) ; 

P = pressure inside globe after cooling to the original tem- 
perature. 

Then, considering the compression as adiabatic, the pressure and 
volume of the enclosed gas before and after opening the tap will be 
represented by 

PiV/ = P V. 

Taking logarithms, this becomes 

y (log V x - log V) - log P - log Pj . . (i) 

If the. temperature at the final reading of the gauge is equal to that 
at the beginning, then, from Boyle's law, 



and 



= (2} 

v ? 



Writing equation (i) in the form 

y 

and substituting 



Adiabatic Changes. 



in 



= log P - log P! 
logP L) -logP/ 

Hence the value of y may be obtained by the observation of the 
three pressures. 

Other methods may also be adopted for finding the ratio of the 
two specific heats. The value of y for a number of gases and vapours 
is appended : 







Cn 






Substance 


&=' 






Air 


i '410 






Oxygen. ..... 


1-402 






Nitrogen .... 


1-412 






Hydrogen ..... 


1-414 






Ammonia ..... 


1-370 






Carbon dioxide .... 


i "261 






Steam ..... 


1-298 






Sulphur dioxide 


.-265 





Calculation of Rise of Temperature due to Adiabatic Compression. 
The equation connecting the volume and pressure of a gas when 
compressed without loss or gain of heat is 



p y = 



(i) 



and from this the volume occupied by the gas after being raised to a 
definite pressure may be calculated, and similarly the pressure pro- 
duced by a given reduction of volume. To obtain the temperature 
resulting from the compression, the above equation must be com- 
bined with the general equation to a gas, viz. 



PV 



Thus from (i) 



and from (2) 



p 

P! 



V J- 1 V T 

r = -[7 & 

v 



T s = p x v 



L 1 2 Heat for Engineers. 



Substituting in (2) the value of ^ in terms of V and V x , we have 



T, - T x (V )- . . . (J) 

y 
Similarly, by substituting in (2) the value of T - in terms of P x and 

and P, we have 

. (4) 



The above substitutions are conducted according to the theory of 
indices, which must be understood in order to follow them. Examples 
of the use of the formula will now be given. 

Example i. 20 cubic feet of air, at 15 C. and 14*7 Ib. pressure, 
are suddenly compressed to 5 cubic feet, all the heat remaining in the 
gas. Find the temperature of the air after compression. 

y ( for air = i '41). 
From equation (3) 

' 41 



but T = 288" absolute, 

1\ = 288 X (5) *4> 

Tj = 506 absolute nearly 
or 506 - 273 - 233 C. 

Example 2. The ignition point of a mixture of gases is 550 C. 
If the mixture be originally at 20 C. and normal atmospheric pressure, 
find the pressure at the moment of ignition when the temperature is 
raised by an adiabatic compression, assuming that y = i "41. 

From equation (4) 

(55 + 273) = 293 

823 = 293 x (1^)0-291 
P! = 34 '75 atmospheres. 

The calculation of the cooling effect produced by an adiabatic 
expansion is not so simple, and will obviously depend upon the 



Adiabatic Changes. 113 

amount of work done by the expanding gas. The work done in an 
adiabatic compression is represented, as in the case of an isothermal, 
by the area bounded by the curve, the ordinates representing the 
initial and final pressures, and the axis of volume. In Fig. 25, for 
example, the work done in compressing a gas adiabatically from a 
volume z\ to a volume v. 2 , is represented by the area A B C D, and is 
definite for a given compression. By integration the work done may 
be shown to be equal to 

//M'i -A>?'2\ 
V y - i / 

where p l is the original, and/., the final pressure. On the other hand 
a compressed gas on expanding from v. 2 to v l may do so with the 
performance of varying quantities of external work, according to the 
arrangement of the experiment. Thus a compressed gas may be 
confined beneath a piston which is open to the atmosphere on its upper 
side, in which case the work done by the expanding gas will be that 
required to overcome the atmospheric pressure only. Again, the 
piston might be connected to a machine, in which case the expanding 
gas would do the additional work of driving the machine ; or, if a 
vacuum existed on the upper side of the piston, no work would be 
done in the expansion save that required to lift the piston itself. The 
amount of work done by an expanding gas may therefore be varied in- 
definitely, and the cooling effect which is caused by the conversion of 
heat stored in the gas into work, will vary in like manner. If it can 
so be arranged that the expanding gas performs an amount of work 
equal to that required in producing the compression, the formulas used 
in the previous examples may be applied, but not otherwise. Thus, 
in Fig. 25, a gas compressed from ^ to z> 2 adiabatically involves the 
performance of work represented by the area A B C D, and undergoes 
a rise in temperature. If the compressed gas can be arranged to ex- 
pand again to z^ so as to perform work equal to the area A B C D 
during the expansion, the temperature will fall to that which existed 
at the commencement of the compression. If less work be done, the 
temperature will not fall to the same extent, and the gas will be hotter 
at the end of the expansion than it was before compression. 

Example. If air, originally at 10 atmospheres pressure and 20 C. 
expand to i atmosphere, doing work equal to that which would be 
required to restore it to its original condition, the temperature would 
be from (4) . y,. 29I 

T, = 293 x (-) 

TI = 149-2 abs. = - 1 23-8' C. 



1 1 4 Heat for Engineers. 

In the cold air refrigerating machine the expanding air does work 
in helping to drive the machine, so as to assist in compressing the 
next charge. A very low temperature is thus obtained, - 62 C. or 
- 80 F. often being observed. 

Mayer's Calculation of the Mechanical Equivalent of Heat from 
the two Specific Heats of Gases. In the year 1842, Dr. Julius Mayer 
published a paper containing a calculation of the value of the 
mechanical equivalent of heat, based on the assumption that the heat 
produced in the compression of a gas, or lost during its expansion, is 
the exact equivalent of work done. The principle of Mayer's calcu- 
lation is as follows : imagine a cylinder containing air, and fitted with 
a weightless piston. For simplicity of calculation, suppose the volume 
of the air beneath the piston to be originally i litre ; the area of section 
100 square centimetres; and the temperature o C. The distance 
between the end of the cylinder and the under side of the piston 
will then be 10 cm. If the temperature be raised to 273 C., the 
volume of air, by Charles' law, will be doubled, and the piston will 
be raised 10 cm. against the pressure of the atmosphere. The 
number of heat units required in the process may be calculated from 
a knowledge of the specific heat of air at constant pressure, for, as 
the piston is free to move, the pressure of the enclosed air will not 
alter. If, however, the piston be fastened down before heating, the 
conditions are those of a constant volume, and a smaller amount of 
heat will be required to raise the temperature of the air to 273 C. 
The difference between the heat quantities in the two cases was 
assumed by Mayer to be the exact equivalent of the work done in 
raising the piston. The calculation, using modern values for the 
constants for air, may then be made as under : 

Constants for Dry Air. 

Weight of i litre at o C. and 760 mm. = i '293 gram 
Specific heat at constant pressure "238 

at constant volume = '169 

Pressure of atmosphere = 760 mm. 
I0 33 grams per sq. centimetre. 
Calories required to raise temperature from 
o C. to 273 C. at constant pressure = i 293 

x 0-238 x 273 . 84-03 

Ditto at constant volume = 1-293 x 0*169 x 

2/3 = 59'67 



Difference = 24-36 



Properties of a "Perfect" Gas. 115 

Work done in raising piston = total 

pressure on piston x distance 

moved = 1033 x 100 x 10 1,033,000 cm. grm. 

Equating, 24-36 calories 1,033,000 cm. grm. 

*. i calorie 42,390 cm. grm. 

The same result will be obtained whatever mass of air, or rise in 
temperature, be considered; the quantities chosen in the above 
example are merely for the purpose of simplifying the calculation. 
Or, if desired, the result may be obtained in British units by a similar 
process. 

The actual figure given by Mayer was 36,700 cm. grm., the 
error being due to the use of inaccurate data. Moreover, the 
assumption is made that the whole of the heat is expended in external 
work, which, as we have seen, is almost, though not quite, correct ; 
but at the time Mayer's calculation was published, no experimental 
evidence of the truth of the assumption was available. Nor could it 
be predicted beforehand that the molecules of a gas would require 
practically no force to drag them apart. Hence, although Mayer's 
result was published prior to those of Joule, it is to the latter that the 
credit of first determining the mechanical equivalent of heat is due. 

Properties of a "Perfect" Gas. The laws concerning gases are 
not exactly obeyed by any known gas, but an ideal gas may be 
imagined which would exactly conform to these laws under all con- 
ditions. A gas, in order to be " perfect," would possess the following 
properties : 

1. It would obey Boyle's law exactly under all conditions. 

2. Its specific heat at constant pressure would be the same at all 
temperatures and pressures. 

3. The external heat required to enable the gas to expand at 
constant pressure would be the exact equivalent of the work done by 
the expansion, />., there would be an entire absence of internal 
molecular work. 

Of the known gases, hydrogen, helium and nitrogen approximate 
most closely in properties to those of a perfect gas. A much greate*' 
deviation is noticed in the case of easily liquefied gases, such as 
sulphur dioxide, ammonia and chlorine, which may be regarded as 
being vapours rather than true gases. The conception of a perfect 
gas is of great service, in forming a standard of comparison for known 
gases. 

Operations Depending on Gaseous Pressure. Explosives. In gas, 
oil and hot-air engines the piston is propelled by the expansive force 

i 2 



1 1 6 Heat for Engineers. 

exerted by a mass of hot gas, which in the process loses heat equiva- 
lent to the amount of work done. The gas, in reality, acts as a 
medium for the conversion of heat into work ; the heat, in gas and 
oil engines, being furnished by the combustion of the fuel in the 
cylinder. The properties of steam or other saturated vapour differ 
entirely from those of a gas, and will be referred to later. 

The heat produced by the compression of a gas is made use of in 
the Diesel engine to ignite the charge in the cylinder. This involves 
the use of a high working pressure, sufficient to raise the temperature 
of the charge to the point of ignition, but results in increased efficiency, 
and renders ignition devices unnecessary. 

The class of substances known as explosives owe their power to 
the generation of a large quantity of gas at a high temperature. If 
a piece of guncotton, for example, be burnt in an exhausted vessel 
the amount of gas collected will be found to occupy several hundred 
times the volume of the guncotton taken. The generation of this 
mass of gas, at a high temperature, gives rise to an enormous pres- 
sure in a closed space, and this pressure constitutes the force of the 
explosion. The magnitude of the force generated may be realised 
from the numerical example which follows : 

One gram of an explosive yields 750 c.c. of gas, measured at o C. 
and 760 mm. pressure. The actual temperature of the gas, at the 
moment of explosion, is 1200'' C. To find the pressure exerted 
immediately after firing i gram in a closed space of 2 c.c. The 
volume occupied by the gas at i20oC. and 760 mm. (i atmosphere) 
pressure, would be 

7^0 x (1200 + 27-3) 

- - 3 - - ' = 4047 c.c. 

273 

From Boyle's law, if 4047 c.c. of gas at i atmosphere pressure, 
be compressed into a space of 2 c.c., the pressure will become 

- 2023 '5 atmospheres. This is equal to nearly 13*3 tons per 

square inch. All explosives may be regarded as bodies which 
possess stored-up energy, which on decomposition, is liberated in 
the form of heat. The most powerful explosive is therefore the one 
that disengages the greatest amount of energy. 

Absorption of Gases by Porous Solids. Many solids, particularly 
those of a porous character, possess the property of absorbing large 
quantities of gases. Spongy platinum, and in a less degree platinum 
wire or foil, are capable of absorbing hydrogen and combustible 
hydrocarbons, the process being attended by the evolution of heat. 



A bsorption of Gases by Solids. 1 1 7 

If a piece of spongy platinum, or a spiral of fine platinum wire, be 
held in a jet of hydrogen or coal gas, the heat generated is sufficient 
to raise the platinum to incandescence, thus causing the jet to ignite. 
Gas-lighters based on this property of platinum are in common use, 
as also is an arrangement for procuring a light, in which the platinum 
is dipped into the interior of an annular wick steeped in spirits, the 
vapour of which is absorbed, producing incandescence, and so light- 
ing the lamp. Whilst platinum is capable of absorbing a number of 
gases and vapours, other substances appear to be able to absorb one 
gas only. Thus the metal palladium absorbs over 600 times its volume 
of hydrogen, but is inert towards other gases ; and similarly molten 
silver occludes oxygen only, which is expelled at the moment of 
setting. Powdered magnesium absorbs hydrogen, which, as also in 
the case of palladium, may be expelled by heating in a vacuum. It 
is probable that every solid, to some extent, is capable of entangling 
gases either in its pores or on its surface. 

Wood charcoal exercises this power of absorbing gases to an 
extraordinary degree, particularly w r hen freshly made. Noxious gases 
such as sulphuretted hydrogen, sulphur dioxide, and ammonia are 
readily occluded, to an amount equal to many times the volume of 
the charcoal. It is to this property that the well-known cleansing 
powers of charcoal, in such processes as filtration, are due. In addi- 
tion, the main constituents of the atmosphere oxygen and nitrogen 
are readily absorbed. Charcoal made from porous woods, such as 
willow or alder, if ground up immediately after making, absorbs 
oxygen so eagerly, and with such generation of heat, that the mass may 
ignite. Charcoal for making gunpowder is obtained from woods of the 
type of willow, and to avert the danger of spontaneous ignition the 
charcoal is kept for at least two weeks before grinding up. The recent 
experiments of Professor Dewar show that charcoal made from cocoa- 
nut fibre possesses a greater absorbing power than any other kind, and 
that the amount of gas absorbed increases enormously when the 
charcoal is kept at a very low temperature. In one experiment 
50 grams of cocoa-nut charcoal were placed in a tube connected to 
a meter, and immersed in liquid air at -i8oC. The air in th ; 
tube was absorbed, causing a reduced pressure, owing to which a 
further quantity of air passed through the meter into the tube, and 
was in turn absorbed. This continued until 8 litres of air were 
registered as having passed through the meter into the charcoal. In 
another experiment a glass tube about 4 feet in length was taken, 
closed at one end, the closed end being bent into a parallel branch 
which contained charcoal, and the open end placed under mercury. 



1 1 8 Heat for Engineers. 

On surrounding the charcoal with liquid air, the enclosed air was 
absorbed so completely that the mercury rose in the tube to a height 
equal to that of a standard barometer. These experiments show 
that it is possible to procure vacua, equal, if not superior, to those 
obtainable with the best mercury pumps, and the process has been 
tried commercially in the manufacture of vacuum tubes and glow- 
lamps. The charcoal-absorption method of obtaining vacua is far 
more expeditious than the mercury pump, which it will doubtless 
largely supersede as liquid air becomes cheaper to obtain. 

Closely connected with this subject is the passage of gases through 
solids. If a closed platinum tube containing hydrogen be heated to 
a white heat, it will be found on cooling that the hydrogen has 
escaped, leaving a vacuum in the interior ; thus showing that whereas 
hydrogen could pass through the hot platinum, air could not, as other- 
wise air would be found in the tube after cooling. For this reason, 
as will be referred to under the subject of Pyrometry, hydrogen gas 
cannot be employed in a gas-pyrometer furnished with a platinum 
bulb. Iron, at a red heat, is similarly penetrated by carbon mon- 
oxide, and this property probably plays an important part in the 
process of converting iron into steel. 

The physical and chemical condition of gases in the interior of 
solids is still a matter of conjecture. The outward appearance of 
the solids is not altered, in general, by the absorption of large quan- 
tities of gas, as would be the case if an ordinary chemical action took 
place. On the other hand, the disengagement of heat appears to 
point to some form of combination occurring, or to some molecular 
change in the gas ; in which latter connection it may b<s noted that 
gases, when absorbed in a solid, are frequently more chemically active 
than when in the free state. Metals in general, when containing an 
occluded gas, offer a higher resistance to electricity than when in the 
pure state. 



CHAPTER VII. 

THE MEASUREMENT OF TEMPERATURE. LIQUID AND GAS 
THERMOMETERS. 

Definition of Temperature. Clerk Maxwell has defined tempera- 
ture as " the thermal state of a body, considered with reference to its 
power of imparting heat to other bodies." Higher and lower tem- 
peratures are defined as follows : " If, when two bodies are placed 
in thermal communication, one loses heat, and the other gains heat, 
that body which gives out heat is said to have a higher temperature 
than that which receives heat from it ; and if neither body loses or 
gains heat, they are said to have the same temperature." The tem- 
perature of a body is therefore its thermal condition, and must not 
be regarded as expressing heat quantity. To raise the temperature 
of a given mass of water through a given interval requires about 
thirty times as much heat energy as that expended in raising an equal 
mass of lead through the same interval. The heat quantity involved 
in a given thermal change therefore depends not only on the tem- 
peratures, but also on the thermal capacity of the body employed. 

Standards of Temperature. Temperature is measured by refer- 
ence to certain arbitrary standards, those now universally chosen 
being the thermal conditions of melting ice, and the steam from 
water boiling at normal atmospheric pressure. These standards, 
originally used by Hooke and Sir Isaac Newton, possess the advan- 
tages of absolute constancy and simplicity, and enable instruments 
made in any place to be standardised so as to be identical. Other 
standards have been used from time to time, but have been abandoned 
in favour of the more convenient ice and steam. 

The difference between the thermal conditions of ice and steam 
at 760 mm. pressure is called 100 on the Centigrade scale of tem- 
perature, the ice point being marked o, and the steam point 100 . 
On the Fahrenheit scale, largely used in Britain and America, the 
same points are labelled 32 and 212 respectively, the interval being 
therefore i8o r . A third scale, known as Reaumur, is used in Eastern 
Europe, in which the ice point, as in the Centigrade scale, is called 



1 20 Heat for Engineers. 

o, and the steam point 80. For scientific purposes the Centigrade 
scale is now generally employed, as the numbers chosen are more 
convenient for use in calculations. The importance of specifying a 
pressure for the steam point is manifest, as the temperature of steam 
alters considerably with slight variations of pressure ; the melting-point 
of ice, on the contrary, is practically unaffected by ordinary fluctua- 
tions in atmospheric pressure. 

Principles of Instruments for Measuring Temperature. In order 
to measure temperatures between and beyond the fixed points, 
advantage must be taken of some regular physical change brought 
about by changes in temperature. Any of the following, for example, 
if uniform, may be utilised : 

1. The alteration in volume of a liquid or gas. 

2. The change of pressure exerted by an enclosed gas or vapour. 

3. The variation in length of a bar of metal. 

4. The alteration in the electrical resistance of a metal. 

5. The varying electromotive force set up at the junction of two 
different metals. 

6. The difference in the quantity of heat radiated by a given 
surface. 

It is essential, however, that the physical change in question shall 
l)e uniform, in order to confer the same value to individual degrees 
of temperature. When this is the case, the change between the ice 
and steam point can be noted, and T -J-g- part of the change will then 
correctly represent i degree Centigrade, and T -|o part i degree 
Fahrenheit. If the change be uniform at temperatures beyond the 
fixed points also, the value of i will be identical on all parts of the 
scale. 

In practice, however, it is not possible to obtain a physical change 
of absolute constancy. The expansion of certain gases, such as 
hydrogen and nitrogen, or the increase of pressure exerted by these 
gases when enclosed, show an extremely close approximation to uni- 
formity at all temperatures well above those at which they liquefy. 
For a practical standard, therefore, temperatures on the gas scale are 
taken as a reference for those arrived at by other methods. On the 
gas scale i degree Centigrade may be defined as T -J^ part of the 
increase in volume (or pressure, if enclosed) of a given mass of the 
standard gas when placed in ice and steam at 760 mm. successively. 
The other physical changes enumerated are all inferior, in point of 
uniformity, to the volume or pressure changes in a suitable gas, and 
when used for measuring temperatures exactly must be compared with 
the gas scale. 



Principles of Temperature Measurement. 121 

In addition to the correctness of the method adopted, the question 
of practical convenience in use also arises. Any instrument for 
measuring temperatures should, as far as possible, be portable, easily- 
read, and inexpensive. These considerations render gas thermo- 
meters of little service for everyday use, as these instruments lack the 
practical qualifications mentioned. For all ordinary purposes, up to 
the temperature of 500 C., and down to - 39 C, mercury thermo- 
meters are by far the most convenient, and, if properly standardised, 
are sufficiently accurate. Beyond these ranges of temperature, other 
instruments must be used, each of which, if accuracy is required, 
should be compared with the gas scale. It will be seen, subsequently, 
that it is possible, by taking advantage of one or other of the physical 
changes previously enumerated, to measure temperatures with con- 
siderable accuracy between the limits of - 260 C. and + 1500 C. ; 
and, with more doubtful accuracy, to more than 3000" C. 

Having regard to the various physical phenomena involved in the 
different methods of measuring temperatures, and the discrepancies 
that might arise, it is highly desirable to have some standard of tem- 
perature independent of the substance used. This standard is fur- 
nished by considerations concerning the conversion of heat into 
work, and is known as the thermodynamic scale. When a perfec- 
engine takes in heat at one temperature and gives it out at another, 
the quantities of heat which it takes in and gives out are propor- 
tional to these temperatures, whatever medium be used in the engine, 
and the work done is the equivalent of the difference between the 
quantities taken in and rejected. It is thus possible to define tem- 
perature with respect to work-producing power, and so to form a 
scale independent of any material. If the interval between ice and 
steam be represented by 100 ideal degrees, as thus deduced, the tem- 
perature of melting ice will be 273*13 of these degrees, and conse- 
quently absolute zero will be 273*13 thermodynamic degrees. A 
hydrogen thermometer based on the alteration in pressure or volume 
of the gas, gives readings practically identical with those of the 
thermodynamic scale over a considerable range ; other gases show 
deviations from it owing to being less perfect than hydrogen. 

The practical forms of instruments for measuring temperatures 
will now be described. 

Liquid-in-Bulb Thermometers. The increase in volume sustained 
by a liquid when heated is the basis of the most common method of 
measuring temperature. A glass bulb, connected to a stem of fine 
bore, is filled with liquid to such an extent that the end of the liquid 
column remains in the stem at all temperatures embraced by the 



i 2 2 Heat for Engineers. 

range of the instrument, and the position of the end of the column in 
the stem is made to indicate the existing temperature. It is evident 
that the increase in bulk observed represents the apparent or relative 
expansion of the liquid, and, if the stem is to be equally divided, this 
expansion should be uniform. For this reason mercury is chosen for 
most thermometers ; other advantages possessed by mercury being 
theVlarge range of temperature it will indicate, its low thermal 
capacity and good conductivity, its visibility even in a thin thread, 
and the fact that it does not cling to the glass. The range of a 
mercury thermometer is restricted by its freezing point ( - 39 C. = 
-38*2 F.), and its boiling point (357 C. = 674*6 F.), but by 
special means it is possible to obtain readings as high as 500 C. 
with mercury. No other ordinary liquid expands so uniformly 
as mercury, and none is capable of being used over so wide a 
range. For special purposes, however, other liquids are sometimes 
employed. 

It is now customary to make mercury thermometers with cylindrical 
bulbs, which are more convenient in practice than spherical bulbs. 
In order to prevent a possible escape of liquid, or the entry of mois- 
ture or dust, the thermometer is sealed at the top, the air having been 
previously displaced by heating the bulb, thus causing the mercury to 
expand and drive out the air, and sealing whilst hot. If necessary, 
the mercury in the bulb may be boiled to insure complete expulsion 
of air so that, on cooling, the space above the column should contain 
nothing but mercury vapour. Before proceeding to mark the stem, 
the thermometer should be put aside for at least six months after 
filling, as the bulb undergoes a gradual contraction during this period 
which would render the readings erroneous if the stem were marked 
immediately after filling. The greater part of this contraction takes 
place during the first month, and is not complete even after the lapse 
of years. After six months, however, the alteration is sufficiently 
small to ignore in ordinary cases. 

The lower fixed point is obtained by placing the bulb, and stem 
as far as the end of the column, in powdered ice contained in a 
tunnel or vessel which allows the water resulting from the melting of 
the ice to drain away. When the column is stationary, a mark is 
made on the stem opposite the end, and is called o Centigrade or 
32 F. The steam point is obtained by surrounding the ther- 
mometer and stem with steam from water boiling at atmospheric 
pressure, the vessel used for this purpose being as shown in Fig. 26. 
It consists of a copper boiler, on the top of which are placed two 
concentric cylinders. The inner cylinder is open at the top, and 



L iqnid-in-Bulb Thermometers. 



123 



contains the thermometer ; the outer one serves as a steam jacket 
and has an opening in the side from which the steam escapes. This 
arrangement insures that the whole of the thermometer attains the 
temperature of the steam, and gives a constant result at a given pres- 
sure which could not be obtained by immersing the thermometer in 
boiling water. The stem opposite the top of the column is marked 
temporarily, as this point will only repre- 
sent 100 C., or 212 F., if the barometric 
pressure is exactly 760 mm. A deviation 
of 26*8 mm. on either side of the 
standard causes an alteration in the 
temperature of the steam of i C., or 
i ' 8 F. Intermediate variations of 
pressure cause a proportional alteration in 
temperature; thus at 750 mm. pressure 
the temperature of the steam would be 

~ 2JF8/ = 99*63C.,or2ii-3F. 
The figure representing the position 
of the top of the column is thus deter- 
mined, and the space between the two 
marks divided into this number of equal 
parts by a dividing engine. Sometimes 
the marks are engraved on the stem ; in 
other cases on a separate scale fastened 
to the stem. For facility in reading, 
longer marks are made at every 5, and 
numbers placed at every 10, or more 
frequently if necessary. The divisions 
are continued geometrically along the 
stem in both directions beyond the fixed 
points. 

Alcohol is sometimes used instead of mercury, either for cheap- 
ness, or for recording temperatures below the freezing-point of 
mercury r or for thermometers for other special uses. Alcohol has - 1 
higher coefficient of expansion than mercury, and consequently a stem 
of .wider bore may be used for a given size of bulb. To render the 
column visible, the alcohol is coloured with a dye, such as rosaniline. 
The boiling-point of alcohol is 79 C., consequently an alcohol thermo- 
meter cannot be standardised in steam. It is customary to mark the 
ice-point in the usual manner, and to obtain the higher temperatures 
by comparison with a good mercury thermometer. The low freezing 




FIG. 26. METHOD OF OB- 
TAINING THE UPPER 
FIXED POINT OF A 
THERMOMETER. 



124 Heat for Engineers. 

point of alcohol (- 112 C.) renders alcohol thermometers of service 
for observing atmospheric temperatures in the polar regions, where 
indications far below the freezing-point of mercury are frequently 
obtained. There appears to be no good reason why turpentine 
should not be used instead of alcohol for many purposes. It boils 
at 159 C., and could therefore be standardised in steam; moreover 
its expansion in glass is more regular than that of alcohol, though not 
quite so uniform as that of mercury between o and 100. Turpen- 
tine has a coefficient of expansion six times as great as that of 
mercury, and is cheaper than alcohol, besides possessing the other 
advantages enumerated. 

Thermometers for reading temperatures below the freezing-point 
of alcohol are now made with pentane (C 5 H 12 ) which freezes about 

- 200" C., and may be used to record temperatures as low as that 
of liquid air. The use of pentane is restricted to low temperatures, 
as it boils at 39 C. Such thermometers may be graduated in ice to 
give one fixed point, and the other points obtained by comparison, 
in cold media, with a gas thermometer. 

Defects of Liquid-in-Bulb Thermometers. All ordinary thermo- 
meters are subject to errors, some of which are inherent, and others 
avoidable. The markings, if measured accurately, are seldom found 
to be equidistant ; and moreover, it is assumed that the bore of the 
tube is perfectly cylindrical, which is seldom the case. Errors may 
also arise from the fixed points being wrongly marked, the author's 
experience being that, whereas the ice point is usually correct, the 
steam point may be wrong by J or more, owing to the barometric 
pressure being ignored at the time of marking. Even if these errors 
were entirely absent, intermediate readings between the fixed points 
and also beyond, do not agree with those of the gas scale, as mercury 
in glass does not show a perfectly uniform expansion, and other 
liquids deviate even more. Thus a mercury thermometer, made of 
ordinary glass, differs from a gas thermometer by + "3 at 50 C.. 

- 2 at 150 C., - '3 at 200 C., + '05 at 250 C., + 1 '08 at 
300 C., and + 4 at 350 C. If contained in a non-expansive envelope 
the differences would be much greater, but, by a fortunate coincidence 
the varying expansion of the glass bulb, up to 250 C., nearly neutralises 
the increased expansion of the mercury. With other kinds of glass 
the discrepancies are usually greater. If exact readings are required 
with a given thermometer, it should be sent to the National Physical 
Laboratory to be compared with the standard instruments, from which 
a table of corrections may be obtained. 

Conversion of Scales. If it be desired to convert readings on the 



T her mome trie Scales. 125 

Centigrade scale into corresponding Fahrenheit readings, the general 
relation 

C reading _ F reading - 32 
5 ~9~ 

maybe used. Thus 40 C. = 104" F., and 122 F. = 50" C. The 
Reaumur reading divided by 4 is equal to either of the above 
expressions, but it is seldom necessary, in this country, to take the 
Reaumur scale into account. It is worthy of notice that any multiple 
of 5 on the Centigrade scale will correspond to a whole number on 
the Fahrenheit scale. This arises from the fact that the distances 
between the fixed points are divided into 100 and 180 respectively, 
consequently, on the same stem, an interval of 5 C. is equal to 9 F. 
As the ice-point is marked o C. and 32 F., it follows that 5 C. 
= (3 2 + 9) = 4 1 " F., and generally^/ 5 C. = (32 + n 9) F. | This 
relation is of service in marking both scales on the same stem. 

The Fahrenheit scale is still extensively used in this country, 
both for meteorological and engineering purposes, as well as domestic. 
It is to be hoped that, for scientific work at any rate, its use will 
gradually die out, as the use of the arbitrary datum number, 32, for 
the ice point, tends to confusion in calculation, and serves no useful 
purpose. This number was arrived at by the use of a mixture of 
snow and salt for fixing the lower point, which was called o, and the 
temperature of the human body for the upper point, which was called 
96". A thermometer constructed on this principle showed 32 in 
melting ice, and 212 in boiling water. Fahrenheit's standards have 
long been abandoned as untrustworthy, but the cumbersome figures 
have been retained, presumably as a concession to custom. The 
fixing of the Reaumur scale was determined by the boiling-point of 
.alcohol which was called 80, and almost agreed with the Centigrade 
scale ; afterwards steam was substituted for alcohol and the figure 
80 retained. 

It should be remembered that where an interval of temperature 
only is considered, i C. is the equivalent of i*8F. \The datum 
number 32 is only necessary to take into account when actual scale 
readings are required. 

Special Range Thermometers. When it is required to measure 
small differences of temperature very accurately, a mercury thermo- 
meter covering a range of nearly 400 C. would be unsuitable, as the 
degrees could not be sub-divided unless the stem were inconveniently 
long. It is possible, however, to construct thermometers to cover 
.any special range, so as to read fractions of a degree. In such cases 



1 2 6 Heat for Engineers. 

the bulb is made large relatively to the bore, and a safety-space pro- 
vided to take the mercury should by chance the range be exceeded. 
For example, a thermometer may be made 1 5 inches long, with the 
mark nearest the bulb o C., and the highest mark 30 C. Each 
degree would then be J an inch long, and could be sub-divided into 
tenths or twentieths. A small bulb is blown at the top into which the 
mercury will pass if 30 C. be exceeded, without danger of bursting the 
thermometer. If observations are required over a small range at a 
higher temperature say 100 to 130 C. the lowest mark on the 
scale is made 100, and a bulb blown between this mark and the 
thermometer bulb, which prevents the mercury reaching the scale 
until a temperature of 100 has been attained. The range is thus 
restricted, and sub-divided degrees can therefore be obtained on a 
thermometer of the usual length. In Beckmann's thermometers, by 
the use of a very large bulb and a narrow-bore tube, the scale is 
divided into T ^. These thermometers are intended to take read- 
ings of differences of temperature varying by a few degrees only. 
The safety-space at the top is bent into a parallel branch with the 
stem, and any excess of mercury will remain in this space. If, at the 
lower temperature, the column shrinks into the bulb, it is possible by 
judicious shaking to cause mercury to pass from the safety-space into 
the bore, until the end of the column is opposite one .of the lower 
marks on the scale, when the higher reading may be taken. If the 
column should stand too high on the scale, the bulb is heated so as 
to drive the excess into the safety-space. These thermometers have 
come into general use for molecular weight determinations from ob- 
servations of the depression in freezing point or rise in boiling point 
of a solvent due to dissolved solids, and for calorimetric observations 
in which great accuracy is desired. 

Registering Thermometers. There are many methods by which 
thermometers may be made to register special temperatures, such as 
the maximum and minimum temperatures experienced during a given 
time. The simplest form for registering the maximum temperature 
consists of a mercury thermometer, in the bore of which is placed a 
glass index, shaped like a dumb-bell. When the mercury rises in 
the tube the index is pushed forward by the end of the column ; and 
if the thermometer is placed horizontally will remain stationary when 
the column shrinks owing to cooling. The end of the index next to 
the column will therefore record the maximum temperature. By at- 
taching a fine steel spring to the index, it may be prevented from 
falling down the bore by its own weight, and the thermometer may 
then be kept in a vertical position. When setting for a given obser- 



Maximum and Minimum Thermometers. 127 

vation the index is shaken down to the top of the column, or, if it 
possess a steel spring, may be dragged down by a magnet. In 
another form of maximum thermometer (Fig. 27 A) the bore of the 
tube near the bulb is made extremely narrow. On heating, the force 
of expansion is sufficient to drive the mercury through this narrow 
passage, but on cooling the friction is too great to allow the column 
in the bore to return to the bulb, and the mercury divides at the con- 
stricted part. The end of the column in the bore therefore records 
the maximum temperature. The mercury in the bore may be made 
to join on to that in the bulb by jerking the thermometer vertically. 
This is the principle of the clinical thermometer, which is graduated 
for the special range of temperature to which the human body is 
liable. 




FIG. 27. MAXIMUM AND MINIMUM THERMOMETERS. 



The simplest form ot minimum thermometer is made of alcohol, 
and possesses an index immersed in the liquid in the bore (Fig. 27 B). 
When the temperature falls, the column of alcohol moves towards 
the bulb, and the surface skin at the end of the column pushes the 
index in front of it, the rounded end of the index being unable to 
penetrate the skin. On the temperature rising, the alcohol expands 
freely round the index without causing it to move ; consequently the 
end of the index next to the top of the column registers the minimum 
temperature. The index may be re-set by shaking, or, if it possess 
a steel spring, by means of a magnet. In Sixe's thermometer 
(Fig. 28) a maximum and minimum arrangement is provided in the 
one instrument. The stem of an alcohol thermometer is bent into 
a U shape, and the column of alcohol interrupted by a thread of 
mercury, which fills the bend and rises to a suitable height in each 



128 



Heat for Engineers. 



branch of the U-shaped portion. An index is placed at the top of 
each of the mercury columns. When the temperature rises, the 
alcohol in the bulb expands, pushing down the mercury in the limb 
nearest to the bulb, and therefore causing it to rise in the other limb, 
pushing the index as it rises, and leaving it, 
sustained by its spring, at the maximum position 
attained. On cooling, the alcohol shrinks into 
the bulb, and the mercury in the column nearest 
the bulb rises, carrying the index in this branch 
upwards, and leaving it nearer the bulb when 
the temperature rises. This therefore records 
the minimum temperature, whilst the other index 
registers the maximum. Two scales are pro- 
vided, the graduations being made to represent 
the position of the top of each mercury column. 
The scale on the branch nearest the bulb there- 
fore reads downwards, whilst the other scale 
reads upwards. Sixe's thermometer is very 
largely used in greenhouses, etc., and is a con- 
venient form of maximum and minimum thermo- 
meter. 

High Temperature Thermometers. The 
upper limit of a mercury thermometer, unless 
specially made, is the boiling point of the 
mercury 35 7C. By employing a strong bulb, 
however, and leaving nitrogen or carbon dioxide 
gas in the bore, it is possible to obtain higher 
readings, as the presence of the gas causes pres- 
sure to be exerted on the surface of the mer- 
cury, and prevents it boiling. By this means it 
is possible to construct thermometers reading as high as 500 C., 
using a special kind of glass, which, at this temperature, does not 
undergo permanent distortion even under the high internal pressure. 
If this temperature be exceeded, however, the glass softens sufficiently 
to cause a permanent alteration in the size of the bulb, and the read- 
ings are then worthless. In Bayly and Chorley's thermometers 
mercury is replaced by an alloy of sodium and potassium, which boils 
at over 700 C. Readings beyond this temperature cannot be made 
with these instruments, as the bulb softens and alters in shape, in spite 
of the absence of internal pressure. It has recently been proposed 
to use thermometers made of quartz instead of glass, and, for readings 
above 250 C., to employ molten tin as the expanding liquid. A 




FIG. 28. 

SIXE'S MAXIMUM 
AND MINIMUM 
THERMOMETER. 



Gas Thermometers. 129 

temperature of 1000 C. might thus be reached without danger of dis- 
torting the quartz bulb. These instruments, however, have not yet 
come into practical use, and for high temperature measurements, 
instruments based on other principles than the expansion of a liquid 
must be used. 

Gas Thermometers. The uniformity of the expansion or increase 
in pressure of the more perfect gases, such as hydrogen or nitrogen, 
render gas thermometers the most accurate of all instruments for 
measuring temperature, when properly constructed. Gas thermo- 
meters are of two types, viz. (i) constant pressure instruments, in 
which the gas is allowed to expand at constant pressure, and the 
temperature deduced from the increase in volume, and (2) constant 
volume thermometers, in which the gas is prevented from expanding, 
and the temperature obtained from the observed increase in pressure. 
Hydrogen is the best gas to use up to 200 C., owing to the accuracy 
with which it conforms to the laws relating to a perfect gas ; above 
200 C., however, it is liable to attack glass and other materials that 
might be used. Nitrogen, although less perfect than hydrogen, is 
free from this objection, and is therefore used when higher tempera- 
tures are measured. There are many forms of gas thermometers, 
and a typical example of each class will now be described. 

Callendar's Compensated Constant Pressure Gas Thermometer. 
Fig. 29 shows a diagrammatic view of this instrument. T is the 
thermometer bulb, which is connected to the bulb M, containing 
mercury, and furnished with a tap. S is a bulb precisely similar 
to T, and is attached to a tube of the same diameter and length as 
that connecting T and M. A U-tube, G, containing strong sulphuric 
acid, connects the two systems of tubes. The bulbs T and S, and 
also their connections, contain dry hydrogen or nitrogen. In taking 
a measurement, the bulbs S and M are surrounded by ice, whilst T is 
placed in the hot space of which the temperature is required. Mer- 
cury is now allowed to flow from M until the pressure inside T is 
equal to that in S, as shown by the sulphuric acid standing at the 
same level in both limbs of the tube G. Originally, when T, S, and 
M are all surrounded by ice, the level of the sulphuric acid must al: o 
be equal. As the pressure in the tube S is constant, that in the tube 
T is brought to its original amount when the gauge indicates equality 
of pressure in the two systems. Any variations in temperature 
experienced by the tube connecting T and M will be equally shared 
by the tube connected with S, any possible error from this source 
being thus compensated. The volume of T being known, the tem- 
perature is calculated from the volume of gas which expands into M, 

K 



1 3 o 



Heat for Engineers. 



which is equal to the volume of mercury run out to equalise pressures. 

This volume is obtained by weighing the mercury and dividing by 
specific gravity. The calculation is made as follows : 
Let V = volume of gas in T, and its absolute temperature. 
v = volume of gas expanded into M. As M is kept in ice, the 

absolute temperature of this gas will be 273 C. 




v 



S 



M 



FIG. 29. CALLENDAR'S COMPENSATED GAS THERMOMETER. 

On heating the gas in the bulb to 0, its volume will become, by 

V 
Charles' Law, , the pressure being constant. The expanded por- 

V ft 
tion, at the same temperature, would have a volume equal to 

273 

- V. But in passing into the bulb M its temperature is reduced to 
that of ice, or 273 C. absolute. Hence the volume of expanded air 
collected in M, which is equal to v, will be 



-V 



- 273 V 

e 



and = -3_ 

V - v 



Gas Thermometers. \ \ \ 

\j 

The result is given in absolute degrees, and it is assumed that 
the gas strictly obeys the gaseous laws, and that the compensation is 
perfect. When used for low temperatures, with hydrogen, the 
deviation from the gaseous laws may be ignored ; with nitrogen, on 
the contrary, a slight correction must be made on this account. The 
error in using this instrument to measure a temperature as high as 
450 C. probably does not exceed o'2, and although the arrange- 
ment is too elaborate for everyday use, it is of great value for stan- 
dardising instruments of a more convenient type. It is the most 
accurate form of constant pressure gas thermometer, and if furnished 
with a quartz or platinum bulb may be used for temperatures ex- 
ceeding 1000 C. This instrument has proved useful in furnishing 
standards for the graduation of pyrometers. 

Example. If the volume of gas in the bulb when in ice is 75 c.c., 
and on heating, 40 9 c.c. pass over into the mercury tube when the 
pressures are equal, the temperature will be 



__7_3 75 _ 600 '4 absolute, 

7 C AO ' Q 



or (600-4 - 273) = 327 -4 C. 

For many determinations dry air, free from CO.,, may be used 
with sufficient accuracy. 

Jolly s Constant Volume Gas Thermometer. The constant volume 
gas thermometer selected for description is one of many varieties, 
and possesses the advantages of simplicity and considerable accuracy. 
In Fig. 30 B is the thermometer bulb, connected by means of narrow- 
bore tubing to the rubber tubing, T, which at the other end com- 
municates with a mercury cistern, The cistern may be raised or 
lowered along the guide G, and clamped in any position. A scale is 
attached to the stand and enables the height to which the mercury 
has been raised to be read off. A mark is engraved on the tube A, 
at which the mercury is retained by raising the cistern when the tem- 
perature of the bulb rises, or lowering when the temperature falls, 
thus keeping the volume of enclosed gas constant. To use the in- 
strument with air, the mercury cistern is lowered below the mark on 
A, and the tap C, connected with a drying tube containing calcium 
chloride, is opened. The bulb is now placed in powdered ice, and 
allowed to remain for some time in order that the temperature of the 
enclosed air may fall to o C. The cistern is then raised until the 
mercury rises to the mark on A, when the tap is closed and the 
height of the surface of the mercury in the cistern read oft' on the 

K 2 



132 



Heat for Engineers. 



scale. The bulb is now placed in the space of which the tempera- 
ture is required, and the cistern adjusted so as to retain the mercury 
at the mark on A. When steady, the height of the mercury surface 
in the cistern is again read, and the temperature deduced as under :- - 




B 



FIG. 30. CONSTANT VOLUME AIR THERMOMETER. 

If the gas used be considered perfect, the relation 

PV P 1 V l 
T TJ 

may be applied at all temperatures and pressures. If the slight ex- 
pansion of the bulb be neglected, V = V 1} therefore 

p p, 

T - i 



Gas Thermometers. 133 

In the experiment, by opening the tap, P = barometric pressure, 
and T = temperature of melting ice = 273 abs. If // = the differ- 
ence in level of the mercury in the cistern when the bulb is in ice and 
the hot space respectively, P l = barometer height + //. 

Hence 

Baro. Baro. + h 



2 3 



When hydrogen gas is used, the above calculation gives an almost 
perfectly correct result for temperatures below 200 C, provided due 
allowance be made for certain incidental errors. A correction is 
necessary for (a) the expansion of the bulb, which cannot be avoided, 
hence V is not exactly equal to V x ; (b) the temperature of the gas 
in the narrow-bore connecting tube, which is not equal to that in 
the bulb ; and (c) the temperature of the mercury column, which, as 
in the case of the barometer, should be reduced to the equivalent 
reading at o C. Owing to the large mass of gas used, the combined 
errors are relatively small, but must be taken into account if standard 
readings are required. If the temperature be less than that of ice, 
the pressure must be diminished by lowering the cistern, in order to 
maintain constant volume, in which case the difference of level (/#, 
will be negative. 

Examples. (i) If the increase of pressure be 241 mm., and '.he 
barometer reading 755 mm., the temperature will be 

(755 JLMI)J1A73 = 360-2 abs., 

or (360-2 - 273) - 87'2C. 

(2) When used to take a low temperature, the mercury in the 
cistern was lowered 310 mm. below the starting point to main'-nin 
constant volume. Height of barometer ^=762 mm. Hence the 
temperature was 



=ll 

762 



or (161 *9 -273) = m'iC. 



134 Heat for Engineers. 

If nitrogen or air be used in the thermometer, the calculation 
must be modified, as the increase of pressure at constant volume 

differs sensibly from -L_ which almost exactly represents the co- 

273 

efficient for hydrogen. Nitrogen is the best gas to employ for 
general work, being inert towards the material of the bulb at all tem- 
peratures. The coefficient of increase of pressure at constant volume 
for nitrogen is not constant, being greater at o than at 100, the re- 
spective values being '003677 and -0036738, or - -and 



271 '9 272 i 

when the original pressure is i metre. Careful investigations of 
the value of the coefficient at different temperatures have been 
made, thus enabling correct calculations to be made. In the previous 
examples, if nitrogen were used, the reciprocal of the coefficient 
known to apply to the range of temperature measured must be used 
instead of the figure 273. Thus in example (i), if the same figures 
had been obtained with a nitrogen thermometer, the temperature 
would be 

(75SJ. L 2 4 i)_x_27 _ 358-9 abs. = 85-9-0. 

since the coefficient has an average value of ^l^ over this range, 
By correcting for the incidental errors previously mentioned, and 
using the proper coefficients, very exact results may be obtained with 
the constant volume nitrogen thermometer, which represents one of 
the best standards for temperature measurement. For rougher deter- 
minations, in which air is used, close results may be obtained in the 
manner described, using the figure 272-5 instead of 273 in the calcu- 
lation. In the standard instruments used at Sevres, the National 
Physical Laboratory, and elsewhere, various refinements are embodied 
which enable very exact readings to be obtained. 

The constant volume hydrogen thermometer is specially suited to 
the measurement of very low temperatures, such as those of liquid or 
solid air. Under the reduced pressure, the gas approaches closely in 
properties to a perfect gas, and accurate readings are obtained. For 
the temperatures of liquid or solid hydrogen (-252-5 and 
- 257 C.), helium may be used in the thermometer, although good 
results may be obtained even with hydrogen, as the enclosed gas,, 
being under a very low pressure, shows no tendency to liquefy, and 
continues closely to obey the gaseous laws. Professor Dewar has 
conducted his low temperature measurements in this manner, and the 
values obtained are very near to the truth. If absolute zero were 



Gas Thermometers. 135 

reached, the mercury in the cistern would have to be lowered by an 
amount equal to the initial pressure, in which case 

Baro. = (Baro. - h} _ o 
873" -T^~ ~TI 

Tj = o abs. 

The physical meaning of this is that the gas would cease to exert 
pressure, and in this respect behave like a vacuum. 

For high temperatures, the bulb of the instrument may be made of 
quartz, platinum, or an alloy of platinum and iridium ; nitrogen gas 
being employed, as hot hydrogen slightly attacks quartz, and is 
occluded by platinum. It has been found possible by this means to 
measure temperatures correctly up to 1150 C., and so to establish 
standards for the graduation of the instruments described in the 
succeeding chapter. 

The most recent development of the gas thermometer is due to 
Day, who has employed a bulb made of platinum, 80 per cent., and 
rhodium, 20 per cent, surrounded by an outer vessel. The space 
between the bulb and its enclosure was kept at the same pressure as 
that existing in the bulb, distortion being thus prevented. It was 
found possible to take accurate readings up to 1550 C., the error 
not exceeding 2 C. This extension of the gas scale has already 
proved of considerable service in checking the readings of other 
instruments used in the measurement of high temperatures. 



136 Heat for Engineers* 



CHAPTER VIII. 

THE MEASUREMENT OF HIGH TEMPERATURES. PYROMETRY. 

THE term " pyrometry " is used to embrace all the methods of 
measuring temperatures above the upper limit of liquid-in-bulb 
thermometers. With mercury, the limit is 500 C., the thermometer 
containing nitrogen under pressure ; and with sodium-potassium 
alloy 700 C. may be measured with fair accuracy. If we except the 
proposed tin-in-quartz thermometer, not yet in practical use, all 
temperatures above 700 C. must be determined by other methods. 
None of these methods, however, can compare in cheapness and ease 
of reading with the ordinary thermometer, which is consequently used 
wherever possible. 

The importance of conducting furnace operations at definite, known 
temperatures is now fully realised by manufacturers. In the manu- 
facture and subsequent treatment of steel, for example, the tempera- 
ture at which the operation is carried out has a determining influence 
on the finished product, which likewise holds true in the casting of 
alloys, the baking and glazing of pottery, and many other industrial 
operations. The recognition of these facts has led to the introduction 
of numerous forms of pyrometers for industrial purposes, and almost 
every establishment of consequence has now its installation of pyro- 
meters. Great advances have been made in recent years in the 
accurate measurement of high temperatures, and it is now possible to 
read the temperature of a furnace with a degree of accuracy equal to 
the reading of a low temperature with an ordinary mercury thermo- 
meter. It will probably be possible, before many years, to measure 
with reasonable certainty temperatures of over 3000 C., such as that 
of the electric arc. So numerous are the modern developments of 
pyrometry, that a special volume would be required for a complete 
treatment of the subject, and it is only proposed in the present 
chapter to give a description of the more typical pyrometers in use at 
the present time, and to indicate their practical utility. It may be 
taken for granted that any workshop pyrometer should, as far as 
possible, give an automatic registration of the temperature, in order 



Measuring High Temperatures. 137 

that workmen who have had no scientific training may be able to 
take the necessary readings. 

The methods in use for obtaining furnace temperatures may be 
summarised as follows : 

1. Wedgwood's Pyrometer, based on the permanent contraction 
of a clay cylinder when heated. The amount of contraction observed 
gives a clue to the furnace temperature. 

2. Calorimetric method, in which a weighed piece of metal is 
taken from the furnace and dropped into water, the temperature 
being obtained from the rise in temperature of the water. 

3. Gas Pyrometers, which are based on the increase in volume 
or pressure of a gas. 

4. Electrical-resistance Pyrometers, which depend on the increase 
in resistance to electricity shown by platinum as the temperature 
rises. 

5. Thermo-electric Pyrometers, which utilise the electromotive 
force developed at a junction of two different metals. With suitable 
metals, the E.M.F. increases in a regular manner as the temperature 
rises. 

6. Heat-Radiation Pyrometers. In these instruments the tem- 
perature is deduced from the heat radiated by a given surface, which 
is a function of the absolute temperature of the surface. 

7. Optical Pyrometers, based on a comparison of tints, or a 
photometric measurement of a given part of the spectrum. 

8. Pyrometers based on the linear expansion of a metal, the tem- 
perature being deduced from the observed elongation. 

9. Fusion method, which consists in the insertion in the furnace 
of a graded series of materials with known melting points, the tem- 
perature being approximately that of the highest member of the series 
which has undergone fusion. 

It may be stated that methods 4, 5 and 6 are the most useful in 
practice, and possess the advantage of being capable of giving auto- 
matic and continuous records of the temperature of a furnace. 

Fixed Points for Graduation cf Pyrometers. In order that pyro- 
meters of different types may read alike, it is necessary to graduate 
them in terms of a common, accurate scale of temperature, for which 
purpose the gas scale is adopted. A series of fixed points, accurately 
determined by means of a gas pyrometer or by other methods, serve 
as standards of temperature for the graduation of the various forms 
of pyrometers, and uniformity is thus secured. Within very narrow 
limits, the table of fixed points given below may be considered as 
correct up to 1150 C., above which it has not yet been found pos- 



Heat for Engineers. 

sible to apply the gas pyrometer method. The melting point of 
platinum is still uncertain, a recent determination by Dr. Marker, 
viz. i7ioC., being 70 degrees lower than the previously accepted 
figure; whilst the still later determination by Burgess is 1753 C. 
Above i r5o C. the values are obtained by assuming that the indica- 
tions of a thermal-couple pyrometer follow the same law as that 
known to exist below this temperature, or by calorimetric, optical, or 
radiation methods ; consequently the accuracy of these higher tem- 
peratures cannot be definitely asserted. The following table gives 
the most accurate results obtained up to the present : 

TABLE OF FIXED POINTS. 

Temp, in deg. C. 
Boiling point of water, at 760 mm. press. . . . 100 

,, naphthalene ,, ... 220 

Free/ing point of pure tin ...... 232 

lead . . . .327 

,, ,, zinc ..... 419 

Boiling point of sulphur at 760 mm. press. . . . 444*6 

Freezing point of pure antimony ..... 632 

,, ,, silver (in absence of oxygen) . 962 

,, ,, gold . . 1065 

,, ,, copper (covered with graphite) . 1084 

,, ,, wrought iron . . . .1510 

,, ,, platinum (formerly called 1780) . 1710 (Harker) 



,, ,, iridium ..... 2250 (?) 

When standardising a pyrometer by means of the above fixed 
points, special precautions are necessary with copper and silver. If 
exposed to air, silver occludes oxygen, and the freezing point is 
lowered. The observation should therefore be taken in an atmo- 
sphere of nitrogen, the silver being melted in a graphite crucible. 
Melted copper oxidises in air, forming an oxide which mixes with the 
metal and reduces the freezing point to 1062. If the copper be 
melted in a graphite crucible and covered with graphite the freezing 
point is 1084; if freely exposed to air the figure 1062 maybe taken, 
as the effect of oxidation reaches a permanent limit, and a steady 
freezing point is then obtained at the lower temperature. It is not 
necessary to employ every fixed point in standardising a pyrometer 
for ordinary use, the following usually sufficing: steam, tin, zinc* 
antimony, silver and copper. Higher points may be obtained by 
extrapolation when required, and a good, cheap substitute for silver is 
furnished by pure anhydrous sodium sulphate, which freezes at 
900' C. approximately. Pure common salt freezes at 800 C. (approx.) 



Wedgwood ' s Pyrometer. 



'39 



Where a number of pyrometers are used, it suffices to standardise 
one instrument exactly, which may then serve to graduate the others 
by comparison, and be kept as a standard for checking the remainder 
from time to time. 

The various types of pyrometer will now be described in the order 
in which they occur in the summary previously given. 

i. Wedgwood's Pyrometer. Wedgwood, the potter, was the first 
to recognise the value of working at uniform temperatures in his 
furnaces, so as to avoid uncertainty in results. He found that mere 
judgment by the eye could not be relied upon, and in the year 1782 
constructed a pyrometer for his own use, which has only been super- 
seded by the more scientific instruments produced during the last 
thirty years, and is still used to some extent. Wedgwood found that 
clay, of definite composition, undergoes a permanent contraction on 




It4o iso MO no coo 1*0 ieo iro 1*0 

ll,.,a;,..l..ii;,.L.,;U,..n;.f.i;J...t...U:...l....t..J. 




FIG. 31. WEDGWOOD'S PYROMETER. 



heating, and the higher the temperature the greater the amount of 
permanent contraction. To establish a standard of reference, he 
made a tapering groove, divided along its length, as shown in Fig. 31. 
The clay cylinder C, is made of such a size that before placing 
in the furnace it slides into the groove down to the mark " o." 
After remaining in the furnace long enough to acquire the existing 
temperature, the clay cylinder is removed and allowed to cool, and 
again placed in the groove. The mark opposite the lower end of the 
cylinder then records the condition of the furnace in terms of the 
scale adopted by Wedgwood, and any considerable variation on 
either side of the desired temperature is thus readily detected. 
Although this method cannot compare for accuracy or convenience 
with modern pyrometers, it is nevertheless a useful guide to the state 



1 40 Heat for Engineers. 

of a furnace, and is further of interest as being the first attempt at 
obtaining precision in work at high temperatures. Wedgwood's divi- 
sions or degrees were taken in terms of ^Q-Q of the initial dimensions 
so that at 240 divisions the diameter was reduced by one half. The 
connection between these divisions and Centigrade degrees has been 
investigated by Le Chatelier, who gives the following figures : 

Degrees Wedgwood 15 30 100 140 

Degrees Centigrade 800 1000 1200 1400 

Wedgwood's pyrometer, on account of its cheapness, is still used 
to some extent by potters and others. 

2. Calorimctric Method of Obtaining Furnace Temperatures. If a 
weighed piece of metal, of known specific heat, be made hot, and 
immersed in a known quantity of water, the temperature of the hot 
metal can be inferred from the rise of temperature produced in the 
water. 

Example. A copper cylinder weighing 140 grams is heated in a 
furnace, and rapidly immersed in 550 grams of water at i8'7C. 
The water is contained in a copper vessel weighing 250 grams, and 
the final temperature is 30'2C. The specific heat of copper is 
0-095. Find the temperature of the furnace. 

Let x = temperature of furnace. 

Heat units lost by hot copper = heat units gained by water and 
essel 

140 x 0-095 x (x - 30-2) = 550 x (30-2 - 18-7) 
+ {250 x 0*095 x (3* 2 ~ I ^'7)l 

x = 526-3 C. 

In attempting to construct an instrument based on this principle, 
several difficulties arise. If the piece of metal is to be used continu- 
ously, it should not oxidise, or its weight would alter. Platinum, in 
this respect, would be most suitable, but the cost of a piece of suffi- 
cient size would be greater than that of a good pyrometer of another 
type. Nickel is the only metal which can be used with advantage for 
this purpose. Again, the specific heat of a metal varies with the 
temperature, and this must be taken into account in the calculation. 
It is also difficult to prevent loss of heat by radiation in trans- 
ferring the metal from the furnace to the water, and in its best 
form a workshop pyrometer on this principle cannot be trusted to 



Siemens Calorimetric Pyrometer. 



141 



25 C. In Siemens' instrument, Fig. 32, the vessel containing the 
water is well insulated with felt, and the outer vessel furnished with a 
handle for convenience of holding near the furnace. A scale C, is 
attached, graduated in such a manner that if the zero mark be placed 
opposite the top of the mercury column in the thermometer before 
starting, the temperature of the hot metal may be read off opposite 
the top of the mercury at the end of the ex- 
periment. Calculations are thus avoided, and 
the instrument may be used by an untrained 
observer. Copper cylinders are sometimes used 
with this apparatus, but are subject to loss of 
weight owing to oxide forming and afterwards 
peeling off. Multiplying factors are sent out 
with the instrument, which enable the error 
due to loss of weight to be allowed for. It is 
preferable, however, to use nickel, which oxi- 
dises very little below 1000 C. 

Whilst the calorimetric method is cheap 
and fairly accurate if carefully used, it suffers 
from the drawback that a continuous reading 
cannot be obtained, and a separate experiment 
must be performed whenever the temperature 
is required. Experience shows that a skilled 
observer is essential if good results are to be 
obtained, as in the hands of workmen errors 
arise through delay in dropping the hot metal 
into the water, or through neglect of other 
necessary precautions. This form of pyrometer 
is fairly extensively used, on account of its 
cheapness, for operations in which an occasional 
reading of the temperature suffices. 

3. Gas Pyrometers. The principle of these 
instruments has been sufficiently indicated in 
the previous chapter. Although furnishing 
a standard of temperature with which other 

pyrometers are compared, gas pyrometers are too elaborate, and re- 
quire too delicate manpiulation to enable them to be used in industrial 
operations. The extensive researches of Holborn and Day at the 
Reichsanstalt with a constant volume nitrogen thermometer have 
resulted in the satisfactory settlement of fixed points up to 1100 C., 
which may be used in graduating other instruments. These observers 
first of all used a porcelain bulb, glazed inside and out ; but after- 





FlG. 32. SIEMENS' 

CALORIMETRIC 
PYROMETER. 



142 Heat for Engineers. 

wards found that a bulb made of platinum-indium alloy is more 
satisfactory, as the latter is not only impervious to nitrogen, but under- 
goes no permanent alteration in shape on heating. More recently, 
Jacquerod and Perrot have used a quartz bulb, which, owing to the 
low coefficient of expansion of quartz, reduces the necessary correc- 
tion for expansion to a minimum. With a platimim-iridium bulb 
the expansion correction at 1000 C. is 40 ; with quartz at the same 
temperature the correction is only 2. It is advisable, in a standard 
constant volume instrument, to employ a bulb of at least 500 c.c. 
capacity, in order that the error due to unheated gas in the connec- 
tions may be less than i. 

In Wiborgh's air pyrometer an attempt is made to read tem- 
peratures from the indications of a Bourdon pressure gauge. A 
definite quantity of air is forced into a porcelain bulb placed in the 
furnace by causing a lens-shaped chamber to collapse and discharge 
its contents into the bulb. The bulb communicates with a pressure 
gauge, and the positions of the index hand of the gauge are made to 
indicate corresponding temperatures. This instrument must not be 
regarded as possessing the accuracy of a standard gas pyrometer, as 
the calibration is purely empirical. There is also a danger of leakage 
at the junction of the porcelain bulb and the gauge tube. 

4. Electrical Resistance Pyrometer. -When platinum is heated, its 
resistance to electricity increases rapidly with the temperature. Thus 
a piece of pure platinum wire, having a resistance of 2 6 ohms at o C., 
increases its resistance to 3*6 ohms at 100 C., that is, gains i ohm 
for a rise of 100. If this increase be considered uniform between 
o and 100, then each increment of T ^ of an ohm resistance would 
indicate a rise of i. As it is easily possible to measure T ^^ of an 
ohm, it follows that on the above assumption -fa of a degree could 
be indicated by noticing the increased resistance of the piece of 
wire. 

Sir William Siemens was the first to propose, in 1871, the utilisa- 
tion of the increase in resistance of platinum for the measurement of 
furnace temperatures; and constructed pyrometers consisting of a 
piece of fine platinum wire wound on a porcelain or fire-clay cylinder 
incased in a steel tube to protect the platinum from the action of 
the furnace gases. The resistance was measured by a set of coils 
and galvanometer, and the temperature deduced from the resistance 
by means of a formula connecting the readings with temperatures on 
the air scale. As constructed, the instrument was found to be unreli- 
able, owing to the resistance of the platinum undergoing a permanent 
increase after heating, as the result of a chemical change due in part 



Callendar s Formulae for Resistance of Platinum. 143 

to the porcelain, and partly also to the furnace gases, which to some 
extent penetrated the iron tube. Later this trouble was overcome 
by the use of magnesia, in which the platinum wire, wound on a special 
kind of fire-clay, was imbedded, a procedure still adopted in Siemens' 
pyrometers as now sold. 

In 1886, Professor Callendar investigated the subject, and showed 
that the method was capable of giving very accurate results under 
proper conditions. Callendar wound the wire round mica, and en- 
cased the arrangement in a glazed porcelain tube, and then found 
that repeated heatings caused no appreciable alteration in the metal. 

The question of the connection between the increase of resistance 
and gas thermometer temperatures w r as investigated by Callendar and 
Griffiths up to 550 C., and formulae deduced from which gas scale 
readings could be obtained to within o'i G by the use of a properly 
wound platinum wire. The formulas are as follows : 

i. Let R = resistance in melting ice 

R 1((0 = resistance in steam at 760 mm. 

Also let R 100 -R be assumed to equal 100 on the platinum 

"O ~D 

scale, then i degree will be equal to -i^ . Assuming that an 

100 

increase of resistance of this amount represents i degree at all parts 
of the scale, then if R be the resistance observed in a given space, 
the temperature, in terms of the platinum scale, will be 

increase of resistance observed 

increase of resistance for i 
or, 

o ~p "p 

^~ ~^~ ^ X ico. 



r? 

- LV 



100 

Example. \.i the resistance in ice be 2 6 ohms, in steam 3 6 
ohms, and in a furnace 12*8 ohms, the temperature of the furnace, 
on the platinum scale, will be 

12 - ( -- x TOO = 1020 (Pt) 
3-6 - 2-6 

2. An increase of resistance at any part of the scale equal to 

RI " ~ R P does not correspond exactly to i degree on the gas scale. 
100 



1 44 Heat for Engineers. 

The connection between the two scales is expressed in the equa- 
tion : 



where / = temperature on the air thermometer 
P / = temperature in terms of platinum scale 
g = a constant, depending on the purity of the platinum. 

This constant must be determined experimentally, and in order 
to obtain the value, P / must be determined at some temperature other 
than o C. and 100 C., at which, by definition, it coincides with the 
air scale. The temperature usually selected is the boiling point of 
sulphur, which Callendar found to be 444*5 C. on the air scale, at a 
pressure of 760 mm. A difference of i mm. alters the boiling 
point of sulphur o'o82 C. The platinum temperature of boiling 
sulphur is found by measuring the resistance at o (ice), 100 (steam) 
and in the boiling sulphur, and calculating as in the previous example. 
A further example will make the procedure clear, and show how 8 is 
determined from the data. 

Example. The resistance of the pyrometer in ice is 2 6 ohms, 
in steam 3-6 ohms, in boiling sulphur 6-815 ohms. Required the 
value of 8. 

The platinum scale temperature of the sulphur will be 

x 100 (see previous example) 

= 421*5 (P/) 

Applying in the formula / - P / = 8 \( V - (-- M, 

IVioo/ Vioo/j 

t air scale temperature = 444 5 
444-5 -431-3=8 j(444- 5Y _ (444.:5\| 

(V 100 / V IOO /J 

from which 8 = i 5. 

The value of 8 for pure platinum is as nearly as possible i 5, but 
should be determined for each batch of wire made into pyrometers 
by the makers, and sent out with the instrument. 



Platinum Resistance Pyrometers. 



When the value of 8 has thus been determined, air-scale tem- 
peratures corresponding to given platinum-scale temperatures may be 
calculated from the equation. A table is appended showing corre- 
sponding temperatures as indicated by the two scales, and also the 
difference between them, when the value of 8 is i 5. 

Comparison of Air and Platinum Scales. 

8-1-5. 



Platinum Thermometer 
Reading (Ft.) 


Air Thermometer Reading 

/ (deg. C.) 


Difference 
Of-Pt.) 


100 


- 97'i 


+ 2' 9 


O 








50 


49-6 


- -04 


100 


IOO 


O 


200 


203' I 


31 


300 


309-8 


9'8 


400 


420-2 


20'2 


500 


534-9 


34 9 


600 


654-4 


54 4 


700 


779-4 


79'4 


800 


910-7 


no'7 


900 


1049-4 


149-4 


1000 


1197-0 


197-0 


1 100 


1355-0 


255-0 


1200 


1526-7 


326-7 


I3OO 


1716-0 


416-0 



From these values a curve may be plotted, by means of which the 
figure to be added to the platinum scale to convert into air-scale 
readings may be deduced for any temperature. Fig. 33 shows such a 
curve, in which the ordinates represent correction numbers (t P /), 
and abscissae values of P / to which the correction is applied. 

The result of the researches of Callendar and Griffiths has been 
to establish the use of the platinum resistance method for temperatures 
between - 200 C. and + 1000 C., when great accuracy is required. 
When the readings are reduced to the air scale, as shown, the differ- 
ence between this corrected result and an actual determination by the 
gas thermometer is extremely small, and the platinum thermometer 
is much simpler to use. Consequently between these ranges the plati- 



146 



Heat for Engineers. 



num instrument is the best practical appliance for accurate working. 
Its chief drawbacks, as will be pointed out later, are the fragile 
character of the porcelain shield and alteration in resistance with 
continuous use. Certain terms connected with the constants of 



t 



FIG. 33. CURVE FOR CONVERSION OF PLATINUM-SCALE INTO 
AIR-SCALE TEMPERATURES. 



platinum resistance thermometers have come into use and will now 
be defined : 

1. The Fundamental Interval is the increase of resistance between 
o C. and 100 C., or R 100 - R . 

2. The Fundamental Coefficient is that fraction of the resistance at 
o C. by which it increases per degree between o C. and 100 C., 
or, 



__ _ 

R x ioo 



3. The Fundamental Zero is the " temperature, in platinum scale 
degrees, at which the resistance would become zero. It is evidently 
the reciprocal of (2) prefaced by a minus sign 



Platinum Resistance Pyrometers. 



147 



or, 



X 100 



4. The Difference Formula is the expression which shows the rela- 
tion between air-scale and platinum temperatures, 



or, 



- P, 



S}( 1 - ( 

TOO 



5. The Platinum Constant is 8 in the above expression. 

The method of measuring the electrical resistance will now be 
explained, and the practical forms of the instrument described. 

Measurement of Electrical Resistance of Pyrometer Wire. The 
Wheatstone Bridge method of measuring resistance is generally 
adopted, although in some forms the differential galvanometer method 




FIG. 34. PRINCIPLE OF WHEATSTONE BRIDGE. 



is employed. The usual quadrilateral representing the principle of 
the Wheatstone Bridge method is shown in Fig. 34, where a and / 
are fixed, known resistances, d an adjustable resistance, and x the 
unknown. When d is so adjusted that on sending a current through 
the system no deflection is obtained on the galvanometer, then 

a x . This principle is applied to the measurement 

b 

of the pyrometer wire as shown in Fig. 35. The pyrometer is placed 
in the branch ,r, and a compensating lead (the use of which will be 

L 2 



a x 

= or x = 
b d 



148 



Heat for Engineers. 



explained in describing the pyrometer) in the arm d, in addition to 
the usual coils, which are adjusted until no deflection is observed, 
and the resistance deduced from the ratio given above, a being made 
equal to b. A modified form of bridge is used for very precise 
measurements ; good results may also be obtained with an accurate 
Post Office box of resistances. 

In the differential galvanometer method, which is less sensitive 
than the foregoing, a current of electricity is made to divide itself 
between the pyrometer wire and an adjustable resistance, the separate 
branches of the current passing round the coils of a differential gal- 
vanometer, so that the tendencies to deflect the needle are opposed. 




FIG. 35. WIIEATSTONE BRIDGE, AS USED FOR MEASURING THE 
RESISTANCE OF A PYROMETER. 



When the needle is not deflected, the current and consequently the 
resistance in the two branches is equal. The resistance indicated 
by the adjustable branch of the circuit, when no deflection is observed, 
is therefore also that of the pyrometer. 

Construction of Platinum Resistance Pyrometers. The Callendar 
and Griffiths instrument, as constructed by the Cambridge Scientific 
Instrument Company, is illustrated in Fig. 36. The lower end con- 
sists of two strips of mica fastened along their length at right angles 
to one another, so as to form a + in section. A thin platinum wire 
is wound in the form of a double thread, round the edges of the mica 
strips, the ends being connected to leads which are threaded through 
mica disks and which pass to the terminals at the head of the instru- 



Platinum Resistance Pyrometers. 



149 




BOXWOOD HEAD 



ment. A pair of dummy leads, similar in every respect to the ordin- 
ary leads, are also threaded through the mica disks, and pass to two 
other terminals in the head. These dummy leads are joined together 
at the lower end ; and the whole arrangement is encased in a porce- 
lain tube, which fits at the top into a wooden head which serves as a 
handle. The thin wire is double-wound to 
prevent the effects of induction when a cur- 
rent of electricity passes in the process of 
measuring its resistance, and the + shape of 
the mica round which it is wound reduces 
the area of contact between metal and mica 
to a minimum. The mica disks prevent con- 
tact between the leads and the porcelain 
cover, and give stability to the whole ar- 
rangement. When the pyrometer is placed 
in a furnace, it is only necessary to insert it 
to a sufficient extent to enable the thin wire 
to acquire the temperature, as, although the 
leads will alter in temperature and resistance, 
the dummy leads, being opposed to them in 
the measuring arrangement, exactly counter- 
balance any changes in resistance which may 
occur in the main leads. Hence the actual 
resistance measured is that of the thin wire, 
which, at o C, ranges in different instru- 
ments from 2 '5 ohms to 10 ohms, the latter 
figure being the normal resistance of a 
modern Siemens' pyrometer. 

Temperature Indicators. Obviously a 
workman could not be expected to manipu- 
late a refined form of Wheatstone Bridge, 
and make the necessary calculations, apart 
from which such an operation would involve 
a considerable time. Accordingly, for work- 
shop and general use, indicators have been devised which give a tem- 
perature reading directly. In the earliest form of Siemens' pyrometer, 
the resistance was measured by a differential galvanometer and box of 
coils, and the temperature corresponding to the resistance, obtained 
by reference to a table furnished with the instrument. A certain 
number of these are still in use, but are gradually being supplanted 
by more modern forms of indicator. 

The pattern now sold by Siemens and Co. is illustrated in Fig. 37. 




PORCELAIN TOBC 
HROUCHOUT WHOLE 
LENGTH 



FIG. 36. PLATINUM 
RESISTANCE PYROMETER. 



1 50 Heat for Engineers. 

It is so arranged that when the lettered terminals of the pyrometer 
tube are connected to the corresponding terminals of the indicator, 
and a battery also connected, a Wheatstone Bridge arrangement is 
formed. The adjustable resistance consists of a wire, wound spirally 




FIG. 37. SIEMENS' INDICATOR FOR PLATINUM 
RESISTANCE PYROMETER. 

round a core, and bent into a circle round the outer side of the in- 
strument. Contact with this wire is made by means of a key, which 
is fastened by an arm to the centre of the indicator, and may be 
revolved round the circumference, so as to oppose a greater or less 
length of wire to the resistance of the pyrometer. A sensitive galva- 
nometer is placed on the top of the indicator, and the key is moved 
and depressed until no movement of the galvanometer needle is 
observed. The dial, instead of recording resistance, is made, by 
calculation, to indicate the corresponding temperature. This arrange- 
ment is simple and accurate, and requires no skill to use, all calcula- 
tions being obviated. 

In the earlier form of indicator made by the Cambridge Scientific 
Instrument Company, a switch moving over a series of studs with 
which it makes contact, introduces a resistance in opposition to the 
pyrometer. The progressive resistance between the studs corresponds 
to 1 00 C., so that if the galvanometer indicated 600 as too little, 
and 700 as too much, the temperature would lie between these limits. 



Indicators for Resistance Pyrometers. 151 

By turning a milled head on the top of the indicator, a scale, divided 
into 100 equal parts, is rotated, the operation adding a gradually in- 
creasing resistance to that already introduced by the switch. Each 
division on the scale represents i, and it is so arranged that the gal- 
vanometer needle, when at rest, lies over the number to be added to 
the reading marked on the plug with which the switch is in contact. 
Thus if the switch be on plug " 600," and " 84 " on the scale opposite 
the galvanometer needle when at rest, the temperature is 684. 
Many of these are in use, and give very good results, but are not so 
simple in use as the Siemens' indicator. 

The latest form of indicator issued by the Cambridge Scientific 
Instrument Company is named after the designer, Mr. Whipple. 
Fig. 38 illustrates the Whipple indicator, which is compact, simple to 




FIG. 38. WHIPPLE'S INDICATOR. 

use, and capable of being read to less than i to temperatures above 
1000 C. The resistance opposed to the wire of the pyrometer is 
vound round a drum, to the axis of which a screw, working in a nut, 
is attached. By turning a handle at the side of the instrument the 



1 5 2 Heat for Engineers. 

drum is rotated, and also, owing to the screw, moved backwards or 
forwards by the same motion. This operation varies the resistance 
opposed to the pyrometer, and is continued until, on pressing a key, 
the galvanometer needle is at rest. The drum is surrounded by a 
paper, on which a spiral line is drawn, divided into degrees, and the 
arrangement is such that the number opposite a pointer fixed in the 
top of the apparatus, and viewed through a narrow window, represents 
the temperature of the pyrometer. This indicator is as simple to use 
as the Siemens instrument, and gives an exact reading. By placing 
the battery in the box containing the rest of the apparatus, portability 
is secured, everything being ready to take a reading as soon as the 
pyrometer is coupled up. It may be pointed out that the readings of 
any indicator, are only correct for the pyrometer with which it is 
intended to be used, and if the pyrometer should alter in resistance, 
the readings will be erroneous. 

Recording Apparatus for Platinum Resistance Pyrometers. It is 
often desirable to obtain a continuous record of the temperature of a 
furnace or other place, so as to be able to detect the fluctuations 
which occur, and thus to form a judgment as to whether the operation 
is being carried out satisfactorily. Cases in point are the tempera- 
tures of the furnaces used in the manufacture of producer gas, the 
hot blast used in blast furnaces, and the temperature of cold stores. 
The recorder designed for this purpose by Callendar is illustrated in 
Fig. 39, and consists, in principle, of an automatic method of 
balancing the resistance of the pyrometer, the moving piece that 
completes the balance carrying a pen at its extremity, so as to make 
a mark on a sheet of graduated paper fastened round a cylinder 
which revolves by clockwork. The galvanometer, shown in the upper 
left-hand part of the illustration, is of the moving-coil pattern, and 
fastened to the suspension of the coil is a boom, which swings with 
the coil. The final adjustment of the resistance opposed to the 
pyrometer is made on a stretched wire, with which the upper part of 
the pen makes contact. The whole arrangement forms a Wheatstone 
bridge, of which the arms b and d (Fig. 35) are represented by the 
two portions of the stretched wire on either side of the pen. If the 
temperature of the pyrometer rises, thereby increasing its resistance, 
the galvanometer coil moves, carrying the boom with it, and causing 
the end of the boom to complete an electric circuit. The completion 
of this circuit, by an electro-magnetic device, liberates a detent and 
sets a train of clock-wheels in motion, which causes the pen to move 
along the wire, tracing a mark on the paper. When at a certain point 
on the wire, a balance is again obtained, the galvanometer coil will 



Callendars Recorder. 



153 



swing back to the central position, thus causing the boom to break 
the electric circuit, and thereby stopping the clockwork. A fall in 
temperature causes the galvanometer coil to swing in the other direc- 
tion, thereby completing a second circuit, and setting in motion a 
second train of wheels which move the pen in the opposite direction. 
If the temperature remain constant, the pen traces a straight line on 




FIG. 39. CALLENDAR'S RECORDER. 



the revolving paper, a fluctuating temperature producing a zig-zag line. 
The divisions on the paper are made to represent actual temperatures, 
and if a drum on which it is wound completes a revolution in 24 
hours, a continuous record of the temperature during this period is 
obtained. Such a record is shown in Fig. 40, which shows the varia- 
tions of temperature in an annealing furnace during a period of nine 



*54 



Heat for Engineers. 



jiours, stoked for one half of the time by a workman A, and the 
remainder by another workman B. The superiority of the stoking of 
A is made manifest by the record. 

The range of temperature covered by the recorder may be arranged 
'by the insertion of suitable resistances, which form part of the instru- 
ment. If, for example, the length of the paper represents 100 C., it 
is possible, by inserting the correct resistance, to take records varying 



MM 




;-B firing - 



FIG. 40. RECORD OBTAINED WITH CALLENDAR'S RECORDER. 

by 100 at any range up to 1200 C., such as -50 to +50; 800* 
to 900, etc. Hence the recorder may be applied to cold stores, 
ordinary or moderate temperatures, and to furnaces. The arrange- 
ment is satisfactory, but costly, which prevents it being more widely 
adopted. Several other forms of recorder for platinum resistance 
pyrometers are made similar in principle to that described. 

Advantages and Drawbacks of Platinum Resistance Pyrometers. 
The chief advantage of the platinum resistance instrument is its 
extreme accuracy over a wide range of temperature, if used in con- 
junction with a reliable indicator or recorder. Very small changes of 
temperature may be detected, and even when encased in porcelain 
the pyrometer is fairly responsive to sudden fluctuations of tempera- 
ture. It has been widely adopted, especially for low temperature 
work, such as in the operations of brewing, jam boiling, cold storage, 
etc. It is also good for moderate temperatures, such as those of flue 
gases and hot blast. A further advantage is that the indicator may 
be kept in an office at any distance from the pyrometer, provided the 
leads are the same throughout, as they nullify each other in the 
measurement. There are many drawbacks, however, attendant on its 
continued use at very high temperatures. The porcelain cover is very 
fragile, and costly to replace ; if further protected by a steel tube the 



Thermo-electric Pyrometers. 155 

instrument is less responsive to sudden changes of temperature. 
Repeated heating at 1000 C. and over causes a permanent elongation 
in the wire, altering its resistance in consequence, and causing the 
indicator readings to be erroneous. The mica supports also deterio- 
rate, and if by any chance metallic vapours enter the pyrometer 
the platinum is attacked, and the instrument rendered useless. In 
case of repairs, great skill is required, it being generally necessary 
to send the apparatus back to the makers, which occasions incon- 
venience and delay. On the whole, for very high temperature work, 
the platinum resistance pyrometer must be regarded as of less 
practical convenience and utility than the thermo-electric instrument, 
although for lower temperatures it is unsurpassed. 

5. Thermo-electric or Thermal Couple Pyrometers. In 1822, 
Seebeck discovered that the heating of a junction of two different 
metals forming part of a closed circuit, causes a current of electricity 
to flow round the circuit. In 1830, Becquerel, using platinum and 
palladium as the metals, attempted to apply the Seebeck effect to the 
measurement of temperatures, but with indifferent success. After- 
wards Pouillet and others attempted to measure temperatures by the 
thermo-electric method, but no accuracy or uniformity in results was 
obtained until 1886, when Le Chatelier showed that if the right metals 
were employed, the method was capable of giving excellent results. 
At the present time the thermo-electric pyrometer is probably more 
used than any other variety. 

The two chief laws of thermo-electricity may be stated as follows : 

1. The electromotive force developed by a heated junction 
depends on the metals used and is independent of the size. 

2. If a complete circuit be made of two metals, joined at the 
extremities, and one junction be heated whilst the other is kept cold, 
the electromotive force generated is proportional to the difference 
between the temperatures of the hot and cold junctions within certain 
limits. 

In attempting to apply these laws to the production of an instru- 
ment for measuring high temperatures, the following conditions must 
be fulfilled : 

(a) The metals must possess high melting-points. 

(b) The electromotive force developed should increase in a uni- 
form manner over the range of temperature embraced by the instru- 
ment, and should be reasonably large. 

(c) There should be no tendency to oxidation on the part of the 
metals used. 

(d) The metals should be capable of being drawn into homo- 



156 Heat for Engineers. 

geneous wires, in order that a junction made of any portions of two 
given pieces may develop the same E.M.F. at the same temperature. 

If the temperature to be measured does not exceed 1000 C, the 
metals copper, gold, nickel, iron, platinum, palladium, rhodium, 
osmium, and iridium might be used, provided a junction of the pair 
selected fulfilled the other conditions. Readings up to i5ooC. 
would lead to the elimination of all save platinum and the rare metals 
which have melting-points well above 1500. At temperatures less 
than 1000 C., however, iron undt. oes certain molecular changes 
which lead to the production of minor or parasite currents in the 
circuit, which are of sufficient magnitude to alter the uniformity in 
the rise of E.M.F. seriously. This was not known to the early 
experimenters, some of whom used thermal couples of platinum and 
iron, and consequently obtained discrepant results. A couple made 
of iron and copper gives curious results. Up to 280 the E.M.F. 
shows a fairly steady rise, but with a further increase in temperature 
it diminishes, and becomes zero ; finally an E.M.F. in the opposite 
direction is set up. Such a couple would therefore be useless for 
temperature measurement. An objection to palladium is its tendency 
to absorb hydrogen in large quantities, which alters its thermo-electric 
properties. Again, iron and copper oxidise readily at temperatures 
below 1000, and above this temperature nickel also oxidises, and 
undergoes molecular changes. It will thus be seen that it is a matter 
of great difficulty to find a pair of metals which fulfil all the necessary 
conditions. 

The first successful thermo-electric pyrometer was made by 
Le Chatelier, who found that uniform and accurate connections 
between E.M.F. and temperature could be obtained by using a couple 
consisting of platinum, and an alloy of platinum and rhodium. An 
alloy containing 10 per cent, of rhodium and 90 per cent, of platinum 
may be made of uniform composition, and is capable of being drawn 
into fine wire. Coupled with pure platinum, the heated junction 
furnishes a steadily increasing E.M.F. as the temperature rises. No 
changes in physical structure or thermo-electric properties occur as a 
result of the heating, and consequently a second set of observations 
at given temperatures will give the same results as the first. More- 
over, the E.M.F. increases with the temperature to such an extent 
that a very small rise of temperature may be detected. Neither the 
platinum nor the rhodium alloy tend to oxidise on heating; both 
have extremely high melting-points ; and, if carefully annealed, wires 
made from both are quite homogeneous, and any portions of a 
given pair of wires will give an identical E.M.F. when joined and 



Thermo-electric Pyrometers. 157 

heated. Barus and Roberts-Austen afterwards found that equally 
good results could be obtained with a couple consisting of platinum 
as one metal, and an alloy of 10 per cent, iridium and 90 per cent, 
platinum as the other. Pyrometers based on the thermo-electric 
principle are now made with either of the couples named, and are 
equally satisfactory. 

The couple introduced by Le Chatelier (Pt Pt + 10 per cent. 
Rh) furnishes an electromotive force of about 500 micro-volts at 
100 C., when the cold junction is kept at o C. The same figure is 
obtained when iridium is substituted for rhodium. At higher tem- 
peratures, however, the E.M.F. is not a simple multiple of that 
observed at 100 ; thus at 500 the E.M.F. would not be five times 
that obtained with the junction at TOO. The two quantities, how- 
ever, have been found experimentally to be connected by the law 

log E = A log / + B, 

where E = electromotive force in micro-volts 

/ = temperature in degrees Centigrade 

A and B = constants depending on the materials used. 

Results calculated from this formula do not differ by more than two 
or three degrees at any part of the scale from actually observed tem- 
peratures. It is therefore possible, by measuring the E.M.F. at two 
fixed points, to calculate the temperature corresponding to any given 
E.M.F. by applying the formula, and the results may be checked, if 
desired, by an experimental determination at another fixed point. 
This would involve the use of an accurate method for measuring 
small electromotive forces, and is not necessary in workshop practice, 
for the purposes of which a good form of galvanometer may be made 
to indicate the temperature of the junction with great accuracy. 

Galvanometers for Use with Thermo-electric Pyrometers. The 
best type of galvanometer to employ with a thermo-electric pyro- 
meter is that of d'Arsonval, suitably constructed to give quantitative 
readings. In these galvanometers the current passes through a coil 
of wire suspended between the poles of a fixed magnet. The 
suspension is formed by a strand of metal wire to which the coil is 
connected, and carries a mirror from which a spot of light may be 
reflected on to a scale. The axial movement of the coil, caused by 
the passing of a current, is thus magnified ; and the position of the 
spot of light on the scale, as indicated by the divisions, should be 
proportional to the strength of the current passing through the coil. 
Such a galvanometer, when joined to a thermal couple, will give 



158 Heat for Engineers. 

indications proportional to the E.M.F. existing at the hot junction,, 
and therefore to the temperature ; for, by Ohm's law, 

E - CR, 

and consequently if R, the resistance, be constant, the current C 
will vary directly as E, the electromotive force. 

In order to ensure accuracy in this respect, the coil of the galvano- 
meter should be made of wire which shows little variation in resist- 
ance when the temperature alters ; suitable materials being manganin, 
German silver, or platinoid. The coil should have sufficient free 
space in which to move between the poles of the magnet, and the 
suspending wire should be strong and yet thin, so as to twist readily. 
A thin, flattened German silver wire makes a good suspension, or 
phosphor-bronze may be used. Care must be taken that the suspend- 
ing wire possess no initial torsion. The type of galvanometer described 
is shown in use in Fig. 44 (p. 162), in conjunction with a recorder. It 
may be added that the coil of the galvanometer should have a resist- 
ance exceeding 400 ohms, so that the increased resistance of the 
wires forming the junction, when inserted at different depths in the 
furnace, does not appreciably alter the strength of the current in the 
circuit. A series resistance may be added, if required, to ensure 
this result. 

Example. If the coil of the galvanometer has a resistance of 
only 50 ohms, and the variation of the resistance of the junction 
wires is 2 ohms, the latter factor will notably affect the current, as it 
is equal to -^ of the total resistance. If, however, the coil has a 
resistance of 800 ohms, the variation due to the junction wires only 
causes an alteration of ? tn: tn P art f tne total resistance, and conse- 
quently the effect on the current is very small. 

In cases where very exact readings are not required, needle 
galvanometers may be used. Siemens-Halske, Paul, Pitkin, and 
others have constructed indicators for thermal-couple pyrometers in 
which the movements of the galvanometer needle over a prepared 
scale give temperature readings directly, to within 5 or 10 degrees C 
Such instruments are correct, within this limit, for the particular pyro- 
meter with which the graduation has been made, but the scale would 
not be correct for another pyrometer obtained elsewhere. When 
the scale may be relied on, such indicators possess the advantages 
of portability and simplicity in use, and consequently have been 
largely adopted. Crompton's indicator is furnished with several 
scales, each corresponding to a given temperature of the cold June- 



Thermo-electric Pyrometers. 



tion, and obviates the necessity for correcting for variations in this 
temperature. 

Practical forms of Thermo-electric Pyrometers. A convenient 
form of pyrometer is illustrated is Fig. 41. The wires from the hot 
junction J, pass through small fire-clay cylinders, which serve to- 
insulate them, into the wooden handle H, which is made so as to 
open. The wires are connected to the brass strips S, which pass out 




FIG. 41. THERMO-ELECTRIC PYROMETER. 

at the end of the handle and are connected to the galvanometer. A 
quantity of spare wire is contained on the reels R, R, from which it 
may be unwound by loosening the strips S. A new junction of the 
same wires may thus be readily made in the event of damage or 
corrosion. The distance between the hot junction and the handle 
is determined by the depth to which the pyrometer is inserted in the 
furnace, and varies from 5 feet downwards. The wires are contained 
in a closed steel or porcelain tube T, which serves as a protection 
from the furnace gases. For temperatures which would cause steel 
to melt, fireclay or silica tubes may be used. If necessary, the hot 
junction J may be further protected by a fireclay cap. 




FIG. 42. METHOD OF USING ONE INDICATOR FOR SEVERAL 
PYROMETERS. 

Fig. 42 shows how the temperatures of a number of furnaces may 
be read by the use of pyrometers in which identical wires are used, 
each of which may be connected by a switch to the same galvano- 
meter. H 1 and H are hot junctions, and Cj. and C 2 cold junctions. 



1 60 Heat for Engineers. 

Corresponding terminals of each couple are connected to one of the 
galvanometer terminals, and the other wire of each couple to the 
positions i, 2, etc. on the switch B. The movable arm D is con- 
nected to the other galvanometer terminal, and serves to connect 
each pyrometer in turn with the galvanometer. The temperature 
of any furnace may be thus correctly read, provided the junctions 
are in all respects identical. 

The wires at the hot junction should be fused together, as, if 
merely twisted, they tend to become loose on heating. This may 
be done by means of the oxy-hydrogen flame. If the temperature 
is never to exceed 1000 C., the couple may be soldered together in 
a Bunsen burner by means of a small quantity of gold, which will 
not alter its thermo-electric properties. 

Standardising a Thermo-electric Pyrometer. The preparation of 
the scale of temperatures in connection with the pyrometer demands 
considerable care, especially when the scale is to be used as a 
standard for the comparison of other pyrometers. The wires form- 
ing the junction should first of all be annealed by passing a current 
of electricity through them so as to heat them to whiteness. The 
temperature of the cold end of the pyrometer should be the same as 
that which will obtain when in actual use, and the total resistance of 
the circuit must also be identical with that possessed when in use. 
The latter point is of great importance when long leads are used to 
connect the pyrometer to the galvanometer or indicator. When 
these precautions have been taken, the pyrometer is placed succes- 
sively in the following, and allowed to remain for a sufficient length 
of time to enable the spot of light to become stationary ; the position 
on the scale then corresponds to the known temperature of the 
surroundings of the pyrometer : 

C. F. 

Steam from boiling water . . . Temp. = 100 212 
Tin at the setting-point , = 232 449. 



Lead ,, ,, 
Zinc ,, ,, 
Antimony ,, 

Common salt ,, 
Copper (uncovered) ,, 



= 3 2 7 620 

= 419 786 

: 632 Il69 

= 8OO 1472 

= IO62 1943 



The above form a set of cheap standards, suitable for a workshop 
calibration. Any of the fixed points given on page 138 may be 
chosen, however, if desired. The steam point may be determined 
by boiling water in a flask, and inserting the pyrometer in the neck, 
into which it must fit loosely, so as to allow a free escape for the 
steam. To determine the setting points of the various substances, 



Thermo-electric Pyrometers. 



161 



a quantity is melted in a graphite or "salamander'' crucible in a 
gas furnace, and the pyrometer inserted in the centre of the molten 
mass, which is then allowed to cool. As the temperature falls, the 
spot of light on the scale moves nearer its zero, but at the setting 
point remains stationary for some time. This is owing to the fact 
that in the act of solidification latent heat is disengaged, sufficient to. 
maintain a stationary temperature for an appreciable time. Hence 
the position at which the spot of light remains at rest represents the 



1800 



16CK, 



1409 



1200 



(0 (000 

14 

(T 

800 

(. 
tU 
a 600 



400 
200 



PT 



ZN 



S. 

ZN, 



H 2 O. 



20 40 60 80 100 120 140 

MIRROR GALV? DIVISIONS. 

FIG. 43. CALIBRATION CURVE FOR THERMO-ELECTRIC PYROMETER. 



freezing point of the substance. A quantity of pure materials shouM 
be kept for the purpose of standardisation, as even small amounts 
of impurities notably alter the freezing points. 

A curve may now be drawn connecting temperatures with deflec- 
tions on the galvanometer scale, from which intermediate readings 
may be obtained. The zero of deflection will correspond to the 
temperature of the cold junction. Fig. 43, which represents a 
calibration curve for a platinum-rhodium alloy couple, is an ex- 

M 



162 



Heat for Engineers. 



ample of this method of graduation, the curve passing smoothly 
between the points. The platinum point may be obtained by heat- 
ing until the couple melts and breaks, the maximum position of 
the spot of light being noted. The curve is produced regularly 
until it cuts the ordinate corresponding to the maximum deflection, 
and the temperature thus obtained by extrapolation. The deter- 
mination of the platinum point, however, is not necessary in practice, 
and would, of course, destroy the junction. From the curve it will 
be seen that 80 scale divisions were equal to 1130 C. ; 40 divisions 
to 610 C. ; and so on. The cold junction in this case was kept at 
oC. 

From the standard scale so obtained, others may be graduated 
by comparison. Any number of pyrometers, if made of the same 
wire as the standard, may be tested by switching on to the standard 
instrument, when the temperature shown by each on its own indicator 
should be made the same as that registered by the standard scale. 
A whole installation of pyrometers may thus be kept in complete 
unison, provided the cold-junction temperatures are constant. 

Recording Thermo-electric Pyrometers. For the purposes of the 
Alloys Research Committee, Roberts-Austen devised the recording 
arrangement shown in Fig. 44. The galvanometer G is enclosed 




FlG. 44. ROBERTS-AUSTEN RECORDER. 

in a box, and a spot of light is thrown from the lamp L (a Welsbach 
burner is preferable) on to the suspended mirror by means of a 
reflecting prism. The spot of light is reflected on to a sensitised 
plate or paper P, which may be moved up or down at any desired 



Roberts-Austen and Thread Recorders. 163 

rate by means of clockwork geared to the wheel W. If the temper- 
ature of the thermal junction remain steady, the spot of light reflected 
from the galvanometer mirror would also be steady, and the discolor- 
ation of the paper would take the form of a straight line. Continuous 
fluctuations of temperature would produce a zig-zag line, and by heat- 
ing the junction to known temperatures the number of degrees corre- 
sponding to a given deviation of the spot of light may be determined, 
and the paper divided accordingly. A complete record over a given 
period is thus obtained. To test the accuracy with which the plate 
moved, Roberts- Austen placed a fixed mirror, M, across the galvano- 
meter magnet, so that the reflected ray from it fell on the sensitised 
plate. A T-shaped interrupter was placed in the centre of the box, 
actuated by accurate clockwork, which caused it to rise periodically 
and shut off the reflected ray from the mirror M. The line traced 
on the plate was then beaded, and as the interruptions took place at 
regular intervals, the beading was spaced out regularly when the 
motion of the plate was uniform, and served as a test of the mechanism 
.actuating the plate. In the modern commer.cial instrument the plate 
is replaced by a drum, revolving by means of clockwork, a strip of 
sensitised paper being fastened on the drum to receive the impression 
of the spot of light. 

A great drawback to the use of this recorder is the necessity of 
a dark room in which to develop and fix the photographic record, 
and the labour entailed in this process. Accordingly, many attempts 
have been made to obtain records in ink, but the great difficulty to 
be overcome is that the needle or any moving part of the gal- 
vanometer cannot be kept continuously in contact with a paper, 
owing to the friction introduced opposing the movement. Various 
arrangements for periodical contact of a pen attached to the moving- 
part have been devised, the pen making a dot on the paper, and then 
being set free to enable the moving parts to attain the correct posi- 
tion before making another contact. A beaded line is thus obtained, 
which indicates the position of the needle or moving coil at any 
time, and which therefore constitutes a continuous record of the 
temperature. The latest and simplest of intermittent contact 
recorders is the "Thread recorder," made by the Cambridge 
Scientific Instrument Company. The action of this instrument is 
illustrated in Fig. 45, where B is the galvanometer suspension, to 
which a boom A is attached. By means of a cam E, rotated by 
clockwork, a chopper-bar D is periodically pressed on to the 
boom A, causing the boom to descend and depress an inked thread 
G, on to the paper wound round the cylinder C. Where the thread 

M 2 



164 



Heat for Engineers. 



touches the paper a dot is made, and the contact may be repeated 
every half-minute, producing a nearly continuous line on the paper. 
The cylinder C makes one revolution in 25 hours, and the tempera- 
ture during that period is thus accurately recorded. A scale of 
temperatures may conveniently be fastened to the front of D for 
direct reading at any moment. The depression arid liberation of 
the boom are so gently performed by this mechanism that the 
galvanometer coil, when freed, comes to its proper position in a few 
seconds. The thread is kept moist by the use of a winding 




FIG. 45. PRINCIPLE OF THREAD RECORDER. 

mechanism, which passes it through an ink-well. The thread 
recorder solves the problem of a suitable ink recorder for a thermo- 
electric pyrometer, and is equally useful in connection with a radia- 
tion pyrometer. The actual instalment is shown in Fig. 46. 

Advantages and Drawbacks of Thermo-electric Pyrometers. One 
of the chief advantages of thermo-electric pyrometers is that a reading 
may be taken on a scale or indicator at any moment, without the 
necessity of any adjustment. They may also be used for higher 
temperatures than is permissible with a platinum-resistance pyrometer. 



Defects of Thermal Couples. 165 

it being possible to measure temperatures of 1500 C. (2732 F.) and 
upwards by their use, the upper limit being that at which the insula- 
tion of the wires fuses or attacks the metals. By passing the wires 
through small silica tubes, and surrounding the whole with a larger 
silica tube, temperatures approaching the melting point of platinum 
may be read. In the event of a junction being damaged, a new one 
may be rapidly made, no great skill being requisite. The thermo- 
electric pyrometer is therefore to be preferred in cases where a certain 
amount of rough usage is unavoidable. 

The chief drawback is the alteration in E.M.F. given by the couple 
on prolonged heating above 1000 C. ; ten hours at nooC. pro- 
ducing an increase of o 5 per cent, in a Pt-Rh couple. The original 




FIG. 46. THE THREAD RECORDER. 

value may be restored by annealing at a full white heat, and, in general, 
the alteration in E.M.F. is small in a well-annealed couple. The 
metals are liable to be corroded under certain conditions, as described 
in connection with the platinum resistance pyrometer. The Pt-Ir 
couple is liable to injury in either a reducing or oxidising atmosphere 
on prolonged heating at 1100 C. and over, the E.M.F. falling off in 
some cases by 12 per cent. At lower temperatures, if well annealed, 
the Pt-Ir couple gives good results. Above 1100 C., therefore, the 
Pt-Rh couple should be used. Finally, the accuracy of the readings 
is less than that obtained with the resistance pyrometer, although the 
approximation to the correct temperature yielded by the thermo- 
electric method is sufficient for all practical purposes. 



1 66 Heat for Engineers. 

Thermal Couples for Extremely High Temperatures. Since the 
commercial introduction of the electric furnace, a means of measuring 
temperatures beyond the melting-point of platinum has become 
desirable. A couple consisting of the metals iridium and ruthenium 
has been used by Herseus for readings up to 2100 C., but the 
graduation, which must be made by extrapolation, is of doubtful 
accuracy. The couple, moreover, is extremely brittle, and therefore 
liable to injury, and cannot be said at present to be of any great use 
commercially. It is possible that metals of still higher melting points, 
such as tantalum and tungsten, may be utilised in this connection 
in the future. Probably more is to be hoped for in the couples 
made of Nernst filament materials, of different composition, as sug- 
gested by Harker. These consist of silicates of the rare earths, and 
are pyro-conductors, that is, conduct electricity only when heated, 
and two filaments when joined and heated give rise to an E.M.F. 
when of different composition. As the melting-point of a Nernst 
filament is much above that of platinum, it may be possible by this 
means to read temperatures as high as 2000 C. For higher tem- 
peratures still, recourse must be had to optical or radiation methods. 

Thermal Couples for Low Temperatures. The drawbacks atten- 
dant on the use of most metals for thermo-electric couples at high 
temperatures, such as melting, oxidation, molecular changes, etc., do 
not apply at low temperatures. Consequently it is found possible to 
measure low temperatures by the aid of suitable couples such as 
copper-constantan, iron-constantan, copper-German silver, etc., the 
couples giving a high E.M.F. being chosen. When the junction is 
colder than the rest of the circuit, a reverse E.M.F. is set up, propor- 
tional to the difference of temperatures as in the converse case. Pro- 
fessor Dewar has employed a copper-German silver couple to measure 
extremely low temperatures, the galvanometer being standardised by 
comparison with a gas thermometer, and a convenient means of 
determining very low temperatures thus obtained. For obtaining 
temperatures in places where thermometers would be unsuitable, such 
as in the cylinders of engines when working, copper-constantan 
thermal junctions are largely used, and prove highly satisfactory. 

Practical Management of a Pyrometer Installation. A brief 
description of the methods adopted in the Royal Gun Factory, 
Woolwich Arsenal, will serve to indicate the uses and practical con- 
trol of a commercial pyrometric installation. The operations include 
the tempering of gun-tubes, lead baths for the treatment of specimens 
used for testing, gas producer furnaces, equipment for determining 
the critical points of steel, and other processes. Thermo-electric 



Workshop Installations. 167 

pyrometers are used, in conjunction with Holden-d'Arsonval galvano- 
meters of about 800 ohms resistance, the metals of the couple being 
platinum and iridium alloy. A large quantity of each wire is obtained 
of uniform composition, so that every junction may give the same 
E.M.F., and may be replaced, when necessary, by an exactly similar 
junction. A standard instrument, carefully calibrated, is kept in the 
metallurgist's office, and each pyrometer may be connected to it. 
The standardising of the pyrometer scales is carried out in situ by 
noting the scale reading at different temperatures, and obtaining the 
degrees corresponding to each by switching on to the standard, due 
allowance being made for the cold- 
junction temperature known to 
exist when in use. Each set of 
furnaces is in telephonic communi- 
cation with the office, and when an 
operation is ready to carry out, as 
indicated by the furnaceman's own 
scale, the office is rung up and 
the pyrometer switched on to the 
standard, as a check. If both read- 
ings agree, word is given to proceed. 

The galvanometer mounting- 
shown in Fig. 47 is used to prevent 
vibration and consequent difficulty 
in reading. It consists of a strong- 
brass tripod, from the rim of which 

the galvanometer is suspended on FlG> 47 ._ HOLDEN AND LAMBERT'S 
three spiral springs, which the ANTI-VIBRATION MOUNTING 
weight of the galvanometer keeps FOR GALVANOMETERS. 

\ in compression. That is, if the 

galvanometer weighs 6 lb., each spring would require 6 Ib. to com- 
press it so that the coils touch. The adjustment of the spot of light 
is obtained by means of the screws at the top of the suspending rods. 
A galvanometer so suspended is singularly unaffected by external 
vibrations, and will give steady indications in the vicinity of sterm- 
hammers, or railway lines over which loaded wagons are running. 

Each pyrometer and scale is checked every morning by placing 
the pyrometer in a bucket of boiling water, and taking the reading. 
Any serious defect is at once detected, and an assistant sent to 
execute the necessary repairs. As a check on the standard scale, 
which might accidentally be displaced, a pyrometer is kept in steam 
in the office, which may be switched on to the standard galvanometer, 




1 68 Heat for Engineers. 

and thus serves to detect any displacement which may have occurred 
by the erroneous reading the scale would then show. The hole in 
the furnace through which each pyrometer passes is luted with clay, 
as otherwise the junctions at the head would be unduly heated. 

Records are taken in special cases only, the Roberts-Austen 
recorder being used, suspended in the same manner as the galvano- 
meters to obviate vibrations, which would be specially objectionable 
in this case. The records are taken on sensitised paper. 

The excellent results obtained by the use of this equipment are 
a testimony to its value. What formerly was a matter of doubtful 
judgment by a workman's eye is now replaced by a method of pre- 
cision, and a variety of operations are now carried out not only with 
certainty of success, but with greater economy, owing to the complete 
control exercised by the metallurgist over all the work conducted in 
the numerous furnaces. 

(6) Heat-Radiation Pyrometers. The great advantage of a 
pyrometer which would indicate the temperature of a furnace from a 
distance has long been recognised. Any form of pyrometer con- 
tinuously subjected to the heat and corrosive action of the gases in 
a furnace is bound to deteriorate, and so necessitate repairs or re- 
placement. Further, the range of a pyrometer, when placed in a 
furnace, is limited by the melting point of its materials, whereas an 
instrument used at a distance would not be subject to this disadvan- 
tage. Work in this direction was attempted by Pouillet, Violle, and 
others, but the results were so discordant that the method was 
regarded as absolutely unreliable. Thus Pouillet found for the tem- 
perature of the sun a value of i3ooC. ; Violle's results indicated 
1500 C. to 2500 C., whilst Secchi actually obtained a figure running 
into millions. All these discrepancies, however, were due to im- 
perfect knowledge of the laws of heat-radiation, which are now 
better understood, with the result that reliable temperature indica- 
tions may be obtained from observations of radiant heat. 

A full discussion of the principles governing the radiation of heat 
will be found in Chapter XIX., and it is only proposed at the present 
juncture to indicate the basis upon which a satisfactory heat-radiation 
pyrometer may be constructed. The amount of energy radiated by 
a " black body," according to the Stefan-Boltzmann law, is propor- 
tional to the fourth power of the absolute temperature. Expressed 
as a formula this law takes the form 

E - K (T 4 - T x 4 ) 
.where E = the total energy radiated by the body at absolute tern- 



Heat- Radiation Pyrometers. 169 

perature T to surroundings at an absolute temperature T 1} and K is 
a constant which depends upon the units employed. 

The correctness of this formula has been amply verified by 
experiment. Thus in a series of observations by Waidner and 
Burgess at temperatures ranging from 850 C. to 1450 C, the values 
calculated from the formula differed by less than i per cent, from 
the actual readings of a thermal-couple pyrometer. It should be 
borne in mind, however, that the formula is only strictly correct for 
"black-body" radiations. An "absolute black-body" is one which 
absorbs all the radiations which fall upon it, and neither reflects nor 
transmits any, and is nearly realised in practice by coal, carbon, and 
heated metals which become coated with black oxides, such as 
copper and iron. If, therefore, any practical means can be found 
of measuring the proportionate amounts of energy radiated by such 
heated surfaces at different temperatures, it is possible to calculate 
the temperature itself from the Stefan-Boltzmann law. The method, 
however, need not be restricted to black surfaces, for, as Kirchoff 
showed, the interior of an enclosure kept at a constant temperature 
gives true black-body radiations. If, for example, a metal box be 
surrounded by steam, and a hole be made in the side, radiations 
passing from the interior through the hole will be black-body radia- 
tions in terms of the definition. If we consider a portion of the wall 
opposite the hole, the energy radiated from this spot must be equal 
to that which it absorbs from its surroundings, or its temperature 
would alter. But equality of temperature in an enclosure involves 
equality in the amounts of energy radiated and absorbed by each 
portion, therefore the spot absorbs all the energy it receives, and, 
irrespective of the nature of its surface, behaves as an absolute black 
body. Hence the radiations received from the interior of a furnace, 
at constant temperature throughout, may be regarded as black-body 
radiations, and the temperature deduced by applying the fourth- 
power law. 

If the energy radiated by a surface which is not a black body be 
measured, and the temperature calculated on the assumption that the 
Stefan-Boltzmann law also applies in this case, a result lower than 
the truth will be obtained, owing to the inferior radiating power of 
the surface. At an actual temperature of 1500 C., for example, a 
platinum surface would only give a calculated temperature of 1320 C. 
But as the radiating power of the platinum surface is constant under 
given conditions, it follows that whenever the temperature, as deduced 
from the radiation law, is 1320 C, its true temperature will be 
1500 C. The thermal condition of platinum is therefore defined 



i 70 Heat for Engineers. 

with the same certainty as if a true reading were taken by another 
method. Whilst this holds true in general for surfaces not altered 
by heat, bodies which oxidise possess a varying radiating power, if 
not enclosed. Thus if a block of steel be heated, and removed 
from the furnace, the temperature indicated by the radiations from 
its surface depend upon the thickness of the film of oxide which 
forms over it. This film of oxide cools rapidly, and the indication 
obtained affords no clue to the temperature of the mass. The only 
safe procedure is to measure the radiations received when the steel 
is under black-body conditions ; that is, when inside the furnace. 
Many failures have resulted owing to the assumption that the 
apparent temperature wrongly called " black-body temperature "- 
bears in all cases a constant relation to the true reading. This is 
only true for unaltering surfaces, such as platinum. 

Fery's Heat-Radiation Pyrometers. Two forms of heat-radiation 
pyrometer, each devised by M. Fery, represent the practical realisa- 
tion of the application of the fourth-power law to temperature 
measurement. In the first form a copper-constantan thermal couple, 
soldered to a copper disc, is placed in the focus of the object-glass of 
a telescope, which thus behaves like a burning-lens. Between the 
object-lens and thermal couple a diaphragm is fixed, which ensures 
that the cone of rays falling on the couple is not changed in size by 
focusing the instrument. The image of the heated body is sharply 
focused on the thermal couple, which is connected through the 
tube of the telescope to a Meylan-d'Arsonval galvanometer. The 
temperature attained by the thermal couple, and consequently the 
deflections of the galvanometer, depend upon the amount of radiant 
heat passing into the telescope ; and this, in turn, depends upon the 
absolute temperature of the hot substance. If the graduations of the 
galvanometer scale are of equal value, and the temperature T, corre- 
sponding to a given reading R, be known, the value to be attached 
to any other reading R 13 may be found from the relation 



RI - ( Ti Y 

R VlV* 



or 

TI= r VR' 

Hence a temperature scale may be readily constructed from one 
exact observation at a known temperature as a starting-point. The 
drawback to the use of this pyrometer is that a quantity of the radiant 



Heat-Radiation Pyrometers. 



171 



heat is absorbed by the glass objective, the amount absorbed varying 
with the temperature. If the objective be made of fluor-spar instead 
of glass, this difficulty is overcome for temperatures above 900 C., 
as beyond this limit the ratio of absorbed and transmitted radiant 
energy is constant in the case of fluor-spar. Hence the arrangement 
is restricted to temperatures above 900 C. ; and as fluor-spar crystals 
large enough to make lenses are difficult to procure, it is necessary to 
use a glass objective, and to standardise the pyrometer by comparison 
with a special instrument which possesses a fluor-spar object-lens. 
The range 700 C. to 900 C. embraces the temperatures at which 
many important processes are conducted, and consequently the first 
form of Fe'ry's heat-radiation pyrometer was not widely adopted. 

In the later form of instrument, the difficulty caused by the 
absorption due to the glass is entirely overcome by the use of a con- 
cave mirror which brings the rays to a focus on the copper-constantan 
couple. Figs. 48 and 49 show the construction of the pyrometer as 




FIG. 48. FERY'S RADIATION PYROMETER, SECTION. 

now made for commercial use. In Fig. 48, M is the concave mirror 
which may be moved backwards and forwards by a rack-and-pinion 
movement controlled by the milled-head P. In early forms this- 
mirror was made with a silvered surface, which tarnished in use, and 
deteriorated in reflecting power ; but by gilding this trouble was over- 
come. The thermal couple is connected to two fixed brass strips, R 
and D, each of which is connected to one of the terminals b, b l on 
the exterior of the instrument, these terminals being insulated from 
one another. The thermal junction is placed at the focus of the eye- 
piece, O, and appears as a circular black disc when viewed through 
the small hole in the centre of the mirror. The image of the source 
of heat must be brought into the focal plane of the eye-piece O, so as 



172 



Heat for Engineers. 



to overlap the thermal junction, and this maybe accomplished by 
moving the mirror M backwards or forwards, according to the distance 
of the pyrometer from the furnace. To secure exact focusing, the 
image of the hot body formed by the concave mirror is reflected to 
the eye-piece by the aid of two small plane mirrors placed near the 
couple, each of which reflects one half of the image ; and it is so 
arranged that when the focus is correct, the separate halves of the 
image are continuous, but are discontinuous when the focus is not 
correct. The rise in temperature of the couple produces an E.M.F. 
which is registered by a Meylan-d'Arsonval galvanometer, and tem- 
perature:'? are deduced from the fourth pov/er law, as previously 
described. 




FIG. 49. FERY'S RADIATION PYROMETER, END VIEW, 
SHOWING REDUCING DIAPHRAGM. 



The galvanometer is furnished with two scales, over which the 
pointer moves, one of which is for use with the full aperture, and 
registers from 600 C. to 1300 C., whilst the second scale is used in 
connection with the diaphragm shown in Fig. 49, which, when swung 
over the end of the tube cuts off a definite fraction of the total radia- 
tion, and enables temperatures to be read which, with full aperture, 
would send the needle off the scale. The higher scale reads from 
1000 C. to 2000 C. The range of temperature recorded might also 
be increased by shunting the galvanometer and maintaining a full 
aperture, provided the temperature of the junction (which, with the 
present arrangement, never exceeds 110 C.) is not unduly raised. 

The distance of the pyrometer from the hot body is immaterial so 



He at- Radiation Pyrometers. 173. 

long as the image completely overlaps the thermal junction. The 
limiting distance, for a given pyrometer, may be calculated from the 
well-known optical principle 

size of image _ distance of image from mirror 
size of object distance of object from mirror 

Example. If the diameter of the thermal-couple disc be T V inch, 
the diameter of the object viewed 12 inches, and the distance of the 
mirror from the thermal-couple 3 inches when the object is correctly 
focused, the limiting distance will be reached when the size of the 
image is equal to that of the thermal-couple, that is, has a diameter 
of ^ inch. Inserting values in the above ratio, 

ii= 3 

12 X 

from which x 432 inches or 36 feet. 

The maximum distance from the source of heat is given with each 
instrument, and is usually i yard for every inch of diameter of the 
heated aperture viewed. On approaching the source of heat, the 
amount of radiation received by the mirror will be greater in the 
inverse proportion of the square of the distances. Thus at 6 feet 
distance the radiations will be four times as great as those received at 
a distance of 1 2 feet. But at the nearer distance a larger image is 
formed, which greatly overlaps the junction, so that at a distance of 
6 feet the proportion of the radiations which impinge on the junction 
are only J of the proportion which obtains at a distance of 12 feet. 
Hence, within the limit given, the actual amount of radiations striking 
the couple is constant at all distances, and the same temperature is 
recorded. 

In using the heat-radiation pyrometer it must always be borne in 
mind that the scale is graduated with respect to black-body radiations. 
Correct readings will be obtained if the instrument be sighted on the 
object whilst in the furnace, or by inserting a fireclay tube, closed at 
one end, in the furnace, and sighting the closed end. In either case 
black-body conditions are realised. On the other hand, the indica- 
tions obtained from the surface of molten metal in a ladle are below 
the truth ; and if fumes arise, as in the case of alloys containing zinc 
or lead, the radiations are seriously interfered with, and the reading 
is far too low. Smoke in a furnace similarly retards the radiations, 
and consequently care must be exercised that no solid particles inter- 
vene between the hot body and the pyrometer. 



1 74 Heat for Engineers. 

Records of temperature may be obtained with this pyrometer when 
used in conjunction with a "Thread" or other intermittent recorder, 
or with a Roberts-Austen photographic recorder, the procedure being 
identical with that adopted in connection with thermo-electric pyro- 
meters. 

Advantages and Drawbacks of Heat- Radiation Pyrometers. The 
lens form of heat radiation pyrometer is little used, owing to its lower 
limit (900 C.) seriously restricting its commercial utility. The 
mirror form, which is capable of reading from 600 C. or lower if 
necessary to an indefinitely high temperature, has become a formid- 
able rival to other forms of pyrometer. The deterioration which 
must inevitably take place in any instrument when constantly heated 
in a furnace is entirely avoided, as no part of the instrument attains a 
higher temperature than 110 C. The unlimited range qualifies this 
pyrometer for use in connection with electric furnaces, and other high 
temperature operations which are beyond the compass of instruments 
which must be placed in the source of heat. It requires no skill in 
use, and the indications are rapid. It has the further advantage over 
pyrometers fixed in position that it may be focused on any part of a 
furnace, or any object in it, and is thus not restricted to recording 
the temperature at one part only. For recording purposes it may be 
mounted opposite a tube with a closed end, inserted to any desired 
depth in the furnace, and focused on the end of the tube. 

The chief drawback is that an installation worked from a central 
standard, cannot be made with these pyrometers, as complete identity 
optical and otherwise is practically impossible to attain. Each 
pyrometer will only yield true readings on its own specially standard- 
ised indicator. 

7. Optical Pyrometers. An investigation of the light proceeding 
from a luminous object may, with proper precautions, furnish a clue 
to the temperature of the object. An instrument working on this 
principle would possess the same advantages as a heat-radiation pyro- 
meter in the respect that its indications could be obtained at a distance 
from the source of heat. Up to the present, however, the various 
forms of optical pyrometers introduced by different investigators have 
received little practical application in the workshop, although of 
service in the laboratory for the determination of the temperature of 
small luminous sources, such as the filaments of incandescent and 
Nernst lamps, and the crater of the arc lamp. The drawback to the 
use of these pyrometers in a workshop is that considerable skill is 
necessary in obtaining correct readings, and that a delicate adjustment 
of parts is necessary, rendering the instruments extremely susceptible 



Optical Pyrometers. 175 

to rough usage. Space will only permit of a description of the method 
adopted in connection with the more important types, and for details 
the reader is referred to special treatises on the subject. 

The colour changes experienced by a substance as its temperature 
rises are well known, and the temperatures corresponding to different 
colours were found by Pouillet as follows : 



First visible red . . 525 

Dull red ... 700 

Turning to cherry . . 800 

Cherry proper . . 900 

Bright cherry . . . 1000 



Dull orange . . 1 100 

Bright orange . . 1200 

^^ 7 hite .... 1300 

Brilliant white . . 1400 

Dazzling white . . 1500 



These colours are used to form a judgment in conducting many 
workshop operations, such as tempering chisels, forging steel, etc., 
but the temperatures attached to them are uncertain, as no two persons 
form quite the same judgment of the colour. At a dull red heat the 
change is most sensitive, a rise of 20 C. being detectable to a trained 
eye ; thus the recalescence of a piece of steel between 700 and 800 C. 
is readily seen. It is the uncertainty of judging colour changes with 
even an approximation to accuracy that has led to the necessity fcr 
pyrometers. 

The photometric measurement of the total luminosity cannot be 
relied upon to furnish a clue to the temperature, as bodies at the 
same temperature may possess widely differing luminosities. If it 
be attempted to obtain the temperature of a hot space by measuring 
the candle-power of a piece of platinum placed in the space, the 
changing colours of the platinum render the method unreliable. 
Definite results can only be obtained by measuring the intensity of 
a radiation of given wave-length, or by comparing the intensities of 
radiations of definite wave-lengths. Both these principles are utilised 
in the construction of optical pyrometers. 

Le Chateliefs Optical Pyrometer. In this instrument the inten- 
sity of the red radiations of the hot body or space are compared 
with those received from a standard source by means of a specir 1 
kind of photometer. The hot body is viewed through a telescope, 
at the object end of which is placed a piece of red glass, and also 
an iris diaphragm which regulates the amount of luminous radiation 
received by the eyepiece. A branch at right angles to the telescope 
contains a standard lamp, the light from which, after passing through 
a piece of red glass, is reflected by a mirror placed at 45 into the 
eyepiece, so as to appear side by side with the image of the hot body. 



176 Heat for Engineers. 

By adjusting the diaphragm, and interposing other glasses when 
necessary, the two images may be made equally luminous. The 
determination of the temperature from these observations is a com- 
plicated matter, involving measurements of the absorption coefficient 
of the glass, the emissive power of the source of luminosity, and a 
knowledge of the connection between temperature and the intensity 
of red radiations. Le Chatelier was enabled, as a result of his 
investigations, to prepare a table for the pyrometer from which 
temperatures could be deduced from the number of absorption 
glasses interposed, and the diameter of the diaphragm when equality 
of tint is obtained. The figure given by this pyrometer for the 
temperature of the arc lamp is 4100 C., or 500 higher than that 
indicated by the heat-radiation pyrometer. In Fery's modification 
a fixed diaphragm is placed in the tube of the telescope, so that the 
angular aperture is fixed, and the result made independent of the 
distance of the furnace within considerable limits. The iris is- 
replaced by a pair of absorbing glass wedges, which may be pushed 
over one another and thus caused to interpose any desired thickness 
of absorbing glass between the object and the telescope lens. The 
calibration is based on the law that the thickness of wedge interposed 
varies inversely as the absolute temperature. 

The Wanner Pyrometer. In this instrument a standard source 
of light is obtained by illuminating a ground-glass surface by means 
of a small incandescent electric lamp. Light from this surface is 
passed through a direct vision spectroscope, furnished with a 
diaphragm which cuts off all but a band in the red portion of the 
spectrum. By means of a second slit in the end of the instrument, 
light from the source under observation is similarly treated. The 
relative intensities are measured by a polarising arrangement, and 
the temperature, deduced from the angle through which the analyser 
must be turned to produce equality of tint in the light received from 
the two slits and a knowledge of the black-body temperature of the 
standard, is marked on the circumference of a dial which rotates 
with the analyser. As the incandescent lamp deteriorates with use, 
it must be compared from time to time with a standard amyl acetate 
lamp, and the voltage increased to bring its illuminating power to 
that which it possessed when the instrument was graduated. Owing 
to the great loss of light caused by the optical arrangements, certainty 
of measurement cannot be obtained below 900 C. (1650 F.). 

Holborris Optical Pyrometer. The principle of this instrument 
is to make a comparison between the luminosity of the filament of 
a small incandescent electric lamp, connected to a rheostat and milli- 



Optical Pyrometers. 177 

ammeter, and that of the source. To this end the filament of the 
lamp is placed in the focal plane of a telescope objective, and may 
be viewed through an eye-piece in which a red glass is placed. If 
the filament be at a different temperature to the object, it will be 
seen superposed on the image of the hot source. By varying the 
rheostat, the luminosity of the filament may be altered until it is no 
longer visible on the bright background. The current passing 
through the lamp is then noted, and the temperature obtained from 
the relation found to exist between the temperature of the lamp 
filament and the current. This relation takes the form 

C = a + b t + c t-, 

where C = current, t = temperature, and a, b, and c = constants 
depending on the kind of lamp used. This method has been found 
to give excellent results up to 1500 C. 

Mesurt and NoueVs Pyrometer. In this apparatus a piece of 
quartz, cut perpendicularly to the axis, is placed between two Nicol 
prisms ; an arrangement which serves to cut out the central portions 
of the spectrum. The relative intensities of the red and green 
portions of the spectrum are then used to indicate the temperature, 
the green portion becoming relatively brighter as the temperature 
rises. One of the Nicol prisms, which serves as an analyser, is 
fastened to a rotating disc, which is graduated. On turning the 
analyser a red colour is observed in one direction, and a green colour 
in the other. The intermediate position, where a neutral tint is 
obtained, alters with the temperature of the luminous source, and is 
determined by the relative brightness of the red and green portions 
of the spectrum. The division on the rotating disc which is opposite 
a fixed mark is noted when the intermediate tint is obtained, and 
the temperature read from a table provided. This table is prepared 
by sighting the pyrometer on a surface, the temperature of which is 
varied, and noted at each reading by means of a thermo-electric, 
pyrometer. The Mesure and Nouel pyrometer is used in cases 
where a rapid, approximate result is desired ; an error of judgment 
in deciding the neutral tint might make a difference of ioo c C. or 
more in the reading. 

Advantages and Drawbacks of Optical Pyrometers. The ability 
to measure a temperature from a distance is a strong point in favour 
of optical pyrometers, and there need be no upper limit to the tem- 
perature measured if the laws of luminous radiations are fully known 
and used in the graduation of the instrument. As the use of the 
electric furnace extends, and operations at extremely high tempera- 



178 Heat for Engineers. 

tures become more common, it is safe to predict that optical pyro- 
meters will be more extensively used than at present. Many 
important researches have already been carried out by the aid of 
these instruments, which, until the introduction of the heat-radiation 
pyrometer, furnished the only means of measuring temperatures 
beyond the scope of a thermo-electric pyrometer. 

The chief drawbacks are the fragile character of the instruments, 
the delicate adjustments required, and the skill necessary to obtain 
correct readings ; all of which militate against their extended use in 
the workshop. In many of the forms, moreover, the temperature 
scales cannot be regarded as certain; and the maintaining of a 
standard illuminating surface is bound, in ordinary practice, to give 
rise to trouble. They are not adapted for obtaining continuous 
temperature records. 

8. Linear Expansion Pyrometers. Brogniart and others designed 
pyrometers based on the expansion of a rod of iron, free to move at 
one end only. The elongation was multiplied by levers, the terminal 
lever causing an index-hand to move round a dial. From the known 
coefficient of the expansion of the iron, or by comparison with a 
standard, the dial could be marked to represent degrees. Pyrometers 
based on this principle are still made, largely for use in bakers' ovens. 
A rod of iron, surrounded by a porcelain or fire-clay tube, touches 
the end of the latter at one of its extremities, and is free to move at 
the other and cause an index to move over a dial. The difference 
between the expansion of the iron rod and the enclosing tube is thus 
made to indicate the temperature. In another form the index is 
actuated by a rod of carbon placed in an iron tube. Such pyrometers 
cannot be regarded as in any sense exact, as the coefficients of 
expansion of the substances are not uniform at all temperatures, and 
alter in value on continuous heating. They are not intended for use 
above 700 C., but at lower temperatures form a sufficiently exact 
guide in many operations, and in addition are cheap and require no 
manipulation. Much greater certainty can be obtained by the use of 
these instruments than by trusting the eye. 

9. Fusion Method of Obtaining Furnace Temperatures. Where 
intermittent readings of a furnace temperature suffice, and it is not 
desired to make the necessary outlay for a pyrometer, the fusion 
method furnishes a cheap and fairly accurate means of obtaining the 
desired readings. A series of substances differing progressively in 
melting-point are obtained, and by placing them in the furnace until 
the temperature existing is attained, some will be found to melt, whilst 
others remain solid. The furnace temperature may then be obtained 



Seger Pyramids. 179 

from the known melting-points of the substances, with an accuracy 
depending upon the interval between the successive fusion tempera- 
tures. As an example of the method, the following salts may be 
chosen : 

Salt. Melting Point. 

I molecule common salt + I mol. potassium chloride . 650 C. 

common salt ...... 800 

anhydrous sodium carbonate .... 850 

anhydrous sodium sulphate .... 900 

sodium plumbate ...... 1000 

anhydrous potassium sulphate . . . 1070 

anhydrous magnesium sulphate . . 1 1 50 

If, in the furnace, it be found that the first two in the series have 
completely melted, whilst the sodium carbonate is intact, it is then 
known that the furnace temperature exceeds 800 C., but is less than 
850. A knowledge of these limits often suffices. 

Instead of salts, a prepared series of metals and alloys may be 
used. It is not necessary to place the whole series in the furnace, 
but only those which are known by experience to have melting-points 
near to that of the furnace temperature. 

Seger Pyramids or " Cones? The fusion method has been brought 
to a high degree of accuracy by Seger of Berlin. Small triangular 
pyramids, 50 millimetres in height, each side of the base measuring 
15 millimetres, are made of silicates of varying composition. The 
pyramids are numbered from " 38," which melts at 1890 C., to " 022," 
which melts at 590 C.; a range of 1300 C. being thus comprehended. 
Altogether 60 different pyramids are used, differing in melting-points 
by intervals of 20 from 1890 to 950, and afterwards by intervals of 
30. The shape is well designed for observations of fusion, the 
method of testing being to place a number of the pyramids, having 
melting-points near to that of the furnace temperature, on an earthen- 
ware support, and insert them in the furnace. The effect is shown 
in Fig. 50; one of the pyramids has completely melted and fallen 
flat; the next has bent over; whilst the other two are intact. The 
temperature of the furnace is taken as that of the melting-point rf 
the pyramid which has bent over, but not collapsed, and which may 
be obtained from the number stamped on it. The most refractory 
pyramids are composed of alumina and silica in varying proportions, 
other ingredients, such as potash, lime, etc., being introduced to 
obtain the more readily fusible pyramids. 

Seger pyramids are largely used by pottery manufacturers, and 
are commercially known as " fusible cones." They possess advan- 

N 2 



1 80 Heat for Engineers. 

tages over other fusion methods not only in respect to the range 
covered, but also in accuracy owing to the nearness of the melting- 
points of consecutive pyramids. They may be used to indicate the 
rise in the temperature of a furnace by observing the bending over in 

B A 




FIG. 50. METHOD OF USING SEGER " CONES." 

turn of a number inserted in the furnace. It may be added that a 
number of pyramids, suited to a given operation, may be purchased 
at a trifling cost. 

Cylinders of fusible materials, which melt completely at specified 
temperatures, have been introduced for use in steel furnaces under the 
name of " Sentinel " pyrometers. 

Other Forms of Pyrometers. In addition to the forms already 
described, numerous other pyrometers have been devised from time to 
time. Amongst these may be mentioned (a) the mercury vapour 
pyrometer, in which mercury is enclosed in a steel tube to which a 
pressure-gauge is attached, and the temperature deduced from the 
observed pressure of the mercury vapour ; (b) pyrometers based on 
the rise in temperature observed in a steady stream of water or air 
driven through a tube placed in the furnace ; (c) pyrometers in which 
the temperature is obtained from the variations in the viscosity of 
gases with temperature, or from the alteration of the refractive index ; 
(d) instruments depending upon the observed pressure of a gas or 
vapour liberated on heating a weighed quantity of solid ; and many 
others. None of these are in such general use as to demand a 
detailed description in the limits of the present treatise. 

High Temperature Data. The following table may be of interest 
as showing the progress made in connection with the measurement of 
very high temperatures. 



High Temperature Data. 



181 



Source 


Temperature, 


Observer and Method 


Incandescent electric lamp j 
(carbon) / 


I800 


Le Chatelier, optical pyrometer 


Arc lamp .... 


4IOO 





Arc lamp .... 


3760 


Fery, heat radiation pyrometer 


Thermit in mould 


2500 


95 > > 


Bunsen flame, open . 


1870 


Fery, spectroscopic method 


,, closed 


I7IO 


5> 5> 55 


Acetylene flame 


2550 


5 55 S> 


Oxy-hydrogen flame . 


2420 


55 5 > 


Melting point of tantalum . 


3000 


(Waidner and Burgess, optical 
\ pyrometer 


tungsten . 


32OO 


JWaidner and Burgess, optical 
\ pyrometer 


Temperature of sun . 


7600 ! Le Chatelier, optical pyrometer 


5 ' ' 


7500 


Fery, heat-radiation pyrometer 



Recent Developments of Pyrometry. Owing to readings on the 
gas scale now being possible up to 1550 C. (p. 135), the uncertainty 
of the indications of instruments between 1000 C. and the above 
temperature has now been removed. Improvements in resistance 
pyrometers have been made by Paul and Northrup, who have intro- 
duced indicators practically automatic in action. Cheap thermo- 
electric pyrometers have been placed on the market by various firms 
for temperatures up to 1000 C., the couples used being iron and 
constantan, nickel and copper, and nickel and carbon; and the 
author has devised a method of automatic compensation for fluctua- 
tions in the temperature of the cold junction. Radiation pyrometers 
have been added to by the Cambridge Scientific Instrument Com- 
pany, who have introduced a' form of Fery pyrometer in which the 
thermal junction is replaced by a compound strip in spiral form, 
which coils up or uncoils with changes of temperature, and carries a 
pointer moving over a scale which is marked so as to give direct 
readings of the temperature of the source. A radiation pyrometer 
which, within moderate limits, requires no focusing, has been devised 
by Foster. Holborn's optical pyrometer (p. 176) is now made in 
commercial form by Messrs. Siemens, and has found a use in the 
treatment of special steels at very high temperatures. 



1 82 Heat for Engineers. 



CHAPTER IX. 

CHANGE OF STATE. FUSION. 

Physical Effects of Heat on Solids. When the temperature of a 
solid is raised, the kinetic energy possessed by its molecules is aug- 
mented, and the freedom of motion of the molecules increases. 
Cooling produces the converse effect, and consequently, at different 
temperatures, the physical properties of solids might be expected to 
differ, and this is generally true. Indiarubber, for example, becomes 
hard in cold weather, an^ ,if dipped in liquid air becomes so brittle 
that it may be broken up with a hammer. In the case of metals a 
molecular rearrangement often results from heating, which may remain 
permanent on cooling. Thus metals which have been rendered hard 
by rolling or drawing into wire are often permanently softened by 
heating, as may be noticed in the case of brass and copper. The 
annealing of metals is explained in this way, and a microscopic 
examination of the etched surface of the metal shows a different 
structure after annealing than before. An interesting example of the 
molecular changes caused by a rise of temperature is furnished by 
zinc, which, if cast, is brittle at ordinary temperatures. On heating 
to ioo-i5o C., however, the metal becomes malleable, and may be 
drawn into wire ; but at 300 C. it again becomes extremely brittle. 
Bismuth, which ordinarily possesses little tensile strength, improves 
greatly in this respect at very low temperatures, and steel which has 
been dipped in liquid air shows a permanent increase in tensile 
strength. 

The electrical resistance of various substances is also modified by 
changes of temperature. Pure metals have in general a high tem- 
perature coefficient ; that is, show a rapid increase in resistance as 
the temperature rises and a correspondingly rapid decrease as the 
temperature falls. Alloys, in general, have a lower temperature coef- 
ficient, and in special alloys such as German silver, platinoid, and 
constantan, the resistance only alters very slightly with the tempera- 
ture. Certain other substances, such as porcelain, are practically 
non-conductors of electricity when cold, but at high temperatures 



Critical Points of Steel. 183 

conduct freely. Such bodies are known as pyro-conductors, the con- 
ducting power being due to molecular alterations caused by the rise 
in temperature. The Nernst lamp consists of a filament of pyre-con- 
ducting material, which after a preliminary heating conducts the 
current, and offers sufficient resistance to remain luminous when a 
current through it is once established. 

Critical Points of SteeL The molecular changes occasioned in 
steel by alterations of temperature call for special mention, as a study 
of these changes may often prove a valuable guide to the successful 
treatment of the metal. The phenomenon of recalescence has already 
been mentioned (see Chapter IV.), and the temperatures at which 
recalescence occurs known as the " critical points " vary with the 
class of steel, and may be used to furnish a clue to the character of 
the steel under test. It being known by experience how to treat 
steels of different kinds for the purposes intended, the determination 
of the critical points becomes a matter of commercial utility. 

One method of determining these points is to place a platinum- 
resistance or thermal-couple pyrometer in a hole drilled in the speci- 
men, the temperature being raised slowly by a gas furnace, or better 
still, an electric furnace. The molecular change with rising tempera- 
ture is accompanied by an absorption of heat, so that at the critical 
points the temperature for a short time will cease to rise. If readings 
be taken every half-minute, and a curve connecting time and tem- 
perature be drawn, it will show a flexure when the critical point is 
reached. The curve will be traced automatically if a recorder is 
used with the pyrometer. On cooling the steel, evolution of heat 
occurs at the recalescent points, and flexures would again be observed 
if a curve were traced as before. Such a cooling curve is shown in 

Fig-.^i- 

A second method, more sensitive than the foregoing, is known as 
the " differential " method. A block of metal known to be free from 
molecular changes of this kind is placed side by side in the furnace 
with the specimen of steel, as indicated in Fig. 52, so that both blocks 
would show the same rise in temperature in the absence of a mole- 
cular change. In a hole drilled in the specimen A, a thermal-junc- 
tion C is placed, connected to a galvanometer G, the scale of which 
has been graduated to read temperatures. The second galvanometer 
H is in circuit with two junctions, D and E, one in the specimen and 
the other in the comparison piece B. So long as the junctions D 
and E remain at the same temperature, no deflection will be observed 
on the galvanometer H, any tendency to send a current on the part 
of either being counterbalanced by an equal tendency on the part of 



1 84 



Heat for Engineers. 



the other to send a current in the opposite direction. If the tem- 
perature of the furnace be raised slowly, no movement on H will be 
noted until a molecular change occurs in the specimen A, which, by 



000 



,800 



700 



600 



500 



\ 



\ 






O 10 2O 30, 4O 

FIG. 51. COOLING CURVE FOR STEEL, SHOWING RECALESCENCE. 

absorbing heat, causes the temperature to lag behind that of B. The 
temperature at which the galvanometer H commences to deflect is 




FIG. 52. DIFFERENTIAL METHOD OF DETERMINING 
RECALESCENCE POINTS OF STEEL. 

recorded on G, and the critical point thus determined. The tempera- 
ture may now be raised some 50 above this point, and then allowed 



Change of State. 185 

to fall gradually, when a deflection on H, bur in the opposite direction, 
will again be obtained at the critical point, as owing to recalescence 
A remains at a higher temperature than B. In performing the ex- 
periment, an electric furnace is suitable, and all the junctions should 
be naked. The wires should be threaded through twin-bore fireclay 
tubes, which rest in the holes in A and B, and prevent contact with 
the mass of metal. The specimen and comparison-piece should rest 
on mica in the porcelain or silica tube of the furnace. This method 
is very sensitive and well adapted for testing steels which do not 
show a marked recalescence. Any undue rise in temperature on the 
part of either piece of metal, due to a more favourable position in the 
furnace, would be detected in the early stages by a movement of H. 

The molecular changes which occur when steel is heated are only 
partially reversed when the steel is rapidly quenched. Hence, a 
piece of hot steel, when cooled rapidly in water or oil, retains to a 
large extent the molecular structure possessed at the higher tem- 
perature, and differs from slowly-cooled steel in being harder and 
more brittle. Tempered steel is intermediate between the hard 
and slowly-cooled or soft steel both in structure and properties. 
The modifications caused by the introduction of metals such as 
tungsten, chromium, etc., cannot be dealt with here, but it may be 
stated that a knowledge of the critical points, in the hands of a 
competent metallurgist, is of great service in guiding the operations 
carried out in working the steel. 

Change of State. -When the temperature of a solid is continu- 
ously raised, a point is reached at which fusion occurs, and the solid 
becomes a liquid. The temperature at which fusion takes place is 
called the " melting-point " of the solid ; and the temperature at 
which the substance, on cooling, re-assumes the solid state is known 
as the " freezing " or " setting point." In most cases these two tem- 
peratures are identical, but when the transition is not abrupt a 
difference of several degrees may exist between the temperature at 
which the substance ceases to be a well-defined solid, and that at 
which it flows freely. Many solids, before liquefying, pass through 
an intermediate or pasty state, in which the properties are miu- 
way between those of a solid and a liquid, as may be observed 
with cast-iron and other metals. It is advisable, therefore, in all 
observations on the change of state, to distinguish between the tem- 
peratures which bound this intermediate condition. 

The liquefaction of a solid is always accompanied by an absorp- 
tion of heat, which is converted into work in conferring increased 
velocities on the molecules, and therefore cannot be detected by a 



1 86 Heat for Engineers. 

thermometer. When the liquid solidifies, the heat absorbed in the 
act of liquefaction is liberated. The term " latent heat of fusion " 
is applied to the heat energy necessary to change the solid, already 
at its melting-point, into liquid also at the melting-point ; or to that 
liberated in the converse change. It is owing to the absorption of 
this latent heat that a block of ice placed in a room, and continuously 
receiving heat from the atmosphere and surrounding objects, remains 
at o C. until completely melted ; moreover, the water resulting from 
the melting has also a temperature of o C. Hence all the heat 
received by the ice has been converted into another form of energy, 
having been utilised in imparting the greater kinetic energy possessed 
by the molecules in the liquid state. The liberation of latent heat 
is noticed when a liquid is cooled until solidification occurs. A 
thermometer placed in the liquid shows a continuous fall of tempera- 
ture until the freezing point is reached, when, owing to the disengage- 
ment of the latent heat, the temperature remains steady for some 
time, falling again when solidification is complete. If a small beaker 
be filled with paraffin wax, and a thermometer be placed in the 
centre of the mass after melting, it will show a continuous fall of 
temperature until 49 C. is reached. At this temperature it will 
remain for 15 minutes or more, depending on the size of the beaker 
and the rate of cooling. The observation of the stationary tempera- 
ture is used to determine the freezing point of solids. 

Determination of the Melting-Point of Solids. First Method, 
for solids which melt below 300 C. A narrow piece of thin- walled 
glass tubing, closed at one end, is fastened to a thermometer by 
means of a piece of wire or a rubber ring. A small piece of the 
solid is placed in the tube, and pushed down with a wire until it is 
opposite the centre of the thermometer bulb. The tube and thermo- 
meter are then immersed in a bath of strong sulphuric acid to a 
sufficient depth to cover the part of the tube occupied by the solid ; 
the open end of the tube, however, or the rubber ring, must not be 
submerged. The bath is gradually heated with a Bunsen burner, 
until the solid is observed to liquefy and trickle down the tube. The 
reading of the thermometer is then taken, and gives the melting- 
point of the solid. To obtain an exact reading, the bath should be 
continuously stirred, and the temperature raised very gradually as 
the melting-point is approached. A quickly performed experiment 
indicates the melting-point to within a few degrees, and a second may 
then be performed in which the final stage is conducted very slowly. 

Second Method, generally applicable. A thin-walled iron or 
platinum tube, ^ inch in diameter, and 4 inches long, closed at one 



Change of State. 187 

end, is filled with the solid and heated until liquefaction occurs. An 
iron or platimm spiral is placed in the molten mass, so as not to 
touch the tube, and the mass is now allowed to solidify, thus fixing 
the wire in the centre of the solid. The tube is now placed in a 
suitable bath, and fixed in position by means of a stand; and a 
thermometer or pyrometer is placed side by side with the tube. 
The free end of the wire is passed over a pulley, and a 5o-gram 
weight attached to it. The temperature of the bath is gradually 
raised until the portions of the solid in contact with the walls of the 
tube become liquid, when the weight will be observed to fall and 
drag out the solid core. The temperature of the bath at this moment 
gives the melting-point, provided that the last stages of the heating 
have been conducted very gradually. 

For melting-points not exceeding 300 C., a bath of strong sul- 
phuric acid may be used. Above this temperature molten tin may 
be used in conjunction with an iron tube, or suitable fused salts with 
a platinum tube. Platinum should never be used when the bath or 
substance tested is metallic in character, or contains free caustic 
alkalies. A platinum-resistance pyrometer may be used for melting- 
points not exceeding i2ooC. ; above this temperature a thermo- 
electric pyrometer is necessary. 

Determination of the Freezing- Point of Solids. A quantity of the 
solid is melted in a crucible or other suitable vessel, and raised to 
30 or 40 above its melting-point. A thermometer or pyrometer- 
according to the temperature is placed in the molten mass, and its 
indications observed as the liquid cools. When solidification occurs, 
the liberation of latent heat suffices to maintain a steady tempera- 
ture for some time, after which continuous cooling will again take 
place. The stationary temperature is taken as the freezing-point of 
the solid. 

The time during which the temperature is steady depends upon 
the rate of cooling, the mass of substance used, and the quantity of 
latent heat disengaged. So long as the latent heat liberated balances 
the cooling due to radiation and other causes, the temperature will 
not alter. Hence at high temperatures, when the rate of cooling due 
to radiation, etc., is rapid, a large mass of substance is necessary if 
the stationary temperature is to continue for any length of time ; or 
the same result may be secured by allowing a smaller quantity of the 
substance to cool in the interior of the furnace in which it was melted. 
The definite character of the freezing-point, as thus observed, renders 
the method suitable for the graduation of pyrometers by the use of 
standard substances of known freezing-points. 



i88 



Heat for Engineers. 



The results may with advantage he recorded graphically, the 
temperature being noted every half-minute, and a curve drawn on 
squared paper connecting time with temperature. The general form 
of curve obtained with a single substance is shown in Fig. 53. At 
the solidification temperature the curve becomes parallel to the time 
axis, to which, at other temperatures, it is inclined. When the cooling 



























IUO 

do 
80 
70 

fiO 


\ 






















\ 






















\ 
























\ 




















50 
40 
30 
20 
10 

c 




X 






























X 


s^ 
























X 
























x 


\ 
















































) 4 8 12 16 20 24 28 32 36 40 



Time, irv minutes 

FIG. 53. COOLING CURVE FOR A PURE SUBSTANCE PASSING 
FROM LIQUID TO SOLID. 



has been too rapid for stationary readings to be observed, a flexure 
of the curve is obtained at the solidification point, sufficient to give 
a clue to the temperature. 

In determining the freezing-point by this method, it may frequently 
be noticed that the substance cools continuously for a time, and then 
undergoes a sudden rise in temperature, at which it remains steady 
until solidification is complete. This failure to set until the tempera'- 



Change of State. 189 

ture has fallen below the normal setting or freezing-point, is known 
as " surfusion," and will be specially referred to later. When solidifi- 
cation occurs, however, the temperature rises at once to the true 
freezing-point, and remains stationary as before ; hence, in all cases 
the steady temperature gives the correct freezing-point. 

The melting-points of metals are in general identical with the 
freezing-points, and consequently the method under notice will 
furnish the melting-points of these substances ; for which purpose it 
is to be preferred to either of the methods previously described. The 
special case of alloys will now be considered. 

" Partial" Melt ing- Points cf Alloys. Eutectics. Alloys of metals 
differ in physical properties from those of the constituents in a marked 
manner, and are not merely simple mixtures of the component metals. 
In the simplest case an alloy may be a true chemical compound, 
with a uniform structure, and will then possess a definite melting-point. 
In a more complicated case, such a compound may be diffused 
through the mass of another metal, and the alloy will then possess 
" partial " melting or freezing points, one for the compound, and the 
other for the metal ; or a number of partial melting-points may be 
observed if the constitution of the alloy is still more complex. The 
constituent which possesses the lowest melting-point is called the 
" eutectic," and, in a given alloy, has a definite composition. In the 
act of solidification, therefore, the constituent of the higher melting- 
point settles out first, leaving the eutectic still liquid, the action being 
comparable to the crystallisation of a salt from the mother-liquor. 
Hence a cooling-curve for an alloy which is not a homogeneous 
chemical compound, will show two or more flexures or straight parts, 
corresponding to the setting of the constituents in turn, each of which 
liberates latent heat in the act of solidification. The structure of an 
alloy will therefore consist of a matrix formed by the eutectic, which 
is the last to solidify, interspersed by the other ingredients. Each 
partial setting corresponds to the separation of a substance from the 
molten mass, and hence the number of distinct components may be 
deduced from the number of the partial setting-points observed. 

It must not be supposed that because a given alloy of two metals 
has two partial freezing-points that these correspond to the separate 
solidification of the pure metals. On the contrary, the first setting 
generally represents the solidification of an alloy of the two metals of 
a definite composition, and the second, that of the eutectic, which also 
contains both metals, but in a different proportion ; and the tempera- 
tures at which solidification occurs is in neither case identical with 
that of either component metal. The whole question of the structure 



190 



Heat for Engineers. 



of alloys and its relation to the freezing-points is dealt with at length in 
the reports of the Alloys Research Committee in the Proceedings of 
the Institution of Mechanical Engineers, to which the reader is referred 
for detailed information. 

Melting-Points of Mixtures. The melting-point of a substance is 
generally lowered by the presence of another substance, a small 
quantity of which may suffice to cause a notable fall in the melting- 
point. Thus pure iron, which melts just above i5ooC., has its 
melting-point reduced by more than 300 when less than i per cent, 
of carbon is present. A mixture of equal parts of common salt and 
potassium chloride melts at a lower temperature than either of the 
constituents, and the same holds true for a mixture of sodium and 
potassium carbonates. In general, the melting-point of a mixture is 
always lower than that of the constituent which has the higher melting 
point, and frequently lower than that of either. 

TABLE OF MELTING-POINTS OF MIXTURES OF LEAD AND TIN. 



Composition : Parts by Weight 


Melting-Point 


Lead 


Tin 


Degrees C. 


Degrees F. 


I 


(Pb) 


327 


620 


7 


i (Pb 4 Sn) 


292 


558 


51 


i (Pb 3 Sn) 


283 


541 


3i 


I (Pb 2 Sn) 


270 


S I8 


if 


I (PbSn) 


235 


455 


7 


8 (PbSn 2 ) 


197 


387 


10 


17 (PbSn 3 ) 


181 


358 


10 


19 (PbSn 3 . 3 ) 


180 


356 


i 


2| (PbSn 4 ) 


1 86 


367 


10 


28 (PbSn 5 ) 


194 


38i 





I (Sn) 


232 


45o 



As the amount of impurity in a substance increases, the melting- 
point usually falls until a minimum is reached, after which further 
additions of the second substance cause a progressive rise in the 
melting-point. The mixture which possesses the minimum melting- 
point is known as the eutectic mixture of the two substances. The 
eutectic for iron and carbon has the composition iron, 99*11 per 
cent, and carbon, 0-89 per cent. Mixtures of lead and tin furnish 



Change of State, 



191 



an interesting example of the lowering of melting-point, and an 
inspection of the table on page 190 shows that theeutectic mixture of 
these two metals melts at i8oC., and is composed of 10 parts by 
weight of lead to 19 parts by weight of tin, or in the proportion of 
i atom of lead to 3 3 atoms of tin. 

The temperatures given above are to be regarded as the melting- 
points of the constituent which first settles out as the liquid is cooled ; 
the lower constituent, whatever the composition, solidifies at approxi- 
mately 1 80, and is the eutectic PbSn 3 . 3 . When the alloy possesses 
this composition, only one setting point is observed, and the whole 
mass consists of the eutectic. Any variation from this composition 
causes a constituent of higher melting-point to separate out before 
the eutectic has solidified. 

Alloys of very low Melting- Point^ or Fusible Alloys. By alloy- 
ing several metals it is possible to obtain a product which possesses 
an extremely low melting-point considerably less than the tempera- 
ture of boiling water. Many of these " fusible alloys " are known, 
and the composition and melting-point of several are appended : 

TABLE OF ALLOYS OF VERY Low MELTING-POINT. 



Composition : Parts by Weight 



Melting-Point 



Tin 


Bismuth 


Lead 


Cadmium Degrees C. 


Degrees F. 


25 


50 


IO 


. . 


1 20 


248 


8 


25 


IO 


.. 


100 


212 


6 


40 


IO 




95 


203 


I 


4 


2 


I 


65 


149 


4 


IS 


8 


3 


60 


140 



By varying the above quantities alloys may be produced which 
possess any desired melting-point between the upper and lower limits. 
Fusible alloys have some important practical applications, which 
will be considered in the succeeding chapter. 

Change of Volume on Melting. In most cases the melting of a 
solid is accompanied by an increase in volume, that is, the liquid 
occupies a greater bulk than the solid from which it was derived. 
Conversely, on solidifying, a decrease in volume is generally observed. 
The density of the solid in such cases is, therefore, greater than that 
of the liquid, and consequently a piece of the solid will sink if dropped 
into the liquid. Exceptions to this rule are found in the cases of 



192 Heat for Engineers. 

water, bismuth, antimony and grey cast-iron ; all of which expand 
in the act of solidification. One cubic foot of water at o C. becomes 
i ' 09 cubic feet of ice at o C. hence ice will float on water, being 
less dense. The force exerted in the act of expanding at the 
moment of solidification is great, and if the water be confined may 
suffice to burst the enclosure. The bursting of water-pipes and the 
breaking up of porous rocks in frosty weather are due to the expan- 
sive force thus exerted ; the result, however, is not made evident 
until a thaw occurs. The expansion on solidification which takes 
placi with grey cast-iron, antimony and bismuth, is manifested by 
the sharp definition of castings obtained from them, as in solidifying 
the metal is squeezed into the finest lines of the mould. Antimony 
and bismuth are mainly used for alloys, to which they impart the 
property of expanding on setting. Most metals and alloys contract 
on solidifying, and castings obtained from them are not so sharply 
defined. Waxes, fats, and organic substances generally, as well as 
salts, show a contraction on entering into the solid condition. 

The finished size of a metal casting will differ from that of the 
pattern used for making the mould, partly because of the alteration 
in volume on setting, and partly because of the contraction of the 
solid in cooling down to the atmospheric temperature. Other factors 
are the expansion of the mould, and the temperature at which the 
metal is poured. A table is given on page 77 which shows the 
allowance to be made in a pattern for various metals, in order to 
produce castings of a given size. 

Effect of Pressure on the Melting-Point. If a solid, just about 
to melt, be subjected to pressure, the tendency to increase in volume 
en liquefying will be opposed ; whilst a tendency to contract on 
liquefying will be assisted. Hence it might be inferred that pressure, 
in the case of ordinary solids, will retard melting, and thus raise the 
melting-point, whilst in the case of ice, bismuth, etc., the process 
will be accelerated, and consequently the melting-point will be 
lowered. These conclusions may be verified by experiment. Thus 
Bunsen found that a sample of wax, which melted at 46*3 C. under 
i atmosphere, fused at 49*9 C. under a pressure of 100 atmospheres. 
Prof. James Thomson showed that when the increase or decrease in 
volume accompanying the change of state was known, the alteration 
in melting-point due to a given pressure could be calculated from 
thermodynamic principles, and thus found that i atmosphere addi- 
tional pressure should lower the melting-point of ice by 'oo75C. 
The experimental verification of this result was made by Lord 
Kelvin, who obtained a figure closely agreeing with the calculated 



Melting Points. 



'93 



TABLE OF MELTING-POINTS. 



Substance 


Melting-Point, Melting-Point, 
Degrees C. Degrees F. 


Metals 






Tungsten .... 


3200 (about) 


5900 (about) 


Tantalum .... 


3000 


5400 ,, 


Platinum (Harker) . 


I7IO 


Siio 


_ (Burgess) . 


1753 3187 


Pure iron .... 


1510 


2750 


Palladium .... 


1500 


2732 


Nickel 


1427 


2600 


Copper (in reducing atmosphere) 


1084 


1983 


,, (in air) 


1064 


1947 


Geld 


1064 


J947 


Silver (free from oxygen) . 


962 


1763 


,, (in air) . 


955 


I75 1 


Aluminium .... 


657 


1214 


Antimony .... 


632 


1169 


Zinc 


419 


786 


Lead 


3 2 7 


620 


Cadmium .... 


321 


610 


Bismuth ..... 


268 


5H 


Tin 


232 


449 


Mercury ..... 


- 39 


- 38 


Non-Metallic Elements 






Sulphur (rhombic) 


114 


237-2 


Phosphorus (yellow) . 


43 '3 


no 


Bromine ..... 


- 7 


19-4 


Chlorine ..... 


- 34 


- 29 


Nitrogen .... 


- 214 


~~ 353 


Oxygen . ... 


- 238 


- 396 


Hydrogen .... 


- 257 


- 43i 


Pure Salts 






Saltpetre .... 


399 


75o 


Potassium chloride . 


735 


1355 


Common salt .... 


800 


1472 


Sodium sulphate (dry) 


900 


1652 


Potassium sulphate (dry) . 


1070 


1958 


Magnesium sulphate (dry) . 


1150 


2IO2 


Calcium silicate 


1700 


3092 


Other Substances 






Glass (soft) .... 


I 100 


2OI2 


Paraffin wax .... 


54-46 


I29-II5 


Ammonia .... 


- 75'5 


IO4 


Alcohol ..... 


112 


- 170 


Ether 


- "3 


- 171 


Nitrous oxide .... 


- 150 


- 2 3 8 


Water 





32 



194 Heat Jor Engineers. 

result. Later work by Prof. Dewar indicates that an additional 
140 atmospheres cause the melting-point of ice to fall by iC. ; 
an average lowering of '0072 C. per atmosphere. 

As a result of the effect of pressure on the melting-point, it is 
surmised that the internal portions of the earth, although possessing 
a temperature much higher than the normal melting-point of the 
materials, is kept in a solid or semi-solid state owing to the enormous 
pressure of the overlying rocks. The anomalous behaviour of ice in 
respect to the increase of pressure explains many curious phenomena 
that may be observed. Thus, as Bottomley showed, if a wire be 
placed across a bar of ice, and a weight be suspended from each end, 
the weighted wire will pass through the ice, but will not leave it in 
two separate pieces. The effect of the pressure on the ice beneath 
the wire is to cause it to melt, but the water produced escapes round 
the wire and freezes again, and this occurs until the wire has passed 
through the bar. The adhesion of snow under compression, as in 
making a snowball, is similarly explained ; the pressure causes a 
partial melting of the particles of snow, and on liberating the pressure 
the water produced freezes and binds the particles together. Simi- 
larly, two pieces of ice, if pressed together, will adhere or join 
together to form a single piece. This property of joining under 
pressure is known as " regelation," and was first called attention to 
by Faraday. 

Melting- Points of Various Substances. The table on page 193 
gives the melting-points of a number of solids at ordinary pres- 
sures. Decimals are in most cases omitted. 

The figures given in the table represent the most recent deter- 
minations. Exact information as to the melting-points of pure salts 
is scanty, and further investigations in 'this direction are desirable with 
a view to establishing cheap standards for graduating pyrometers. 
The very low temperature data represent the observations of Professor 
Dewar. 

Surfusion, or Delayed Solidification. The fact that water, if free 
from suspended matter, may be lowered considerably below the 
freezing point and yet remain liquid, was noticed by Fahrenheit in 
1724. This phenomenon has since been observed with many other 
substances such as phosphorus, sulphur, tin, antimony, and fused salts, 
and is termed " surfusion." If a surfused liquid be shaken, it will 
frequently solidify, and in all cases the insertion of a fragment of the 
solid will cause solidification. The disengagement of latent heat on 
setting raises the temperature to the melting-point; obviously the 
temperature cannot exceed this, as some of the solid would be re- 



Sur fusion. 



195 



melted, and the latent heat re-absorbed. The converse phenomenon 
of delayed melting may also be observed in certain cases, where the 
temperature must be raised above the normal melting-point before 
liquefaction commences. 

A surfused liquid, if continuously cooled, will ultimately solidify 
without shaking or dropping in a piece of the solid. A mass of molten 
antimony, for example, may be noticed to cool down to 600 C., 



5 10 15 20 25 30 35 4O 45 SO 55 60 




530 



FIG. 54. COOLING CURVE FOR ANTIMONY, SHOWING SURFUSION. 

showing 32 of surfusion; it then sets spontaneously and the tem- 
perature rises to the melting-point, 632 C. A cooling curve under 
these circumstances takes the form shown in Fig. 54. Water in the 
surfused condition in a Bunsen calorimeter may always be made to 
freeze by placing solid carbon dioxide in the inner tube. 

The supersaturation of solutions in some respects resembles the 

o 2 



196 Heat for Engineers. ( 

phenomenon of surfusion. If water be made to dissolve as much as 
possible of a salt when boiling, and the solution be kept still and free 
from dust on cooling, the crystals which usually deposit, owing to less 
solubility at lower temperatures, remain in solution. Shaking, or 
dropping in a crystal of the solid, will cause crystallisation to occur, 
with considerable generation of heat. So small is the crystal required 
to initiate the deposition, that a knitting-needle dipped in a mass of 
crystals, and afterwards cleaned with emery paper, will often retain 
sufficient of the solid to cause crystallisation when the needle is placed 
in the solution. 

The phenomena of surfusion and supersaturation are due to the 
molecules having attained a state of unstable equilibrium, which a 
slight disturbance of the right kind serves to upset. An analogy may 
be drawn from a row of bricks placed on end within reach of one 
another, when knocking over the end brick causes the whole row 
to fall. 

Latent Heat of Fusion. Reference has already been made to the 
absorption of heat by a substance on melting, which is restored on 
solidification. The numerical value of the heat quantity involved is 
denned as follows : The latent heat of fusion of a substance is the 
number of calories absorbed by i gram on being converted from the solid 
to the liquid state, without change of temperature. Thus by saying that 
the latent heat of fusion of ice is 80 calories per gram, is meant that 
one gram of ice at o C., on becoming water at o C., absorbs 80 
calories. Black found the value for ice by trial with different 
quantities of water and ice, which he mixed and noted the result. 
He ultimately found that when i Ib. of water at 79'4C. (or its 
equivalent in degrees F.) was mixed with i Ib. of ice at o C., the 
temperature of the whole after mixing was o C., and all the ice was 
melted. With a less quantity of ice the temperature of the mixture 
did not fall to o C., with a greater quantity some remained unmelted. 
Hence i Ib. of ice on melting to water at the same temperature 
absorbed 79*4 lb- C. units of heat. More exact methods indicate 
80 calories per gram, or 80 lb- C. units per pound, as the correct 
value for the latent heat of fusion of ice. 

The value of the latent heat of fusion of ice may be determined 
by adding dried ice (prepared by squeezing between blotting-paper) 
to a known quantity of water at a known temperature, and noting the 
temperature of the mixture after the ice has melted. The increase 
in weight of the water gives the amount of ice added, and the latent 
heat of fusion is calculated by equating the heat lost by the water and: 
vessel to that gained by the ice. 



Latent Heat of Fusion. 197 

Example. A calorimeter weighs 100 grams, and is made of 
material of specific heat OT. It contains 520 grams of water at 
19 ' 8 C., and on adding a quantity of ice temperature falls to 10 5 C. 
The weight of ice added, as determined by weighing the calorimeter 
and its contents, is 55 grams. Then from the equation 

Calories gained by ice = J calori f s '? St ^ wator 
( and calorimeter 

we have 

(L x 55) + (55 x 10-5) = 520 x (19-8 - 10-5) 
+ {(100 x o - i) x (19*8 - 10*5)} 

and L = 79 calories per gram. 

It should be noted that the calories gained by the ice represent 
(a) the heat required to melt it, producing water at o C., which is 
the latent heat ; and (b) the heat required to raise the water formed 
from o c C. to that of the mixture. 

The drawback of this method is the difficulty of obtaining perfectly 
dry ice. When wet, a low result will be obtained, and more accurate 
results are furnished by the use of a Bunsen calorimeter. If 10 grams 
of water at 10 C. be placed in the tube of this calorimeter, 100 
calories will be given out on cooling to o C. The amount of ice 
melted by this quantity of heat is found from the observed contraction, 
and hence the calories required to melt i gram of ice are readily 
calculated. 

It is more difficult to find the value of the latent heat of fusion of 
other solids by this method, as the specific heat of the substance both 
in the liquid and solid state must be known. A table of latent heats 
of fusion is appended, the values being given both in heat and work 
units. 

An inspection of the table on page 198 shows that the latent heat 
of fusion of ice is much greater than that of any of the other sub- 
stances enumerated. The value of ice as a cooling agent is thus 
greater than that of any other solid which might be used ; hence for 
cooling purposes ice is not only cheapest, but best. The value f r 
metals varies considerably ; thus the melting of grey cast-iron involves 
an absorption of heat five times as great as that required for an equal 
weight of nickel. 

The amount of energy absorbed in the process of melting is best 
judged by a consideration of the work equivalent of the latent heat. 
In the case of ice, the energy absorbed by i Ib. on becoming water 
at o C. would suffice to raise a weight of i ton through a height of 



198 



Heat for Engineers. 



TABLE OF LATENT HEATS OF FUSION. 



Substance 


Latent Heat of Fusion 


Calories 
per gram 


B.Th.U. 

per Ib. 


Ergs per gram 


Ft-lb. per Ib. 


Metals 










Bismuth 


12*6 


22'7 


52-9 x io 7 


17,640 


Cadmium . 


13*7 


24-7 


57'5 


I9,l8o 


Cast iron (grey) . 


23-0 


41-4 


96-6 


32,200 


(white) 


33*o 


59'4 


138-6 


46,200 


Lead . . . . 


5*4 


9*7 


22-7 ,, 


7,560 


Mercury 


2-8 


5'4 


11-8 


3,920 


Nickel 


4-6 


8'3 


19*3 


6,440 


Platinum 


27-2 


49-0 


114-2 


38,080 


Silver 


21*1 


38-0 


88-6 


29,540 


Tin . 


I4'3 


25*7 


69-1 


2O,O2O 


Zinc .... 


28-1 


50-6 


Il8'2 ,, 


39,340 


Other Substances 










Ice . 


80'0 


144-0 


336-o 


112,000 


Bromine 


16-2 


29-2 


68-0 


22,680 


Phosphorus (yellow) 


5*2 


9*4 


21'8 


7 ,280 


Sulphur (rhombic) 


9*4 


16-9 


39'5 


13,160 


Hydrogen . 


i6'o 


28-8 


'67*2 ,, 


22,400 



50 feet, or is equal to 50 foot-tons. The energy possessed by the 
molecules of i Ib. of water at o C. therefore exceeds that contained 
by i Ib. of ice by 50 foot-tons. 

Effect of Dissolved Solids on the Freezing- Point. The freezing 
point of liquids in general is lowered by the presence of dissolved 
solids, the depression being, within limits, proportional to the amount 
of solids dissolved. Strong solutions of salt or calcium chloride may 
be cooled to 20 C. or lower without freezing, and for this reason 
are used to circulate at a low temperature in cold stores. Sea water, 
for the same reason, does not freeze so readily as fresh water. It 
has been found that if quantities of different salts be dissolved in 
equal quantities of a given liquid, in the proportion of the molecular 
weights of the salts, the various solutions will possess the same 
freezing-point. Thus a solution of 40 grams of caustic soda in 



Fusion. 199 

1000 grams of water, will freeze at the same temperature as a solu- 
tion of 101 grams of saltpetre in 1000 grams of water, the molecular 
weights of the salts taken being 40 and 101. In the case of non- 
electrolytes, such as sugar, the depression in freezing-point is only 
one-half that occasioned by the molecular equivalent of salts. These 
observations have been applied to the determination of molecular 
weights. 



2OO Heat for Engineers. 



CHAPTER X. 

PRACTICAL APPLICATIONS OF FUSION AND ALLIED PHENOMENA. 

Welding. Two pieces of iron may be made to unite perfectly 
by the operation known as welding. The surfaces to be united are 
raised to the fusion point, and placed together, a little sand or 
borax having first been thrown on each to form a flux with any 
oxide that may have formed. The adhering surfaces are then well 
hammered, and the iron remains in a pasty condition for a sufficient 
time to allow the two metallic surfaces to be thoroughly incorporated 
with each other. A good welded joint should be as strong as any 
other part of the pieces joined. The ends of the separate links of 
iron chains are joined together by welding, and the operation is a 
very common one in the work of a blacksmith. The welding of 
steel may also be accomplished, but demands greater care and a 
more exact judgment of the correct temperature. Only those metals 
can be welded which remain in the pasty state for a considerable 
time a property possessed by iron, steel and platinum. Others, 
such as copper, solidify too abruptly for the process to succeed. 

Soldering. The common method of uniting two metallic surfaces 
by the aid of a metal or alloy, known as soldering, is usually carried 
out by the use of an alloy of lead and tin, called " solder." Coarse 
solder contains 2 parts by weight of lead to i part of tin, and flows 
at 240 C. ; common solder consists of equal parts of lead and tin, 
melting at 200 C. ; whilst fine solder is composed of 2 of tin to i of 
lead, and fuses at 180 C. These alloys possess a lower melting- 
point than the metals they are used to unite, and if the surfaces be 
clean, and sufficiently hot, the alloy adheres to both, forming a 
perfect joint. For cleaning the surfaces, zinc chloride or " killed 
spirit" is used for ordinary work; and resin for electrical work, 
such as joining cables and wires. In making a large " wiped" joint, 
as on water pipes, a large mass of solder is placed on the joint, and 
heated to its melting-point. It remains plastic for a sufficient time 
to enable the plumber to work it into any desired shape by means of 
a piece of leather held in the hand. 



A utomatic Water -Sprinklers. 



201 



Automatic Water- Sprinklers. The production of alloys which 
melt at low temperatures is utilised in the construction of automatic 
water-sprinklers, in which a water supply is held in check by means 
of a fusible alloy. When the temperature rises to a dangerous point, 
owing to an outbreak of fire, the fusible alloy melts, and allows 
water to be sprinkled into the room ; thus enabling a fire to be 
extinguished in the early stages. These appliances are now exten- 
sively used in cotton mills, cabinet-making factories, and other places 
where inflammable materials are kept, and have undoubtedly been 
successful in preventing many serious fires. Many forms of water 
sprinklers are in use, and several typical examples will now be 
described. 

A B 





FIG. 55. GRINNELL'S SPRINKLER : A, CLOSED ; B, OPEN, 



Grinnell's sprinkler (Fig. 55) consists of a pipe P, connected to 
the watei supply, and closed at the lower end by the valve V, which 
rests on the splash-plate D. The valve is kept closed by the levers 
L L, of which the lower one is fastened to the yoke K, by means cf 
fusible alloy at S. When the surrounding temperature rises to the 
melting-point of the alloy, the levers give way, and the pressure of 
the water opens the valve. The splash-plate D falls to a lower 
position, and its serrated edge causes water falling upon it to be 
scattered in all directions. The illustration shows the sprinkler 
before and after the melting . of the alloy. A more recent form of 
Grinnell sprinkler is shown in Fig. 56, the valve in this case con- 



2O2 



Heat for Engineers. 



sisting of a hemisphere of glass V, on the convexity of which is placed 
a covering of Babbitt metal. A flexible diaphragm is pressed against 
V by the water pressure in P, and a water-tight joint is thus secured. 
The valve is held in position by the strut 
S, formed of several pieces of metal sol- 
dered together with fusible alloy, and 
resting on the yoke K, which also carries 
the splash-plate D. This arrangement is 
simpler than the earlier form, and easier 
to restore after having been in operation. 
In Wai worth's sprinkler, Fig. 57, the 
soldered part consists of a link only, and 
not only is such an arrangement prompt 
in action, but restoring after use involves 
the minimum of labour. The splash-plate 
D is stationary, and the valve V is pressed 
firmly against its seat by means of the lever 
FIG. 56. GRINNELL'S A > which causes the eccentric C to turn 
SPRINKLER (Later form.) and raise the valve. The lever A is held 
in position by a link L, made of fusible 

alloy. When the link gives way, the water-pressure forces the valve 
downwards, causing A to fall. At its lowest position the upper surface 





FIG. 57. WALWORTH'S SPRINKLER. 



of the valve V is level with the deflector D, of which it now forms a 
part. The pipe P, as usual, is connected to the water-supply. The 



Automatic Water-Sprinklers. 



20 



illustration gives a front view of the sprinkler with the valve closed, 
and a side view showing the position of the parts when the link has 
given way. 

The "Morris" sprinkler, Fig. 58, is one of the latest forms, and 
combines simplicity of construction and replacement with a very 
sensitive action. The valve consists of a hollow cap A, in the 
interior of which is placed a thin disc of phosphor-bronze, resting on 
soft metal. The joint is made by pressing this disc against the enc 
of the pipe P, by means of the screw S, which acts through the levers 
L L. These levers are held in position by the brass strip B, which 
is made of two pieces, corrugated and soldered together with fusible 




FIG. 58. THE "MORRIS" SPRINKLER. 



alloy, a greater strength being attained than if the surfaces were flat. 
The levers are independent of each other, save for a bearing surface 
at the point of contact, made by grooving one lever and making a 
knife-edge on the other. When the fusible solder melts, the two 
portions of the link B separate, and the water-pressure pushes th-i 
the groove of the upper lever over the knife-edge of the lower. The 
levers and valve then fall to the ground, and nothing intervenes 
between the water-supply and the splash-plate. By having the 
soldered surface at the end of the levers, away from the body of the 
sprinkler, a more rapid action is secured than occurs when the solder 
is on the yoke itself, as in the latter case a larger mass of metal must 
be heated up before the solder melts. After being in action, it is easy 



204 Heat for Engineers. 

to replace the parts, a number of spare links being kept for this 
purpose. 

Water-sprinklers in general are 3 or 4 inches long, with other 
dimensions in proportion. It is customary to place them near the 
ceiling of the room, a short distance apart, so that all come into 
operation simultaneously and distribute water over the whole room 
and also on to the ceiling. In some of the earlier forms the water 
was distributed through a rose, but it was found that the holes fre- 
quently became choked with dust, thus greatly impairing the efficiency 
of the sprinkler. The full discharge of the supply on the splash-plate 
overcomes this difficulty completely, and is the plan adopted in all 
modern forms. Another early trouble was the sticking of the valve 
due to lead being used to make the contact with the seating at the 
end of the brass supply pipe, as after a time the lead and brass 
adhered so firmly that the water pressure was insufficient to cause 
separation, with the result that the sprinkler failed to act. This 
defect was remedied by the use of Babbitt metal instead of lead : and 
the more recent plan of making both bearing surfaces of bronze, as 
in the Morris sprinkler, is better still. 

An automatic alarm is generally arranged in conjunction with an 
installation of sprinklers. When the water in the pipes commences 
to flow, a bell mechanism is set in motion by the turning of a hinged 
valve placed in the pipes, or by some similar means ; so that the 
existence of the fire is immediately notified. 

The alloy generally used for sprinklers is composed of bismuth, 
4 parts (by weight) ; lead, 2 parts ; tin, i part ; and cadmium, i part. 

It melts at 150 F., or 65 C., which is well above the limits of 
atmospheric temperatures, but considerably below the boiling-point 
of water, and consequently a sprinkler will come into action before a 
fire has made much progress. The alloy has poor mechanical pro- 
perties, and when used in the mass tends gradually to flow under 
pressure. It is difficult to use as a solder, and considerable skill is 
necessary to fasten two pieces of brass together securely by its aid. 
As the fusible solder is the vital part of the sprinkler, the soldering 
operation must be conducted with great care if a successful result is 
to be obtained. 

Other Uses of Fusible Alloys.- Fusible alloys have been employed 
in the construction of automatic fire-proof doors and screens, which 
are held back by brass links soldered together with fusible alloy, which 
on melting, allows a spring or suitable mechanism to close the door 
or screen. Fusible alloys are also used for sealing joints in cases 
where a high temperature cannot be employed with safety ; and for 



Fusible Plugs. Fitrnace Linings. 205 

obtaining moulds of plaster or clay models in certain electrotyping 
processes, for which the expansion on solidification, due to the bis- 
muth present, renders these alloys suitable. In all cases where it is 
desired to take a metal mould at a low temperature, fusible alloys are 
used. 

Fusible Safety-Plugs. When, from any cause, the water in a boiler 
runs too low, there is a danger of the upper part of the furnace becoming 
red-hot, and yielding to the internal pressure. In order to give warning 
that the water is too low, a fusible plug is fastened into the crown of 
the furnace, which melts when the temperature rises to a dangerous 
point, and causes steam to escape into the furnace. These plugs are 
made by filling holes made in a hollow piece of brass threaded so 
as to screw into the crown of the furnace with lead or suitable alloy. 
So long as the upper surface of the plug is covered with water, the 
lead will not melt ; but when the water level is below the crown of 
the furnace, the lead fuses, and the escaping steam gives warning of 
the danger. The choking of the water-gauge may lead the attendant 
to believe that the water-supply in the boiler is sufficient, and a 
serious accident might happen in the absence of a safety-plug to indi- 
cate the danger. A temperature of 327 C., which is the melting- 
point of lead, cannot be exceeded without warning being obtained. 
It may be added that the upper side of the plug must be kept free 
from scale, which would prevent the heat of the furnace passing freely 
from the lower side to the water, and thus cause premature melting, 
Uses of Substances of High Melting- Points. Furnace Linings. 
When metallurgical or other operations are conducted at high tem- 
peratures, it is necessary to provide an enclosure which will not melt 
at the temperature employed. Furnaces are therefore built of sub- 
stances which possess high melting-points, and which are termed 
" refractory " materials. Carbon, which has the highest melting-point 
of any known substance, cannot be generally used on account of its 
tendency to oxidation ; in the forms of graphite and gas carbon, 
however, it is used in some forms of electric furnace. These varieties 
of carbon oxidise slowly, and, mixed with silica and other materials,, 
are used in the manufacture of crucibles for containing molten metis- 
at very high temperatures. Two chief varieties of linings are used 
in steel furnaces, the " acid " lining, consisting mainly of silica, and 
used in the absence of phosphorus; and the "basic" lining, made 
from dolomite or magnesian limestone, which combines with any 
phosphorus present in the metal, and hence is used to remove this 
constituent. Magnesite (magnesium carbonate) is now largely used 
instead of dolomite, owing to its greater durability. Fire-bricks for 



206 Heat for Engineers. 

temperatures lower than that of the steel furnace are made from 
special clays, and in composition are silicates of alumina. The actual 
melting-points of these materials are not accurately known : that of 
silica, as used for the " acid " lining, is probably about 2000 C., whilst 
that of dolomite is equally high. Magnesite, when calcined, gives off 
carbon dioxide, and the resulting magnesia is not completely fluid 
even in the electric furnace, in which the temperature exceeds 3000 C. 
The most refractory fireclays melt below 2000 C., the investigations 
of Seger showing that the clay in which the alumina and silica are 
present in the proportions of (iA! 2 O 3 , iSiO 2 ) has the highest melting 
point, viz., 1890 C. 

The necessity of refractory materials possessing much higher 
melting-points than silica or fireclay, for use in electric furnaces, 
has largely been met by electric furnace products. When sand 
and coke are heated together in an electric furnace, combination 
occurs, with the production of compounds of the two ingredients, 
varying with the temperature and proportions of the materials. At 
about 3300 C. the sand and coke form a crystalline compound known 
as carborundum, which chemically is silicon carbide, SiC, and is 
practically infusible even in the electric furnace. At 2500 C., when 
an excess of sand is used, a body of composition SiCO is obtained, 
which has been called " siloxicon," and which may be used in a 
reducing atmosphere up to 3000 C. without decomposition. On 
breaking up at this temperature, oxygen is given off, and carborun- 
dum formed. Both these materials are now largely used as furnace 
linings ; but being comparatively good conductors of heat it is pre- 
ferable to use them as coatings on fire-bricks rather than in the mass. 
By the use of such a coating the life of an ordinary furnace lining is 
greatly increased, as these compounds are unaffected by most of the 
substances which unite chemically with ordinary refractory materials, 
and so destroy the lining. The use of carborundum and siloxicon, 
therefore, is not restricted to the electric furnace, to which, however, 
they are well suited, owing to being practically infusible. An excellent 
lining for electric furnaces is also made from magnesite, which is 
calcined by passing the material gradually through an electric arc. 
The product, known as " electrically shrunk " magnesite, forms a solid 
block from which furnace linings may be made, and, if pure magnesite 
be used, does not melt at the temperature of the electric furnace or 
that attained by " thermit " compounds. 

Utilisation of Latent Heat of Fusion for Heating Purposes. Rail- 
way " Foot- Warmers" It has previously been pointed out that the 
latent heat disengaged when a liquid solidifies causes the temperature 



Freezing Mixtures. 207 

to remain at the melting-point for a period of time depending upon 
the quantity of liquid and the rate at which heat is lost by radiation, 
etc. Advantage has been taken of this phenomenon in the construc- 
tion of foot-warmers for use on railways, by filling a flat metal vessel 
with a substance which solidifies at a temperature conveniently warm 
to the feet. Sodium acetate, which sets at about 60 C., has been 
largely used for this purpose by the London and North Western and 
other railways. The solid is melted in the foot-warmers by steam, 
and after placing in the compartment the temperature falls gradually 
until the freezing point of the solid is reached, at which, owing to the 
large amount of substance used, it remains stationary for several 
hours. The quantity of heat disengaged in the cooling is much 
greater than if hot water were used, as in the latter case no latent 
heat is set free. A drawback to the use of these foot-warmers is the 
tendency of the salt to become surfused, when, owing to solidification 
not taking place, the foot-warmer cools sooner than one containing 
hot water. The tendency to surfusion becomes more marked after 
repeated meltings, and to ensure solidification an iron ball is sometimes 
placed in the liquid, which, by rolling about generally causes setting 
to occur. Shaking the foot- warmer, as many travellers are aware, 
often causes the temperature to rise, as any form of agitation tends to 
bring about solidification. The success of these appliances has been 
greatly discounted by the uncertainty of the setting, and consequent 
loss of efficiency. 

Utilisation of Latent Heat of Fiisioii for Cooling Purposes. 
Freezing Mixtures. When a solid liquefies, heat is absorbed; and if 
the process of liquefaction be conducted without external heat being 
applied to the solid, the heat necessary for the change of state is 
extracted from the solid itself, and a fall of temperature results. Thus 
a solid may be caused to liquefy by the addition of another substance, 
in which case the latent heat of fusion will be extracted from the 
mixture ; and if a lowering of temperature occur, the ingredients form 
what is known as a " freezing mixture." 

A simple example is furnished by the solution of sal ammoniac in 
cold water, by means of which a temperature of - 10 C. may b^ 
attained. The molecules of the solid on dissolving, possess a greater 
amount of kinetic energy, obtained by extracting heat from the 
solution hence the fall of temperature. There is, however, a 
secondary influence which must be taken into account, namely, the 
possibility of chemical action taking place between the two substances 
and the consequent evolution of heat. This is exemplified when 
caustic soda or potash or anhydrous sodium carbonate are dissolved 



208 



Heat for Engineers. 



in water, as a rise of temperature is then noticed. Generally speak- 
ing, therefore, the heat disturbance occasioned when a solid dissolves 
is the sum of two factors ; one, the latent heat absorbed owing to 
change of state, which tends to lower the temperature ; and the other 
the heat evolved owing to chemical action, which tends to raise the 
temperature. In freezing mixtures the latent heat absorbed exceeds 
the heat due to chemical action, and the temperature falls ; whilst the 
converse holds true in other cases, and " heating mixtures " result. 
In a few instances the two effects are practically balanced, and the 
temperature therefore does not alter. The heat change may be 
expressed as follows. 

Solution of a solid causes : 



/Heat of chemical\ 1 /Absorption of latent 
( action ( + ) ; ana V heat(-) 



If A be greater than B the temperature will rise ; if B exceed A 
the temperature will fall. 

These considerations explain why only a comparatively few solids 
are capable of forming freezing mixtures. A table of freezing 
mixtures is appended, showing in each case the lowering of tempera- 
ture observed; in the cases in which ice is used, the ingredients are 
all supposed to be at o C. before mixing ; in all other instances the 
starting temperature is taken as 10 C. 



TABLE OF FREEZING MIXTURES. 



Composition, by Weight 


Reduction of Temperature 


Degrees C. 


Degrees F. 


Ammonium nitrate . . . I 1 
Water I / 


2 5'5 


4 6 


Sodium nitrate . . . . 3 ) 
Dilute nitric acid . . . 2 / 


*9'4 


53 


Sal-ammoniac . . . . 5 j 
Saltpetre . . . . . 5 \ 
Water 16 | 


22'2 


40 


Sodium phosphate . . . 9 "1 
Dilute nitric acid . . 4 J 


34-4 


62 



Freezing Mix hires. 

TABLE OF FREEZING MIXTURES continued. 



209 



Composition by Weight 


Reduction of Temperature 


Degrees C. 


Degrees F. 


Sodium sulphate 
Hydrochloric acid 


9 8 1 ^ 


50 


Snow or pounded ice . 
Common salt 


1} 


39-6 


Snow or pounded ice . 
Common salt .... 
Ammonium nitrate 


12 I 
5J 3-7 


57 


Snow ..... 
Calcium chloride (crystals) . 


3 ) 


82 


Snow ..... 
Dilute sulphuric acid . 


I } 30-6 


55 


Snow or pounded ice . 
Common salt .... 
Sal-ammoniac .... 


24-4 
i ) 


44 



Of all the above mixtures, ice and salt is the cheapest, and 
although this mixture does not yield the lowest temperature, the 
quantity of heat absorbed is greater than in the case of equal weights 
of other mixtures not containing ice. This arises from the superior 
latent heat of fusion of ice, and it should be clearly understood that 
the actual temperature obtained is no criterion of the quantity of heat 
absorbed. Guthrie's investigations have shown that a definite limit 
of low temperature is reached in freezing mixtures, which corresponds 
to the melting-point of a compound formed in the solution. Ice and 
salt, for example, when mixed, yield a solution of salt in water, in 
which a definite compound of the two exists. This compound freezes 
at - 22 C., and if actual freezing took place, the act would be accom- 
panied by the disengagement of latent heat, which would tend to raise 
the temperature. In practice, therefore, the temperature cannot fah 
lower than - 22 C., which represents the lowest limit obtainable with 
.a mixture of ice and salt. The compound formed when ice and 
calcium chloride crystals mutually liquefy freezes at - 45 5 C., which 
therefore represents the limit for this mixture ; and similarly other 
mixtures have a limit represented by the freezing-point of a compound 
produced in the solution. Hence the actual temperature obtained 
is not a measure of the quantity of heat absorbed; and ice and salt, 

p 



2io Heat for Engineers. 

for example, occasion a much greater absorption of heat than phos- 
phate of soda and nitric acid, although the latter mixture yields the 
lower temperature. 

Freezing mixtures are largely employed in the making of iced 
confections, and in minor cooling operations, ice and salt being used 
for these purposes on the grounds of cheapness and efficiency. When 
a specially low temperature is desired, a mixture of ice and crystallised 
calcium chloride is used. Before the introduction of economic 
refrigerating machines attempts were made to produce artificial ice on 
the large scale by the use of freezing mixtures. The general pro- 
cedure was to dissolve a suitable salt in water nitrate of ammonium 
for example and to pump the cold solution through a series of pipes 
surrounded by the water to be frozen. The pipes were continued into 
a second vessel, containing water intended to dissolve the ammonium 
nitrate, which was thus cooled before use. Finally, the solution was 
conducted into an evaporating tank, and the salt recovered and used 
over again. Such a process is continuous, and capable of producing 
a good supply of ice ; but as the cost of production is greater than 
when a modern refrigerating machine is used, the method is no longer 
employed. 



21 I 



CHAPTER XT. 

VAPOURS. 

Molecular Changes in Liquids due to Heat. As a general rule, a 
liquid on heating becomes more mobile, that is, flows more freely. 
Hence hot liquids pass more readily through the pores of filter-paper, 
or through a fine orifice, than when cold. This increase of mobility 
is in all probability due to the increased freedom oi motion of the 
individual molecules, which show a diminished tendency to adhere 
when the temperature is raised. 

In certain cases a rise of temperature induces molecular rearrange- 
ment, and thereby causes considerable alterations in the properties 
of the liquid. A notable instance of such changes is furnished by 
sulphur, which at 115 C. forms a clear, amber-coloured liquid, which 
flows readily. On raising the temperature the colour darkens, and 
the liquid becomes less mobile, until at 230 C. the mass is almost 
black, and so viscous that it cannot be poured out of a vessel. A 
further increase of temperature largely restores the mobility, and at 
the boiling-point 444*5 C. the liquid flows with a fair amount of 
freedom, but still remains black. If cooled, the same changes are 
observed in the converse order ; the progressive alteration in physical 
properties being in each case due to molecular rearrangement. 
The great difference in properties of metals and alloys cast at different 
temperatures may be in part due to the suppression of molecular 
changes by sudden cooling in the mould, which changes would take 
place on slower cooling. The solidifying of albumen (white of egg) 
on heating is a further example of molecular change induced by heat 
which in this case is permanent in character. 

Change of State from Liquid to Vapour. At all temperatures 
an unconfined liquid passes into vapour at its surface. Thus a vessel 
of water, if exposed in dry weather, evaporates completely if left for 
a sufficient length of time. Other liquids, such as petrol, ether, and 
alcohol evaporate very rapidly when exposed, and hence are called 
" volatile " liquids. Even in the case of mercury, the process of 
passing into vapour at ordinary temperatures, although extremely 

P 2 



2 1 2 Heat for Engineers. 

slow, may be detected. As the temperature is raised, the rate of 
evaporation increases, and an increase is also observed when the 
pressure on the surface of the liquid is diminished. 

If the liquid be confined, as in a stoppered bottle, a certain 
quantity will become vapour and enter the space above the liquid. 
The molecules of vapour present in the space will exert a pressure 
on the surface of the remaining liquid in the same way that the 
molecules of a gas exert pressure ; and when the pressure due to the 
vapour attains a certain value, which for a given liquid at a given 
temperature is constant, evaporation ceases, or is balanced by an 
equal amount of condensation. In a closed space, therefore, only a 
limited amount of vapour can be held at a given temperature, and 
when this limit has been reached the space is said to be " saturated," 
and the vapour present in the space is called a " saturated " vapour. 
If a less quantity than the maximum be present, the space is referred 
to as " unsaturated," and the vapour itself is also termed an " unsatu- 
rated " vapour. As examples, the space above ,a liquid in a partly- 
filled bottle is saturated with the vapour of the liquid in the bottle ; 
whilst the atmosphere is usually unsaturated with respect to water 
vapour, being capable of holding further quantities, as witnessed by 
the evaporation of an exposed surface of water. As will be seen 
later, the properties of saturated and unsaturated vapours differ con- 
siderably, and it is therefore necessary, in describing the properties 
of vapours, to take the condition with respect to saturation or other- 
wise into account. 

Pressure of Saturated Vapours. The pressure exerted by a 
vapour in contact with its liquid which is, therefore, a saturated 
vapour increases as the temperature rises. The increase in pres- 
sure, however, is not uniform ; being comparatively small at low 
temperatures, and large at higher temperatures. When a point is 
reached at which the pressure of the vapour is equal to that exerted 
on the surface of the liquid by its surroundings, the liquid gives 
rise to vapour not only on its surface, but throughout its mass, and 
is then said to boil. Thus if water in an open vessel be heated 
when the atmospheric pressure is 760 mm., or 14*7 Ib. per square 
inch, it will boil when the pressure exerted by the escaping vapour 
is also 760 mm., or 14*7 Ib. per square inch. The temperature at 
which this occurs is iooC., which is called the boiling-point of 
water under normal atmospheric pressure. In general, therefore, 
the boiling point of a liquid may be defined as the temperature at 
which the pressure of its saturated vapour is equal to the surround- 
ing pressure-, and consequently any reduction of the latter will 



Vapours. 



21 



lower the boiling-point, whilst an increase will cause a ri<e in 
boiling-point. 

A knowledge of the extent of the pressure exerted by saturated 
vapours at different temperatures is of great importance, particularly 
in the case of water. Numerical values below i atmosphere may be 



which represents 



obtained by the apparatus illustrated in Fig. 59, 
Dalton's method as modified by the author. The 
barometer tube B, graduated in millimetres, con- 
tains a small quantity of the liquid floating on the 
surface of the mercury, and is surrounded by a 
water-bath which may be heated by passing steam 
through the metal pipe P. The mercury in the 
cistern is brought to the level of the zero mark on 
the barometer tube by means of the siphon S, 
the short limb of which terminates at the mercury 
surface in the cistern, whilst the long limb passes 
beneath the mercury in the bottle C. On blowing 
into the bottle by the tube T, the siphon is filled, 
and on releasing the pressure mercury will siphon 
over from the cistern into the bottle until the end 
of the small limb is just above the mercury in the 
cistern. The siphon is adjusted until the mercury 
level in the cistern, at the commencement of the 
experiment, is brought opposite the zero mark on 
the tube by the action of the siphon. As the 
temperature rises, mercury leaves the barometer 
tube and enters the cistern, thereby raising the 
mercury level above the zero mark ; but on work- 
ing the siphon the surplus mercury passes over into 
the bottle, and the level again falls automatically 

to zero. This arrangement enables the height of 

the mercury in the tube to be read off directly, 

without requiring a correction for alteration of FlG- 59- 

APPARATUS FOR DE- 
level in the cistern. 

The presence of vapour in the otherwise vacu- 
ous space at the top of the barometer tube causes 
the column of mercury to be depressed, and the 
amount of depression is a measure of the pressure exerted by the 
vapour. If no liquid were present, the mercury column would stand 
at the same height as the barometer ; hence the vapour pressure at 
any given temperature is expressed by the difference between the 
height of the barometer and the height of the column of mercury 




TKRMINLNG THE 

VAPOUR PRES- 
SURE OF WAFER 

I5ELOW 100 C. 



214 



Pleat for Engineers. 



in the tube containing the liquid. In performing the experiment, 
therefore, the temperature of the bath is raised, and the height of 
the column of mercury in the tube noted at intervals, care being 
taken to allow the bath to attain a steady temperature, and to adjust 
the mercury level in the cistern, before the readings are taken. Each 
reading, on being deducted from the height of the barometer, gives 

the vapour pressure corre- 
sponding to the temperature 
at which the reading is taken. 
When the temperature rises to 
the boiling-point of the liquid, 
the mercury in the barometer 
tube will be level with the 
surface of the mercury in the 
cistern, as, by definition, the 
pressure of the vapour is then 
equal to the surrounding pres- 
sure, which in this case is i 
atmosphere. In order to ob- 
tain this result and adjoining- 
readings it would be necessary 
to prolong the bath into the 
cistern ; or other methods 
might be adopted. If very 
accurate results are required, 
the height of the column of 
mercury in the tube should be 
read oft' by cathetometer, and 
corrections applied for the ex- 
pansion of the mercury. The 
barometer should also be cor- 
rected for temperature, so that 
the vapour pressures may be 
obtained in terms of a column 
of mercury at o C. 

When the temperature is such that the vapour pressure exceeds 
i atmosphere, the values may be determined by means of the apparatus 
shown in Fig. 60, which represents Marcet's boiler. This is a strong 
steel vessel, in the lower portion of which a quantity of mercury is 
placed, on the surface of which floats the liquid under test. Through 
the top of the vessel a stout glass tube T, open at both ends, is passed 
beneath the mercury surface, and outside the boiler this tube is 




FIG. 60. MARCET'S BOILER. 



Vapours. 2 1 5 

fastened to a scale S. A stuffing-gland is provided at the place where 
the tube enters the boiler, in order to prevent leakage of the vapour, 
and a thermometer A, is also fixed in the top of the boiler by similar 
means. The boiler is also furnished with a tap B, which serves to 
regulate the pressure, and which may be screwed out so as to permit 
of the introduction of the liquid. In performing the experiment, the 
liquid is made to boil by means of a Bunsen burner, the tap beino- 
kept open. After boiling for one or two minutes, so as to ensure that 
all air has been expelled by the vapour, the tap is closed, and on 
continuing the heating the pressure inside the boiler rises, forcing the 
mercury up the tube. When the column of mercury appears in view 
outside the boiler, the flame is adjusted until the height of the column 
is stationary, when the readings on the scale and thermometer are 
taken. The temperature is then allowed to rise, the flame again 
adjusted until the column is stationary, and a second pair of readings 
taken. All heights must be measured from the level of the mercury 
in the boiler, which represents the zero of the scale. The vapour 
pressure at any temperature is then found by adding the height of the 
barometer to that of the mercury column, as the commencing pressure 
before closing the tap is equal to i atmosphere, and at this stage the 
mercury in the boiler and tube stands at the same level. Corrections 
are again necessary for the temperature of the mercury, and also for 
the altering level in the boiler as the mercury rises up the tube. It 
is not easy to make these corrections accurately, but as the increase 
of pressure with temperature is relatively large, the corrections do not 
affect the results to any marked extent, and may be ignored except 
when very accurate results are required. 

In either of the preceding experiments the values obtained are 
independent of the amount of liquid present, so long as some remains 
in the liquid state throughout. The pressure is determined by the 
number of molecules of vapour present in unit space, which is con- 
stant for a given temperature. So long as sufficient liquid is present 
to yield this number, therefore, the same result will be obtained, any 
liquid beyond this amount remaining as surplus. As distinct from 
this, however, the weight of the liquid will tend to lower the mercury 
column in the .barometer tube, and to raise it in the Marcet boiler. 
This may be allowed for when the specific gravity of the liquid is 
known; thus in a barometer tube a column of water 13 '6 mm. long 
would depress the mercury by i mm., whilst a column of alcohol 
(sp. gr. = 0*79) of length 17*2 mm. would also cause a depression 
of i mm. The actual vapour pressure, however, is quite independent 
of the quantity of residual liquid. 



2l6 



Heat for Engineers. 



Saturation Pressure of Water Vapour. As it will frequently be 
found necessary in following chapters to perform calculations involv- 
ing a knowledge of the saturation pressure of water vapour, a table is 
appended giving the values obtained by Regnault between - io c C. 
and + 120 C. Figures for temperatures above 120 C. will be found 
in the special steam tables in Chapter XIII. 

PRESSURE OF AQUEOUS VAPOUR IN MM. OF MERCURY. 



tC. 


mm. 


tC. 


mm. 


tC. 


mm. 


IO 


2 - o8 16 


i3"54 


90 


525-39 


- 9 


2-26 17 


14-42 


95 


633-69 


- 8 


2-46 18 


i5-3 6 


99 


733'2i 


- 7 


2-67 19 


i6'35 


99-1 


735-85 


- 6 


2 ' 89 2O 


I7-39 


99'2 


738-50 


- 5 


3-I3 21 


18-50 


99-3 


741-16 


- 4 


3-39 22 


19-66 


99-4 


743-83 


- 3 


3-66 23 


20-89 


99'5 


746-50 


2 


3-96 24 


22-18 


99-6 


749-18 


I 


4-27 25 


23 '55 


99'7 


75 I-8 7 





4-60 26 


24-99 


99-8 


754-57 


I 


4*94 27 


26-51 


99-9 


757-28 


2 


5-30 28 28-10 


ICO 


760-00 


3 


5-69 29 


29-78 


lOO'I 


762-73 


4 


6-10 30 


3I-55 


100-2 


765-46 


S 


6'53 35 


41-83 


ioo"3 


768-20 


6 


7-00 40 


54-9I 


ioo'4 


77i'95 


7 


7 '49 


45 


7i'39 


100-5 


773-71 


8 


8'02 


5 


91-98 


loo 6 


776-48 


9 


8-57 


55 


117-48 


100-7 


779-26 


IO 


9-17 


60 


148-79 


100-8 


782-04 


ii 


9-79 65 


186-94 


100-9 


784-83 


12 


10-46 


70 


233-08 


IOI 


787-59 


13 


ii'i6 


75 


288-50 


105 


906-41 


I 4 


11*91 


80 


354-62 


1 10 


I075-37 


15 


12 - 7O 


85 


433-00 


120 


1489-6 



A curve, connecting temperature with the corresponding vapour 
pressure, is shown in Fig. 61, from which it may be noticed that up 



Vapours. 



217 



to 40 C. the pressure shows only a small increase with the tempera- 
ture, but afterwards rises rapidly, as indicated by the increasing steep- 
ness of the curve. It should be noted that the vapour pressure does 
not vanish when the water freezes, as ice at o C. gives off sufficient 
vapour to generate a pressure of 4 6 mm. of mercury in a closed space, 



I2OO 

1 100 
























// 


irvnn 






















1 


/ 
























it 




> aou 
"^ o/%n 






















/ 




^ 

3 7QO 




















: 


1 
























I 






o ***' 

(CQA 


















j 


i 






s 

S> 40O 


















// 








o 
f\ -nn 
















/ 


/ 1 

1 








200 














/ 


/ 


/ 








100 












x 


/ 


1 
1 


















i ' 


-^^ 


^-"" 






/A 




B 


_ 





10 26 30 4O 5O 6O 70 8O 9O IOO HO I2O 



FIG. 61. CURVE SHOWING VAPOUR PRESSURE CF WATER 
AT DIFFERENT TEMPERATURES. 

and even at - 10 C. a pressure of 2 mm. is still observed. No 
exact equation to this curve is known, but the portion lying beyond 
80 C. may be approximately represented by Dulong's formula, which 
is as follows : 

P (atmospheres) = 



where t is the temperature in Centigrade degrees. 



2 1 8 Heat for Engineers. 

Pressures calculated from this formula differ by about i\ percent, 
from the observed results at 80 C. and 225 C., whilst the formula is 
correct at 100 C. Between 100 C. and 80 C. the error rises from 
o to ~L\ per cent., and similarly between 100 C. and 225 C. This 
formula may therefore be used to calculate approximately the tem- 
perature in a steam boiler when the pressure is known, or the 
converse. 

Example i. If the absolute pressure in a steam boiler be 12 
atmospheres (172*4 Ib. per square inch), the temperature of the steam 
will be 190 C., since 

12 = ( ) ; and taking logarithms, 
\ 140 / 

log 12 + 5 log 140 = 5 log (40 + /), from which 
log (40 + /) = 2-3619 

and 40 + / = 230 

t = 190 C. 

It must be remembered that absolute pressure = (gauge pressure 
+ i atmosphere). 

Example 2. A temperature of 200 C. in a steam boiler will 
correspond to an absolute pressure of 14*8 atmospheres, or approxi- 
mately 220 Ib. per square inch. The pressure gauge should therefore 
read 13*8 atmospheres, or approximately 205 Ib. per square inch. 

As indicated in the two examples, the readings of a thermometer 
placed in a steam boiler serve as a check on the readings of the 
gauge, when the vapour pressure of water at different temperatures 
is known. 

The boiling-point of water at any given pressure may be obtained 
directly from the table of vapour pressures. Thus if the pressure on 
the surface of water were 433 mm., the water would boil at 85 C., 
as the vapour pressure of water at 85 C. is 433 mm., and boiling- 
point is denned as the temperature at which the vapour pressure 
equals the surrounding pressure. In order to boil water at o C., it 
would therefore be necessary to reduce the pressure on the surface 
of the water to 4*6 mm., which can be done by special means to be 
described later. The rate at which the pressure changes at any 
given temperature may be determined by drawing a tangent to the 
curve at the point which corresponds to the given temperature. Such 
a tangent is drawn in Fig. 61, to show the rate of change at 100 C., 
and on dividing the millimetres represented by the ordinate through 



Vapours. 2 1 9 

100 by the degrees represented by the distance A B, bounded by 
the ordinate through 100 C. and the point of intersection of the 
tangent with the horizontal axis, the change is found to be at the 
rate of 26*8 mm. per degree. This figure has previously been used 
in Chapter VII. in connection with the correction of the boiling-point 
of water for small changes of pressure on either side of the normal 
760 mm. A different value will be obtained at other temperatures, 
as the slope of the curve varies considerably. 

The increase of steam pressure with rise of temperature is 
much greater than that observed with a gas. In order to double the 
pressure of a gas, initially at 100 C. and one atmosphere pressure, it 
will be necessary to raise the temperature to 473 C, whereas in the 
rase of saturated steam at 100 C. the pressure becomes 2 atmospheres 
at 120 C. The reason for this great difference is that in the former 
case the number of molecules is fixed, whilst in the latter instance a 
continuously increasing number of molecules enter the space as the 
temperature rises, and the pressure increases rapidly in consequence. 
On cooling a saturated vapour, the surplus molecules assume the 
liquid state, only sufficient remaining in the space as vapour to furnish 
the pressure corresponding to the existing temperature. 

As might be expected, liquids possessing a higher boiling-point 
than water, such as mercury, glycerine, and strong sulphuric acid, 
exert a less vapour pressure than water at a given temperature ; 
whilst liquids of lower boiling-point, such as alcohol, ether, and petrol, 
give higher values than water. The vapour pressure of mercury at 
ordinary atmospheric temperatures is extremely small hence its 
suitability for barometers and for air-pumps. The limit of vacuum 
obtainable with a pump in which a liquid is used is obviously the 
vapour pressure of the liquid at the working temperature ; thus a 
pump in which water is present cannot possess, at 15 C., a less 
internal pressure than 12-7 mm., or about -J Ib. per square inch. It 
is customary for engineers to speak of the difference between 
i atmosphere and the internal pressure as the " vacuum," and adopt- 
ing this mode of expression the best vacuum obtainable in the 
presence of water at 15 C. is 7 47 '3 mm., or 29*4 inches, when th 
barometer is at the normal height. The use of a heavy oil in an 
air-pump enables a very good vacuum to be obtained, owing to the 
low vapour pressure of the oil ; and by the aid of the Fleuss pump, 
in which the moving parts are oil sealed, the internal pressure of a 
vessel may be lowered below i mm. The highest degree of exhaus- 
tion, however, is obtained by means of the mercury pump, which is 
used in the final stao-es of the removal of air from incandescent 



22O Heat for Engineers. 

electric lamps and vacuum tubes. The vapour pressure of mercury 
at ordinary temperatures is only a minute fraction of i mm., and 
this small pressure exists in the space above the mercury in a baro- 
meter, tending to depress the column. The depression caused, 
however, is so small as to be negligible. 

Pressure of Mixed Gases and Vapours. Daltorfs Laws. Many 
cases arise in which gases and vapours are mixed, e.g. a bottle half- 
filled with a liquid contains in its upper part a mixture of air and the 
vapour of the liquid. With a view to discovering whether the pres- 
sure due to the vapour is modified in any way by the presence of the 
gas, Dalton carried out a series of experiments and arrived at the 
following conclusions, which are known as Dalton's laws : 

1. In any mixture of gases and vapours, each constituent exerts 
its own pressure independently, and the extent of this pressure is the 
same that the vapour would exert if present in an otherwise vacuous 
space. This law does not apply to mixtures in which the constituents 
act chemically upon each other. 

2. The number of molecules of a given vapour which can be 
contained in a given space is the same whether the space contains 
the vapour alone, or other gases or vapours in addition. 

Several important conclusions may be drawn from these laws. It 
is evident, for example, that the total pressure exerted by the mixture 
is the sum of the several individual pressures. If, therefore, one con- 
stituent be removed, the pressure will fall by the amount exerted by 
this constituent, and, assuming Boyle's law to hold for the mixture, 
the volume will be diminished in a like ratio. This conclusion is of 
service in correcting the volume of a gas for the presence of water 
vapour. 

Example. A quantity of gas, collected over water at 15 C, 
occupies a volume of 250 c.c. Find the volume the gas would 
occupy if dry, the barometric pressure in each case being 760*7 mm. 

The total pressure due to the wet gas (760-7 mm.) is made up 
of two factors (a) the pressure due to the gas molecules, and (If) the 
pressure due to the water vapour molecules. At 15 C. water vapour 
exerts a saturation pressure of 12*7 mm., hence the pressure (!ue to 
the gas is (760-7 - 12-7) = 748 mm. If the water vapour could 
be extracted, the pressure of the gas would fall to 748 mm., provided 
the volume remained at 250 c.c. If the dried gas were then com- 
pressed to 760-7 mm., its volume, by Boyle's law, would become 



Storage of Volatile Liquids. 221 

Another conclusion to be drawn from Dalton's laws is that if a 
vapour were liberated in a space whether empty or otherwise the 
pressure would increase by the amount due to the vapour. Hence, 
if a vessel containing ether, for example, be broken in an air-tight 
space, the pressure in the space would be augmented by an amount 
equal to the pressure of ether vapour at the existing temperature, 
provided some of the liquid remained. 

Pressure Exerted by Volatile Liquids luhcn Stored. The safe 
storage of volatile liquids (i.e. liquids of high vapour pressure) is a 
matter of considerable importance, particularly when the vapour is 
inflammable or dangerous, as in the cases of petrol, ether, alcohol and 
chloroform. Not only must the storage vessel be strong enough to 
withstand the enhanced internal pressure occasioned by rise of tem- 
perature, but an additional margin must be allowed for rough usage 
during transport. Neglect of these precautions has led to numerous 
accidents, many of w^hich might have been avoided if the factors 
which give rise to the increase of pressure on heating had been allowed 
for in the construction of proper storage vessels. 

When a barrel or other receptacle is charged with a liquid, a 
space must be left at the end, to allow for the expansion of the liquid, 
before closing. This space, at the moment the bung is inserted, 
contains a mixture of air and the vapour of the liquid, and the pres- 
sure due to this mixture is equal to that of the atmosphere. When 
the temperature rises, the internal pressure rises owing to three causes, 
namely (a) the increased vapour pressure of the liquid, (b) the 
enhanced expansive force of the enclosed air, and (<r) the compression 
of this air due to the expansion of the liquid. The compression of 
the vapour in the space merely causes a portion to condense, without 
altering the pressure due to the vapour. The total rise in pressure is 
therefore determined by these three factors, and with a volatile liquid 
stored with a small expansion space, may be a considerable amount. 

Example. A cylindrical keg is filled at 20 C. with a liquid which 
under normal atmospheric pressure boils at 45 C., and at 20 C. 
exerts a pressure of 380 mm. To find the internal pressure if the 
keg be 105 cm. long, the expansion space 5 cm. long, the pressure 
of the atmosphere at the moment of closing 760 mm., and the coeffi- 
cient of expansion of the liquid o'ooi, when the temperature rises to 
45 C. 

a. The vapour pressure of the liquid at 45 C. (its boiling point), 
will be 760 mm., and as the pressure is 380 mm. at 20 C. (the tem- 
perature of filling) the increase under this head will be (760 - 380) 
= 380 mm. 



222 Heat for Engineers. 

b. The expansive force of the air will be 

780 x l7-3__45 =412-5 mm. at 45 C. 
273 + 20 

an increase of 32*5 mm., as from Dalton's law the pressure due to 
the air in the space at starting is equal to the total pressure less that 
due to the vapour, or (760 - 380) = 380 mm. This pressure, 
according to the gaseous laws, rises in the direct ratio of the absolute 
temperatures. As the pressures of the air and vapour are independent 
each may be considered separately. 

c. As the coefficient of expansion of the liquid is 0*001, a column 
TOO cm. long, when heated through 25 C., will elongate by (100 x 
25 x o'ooi) = 2*5 cm. The space, originally 5 cm. long, will 
therefore be halved, and the pressure of the enclosed air doubled. 
The pressure of the vapour will be unaffected by alterations in the 
space. Hence the pressure of the enclosed air, at 45 C., will be 
(412-5 x 2) = 825 mm. 

Consequently, the total internal pressure will be 760 mm., due to 
the vapour, plus 825 mm. due to the enclosed air, or a total of 1585 
mm., or 2-08 atmospheres. 

It is evident, from the above considerations, that if the space in 
the storage vessel be freed from air, the internal pressure will be 
entirely due to the vapour of the liquid. Should the temperature 
rise above the boiling-point of the liquid, the internal pressure may 
increase to several atmospheres. Calculations of the pressure, as 
shown in the foregoing example, involve a knowledge of several 
constants, and it is better to subject the liquid to an actual test, under 
the same conditions as those existing in the storage vessel, in order 
to determine whether a sufficient margin of sa'fety has been allowed. 
This may be accomplished by means of the apparatus shown in Fig, 
62, devised by the author for this purpose. A glass tube, of narrow 
bore, divided into millimetres, is sealed into a glass vessel of about 
250 c.c. capacity, so that the lower end of the tube is just clear of 
the bottom of the flask. A neck, fitted with a tight stopper which 
may be fastened down, is inserted at the side of the flask. In per- 
forming a test, 100 c.c. of mercury are poured into the flask through 
the neck, by means of a funnel with a fine stem, after which the liquid 
under test is added, and the stopper securely inserted. The space 
left in the flask should bear the same ratio to the volume of the liquid 
under test as will obtain in the barrel; thus if 150 c.c. be the volume 
left after pouring in the mercury, the minimum space allowed, calcu- 
lated from an assumed coefficient of expansion of o ooi and a possible 



Storage of Volatile Liquids, 223 

rise of temperature of 50 C, must be 7-5 c.c. to permit of the 
expansion of the liquid only. If twice this volume be allowed as 
space equivalent to T V part of the length of a cylindrical keg then 
the quantity of liquid poured in will be 135 c.c. Before closing the 




FIG. 62 APPARATUS FOR TESTING THE STORAGE PRESSURE 
OF VOLATILE LIQUIDS. 

neck, the vessel is placed in a water-bath, the temperature of which 
is kept at that which is likely to exist during the filling of the barrels. 
Having attained this temperature the stopper is inserted, and the 
arrangement is then identical with a vessel filled for storage. The 
temperature of the bath is then slowly raised to the highest point to 



224 Heat for Engineers. 

which the liquid will be subject in a hot climate say 60 C. or 
140 F. or to the highest temperature to which it will be liable. As 
the temperature rises, mercury will be forced up the tube, and the 
height of the column, measured from the mercury level in the flask, 
is read, and corrected, if desired, for the weight of the liquid floating 
on the mercury in the flask. The total internal pressure will be 
given by adding the height of the barometer to that of the mercury 
in the tube, and, if necessary, a series of readings may be taken at 
different temperatures. 

It may not be out of place here to utter a caution against using 
large quantities of inflammable liquids for such a test as the foregoing, 
as this procedure has been known to cause loss of life owing to the 
ignition of vapour which has been allowed to escape, or to the bursting 
of the vessel and subsequent explosion of its contents. The results 
obtained with the apparatus described are just as accurate as any 
which might be determined by the use of a larger quantity ; and the 
test may be conducted without danger. 

In storing volatile liquids, therefore, a space must be left in the 
vessel sufficient to permit of the expansion of the liquid, with a liberal 
margin to prevent any air remaining in the barrel from being com- 
pressed to a dangerous point by the expanding liquid. The strength 
of the vessel should be such as to enable it to resist a total internal 
pressure several times as great as the combined air and vapour pres- 
sure ; and great care should be taken that the bungs or stoppers are 
secured so as to remain fixed and not liable to leakage at the highest 
pressures to which the vessel will be subjected. For petrol, kegs or 
drums of mild steel, closed with a screw stopper fitted with a leather 
washer, form a safe and convenient means of storage, capable of 
standing a fair amount of rough usage. It should be remembered 
that the pressure in a small vessel of petrol or other liquid is the same 
per unit area as in a large drum, and this and other dangerous liquids 
should therefore never be stored in weak vessels if subject to high 
atmospheric temperatures. Neglect of this precaution has been the 
cause of most of the fires and accidents which have occurred with 
stored petrol. 

Vapour Pressure of a Liquid in Communication with a Cold Space. 
Waffs Separate Condenser. In all the instances of vapour pressure 
hitherto considered, the liquid and vapour have been assumed to be 
at the same temperature as their surroundings, as also any space 
containing the vapour. If, however, the space into which a liquid 
evaporates be colder than the liquid, the pressure exerted by the 
vapour will be the saturation pressure corresponding to the tempera- 



Vapours. 

turc of the cold space and not to that of the liquid. Thus if the 
barometer tube in Fig. 59 were prolonged above the bath, and 
terminated in a bulb surrounded by ice, the depression of the mercury 
column would only be 4* 6 mm., whatever the temperature of the bath. 
The reason for this is that vapour given off from the liquid in greater 
quantity than that required to saturate the space at o C. will condense 
in the bulb, and hence the pressure is determined by the coldest 
part of the vapour. This is the principle of the " separate condenser " 
introduced by James Watt in the steam-engine. When the steam in 
the cylinder is made to communicate with the condenser the pressure 
falls to that which corresponds to the temperature of the condenser, 
and the same effect is produced as if the steam were cooled in the 
cylinder itself. 

If the cold portion of the space be small in comparison with the 
heated portion, as in the case of the barometer tube in Fig. 59 being 
allowed to protrude just above the surface of the bath, only a slight 
lowering of the vapour pressure due to the higher temperature is 
observed, as condensation does not occur to a sufficient extent to 
reduce the pressure by any considerable amount. The pressure of a 
vapour is determined by the number of vapour molecules in the space, 
more being present at high temperatures than at low ; and unless the 
cool part of the space is capable of condensing these molecules to 
such an extent as to maintain the lower number, the lower pressure 
will not be reached. Thus the pressure-gauge of a steam boiler 
records the pressure of water vapour at the temperature existing in 
the boiler, as the reduction of vapour molecules caused by condensa- 
tion in the gauge is infinitesimal compared with the total number in 
the boiler itself. 

Differences between Gases and Vapours.- If a given space be 
capable of holding i gram of a certain vapour at a given temperature 
and only a portion say T T o of a gram were actually present, the 
properties of the vapour under these circumstances would differ in 
degree only from those of a gas. The vapour would for example 
approximate less closely to a perfect gas than air or hydrogen. On 
diminishing the space to T ^ its former volume, it would now b? 
charged to its maximum capacity with vapour, and the pressure per 
unit area will be ten times as great as previously. So long as the 
vapour remains unsaturated that is, so long as liquefaction does not 
commence, it would approximately obey the gaseous laws ; and the 
further the vapour is removed from saturation, the more closely will 
it approximate in properties to a perfect gas. Inasmuch as a hot 
space is capable of holding more vapour molecules per unit volume 

Q 



226 Heat for Engineers. 

than a cold space, the effect of heating a vapour apart from its liquid 
is to remove it further from the state of saturation, and consequently 
to cause the vapour to obey more closely the gaseous laws. Thus at 
very high temperatures unsaturated water vapour is a true gas ; and 
conversely, at very low temperatures gases such as air or hydrogen 
oehave as vapours. An unsaturated vapour, therefore, may be 
regarded as a gas under conditions such that liquefaction may easily 
be brought about, either by an increase in pressure or reduction of 
temperature. Gases which are fairly easily liquefied, such as sulphur 
dioxide and ammonia, are in reality unsaturated vapours not differing 
greatly in properties from water vapour ; and even air and hydrogen 
under usual atmospheric conditions, merely represent unsaturated 
vapours at a temperature greatly above the liquefying point. Evi- 
dently therefore the state of a gas differs only in degree from that of an 
unsaturated vapour, and the two cannot be regarded as actually distinct. 
When, however, a space becomes saturated that is cannot hold 
more molecules in the condition of vapour an entirely different 
behaviour is shown by the contained vapour. If, for example, a space 
at a given temperature be saturated when it contains i gram of vapour, 
and this amount of vapour is actually present, a reduction of the 
volume will not cause an increase of pressure. On reducing the 
volume by one-half, vapour to the amount of \ gram would condense to 
liquid, leaving the number of vapour molecules per unit volume the 
same as before. On again increasing the volume to its original size 
the liquid previously formed will evaporate, and the pressure remain 
constant owing to this reason. Hence a saturated vapour in no sense 
obeys Boyle's law, as the pressure is independent of the volume ; that 
is, P (at constant temperature) = a constant. A saturated vapour 
really represents the transition state between a gas and its liquid, and 
its properties differ from both. An idea of these differences may be 
obtained by considering a cylinder, fitted with a pressure-gauge, into 
which carbon dioxide is continuously pumped. On commencing, the 
pressure will be observed to rise until a point is reached at which 
liquefaction occurs. At this point the gauge will remain steady, any 
gas pumped in being converted at once into liquid, and therefore 
failing to add to the pressure. When the cylinder is absolutely full of 
liquid, the pressure will again rise, as the incoming gas now tends to 
compress the liquid. Conversely, on opening the valve of a cylinder 
containing liquid carbon dioxide, the pressure remains steady so long 
as any liquid remains; but after all the liquid has evaporated, the 
pressure of the residual gas will fall off according to Boyle's law. 
These observations are shown in graphic form in Fig. 71. 



Vapours. 227 

It may again be emphasized that the condition of saturation is 
determined by the presence of a definite number of molecules per 
cubic centimetre, which at a given temperature cannot be exceeded. 
Reduction of volume therefore causes the surplus molecules above 
this number to settle out as liquid ; and an increase of volume causes 
more liquid to evaporate until the requisite number are present. In 
the absence of the liquid, an increase in volume will reduce the 
number of molecules per cubic centimetre, and the pressure will there- 
fore diminish, and the vapour no longer be saturated. Hence the 
spontaneous maintenance of a constant pressure at a given tempera- 
ture distinguishes a saturated vapour from a gas or unsaturated 
vapour. 

Vapour Density. A knowledge of the vapour density of a sub- 
stance is of great importance in chemistry, as it furnishes a clue to 
the molecular weight. Vapour densities may be determined by 
directly weighing a known volume of the vapour under specified 
conditions of temperature and pressure ; or by measuring the volume 
of air displaced when a known weight of liquid is vaporised in a tube 
containing air, as in Victor Meyer's method. It is customary, for 
chemical purposes, to express the figure as the weight of the vapour 
compared with that of an equal volume of hydrogen under the same 
conditions. Thus by stating that the vapour density of alcohol is 
23, is meant that alcohol vapour is 23 times as heavy as hydrogen 
under the same conditions of temperature and pressure. The density 
of water vapour and steam are frequently referred to liquid water as 
a standard, as is usual for solids and liquids. Compared with water 
at 4 C. as unity, water vapour has a density of * 00080 when at a 
pressure of 760 mm., and a temperature of o C. Hence at normal 
temperature and pressure i litre of water vapour w y eighs 80 gram, 
and is, therefore, lighter than dry air, i litre of which weighs 1*293 
grams under the same conditions. 

''Flash Point" of Inflammable Liquids. All inflammable liquids 
give off vapour, the quantity evolved increasing with the temperature. 
When the quantity of vapour present in air rises to a definite amount, 
the mixture explodes on applying a light ; but if the amount of 
vapour mixed with the air be in less proportion, no explosion occurs. 
The temperature at which the vapour is liberated in sufficient amount 
to form an explosive mixture with air is termed the " flash-point." 
The figure for petroleum is determined by means of the standard 
apparatus designed by Sir F. Abel, and illustrated in Fig. 63. The 
petroleum under test is placed in the closed vessel A, and its tem- 
perature raised by means of the water-bath B. The lid of the vessel 

Q 2 



228 



Heat for Engineers. 



A is furnished with a sliding-piece which carries a small lamp, and 
on drawing out the slide the lamp is tilted so that the flame enters 
the interior of A, when, if sufficient inflammable vapour be present 
in the space, a flash will be observed. In conducting the experiment 
the water-bath is raised to a steady temperature (which exceeds the 
flash-point of the oil under test) and the vessel A then placed in 

position. At frequent intervals 
the slide is withdrawn, until a 
flash is observed ; when the 
temperature recorded on the 
thermometer placed in the 
petroleum is read, and consti- 
tutes the flash-point. Abel's 
apparatus is made to standard 
size, and to secure uniformity 
of results must be worked under 
prescribed conditions as to the 
starting temperature of the 
bath, the interval between 
each withdrawal of the slide, 
and the size of the flame of 
the lamp. These instructions 
are furnished with the appar- 
atus. Burning-oil for use in 
Britain must not flash at a 
lower temperature than 73 F.; 
in other countries a minimum 
of 1 00 F. or more is pre- 
scribed. It would evidently 
be dangerous to have a naked 
flame in the vicinity of oil 
stored at a temperature equal to or exceeding the flash-point. 

The above method of determining the flash-point is known as the 
" close " test, as the vessel is shut during the intervals between each 
application of the flame. The " open " test is frequently adopted 
for lubricating oils which possess high flash-points, In this test the 
oil is heated in an open vessel by a small flame, and a lighted taper, 
or small gas-jet, brought near the surface at frequent intervals until 
a flash is observed. A thermometer placed in the oil registers the 
temperature, and is read when the flash is obtained. To secure a 
sharply-defined result, the rise of temperature near the flash-point 
should be conducted slowly. 




FIG. 63. ABEL'S FLASH-POINT 
APPARATUS (Close test). 



22Q 



CHAPTER XII. 

EBULLITION. 



Determination of the Boiling-Point of Liquids. The boiling-point 
of a liquid has previously been defined as the temperature at which 
the pressure of its vapour is equal to the pressure on its surface. 
The value, therefore, will vary according to the pressure, and the 
normal boiling-point is taken 
as the temperature at which 
the vapour pressure is 760 
mm., or one atmosphere. 
The boiling - point under 
existing atmospheric condi- 
tions may be obtained by 
boiling the liquid in a flask 
furnished with a free outlet, 
and placing a thermometer 
in the vapour so that the bulb 
is about i inch above the sur- 
face of the liquid. The value 
at 760 mm. may be found by 
raising or lowering the pres- 
sure to 760 mm. by artificial 
means, or the pressure corre- 
sponding to the given boiling- 
point may be recorded. The 
thermometer should not be 
placed in the liquid if this can 




FIG. 64. ^-DETERMINATION 
OF THE BOILING-POINT OF A LIQUID. 



be. avoided, as unless special 
care be taken this tempera- 
ture may vary considerably, 

whereas that of the vapour is constant for a given pressure if the 
liquid be pure. 

An alternative method, useful for small quantities of liquids, or for 
liquids which are dangerous to boil in a flask, is illustrated in Fig. 64. 



230 Heat for Engineers. 

A glass tube is bent into two parallel branches, the shorter of which 
is closed, and the longer left open to the atmosphere. A small 
quantity of the liquid is introduced into the closed limb, so as to 
occupy the space at the closed end, and the remainder of the tube 
contains mercury up to some point in the open branch, so that the 
level is below that in the closed branch. The tube is now immersed 
in a bath, and the temperature raised until the mercury is level in 
both limbs. The temperature of the bath is then the boiling-point 
of the liquid at existing atmospheric pressure, as the pressure of the 
vapour in the closed limb is then equal to that exerted by the atmo- 
sphere down the open limb. To find the normal boiling-point, it is 
only necessary to take a reading of the temperature of the bath when 
the vapour pressure of the liquid is 760 mm. Thus if the atmospheric 
pressure at the time of the experiment be 750 mm., the heating is 
continued until the mercury in the open limb is 10 mm. above that 
in the closed limb ; when the pressure exerted by the vapour will be 
(750 + 10) = 760 mm. The last stages of the heating should be 
conducted very slowly to ensure an accurate result. 

The following table gives the boiling-points of a number of liquids 
at normal atmospheric pressure : 



Liquid 


Boiling Point in 


Degrees C. 


Degrees F. 


Ordinary Liquids 






Ether 


35 


95 


Carbon disulphide .... 


46-2 


"5 


Chloroform ..... 


61-2 


142 


Alcohol 


77-9 


172-2 


Benzene ...... 


80-4 


176-7 


Water 100 


212 


Turpentine ..... 


159 


318 


Aniline ...... 


184 


363 


Naphthalene (solid to 82 C.) 


220 


428. 


Glycerine ...... 


290 


554 


Olive-oil ...... 


3i5 


599 


Strong sulphuric acid .... 


325 


617 


Mercury ...... 


357 


675 


Sulphur (solid to II4'5C.) 


444-6 


833 



Ebullition. 



231 



Liquid 


Boiling Point in 


Degrees C. 


Degrees F. 


Liquefied Gases 






Sulphur dioxide. .... 


IO 


H 


Ammonia ...... 


- 34 


- 2.J 


Carbon dioxide ..... 


78 108 - 5 


Liquid air ; 


-i9i'5 -3i3 


Oxygen ...... 


-182-5 


-296 


Nitrogen ...... 


-193 


-3I5-5 


Argon ...... 


-i 86 


-303 


Hydrogen ...... 


-252-5 


-422 



A definite boiling-point cannot in most cases be assigned to a 
mixture of liquids, such as go to form petroleum. In such cases, 
if heat be gradually applied, the thermometer will remain fairly steady 
for a time, and a portion of more or less definite composition will 
evaporate ; after which the thermometer rises to some higher tem- 
perature, and again remains nearly steady. Several successive 
readings may thus be obtained, corresponding to the boiling-points 
of the various fractions. The temperature at which the vapour 
pressure of the mixture is equal to 760 mm. can, however, be 
obtained by means of the bent tube method used to determine the 
boiling-points of pure liquids (Fig. 64). Only in rare cases does a 
mixture possess a constant boiling-point. 

Effect of Pressure on the Boiling-Point. The lowering of boiling- 
point caused by reduction of pressure may readily be demonstrated 
by placing a beaker of warm water under the receiver of an air-pump, 
and exhausting the air. When the pressure is reduced to such an 
extent as to be equal to the vapour pressure of the warm water, 
rapid boiling will be observed. The same phenomenon is observed 
in the experiment due to Franklin, in which water is boiled in a 
flask until the air is expelled, and the flask then corked up. On 
cooling the flask by pouring water over it, the steam in the interior 
condenses, and thus lessens the pressure on the contained hot water, 
which then boils vigorously. Hence the seeming paradox of the 
water boiling owing to the cooling of the flask. 

The rise of boiling-point under increased pressure may also be 
simply demonstrated by heating water in a flask furnished with a 
cork, and a bent outlet-tube which dips under a column of mercury. 



232 Heat for Engineers. 

through which the steam must escape. As the length of the mercury 
column is increased, a thermometer in the interior of the flask will 
show a progressive rise of temperature. Similarly, the water in a 
steam boiler increases in temperature as the pressure rises. 

The reduction of boiling-point under diminished pressure is taken 
advantage of in the evaporation of liquids at a low temperature, in 
cases where a temperature equal to the normal boiling-point is 
undesirable. In the manufacture of sugar the solutions are boiled 
in air-tight vessels, known as vacuum-pans, the pressure in the 
interior of which is reduced so that the solution boils at about 70 C., 
exhaust pumps being employed for the purpose. The same process 
is employed in the preparation of many chemical substances which 
would undergo decomposition at the normal boiling-point of the 
mother liquor. The drying of substances at a low temperature can 
be rapidly accomplished in a similar manner. In many cases it is 
desirable to raise the boiling-point for example, in the cooking of 
food at high altitudes, where the pressure is low and the boiling-point 
below the normal in consequence. Foods such as eggs and vege- 
tables cannot be properly cooked unless the temperature borders on 
iooC. ; hence boilers, fitted with an adjustable valve, are used as 
cooking vessels, the valve being arranged to blow off at 100 C. 
Such boilers are known as " digesters," and are also used in the 
conducting of chemical processes in which the desired reaction only 
occurs above the normal boiling-point of the solution used. 

Determination of Altitudes by Observations of the Boiling- Point of 
Water. On ascending into the atmosphere the pressure diminishes, 
and consequently the boiling-point of water will be lowered. The 
barometric pressure at a given elevation may be determined by 
observing accurately the temperature at which water boils, and 
referring to a table of vapour pressures ; for the vapour pressure at 
the boiling-point observed is equal to the surrounding pressure. 
Thus if the water boiled at 95 C., its vapour pressure 633*7 mm - 
of mercury must also represent the atmospheric pressure. The 
height may then be deduced from the tables employed for obtaining 
elevations by the aid of a barometer. When only an approximate 
result is required, it may be assumed that an elevation of 900 feet 
causes a fall of iC. in the boiling-point of water. The apparatus 
employed consists of a boiler furnished with a long, telescopic tube, 
in which a delicate the-mometer may be placed so as to be sur- 
rounded by steam, which escapes at the top of the tube. In order 
to ensure an accurate reading, the thermometer is constructed so 
that the lowest mark on the scale represents 85 C., and the highest 



Ebullition. 233 

105 C., the whole stem thus being covered by a range of 20, and 
consequently capable of fine sub-division. The apparatus is known 
as the hypsometer, or height-measurer, and is obviously more portable 
than the mercury barometer, which it was designed to supersede for 
this purpose. It is, however, much inferior in this respect to the 
aneroid barometer, and its use is now restricted to checking the read- 
ings of the latter type of barometer. 

Effect of Dissolved Solids on the Boiling- Point. The boiling- 
point of a liquid is invariably raised when a solid is dissolved in it, 
and consequently the vapour pressure is lowered. The rise in boiling- 
point is progressive as the amount of dissolved solid present in a 
given volume of liquid is increased, and reaches a maximum when 
saturation occurs. The rise in boiling-point, moreover, bears a 
definite relation to the molecular weight of the dissolved solid. 
Taking 100 c.c. of water as the standard, the rise occasioned by 
i gram-molecule of any salt is approximately 10 C. Thus the 
molecular weight of calcium chloride (CaQ 9 ) is in, and of sodium 
nitrate (NaNO 3 ), 85; and if in grams of calcium chloride and 
85 grams of sodium nitrate each be dissolved in separate 100 c.c. 
of water, the boiling-point of the solution in each case will be 110 C. 
at 760 mm. pressure. With non-electrolytes, such as sugar, the 
molecular rise is only one-half that occasioned by salts, or 5 C. 

In taking the boiling-point of a solution the thermometer bulb 
must be placed in the liquid, as the temperature of the steam is 
intermediate between those of the solution and the pure liquid, owing 
to condensation and evaporation taking place on the thermometer 
bulb. A piece of platinum wire placed in the solution ensures steady 
boiling. 

Normal and Abnormal Boiling. When a vessel containing a liquid 
is heated from below, the layer of liquid nearest the flame becomes 
notter than the rest and rises, colder liquid falling to take its place. 
A circulation is thus set up, and the temperature of the whole mass 
is raised. After a time large bubbles of vapour are observed to form 
in the layer nearest the source of heat, which rise towards the surface, 
but condense before reaching it owing to the lower temperature of 
the upper portions of the liquid. This condensation is accompanied 
by a noise known as " singing," due to the liquid being set into a 
state of vibration by the collapsing of the bubbles. Finally, the 
bubbles of vapour are no longer condensed by the overlying liquid, 
which has now become too hot to effect the condensation ; and con 
sequently the bubbles reach the surface and pass into the space above 
The liquid is then said to boil, or to be in a state of ebullition. 



234 Heat for Engineers. 

If a thermometer be placed in a boiling liquid its readings will be 
practically steady until all the liquid has boiled away. This is owing 
to the fact that the heat energy of the flame is converted into kinetic 
energy in order to bring about the change of state from liquid to 
vapour, and a stationary temperature results as in the case of a melting 
solid. The temperature of the boiling liquid is not quite the same at 
all parts, although, owing to the thorough mixing caused by the vapour 
bubbles, the variation is but slight, the highest temperature being 
recorded nearest the source of heat. Hence one reason why in 
standardising a thermometer the temperature of the steam, and not of 
the water, should be taken. 

Under special conditions, however, the boiling of a liquid may 
take place in a manner very different to the foregoing. Water, for 
example, normally contains a quantity of dissolved gases, which may 
be driven off by prolonged boiling. When all the gases have been 
expelled, the numerous vapour bubbles previously observed cease to 
be evolved, and the temperature rises considerably above the usual 
boiling-point. Ultimately a layer of vapour is suddenly formed over 
the portion of the vessel in contact with the source of heat, and this 
layer of vapour is frequently of sufficient dimensions to lift the over- 
lying liquid bodily, and sometimes to eject it from the vessel. This 
violent boiling is known as " bumping," and is particularly noticeable 
in the case of liquids of an oily character, such as strong sulphuric 
acid, solutions of caustic soda and potash, olive-oil, linseed-oil, and 
heavy oils generally. The explanation of this abnormal boiling is 
that dissolved gases, when present, serve as nuclei round which 
vapour bubbles readily collect, but in the absence of such nuclei the 
formation of vapour is less easily accomplished and only takes place 
at a higher temperature, at which vaporisation occurs simultaneously 
over the hot part of the vessel. Donny, Dufour, and others have 
shown that the temperature of water may be raised to 140 C., and 
even higher, without boiling, although the pressure is kept normal. 

When it is necessary to boil liquids which are specially liable to 
exhibit the phenomenon of bumping, tranquil boiling can generally be 
ensured by bubbling air continuously through the liquid ; or by using 
a ring burner, which heats the upper portions of the liquid and obviates 
the danger of ejection. On the small scale bumping can be prevented 
by introducing a few pieces of clay tobacco pipe stem, or a piece of 
platinum wire into the liquid, the air contained in the pores of the 
former, and the gases occluded by the latter, serving as nuclei round 
which the vapour can collect. On the commercial scale pieces of 
silica firebrick serve the same purpose, but in all cases, when the gases 



Ebullition. 235 

have been expelled, bumping will recur, and fresh deterrent material 
must be added. 

The phenomenon of suspended boiling is analogous to the 
reluctance to melting occasionally shown by solids, and to the surfu- 
sion of liquids. In each case the change of state is retarded unless 
assisted extraneously. 

Spheroidal State. When a drop of water is allowed to fall on a 
very hot metallic surface, it does not spread out into a thin layer, but 
assumes a spheroidal form, and either rolls about or rotates on its axis. 
The globule does not touch the plate, as may be observed with the 
naked eye. Moreover, the temperature of the globule is less than the 
boiling-point of water, which may be proved by placing a small thermo- 
electric junction in the interior, when a temperature as low as 96 C. 
may be observed. The spheroid evaporates away tranquilly, no signs 
of " steaming" being visible, but if the plate be allowed to cool to 
150 C., or thereabouts, the water comes into actual contact with the 
surface and spreads out, the contact being accompanied by a hissing 
noise and the evolution of a cloud of steam. Many other liquids 
behave in a similar manner to water. 

When a piece of red-hot iron is plunged into water, a layer ot 
vapour forms round the metal, which does not actually touch the 
liquid until the temperature has fallen considerably, and a similar 
layer of vapour exists between a globule of liquid and a hot plate. 
No satisfactory explanation of these phenomena has yet been given. 

It has been suggested that boiler explosions may occasionally be 
due to the water entering the spheroidal state in the vicinity of the 
heating surface. If coated with scale internally, it is possible that the 
plates may become very hot on the inner side, being protected from 
contact with the water by the scale, which is a bad conductor of heat. 
The effect of heating is to cause the scale to chip off, and the water, 
being presented to the hot surface, would assume the spheroidal state. 
On the plate cooling sufficiently to permit of actual contact with the 
water, a sudden generation of steam would occur, and the pressure 
might rise to such an extent as to burst the boiler before the steam 
had time to escape through the safety-valve. 



236 Heat for Engineers 



CHAPTER XIII. 

LATENT HEAT OF VAPORISATION. PROPERTIES OF STEAM. 

Latent He.at cf Vaporisation. The change of state from liquid 
to vapour is accompanied by an absorption or disappearance of heat 
energy, which confers on the molecules of the vapour a greater 
kinetic energy than that possessed in the liquid state. One volume 
of water yields nearly 1700 volumes of steam at 1 00 C., and it is 
therefore evident that the molecules of the steam move over much 
longer paths than those of the liquid, the extra energy necessary 
to accomplish this being derived from the source of heat. The 
heat energy thus expended is termed " latent heat of vaporisation," 
and is expressed numerically as the number of heat 2inits required 
to convert unit weight of a liquid into vapour, without change oj 
temperature. An equivalent definition is the number of heat units 
evolved when unit weight of vapour condenses to liqiiid, without 
change of temperature. The figure may be expressed in terms of 
calories per gram ; lb-C. units per pound, or British thermal units 
per pound. 

The latent heat of steam at atmospheric pressure may be deter- 
mined by passing dry steam from a small boiler into a known quan- 
tity of water contained in a calorimeter. The rise in temperature 
is noted, and the weight of steam condensed determined by weighing 
the calorimeter and its contents at the end of the experiment, 
when the increase in weight will represent the condensed steam. 
The method of calculating the result is shown in the following 
example. 

Example. A calorimeter, of water equivalent 19 grams, contains: 
450 grams of water at 15 C. Steam at 100 C. is passed in, and the 
temperature rises to 36 C. The increase in weight of the calori- 
meter and water is 16-4 grams. To find the latent heat of steam at 
100 C. : 

Let L = the latent heat = the number of calories given out when 
i gram of steam at 100 condenses to water at 100. 



Latent Heat of Vaporisation. 237 



Total heat units given out 
by steam 



Heat units gained by water 
and calorimeter 



16*4 x L = calories given out in \ 

condensing to water at 100 (450 + 19) x (36 - 15) =calories 

16*4 x (100 - 36) = calories given I gained by water and calori- 

out by resulting water on cool- meter 

ing from 100 to 36 

Equating, 16-4 L + 16-4 (100 - 36) = 469 (36 - 15). 
From which L == 536*5 calories per gram. 

The chief source of error in the experiment is the presence of 
water particles in the steam, which add to the weight of the latter. 
By passing the steam through an oil bath, kept at 110 C., this error 
can be avoided, and the additional heat liberated may be allowed 
for in the calculation by multiplying the weight of steam by its 
specific heat ('48) and the fall in temperature from that of the 
oil-bath to the temperature of condensation. This quantity would 
be placed on the left-hand side of the equation in the foregoing 
example. 

The latent heat of vaporisation of other liquids may be found in 
the same manner, allowing the vapour to condense in a known weight 
of its own liquid in a calorimeter. The specific heat of the liquid 
must be known in order to obtain the number of heat units given out 
after condensation, and also the heat units gained by the cold liquid. 
The equation would then become : 

(Weight of vapour condensed x L) + (Weight of vapour x sp. 
ht. of liquid x fall in temp.) = (Weight of liquid x sp. ht. x rise in 
temp.) + (Water equiv. x rise in temp.). From this L may be 
obtained by calculation. Or the vapour may be allowed to condense 
in water, if it be certain that no chemical action takes place between 
the vapour and water. A table of latent heats of evaporation of 
different liquids, when evaporating under a pressure of 760 mm., is 
appended (page 238). 

It will be observed that water possesses a higher latent heat of 
vaporisation than any other liquid, and consequently requires more 
heat to be converted into vapour. Conversely, when steam con- 
denses, the amount of heat disengaged is greater, weight for weight, 
than in the case of any other vapour. Hence the superior cooling 
power of evaporating water, and heating power of condensing steam. 
An idea of the amount of energy involved in the change of state may 
be obtained by converting the heat units into work units, when it 



Heat for Engineers. 



will be seen that the evaporation of one pound of water at 100 C. 
absorbs 967 x 778 = 750,000 ft.-lb. (approx.). 





Latent Heat of Vaporisation at 




760 mm. Pressure 


Liquid 






Calories par Gram 


B.Th.U. per Pound 


Ordinary Liquids 






Water 


537 


967 


Alcohol (ethyl) .... 


209 


376 


,, (methyl) .... 


264 


475 


Ether. .... 


9i 


164 


Carbon disulphide 


87 


157 


Mercury ..... 


62 


112 


Turpentine ..... 


74 


133 


Sulphur (solid to 1 14 -5) 


363 


6 54 


Liquefied Gases 






Air 


55 


99 


Carbon dioxide .... 


49 


88 


Ammonia ..... 


295 


53i 


Oxygen ..... 


56 


101 


Hydrogen ..... 


200 


360 



Effect of Temperature of Boiling on Latent Heat. The tem- 
perature at which a liquid boils depends upon the pressure, and it is 
found that the latent heat of vaporisation of liquids is greater when 
boiling occurs at a low temperature (or pressure) than is the case at 
a higher temperature (or pressure). Thus the latent heat of vaporisa- 
tion of water boiling at o C. is 606*5 calories per gram ; at 100 C. 
537 calories per gram ; and at i5oC, 502 calories per gram. A 
falling off in the value of the latent heat is similarly observed with 
all liquids when the boiling-point is raised by increasing the pressure. 
This result might be anticipated, as a rise in temperature signifies 
an increase in the kinetic energy of the molecules, which conse- 
quently require less additional energy to enable them to become 
vapour. 

In the case of steam, Regnault found that up to 230 C. the latent 
heat of vaporisation is closely represented by the equation 

L = 606 '5 - '695 /, 



Latent Heat of Vaporisation. 239 

where / is the temperature at which boiling occurs. If this equation 
held true at all temperatures, L would become zero at 873 C. ; but 
the zero value is actually attained at 365 C., which is the critical 
temperature of water. Hence above 230 C. the value of L must 
diminish at a much greater rate than is indicated by the above 
equation. 

Total Heat of Saturated Vapours. The amount of heat required 
to convert unit weight of liquid at o C. into vapour is termed the 
" total heat" of the vapour. It evidently comprises the heat required 
to raise the liquid from o C. to the boiling temperature, and the 
latent heat absorbed in boiling. Thus to raise i gram of water from 
O D C. to 1 00 C. requires 100 calories; to evaporate it at 100 C. 
requires 537 calories ; hence the total heat of steam at ico C. is 
637 calories. 

The total heat of steam, up to 230 C., was found by Regnault to 
be expressed by the formula 

Q = 606-5 + "305 4 

where / is the temperature at w r hich boiling takes place. But since 
Q is composed of two quantities, viz. latent heat and heat required to 
raise the liquid from o to /, it follows, if C represent the latter 
quantity, that 

L + C = 606-5 + -305 /, 
or 

L = 606-5 + -305 t - C. 

But to raise unit weight of water i C. requires i heat unit, and 
hence a rise of t will require / units ; therefore C = /. Hence the 
equation becomes 

L = 606-5 + *35 t ~ *> 
or, 

L = 606 -5 - -695 t 

which is the formula previously used for the latent heat of steam. 

From the above expression the quantity of heat required to con- 
vert water at any temperature into steam may easily be calculated. 
Thus if the feed-water of a boiler be at a temperature of 15 C., and 
the temperature of the steam produced be 140 C., the total heat at 
the latter temperature will be 648 calories per gram, or lb-C. units 
per pound. But the total heat is measured from oC., and as the 
water commences at 15 C. the actual amount of heat required will 



240 



Heat for Engineeers. 



be (648 - 15) = 633 calories per gram, or lb-C. units per pound. 
Or, in general, the heat required to convert i Ib. of water at a tem- 
perature / into steam = (total heat - temperature of water in C.) 
lb-C. units. 

In expressing the total heat of steam in British thermal units per 
pound, the quantity is frequently reckoned from o F. No useful 
purpose is served by adopting this temperature, at which water would 
exist as ice, and consequently the latent heat of fusion should be 
taken into account, as well as the fact that the specific heat of ice is 
only 0*52. In many tables, however, both these points are ignored, 

PROPERTIES OF SATURATED STEAM. 



Absolute 
Pressure in 
Lb. per Square 
Inch 


Boiling 
Point in 
Degrees C. 


Total Heat 
in Calories 
per Gram or 
Lb-C. 
Units per Lb. 


Total Heat 
inB/lh.U. 
per Lb. 

(from 32 F.) 


Weight of Volume of 
i Cubic Foot i i Lb. in 
in Lb. Cubic Feet 


0-177 


10 


610 


1098 


0-00057 1752 


0-333 


20 


613 


1103 


0*00109 9 2 7 


0'6l2 


30 


616 


noS 


0-00184 544 


I -06 


40 


619 


II 14 


0-0031 3 22 '5 


1-78 


50 


622 


III9 


0-0056 i/S'5 


2-88 


63 


625 


1124 


0*0083 i 20 -5 


4'5o 


70 


628 


1129 


0*0124 So'7 


6-85 


80 


631 


"35 


0-0186 


53'S 


10-18 


90 634 


1140 


0-0268 


37 ' 2 


H'7 


100 


637 


iH5 


0-0380 


26-2 


20 "6 


110 


639 "5o 


0-0525 


19-1 


28-8 


120 


642 


"55 


0*0714 


14-0 


39'<2 


130 


645 


1160 


0-0955 


10-5 


52-5 


140 


648 1165 


0*126 


7'95 


69-1 


ISO 


651 


1170 


0*163 6-14 


89-7 


1 60 


654 


"75 


0-208 


4-81 


114-7 


170 


656 


1180 


0-263 


3 'So 


HS'S 


1 80 


659 


1185 


0-329 


3-20 


182-2 


190 


662 


1190 


0-406 


2-46 


226-2 


2OO 


664 


"95 


0-495 


2 -O2 


276-1 


210 


667 


1 200 


0-575 


i '74 


336-3 


220 


669 i 205 


0-695 


1-44 


404-0 


230 


672 


1210 


0-815 


1-23 



Properties of Steam. 241 

and it is assumed that the water exists as liquid down to o F. 
Such an assumption is misleading, and tables based upon it are 
incorrect, as they do not give the total heat as previously denned. 
An abridged table of the properties of saturated steam is given on 
page 240, in which the total heat is reckoned from o* C., or 32 F., 
and in which other useful constants are also given. 

Superheated Steam. If saturated steam be raised in temperature, 
out of contact with the water from which it is generated, it is said to 
be superheated. In this condition it is really unsaturated, as the 
number of molecules per cubic centimetre is less than the maximum 
at the higher temperature. Superheating may be carried out by pass- 
ing the steam through pipes heated externally, and in engines using 
superheated steam this is effected by allowing the steam pipe to pass 
through the furnace on its way to the cylinder, or through a special 
superheater. A higher working temperature is thus secured without 
causing a corresponding increase in the boiler pressure, and any water 
mixed with the steam is evaporated. The limit of superheating is the 
temperature at which the materials in contact with the steam are 
deleteriously affected. 

Moisture in Steam from Boilers. Saturated steam, as generated 
in a boiler, is seldom free from particles of liquid, which may be 
entangled mechanically as the steam forms, or arise from condensation 
due to a subsequent fall in temperature. The moisture present in 
steam is referred to as " priming water," and may be determined by 
one of the three following methods : 

Method I. Steam from the boiler is passed into a known quantity 
of water, and the rise in temperature and weight of steam condensed 
are noted. If the steam were pure, the heat gained by the water and 
vessel would exactly equal the calculated amount that should be given 
by the known weight of steam ; any deficiency observed is due to 
moisture, and furnishes a clue to the amount present. 

Example. 2 Ib. of steam, at a pressure (absolute) of 114*7 lb. 
per square inch, are passed into 100 lb. of water at 10 C., the water 
equivalent of the vessel being 2 lb. The temperature rises to 22-3. 
To find the percentage of moisture. 

From the table on page 240, the temperature corresponding 10 
a pressure of 114*7 lb. per square inch is 170 C, and the total 
heat at 170, measured from o C., is 656 lb-C. units per pound. 
The latent heat is therefore (656 - 170) - 486 lb-C. units per pound. 
Equating heat lost by steam to heat gained by water and vessel, we 
have 

(2 - x) X 486 + 2 (170 - 22-3) = 102 X (22'3 - TO), 

R 



242 Heat for Engineers. 

where x = weight of water in the steam. This gives the value of x 
to be -0263 Ib. ; or, 

0263 ^oo = ,.3,5 percent . 

2 

No accuracy can be secured by this method unless very large 
quantities are worked with, and a very delicate thermometer used. 
If, in the above example, the final temperature recorded were 22*4, 
or only T V degree higher, the percentage of water calculated would 
be -247, or less than -J of the figure previously obtained. It is 
evident, therefore, that a slight error of observation may cause a great 
discrepancy in the result. 

Method II. The " Throttling" Calorimeter Steven from the 
boiler is allowed to escape from an orifice ^ of an inch in diameter, 
the temperature being observed on each side of the orifice. After 
escaping, the steam expands to atmospheric pressure, and is no longer 
saturated ; any moisture present is therefore evaporated. The greater 
the amount evaporated, the lower will be the reading on the thermo- 
meter placed on the low-pressure side of the disc. The thermometer 
on the high-pressure side serves to record the temperature of the 
steam before expanding; and the amount of moisture present maybe 
deduced from the combined readings of the two thermometers. As 
no heat is supposed to be lost owing to extraneous causes, such as 
radiation, it may be assumed that the total heat of the mixture of 
steam and water is the same before and after escaping. The total 
heat of the escaping steam will be 

(Total heat at atmospheric pressure, or at 100 C., + heat 

given out on steam cooling to 100 C.) 
or 

637 + -48 (/ - 100) calories per gram 

where / is the reading of the low-pressure thermometer, and 48 the 
specific heat of steam. The total heat of the steam and water before 
escaping will be H - x L, where H = total heat of dry steam at the 
boiler temperature, x = weight of water present in i gram, and L = 
latent heat of steam at boiler temperature ; both heat quantities being 
expressed in calories per gram. Equating, 

H - #L = 637 + -48 (/ - roo) 

and x = H-6 37 - -48 (/ - 100) 
L 



Properties of Steam. 243 

Example. To find the percentage of moisture when the tempera- 
ture before throttling is i8oC., and after throttling 126 C. From 
the table the total heat of steam at 180 C., is 659, and the latent 
heat (659 - 1 80) = 479 calories per gram. Inserting in the above 
expression, x = '02, or 2 per cent. 

This method is much more reliable than (I.) as a small error of 
observation in the temperature makes only a little difference in the 
result. To obtain a fair estimate of the percentage of moisture the 
steam should be passed for several minutes, and the average tern j era- 
tures taken over the whole period. 

Method III. The " Separating" Calorimeter. In this method the 
particles of water are separated mechanically from the steam, and the 
quantity of moisture obtained by direct measurement. The apparatus 
used consists of a double cylinder, the inner of which is furnished 
with a perforated cup, fitted with small baffle-plates at its upper end, 
and connected at its lower end with a gauge-glass placed outside 
the apparatus, by means of which the height of the water in the 
interior may be observed. The outer cylinder is furnished with an 
inlet at the upper end, which delivers steam into the bottom of the 
perforated cup, and an outlet at the lower end ; a pressure-gauge is 
also fitted, graduated so as to read pressures and quantities. On 
admitting steam to the apparatus, any moisture present settles on the 
sides and baffle-plates of the perforated cup, and trickles down to the 
bottom of the inner cylinder. The dried steam rises vertically from 
the cup and passes round the inner cylinder, finally escaping at the 
outlet. The inner vessel and gauge-glass are calibrated so that a 
scale, placed behind the glass, reads the weight of water, in pounds, 
corresponding to given levels, and hence the weight condensed in a 
given experiment may be read off directly. The pressure-gauge is 
graduated by allowing steam at a known pressure to flow through for 
a given time, the escaping steam being condensed and weighed. As 
the amount of steam escaping through an orifice is proportional to 
its absolute pressure (provided the opposing pressure does not exceed 
6 of the steam pressure, according to Napier's law), one good reading 
will suffice to graduate the whole gauge. Thus if the absolute pressure 
(= gauge pressure +14*7 lb, per sq. in.) be 95 Ib. per sq. in., and 
4-5 lb. of steam are condensed in 20 minutes, the mark on the gauge 
corresponding to (95 - 14*7) = 80*3 lb. may be marked -225, 
meaning '225 lb. per minute, or 4-5 lb. in 20 minutes. An absolute 
pressure of 190 lb. per sq. in., or 175*3 on the gauge, would give a 
flow of 9 lb. in 20 minutes, and this point on the gauge would be 
marked "45 lb. per minute ; and similarly over the whole scale. 

R 2 



244 Heat for Engineers. 

Hence the steam passing in a given time may be read off by multi- 
plying the reading on the gauge by the time in minutes. 

Example, On passing steam through the calorimeter for 25 
minutes, '15 Ib. of water was collected in the inner vessel, whilst the 
pressure-gauge indicated that 5-45 Ib. of steam had passed through 
the orifice during the test. The total weight of the wet steam was 
(5*45 + ' T 5) = 5 '6 Ib., and the percentage of moisture 

I 1 - 5 x 100 =3-68. 
5'6 

In all cases where the sample of steam is taken from a pipe, 
instead of from the boiler directly, a vertical pipe should be chosen 
when possible, and the take-off tube inserted so as to terminate in the 
centre of the pipe. A sample drawn from a spot near the wall, 
especially in the case of a horizontal pipe, would give too high a 
result, owing to the greater condensation which takes place on and 
close to the wall of the pipe. 

Dryness Fraction. The condition of steam with respect to the 
moisture present is frequently expressed in the form of a " dryness 
fraction." This fraction for dry steam would be i ; for steam con- 
taining 2 per cent, of moisture 98 ; and so on. 

Use of Steam for Heating Purposes. Buildings are sometimes 
heated by means of steam pipes, connected with a suitable boiler 
and furnished with cocks from which the condensed water may be 
drawn off. This method is economical if waste steam be utilised for 
the purpose, but hot-water circulation is generally preferred to the 
special generation of steam for heating buildings. In many chemical 
processes, where only a moderate temperature is required, and 
especially when inflammable substances are being dealt with, steam 
heating is used in preference to a fire or gas-flame, being safer and 
more easily controlled. 

The feed-water for boilers is frequently heated by passing through 
a series of small pipes round which exhaust steam is circulated, thus 
saving a large quantity of heat which would otherwise be lost. A 
further effect of the heating of feed-water is to cause a precipitation 
of a portion of the salts of lime and magnesia held in solution, and 
special appliances are constructed for the double purpose of heating 
and softening the water prior to its being admitted to the boiler. The 
high latent heat of steam renders it extremely effective as a heating 
agent, the condensation of i Ib. at 100 C. being sufficient to raise 
5*37 Ib. of water from the temperature of melting ice to the boiling- 
point. 



Distillation. 



245 



Distillation. A liquid containing solids in solution may be 
obtained pure by the process known as distillation. The liquid is 
boiled in a vessel known as a still, which is furnished with a widened 
portion at the top known as the still-head, on which a quantity of the 
vapour condenses and falls back into the still. The vapour which 
does not condense on the still-head is, in general, pure ; and passes 
into a spiral tube or worm surrounded by running water, which cools 
and condenses the vapour. The purified liquid is collected at the 
end of the worm ; and in this manner water or other liquids may be 
separated from solid matter. 

The separation of two liquids, of different boiling points, may be 
effected by the employment of a more elaborate form of still-head. 
A simple distillation only will not suffice to separate two liquids 
completely, even though the boiling-points are considerably removed 
from each other, as partial evaporation takes place with all liquids at 
all temperatures. If, however, a succession of widened spaces be 
made in the still-head, which is elongated for this purpose, an almost 
complete separation can be effected. For example, the vapour 
reaching the first portion of the still-head might consist of equal parts 
of each constituent, and on condensing the latent heat of each would 
be disengaged. This latent heat would cause a certain amount of 
re-evaporation, and the mixed vapour thus produced would be richer 
in the constituent of lower boiling-point than the original mixture. 
This process of condensation and re-evaporation is repeated at every 
widened space in the still-head, the mixture becoming richer and 
richer in the lower boiling-poinl constituent, until on escaping it con- 
sists of this substance practically pure. The temperature at the 
entrance of the still head is that due to the mixture ; at the exit it is 
the boiling-point of the pure liquid which escapes and is afterwards 
condensed. 

In " patent " or Coffey stills for the production of pure alcohol by 
distillation from grain or other vegetable matter, a process of succes- 
sive condensations and re-evaporations is carried out to separate the 
alcohol from the water which also evaporates from the mash. The 
still-head in this case consists of a chamber, in which perforated plates 
are placed at intervals, upon which the mixed vapours condense. Any 
liquid failing to re-evaporate falls through the perforations back into 
the still; and as alcohol has a lower boiling-point than water, the 
vapour between each successive pair of plates contains an increasing 
proportion of alcohol. If a sufficient number of plates be employed, 
the escaping vapour is practically pure alcohol, and is known as 
" silent " spirit, or spirit that does not indicate its origin, as small 



246 Heat for Engineers. 

quantities of distinctive substances, which would serve to show 
whether the alcohol had been derived from grain, are separated in the 
distilling process. These substances, which impart a flavouring to the 
alcohol, would not be separated by a less elaborate distillation. 

At sea, fresh water is obtained from sea water by a process of 
distillation, the sea water being boiled by immersing in it a coil of 
piping through which high-pressure steam from the boilers is passed. 
In some recent forms of apparatus for this purpose a perforated metal 
plate is interposed between the still and condenser, which serves to 
intercept any spray or priming water that might be mechanically en- 
tangled in the steam, and which, if allowed to pass over, would impart 
a saline flavour to the water. 

Condensers. In steam-engines working with a condenser, the 
steam, after completing its work in the cylinder, is passed over a 
series of tubes through which water is flowing, and is thereby con- 
densed. The condensed steam, being free from dissolved salts, is 
returned to the boiler, being preferable to ordinary water containing 
saline matter. At sea a condenser is essential, owing to the large 
quantity of salts present in sea-water, the condensation being effected 
by using sea-water to circulate through the condenser tubes. The 
special forms of condensers used in refrigerating machines are de- 
scribed in Chapter XVI. 

Korting's Cooling Jets. When water employed for cooling con- 
densers is required to be used over and over again, to save the cost 
of a fresh supply, it is customary to cool the hot water escaping from 
the condenser by passing it through a specially-constructed jet, from 
which it escapes as a revolving spray. A large surface is thus exposed 
to evaporation, and the. latent heat absorbed by the portion which 
evaporates is extracted from the residual water, which consequently 
undergoes a considerable fall in temperature. One gram of water at 
80 C., on evaporating, absorbs 551 calories, which, if extracted from 
ii grams of water, initially at 80 C., would reduce the temperature 
to 30 C. Korting's jets maybe used with advantage whenever it is 
desired to cool a large mass of hot water rapidly. 



247 



CHAPTER XIV. 

ATMOSPHERIC MOISTURE. HYGROMETRY. 

Existence of Moisture in the Atmosphere. The presence of water 
vapour in the atmosphere may be detected in many ways, as, for 
example, by exposing strong sulphuric acid or other hygroscopic 
substance, when an increase in weight, due to the absorption of 
moisture, will be noted after a time. By leading air through a tube 
surrounded by a freezing mixture, a quantity of water, extracted from 
the air, will be deposited. The water vapour present in the atmo- 
sphere is derived by evaporation from the surface of the sea and 
other masses of water, and is precipitated from time to time in the 
form of rain, snow or hail. The quantity of moisture present in a 
given quantity of air varies from day to day, and differs according 
to locality. The atmosphere is seldom saturated with water vapour, 
as a dish of water exposed to it almost invariably undergoes a diminu- 
tion in weight. The normal condition of the moisture in the atmo- 
sphere is therefore that of an unsaturated vapour. 

Effect of Temperature on Atmospheric Moisture. As the quantity 
of vapour which can exist in a given space increases with the tem- 
perature, it follows that warm air can hold more moisture than cold 
air. At 10 C., for example, i cubic metre of air can hold 9-3 grams 
of water vapour, whilst at 20 C. the amount required to produce 
saturation is 17*1 grams, and at 35 C., 39*2 grams. Hence warm 
winds, which have travelled over the ocean such as the S.W. winds 
in Britain contain a much larger quantity of moisture than cold 
winds from the N. or E. 

The maximum quantity of moisture that can be held by i cvbic 
metre of air at different temperatures is shown graphically in Fig. 65. 
The ratio of the weights at two different temperatures is practically 
the same as the ratio of the saturation pressures. Thus at 12 and 

24, the ratio of the weights is - = "49 ; and of the saturation 

pressures IC L_4 = -47. This approximate identity will be used later 
22-1 



248 



Heat for Engineers. 



in calculations concerning the condition of the atmosphere with 
respect to moisture. 

Deposition of Moisture. Dew Point. It has heen stated that the 
atmosphere is seldom saturated with moisture, and on a given day, 
with a temperature of 25 C., the actual amount of water vapour per 
cubic metre may he only 15 grams or less, whereas the quantity 



























































































3U 








































I 






















































































1 












































/ 










































j 








4O 




































y 






















































































y 










































/ 












































/ 












> 


10 

{ 






























^ 










































^ 








































/ 








































/* 








































^ 








































y 








































^ 


[ 






































A 


(* 







































/^ 


' 






































/^ 






































^X 


^ 






































X* 




































^* 


-*" 1 




























































































































10 




20 3O 40 



Temperature Deg. C 



FIG. 65. CURVE SHOWING WEIGHT OF WATER VAPOUR PRESENT 
IN i CUBIC METRE OF SATURATED AIR AT DIFFERENT TEMPERATURES. 



would he 22-8 grams if the air were saturated. Assuming 15 grams 
to be present, and the temperature to fall, a point will be reached 
when the air, owing to its lessened power to hold moisture, will be 
saturated by the 15 grams present. Reference to the curve (Fig. 65) 
will show that saturation will occur at 18 C. ; and if the temperature 
be lowered further, some of the moisture will be deposited. At 
nC. one cubic metre of air can only hold 10 grams of water 
vapour; hence if the temperature fell to 11, a deposition of (15 - 10) 



Atmospheric Moisture. 249 

= 5 grams would ensue. In general, if moist air be cooled, a 
temperature will be reached at which deposition will commence. 
This temperature is called the dew point, and is obviously the tem- 
perature at which the moisture present causes saturation. It is evident 
that the dew point will vary according to the amount of water vapour 
existing in the atmosphere. 

Hygroinetric State or Relative Humidity. It is customary to 
express the condition of the atmosphere with respect to moisture in 
the form of a ratio, which is termed the " hygrometric state " or 
" relative humidity," which is denned as the ratio of the amount of 
moisture present in a given volume of air, to the amount required 
to saturate this volume at the existing temperature. Or, 

Hygrometric State or Relative Humidity 

Weight of water vapour present in unit volume of air 
Weight required to saturate unit volume at temp, of air* 

A numerical example may be given to illustrate the definition. If 
it be found that i cubic metre of air at 25 C. contain 16 grams of 

water vapour, the hygrometric state will be = '70, or 70 per 

cent., since 22*8 grams are required for saturation at 25 C. This 
method of expressing the result is apt to be misleading, as a higher 
hygrometric state may be associated with a less actual quantity of 
moisture. If at 15 C. the moisture present were 10 grams per cubic 

metre, the hygrometric state would be - = '79 or 79 per cent., 

12-7 

although the actual amount is 6 grams less than in the previous case. 
The experimental determination of the hygrometric state may be 
carried out by the aid of instruments known as hygrometers, some 
forms of which will now be described. 

The Chemical Hygrometer. In this instrument a known volume 
of air is drawn through a series of drying-tubes, containing strong 
sulphuric acid or phosphorus pentoxide, which retain the moisture. 
The drying-tubes are accurately weighed before and after the experi- 
ment, the increase being the weight of water vapour in the known 
volume of air. In order to measure the quantity of air, a bottle of 
known capacity, fitted with an escape-tap at the lower portion, is 
filled with water and connected to the drying-tubes. The tap is then 
opened, and as the water escapes an equal volume of air is drawn 
through the tubes. The hygrometric state may be calculated from 
the increase in weight of the tubes, and a knowledge of the amount 



250 Heat for Engineers. 

required for saturation at the existing temperature, which may be 
obtained from tables or a curve similar to Fig. 65. 

Example. Five litres of air were drawn through drying-tubes, 
the observed increase in weight being -073 gram. Temperature 
of air = 22 C. To find the hygrometric state. 

By definition, hyg. state 

_ amount present in 5 litres 

amount required to saturate 5 litres at 22 

From curve (Fig. 65) amount required to saturate i cubic metre, 

or 1000 litres at 22 = 19 grams. To saturate 5 litres 2- = '095 

200 

grm. will be required. Hence the hygrometric state is -^ = -77 

or 77 per cent. 

The chemical hygrometer is accurate, but tedious to use, as it is 
necessary to drag the air slowly through the tubes to ensure complete 
retention of the moisture. It is only employed practically when a 
very accurate result is desired. 

Dines' Hygrometer. The principle adopted in this and several 
other hygrometers is to ascertain the dew point, and also to note the 
temperature of the air, when the hygrometric state may be calculated 
by the use of a table of vapour pressures of water. Dines' hygro- 
meter (Fig. 66) consists of an observation surface O, which may be 




FIG. 66. DINES' HYGROMETER. 

cooled by iced water flowing on its under side from a tank T. The 
bulb of a thermometer, fixed horizontally, touches the under side of 
O, and the small chamber of which O is the cover is provided with 
an outlet for the water at its upper part. The rate at which the water 
flows may be controlled by a tap A. In conducting the experiment, 
the iced water is allowed to pass slowly through the chamber until a 
film of moisture is observed to form on the observation surface O, 
when the thermometer is read. The tap is then closed, and the tem- 
perature allowed to rise until the film of moisture vanishes, when a 



Hygrometry. 2 5 1 

second reading of the thermometer is taken. The mean of the two 
temperatures is taken as the dew point ; thus if the film formed at 
8 5 and disappeared at 9*5, the dew point would be 9. This 
means that the water vapour present would saturate the air if the 
temperature were 9, and by noting the atmospheric temperature the 
hygrometric state may be determined by the ratio 

Weight per unit volume required to saturate at dew point 
Weight per unit volume required to saturate at temperature of air 

These quantities may be obtained from the curve in Fig. 65, or 
instead of taking weights, the ratio of the saturation pressures at the 
dew point and atmospheric temperature may be used, with a practic- 
ally identical result. 

Example. To find the hygrometric state when the dew point is 
9" C., and the temperature of the air 15 C. From the curve of 
weights required to saturate i cubic metre of air (Fig. 65) the amount 
corresponding to 9 C. is 8'8 grams, and to 15 C. 12-7 grams. 

8 * 8 
Hence the hygrometric state is - = '69, or 69 per cent. Or, 

taking saturation pressures from the table on page 216, the ratio 
becomes " = '675, or 67^5 per cent. The difference of 1*5 

per cent, between the two results is well within the limits of error of 
the experiment. 

In order to obtain a close result with Dines' hygrometer, several 
precautions must be taken. The observation surface should be made 
of a thin sheet of metal, a copper surface, lightly silvered, being the 
best for detecting the formation of the film of moisture. A thin piece 
of metal will also possess practically the same temperature on the 
under and upper surfaces, so that the thermometer will record the 
temperature of the air in contact with the upper surface which is the 
temperature sought nearly correctly. The instrument is frequently 
sold with a thick, black glass observation surface, when the formation 
of moisture is not only difficult to detect, but the temperature of the 
under surface, as recorded by the thermometer, may differ greatl 
from that of the upper surface, owing to the poor conductivity of glass, 
thus giving an erroneous value for the dew point. The water should 
be allowed to flow slowly, and should be stopped immediately the 
film is detected. If a thick layer of moisture be allowed to deposit, 
it will take a considerable time to evaporate, and give a false reading 
for the temperature of disappearance. The modification due to Pro- 
fessor Barrett, in which a second tank is provided, containing water 



252 Heat for Engineers. 

warmer than the air, enables a more certain reading of the tempera- 
ture of disappearance to be taken, the procedure being to turn oft" the 
cold water immediately the film is observed, and then to turn on the 
warm water. This prevents a thick film from forming, and warms up 
the apparatus far more quickly than by allowing it to stand in air. 
A more sharply defined second reading is thus secured in a shorter 

time. 

Daniell's Hygrometer. This is another form of dew-point hygro- 
meter, differing from the foregoing in the method of cooling the 
observation surface. Daniell's hygrometer (Fig. 67) consists of a 
tube furnished with a bulb at either end, and containing ether and 
ether vapour only, the air having been expelled by boiling before 
sealing up. A muslin cover is tied round one 
of the bulbs B, and the other bulb A is made 
of blackened glass, or has a band of gold leaf 
surrounding it to act as an observation surface. 
A thermometer is placed in the portion of the 
tube connected with A, and serves to record 
the temperature of the ether in the latter. A 
second thermometer fixed to the stand, enables 
the temperature of the atmosphere to be read. 
In using the instrument, a volatile liquid is 
poured over B, where it is retained by the 
muslin. The evaporation of this liquid lowers 
p 1G 67 DANIELL'S tne temperature of the bulb B, and causes 
HYGROMETER. the ether vapour in the interior to condense. 

This lowers the pressure on the surface of the 

liquid ether in the bulb A, which accordingly evaporates and by absorp- 
tion of latent heat lowers the temperature of A and its contents. The 
evaporation of the ether in A, and the consequent fall of temperature, 
continue so long as B is cooled, and finally moisture makes its appear- 
ance on the surface of A. The temperature on the inner thermometer 
is noted when this occurs, and the apparatus is then allowed to warm 
up until the film disappears, when the inner thermometer is again read. 
As before, the mean of the two temperatures is taken as the dew point, 
and the hygrometric state calculated in the usual way. 

The liquid generally used for external application to the bulb B is 
ether, which evaporates rapidly and so ensures the necessary cooling 
effect. Whilst Daniell's hygrometer is simple to use, some uncertainty 
must exist as to the accuracy with which the thermometer in A records 
the temperature of the outer surface of the bulb, that is, of the air at 
the moment it begins to part with its moisture. 




Hygrometry. 



253 



Regnaulfs Hygrometer. This hygrometer is shown in Fig. 68, and 
consists of two tubes, furnished with silver caps. One of the tubes is 
connected by a T-piece to an aspirator, and is partly filled with ether 
in which the bulb of a thermometer is immersed. The other tube 
contains air and does not communicate with the aspirator, its function 
being to furnish a comparison surface for the working-tube T, and to 
contain a thermometer which records the atmospheric temperature. 
The experiment is conducted by connecting the tube A to an aspirator, 
the result of which is to extract the air and ether vapour from the 
upper part of T, and to cause air to enter by the tube B and bubble 
through the ether. Each bubble of air becomes saturated with ether 
vapour, and the result of the evaporation is to cause a lowering of 
temperature in the residual ether. This is allowed to proceed until 



B 




FIG. 68.- RKGNAULT'S HYGROMETER. 

moisture is observed to form on the silver cap on T, which then 
appears dimmer than the comparison surface on C. The aspirator is 
then stopped and the temperature at which the film disappears noted, 
judgment in this case also being aided by a comparison of the bright- 
ness of the two silver caps. The mean of the temperatures of appear- 
ance and disappearance, as usual, gives the dew point. 

This instrument, if properly made, is the most accurate of the 
various forms of dew-point hygrometers. The rate at which the 
temperature falls can be completely controlled by the aspirator, and 
by cooling slowly near the dew-point a fine reading to a fraction of a 

degree may be obtained. The ether should be in actual contact with 

the silver cap, in which case the thermometer will correctly record 
the temperature of the outer surface of the silver, or very nearly so. 



254 



Heat for Engineers. 



The advantages of Regnault's hygrometer are often nullified by the 
makers, who place the silver cap of the working-tube over a glass tube 
with a closed end, so that a layer of glass is interposed between the 
ether and the observation surface. This mistake is sometimes further 
aggravated by cementing the silver cap over the closed glass tube with 
plaster of Paris, thereby completely destroying the reliability of the 
indications. 

The Wet and Dry Bulb Hygrometer. All the hygrometers previ- 
ously described require an experiment to be performed in order to 
obtain the hygrometric state, which, in the instrument under notice, is 
deduced by the aid of tables from the readings of 
two thermometers. As shown in Fig. 69, this 
hygrometer consists of two similar thermometers, 
hanging side by side, the bulb of one thermometer 
being dry, and recording the atmospheric temper- 
ature, whilst the other bulb is kept wet by surround- 
ing it with a piece of muslin connected to a wick 
immersed at its end in water. Owing to evaporation 
constantly taking place on the surface of the wet 
bulb, heat is extracted from the contained mercury, 
and consequently the wet-bulb thermometer shows 
a lower reading than the other, which is exposed 
to the atmosphere. If the air were saturated with 
moisture, no evaporation would occur, and in this 
case the two thermometers would read alike. On 
the other hand, if the atmosphere were very dry, 
rapid evaporation would take place on the surface 
of the wet bulb, and this thermometer would con- 
sequently indicate a much lower temperature than 
that of the atmosphere. Between these two ex- 
tremes, the difference between the two readings 
will vary according to the amount of moisture 
present, which determines the rate of evaporation. 
Numerous attempts have been made to establish 

a simple formula by the aid of which the hygrometric state might be 
deduced from the two readings, but without success. It has been found 
possible, however, to compile tables from which the desired result may 
be obtained, the figures in the tables having been arrived at as a result 
of daily comparisons between the readings of the wet and dry bulb 
thermometers and a dew-point hygrometer. These daily observations 
were conducted in several countries, and were extended over a number 
of years, so as to embrace a very large variety of atmospheric con- 




FIG. 69. WET 

AND DRY BULB 

HYGROMETER. 



Hygrometry. 



255 



ditions. The results obtained are embodied in the following table, in 
a form convenient for calculating the hygrometric state. 

In the table the first column, headed " t C.," represents the 

THE WET AND DRY BULB HYGROMETER. 



t C. 


o 


I 


2 


3 


4 


5 


6 


7 


8 


9 


10 





4-6 


3*7 


2'9 


2'I 


i'3 








.. 






i 


4"Q 


4* I 


T." 2 


2 '4 


1-6 














2 


T* -7 

5'3 


t 

4'4 


re 


2-7 


1-9 


i* i 


0-3 










3 


5'7 


4'8 


3'9 


3-1 


2'2 


i'4 


0-6 












6-1 


C'2 


4* ^ 


7'4 


2'6 


1-8 


O'Q 












6-<> 


D 

T6 


T 1 O 

A' 7 


J T^ 

S'8 


2'Q 


2' I 


-7 

I *2 












J 


3 


T" / 


O 


.7 














6 


7-0 


6-0 


5-1 


4*2 


3'3 


2- 4 


1-6 






.. 




7 


7'5 


6-5 


5'5 


4-6 


3'7 


2-8 


1-9 


i *i 


O'2 






8 


8-0 


7-0 


6-0 


5'o 


4'i 


3*2 


2-3 


i'4 


0-6 






9 


8-6 


7'5 


6'5 


5'5 


4'5 


3'6 


2-7 


1-8 


0-9 


.. 




10 


9-2 


8'i 


7-0 


6-0 


5'o 


4-0 


3'i 


2*2 


1-3 


.. 




ii 


9-8 


8-7 


7'6 


6'5 


5'5 


4'5 


3-5 


2'6 


i*7 






12 


10-5 


9*3 


8-2 


7-1 


6-0 


5'o 


4-0 


3 -0 


2' I 


1*2 


0-3 


13 


II'2 


I0'0 


8-9 


7-6 


6'5 


5'5 


4'5 


3"5 


2'5 


1-6 


0-7 


14 


11-9 


10-7 


9'4 


8'3 


7' 1 


6-1 


5'o 


4*o 


3 -0 


2'0 


i'i 


15 


12-7 


11-4 


lO'I 


9-0 


7-8 


6-6 


5'5 


4'5 


3*4 


2'5 


i'5 


16 


I3-5 


I2'2 


10*9 


9'7 


8-4 


7'3 


6-0 


5' 


4-0 


3 -0 


1-9 


17 


14-4 


I3-0 


11-7 


io*4 


9-1 


8-0 


6-7 


5'6 


4'5 


3'5 


2-4 


18 


I5-4 


i3'9 


12-5 


II'2 


9'9 


8-6 


7'4 


6'3 


5'i 


4'0 


3-0 


19 


16-3 


14-9 


I3'4 


I2'0 


10-7 


9'4 


8-1 


6-9 


5'7 


4-6 


3'5 


20 


17-4 


i5'9 


I4-3 


I2'9 


n'5 


IO'2 


8-8 


7'6 


6-4 


5' 2 


4'i 


21 


18-5 


16-9 


i5'3 


13-8 


12-4 


II'O 


9-6 


8-4 


7-1 


5'9 


4"7 


22 


19-7 


iS-o 


i6'4 


14-8 


i3'3 


II'9 


10-5 


9-1 


7-8 


6-6 


5'4 


23 


20*9 


19-2 


17*5 


I5'9 


14-3 


12-8 


11-3 


I0'0 


8-6 


7'3 


6'i 


24 


22'2 


20-4 


18-6 


I7-0 


I5-3 


13-8 


12-3 


10-9 


9'4 


8-1 


6-8 


25 


23^ 


21-7 


19-9 


18-1 


16-4 


14-8 


I3-3 


ii-S 


10-3 


9-0 


7-6 


26 


25-0 


23-1 


2I'I 


19-4 


17-6 


15-9 


I4-3 


12-8 


11-3 


9-8 


8-4 


27 


26-5 


24-5 


22 '5 


20-7 


18-8 


17-1 


I5-4 


13-8 


12-3 


10-8 


9'3 


28 


28-1 


26-0 


24'O 


22'0 


20'I 


18-3 


16-6 


14-9 


i3'3 


11-8 


IO'2 


29 


2 9 -8 


27-6 


25*5 


23-5 


21'5 


19*6 


17-8 


16-1 


14-4 


I2'8 


II'2 


3 


3^5 


29-3 


27-I 


25-0 


22'9 


21'0 


19-1 


I7'3 


i5'5 


13-9 


12-3 



256 Heat for Engineers. 

temperature of the atmosphere, as recorded by the dry bulb, whilst 
the figures under the columns headed o, i, 2, 3, etc., give the 
vapour pressure at the dew point corresponding to differences of 
o, i, 2, 3, etc., degrees C. between the wet and dry bulb readings. 
Taking the dry bulb reading as 21 C., and the wet bulb 18 C., the 
difference is 3, and to find the hygrometric state, the figure opposite 
21 in the column headed "o" is divided into the figure opposite 21, 
in the column headed " 3." The hygrometric state is, therefore, 

-3- = "75 or 75 per cent. The column headed "o" is identical 
18-5 

with a table of saturation pressures, and if the two bulbs showed the 
same reading at any temperature, the difference would be o, and the 
hygrometric state 100 per cent. Further examples in the use of the 
table are appended. 

Example i. The dry bulb temperature being i6 c C., and the 
wet bulb 12 C., to find the hygrometric state and also the dew point. 

Difference between readings = (16 - 12) = 4. 

Vapour pressure at dew point, obtained from column 4, in hori- 
zontal row opposite 16 = 8*4 mm. 

Saturation pressure at 16 C., from column o = 13*5 mm. 

Hygrometric state = - = '62 or 62 per cent. 

As the vapour pressure at the dew point is 8-4 mm., the dew 
point must be the temperature at which the saturation pressure equals 
8 4 mm. Looking for the figure 8 4 in the column headed o, or in 
a table of vapour pressures of water, it is seen that this value obtains 
between 8 and 9, the figures for which are 8'o and 8*6 mm. 
respectively. The dew point would, therefore, be 8*6 C. approxi- 
mately. 

Example 2. To find the hygrometric state and dew point corre- 
sponding to readings of 24-5 on the dry bulb, and 20-2 on the 
wet bulb. 

The table only gives values for whole degrees, but proportionate 
parts may be taken for fractions of a degree. The saturation pressure 
at 24*5 may be taken as intermediate between the values at 24 and 

25, or 22 2 + 2 3 5 = 22-85 mm. The difference between the 

2 

readings is 4*3. Under column 4, opposite 24, the figure is 15 '3 
mm., and under column 5, 13-8 mm. The proportionate value for 
4 '3 is, therefore, 14*85 mm. Similarly, in the row opposite 25 C., 
the figure under column 4 is 16-4, and under 5 is 14*8 ; whence the 
proportionate value for 4*3 is 15*92 mm. The value for 24-5, 



Hygrometry. 



257 



with a difference of 4*3, is, therefore, 






15.37 mm - 



Hence the hygrometric state is I -^ ~ = 67 or 67 per cent. The 

22 '85 

dew point, or temperature at which 15 .37 mm. represents saturation 
pressure, is seen from column o to be 17*8' C. 

It will be seen from the latter example that when fractions of a 
degree are involved, the calculation is somewhat complicated. For 
the use of unskilled observers approximate tables have been compiled, 
which assume that the thermometers are only read to the nearest J C. 
or whole degree F. The results obtained are sufficiently close for 
ordinary purposes. 

When in use, the wet and dry bulb hygrometer should be freely 
exposed to air, but should be kept in the shade. The dish of water 
should be well removed from the dry bulb, and the cover of the wet 
bulb washed or renewed periodically, as it tends to become choked 
with dust. Owing to the ease with which readings may be taken, 
this hygrometer is far more extensively used than other types, which 
are only employed for precise readings. 

Hygroscopes, or Moisture Indicators. Many appliances are in use 
designed to indicate, rather than measure, the relative humidity of 
the atmosphere. Some varieties of sea-weed, and other 
forms of vegetation, absorb moisture from a damp at- 
mosphere, which evaporates again on the air becoming 
dry, thus enabling an indication to be obtained from 
the condition of the plant. A paper soaked in a solu- 
tion of cobalt chloride is pink when damp, and blue 
when dry, and furnishes, by its colour changes, a guide 
to the state of the atmosphere with respect to moisture. 
A human hair, free from grease, contracts in length on 
absorbing moisture, and in the atmosphere will either 
increase or decrease in length according to the variations 
in the proportion of water vapour present. Hygroscopes 
based on the alteration in length of hair have been 
devised by De Saussure, Monnier, and others, in which 
the movements of the hair are communicated to an 
index hand, behind which a dial is placed. The scale 
on the dial is usually marked to read directly the per- 
centage of relative humidity, but the readings are at best only approxi- 
mate. The most recent form of this type of hygroscope is Lambrecht's 
polymeter (Fig. 70). The dial, over which the index connected to 
the hair moves, is furnished with two scales, one of which is gradu- 

s 




FIG. 70. 

LAMBRECHT'S 

POLYMETER. 



258 Heat for Engineers. 

atecl so as to give the hygrometric state directly, whilst the second 
scale is divided in such a manner that the figure opposite the index, 
when subtracted from the reading of the thermometer placed above, 
gives the dew point. The attached thermometer is graduated in 
ordinary degrees on one side, whilst on the other side saturation 
pressures are marked opposite corresponding temperatures. Instead 
of using a single hair to move the index, a number of hairs are 
fastened together so as to form a single strand, greater strength being 
thus secured. Lambrecht's polymeter is one of the most suitable 
instruments to use when approximate readings only are required. 
Other forms of direct-reading hygroscopes have been based on the 
alteration in length of whipcord, catgut, and other materials, under 
varying conditions of atmospheric moisture. 

Uses of Hygrometric Observations. Daily observations of the 
hygrometric state of the atmosphere are made at meteorological 
stations, and assist in obtaining a forecast of the weather; thus a 
generally dry condition of the atmosphere over the country would 
indicate the probable absence of rain, and vice versa. A series of 
observations would also serve to indicate whether the climate of a 
place were generally damp or otherwise, and so furnish a clue as to 
its desirability for residential purposes. The existence of abnormal 
dampness in a house or building can be detected by hygrometers, or 
even by hygroscopes, such observations being of value from a hygienic 
standpoint. In weaving delicate fabrics a certain minimum of atmo- 
spheric moisture is essential, as in a dry atmosphere the strands would 
become brittle and snap, consequently the atmosphere is artificially 
moistened by steaming when the normal hygrometric state is too 
low. The dangers attendant on the manufacture of gunpowder, 
and of explosives and ammunition generally, are greater in a dry 
than in a moist atmosphere, hence in factories where explosives are 
handled it is arranged that the hygrometic state shall not fall below 
a certain minimum, and the same applies to storage magazines for 
explosive materials. In horticulture, hygrometers are employed to 
register the percentage of moisture in the atmosphere of greenhouses, 
so that a deficiency may be detected and remedied by sprinkling with 
water. The allowance for evaporation to be made in constructing a 
large water reservoir depends in part upon the average hygrometric 
state of the atmosphere in the locality, the evaporation being greater 
in a dry atmosphere. 

Dew. On clear nights, when radiation can take place freely from 
the surface of the earth, the temperature of the ground falls consider- 
ably. When this occurs to such an extent that the ground and objects 



Mists and Fogs. 259 

near it sink in temperature below the dew point of the air near the 
surface, the surplus moisture is deposited in the form of globules on 
the various objects. ' Moisture so deposited is called dew, and if the 
temperature should fall still further, until the freezing point is reached, 
the dew freezes and forms hoar frost. Most of the moisture which 
goes to form dew rises in the form of vapour from the porous ground. 
This may be proved by placing a metal vessel such as a dish-cover 
on the ground, mouth downwards, on a suitable night, when, on 
examination in the early morning, the deposit of dew will be found 
in the interior of the vessel. If the moisture had condensed from 
the atmosphere itself, the dew would have formed on the exterior of 
the vessel. Owing to the evaporation of underground water, vapour 
is continuously rising from porous ground, and on a cold night is 
condensed on the nearest objects on reaching the surface. Some- 
times, however, ordinary atmospheric moisture is also deposited, as 
the roofs of houses may often be observed to be covered with moisture 
or hoar frost. 

Mists and Fogs. The condensation of moisture in the atmosphere 
itself results in the formation of small spheres of water, which, owing 
to their small size, and the consequent large surface in comparison 
with mass, remain floating for a considerable time in the air. The 
ratio of the surface exposed to friction to the mass is very large in a 
tiny sphere, and although the density of liquid water is 770 times that 
of air, the friction suffices to hold very small globules in suspension. 
When the atmosphere is charged with these small spheres of water, 
the appearance is known as a mist or fog. The cloud resulting from 
the escape of a jet of steam into air is similarly constituted. 

It has been shown by Aitken that each little sphere of water con- 
tains a speck of dust in the centre round which the moisture has 
condensed, and that in the absence of dust a mist could not form. 
When a jet of steam is led into dust-free air no cloud is formed, and 
condensation only occurs when the steam comes into contact with 
cold, solid matter, such as the sides of the vessel containing dust-free 
air. An obvious analogy is here suggested to the phenomena of 
surfusion and abnormal boiling, as in each case external aid is neces- 
sary to initiate the change of state. So small a nucleus is required to 
enable water vapour to liquefy, that the excessively minute particles 
known as " electrons " are capable of effecting the condensation. 

Mists are generally confined to a region near the surface, and are 
caused by the cooling effect of the ground on the atmosphere, the 
result being that the adjacent air is cooled below the dew-point, and 
the surplus moisture settles on the particles of dust always present. 

s 2 



260 Heat for Engineers. 

Hence mists may generally be observed over moist land on cool 
evenings, the vertical extent being determined by the height to which 
the atmosphere is affected by the cold surface. In fogs, on the other 
hand, a general cooling of the atmosphere occurs, probably due to a 
gentle admixture of cold air, the excess of moisture again being- 
deposited round dust nuclei. A fog may extend to a vertical height 
of several hundred feet, and it sometimes happens that during a fog 
the ground is warmer than the overlying air, thus indicating a differ- 
ent origin to that of a mist. In large cities where the atmosphere is 
laden with smoke particles, a yellowish-brown colour, due to the 
smoke, generally accompanies the fog, and adds greatly to the density. 
This colour is usually associated with London fogs, the atmosphere 
being laden with smoke particles from factories and domestic chim- 
neys, and dust caused by the enormous street traffic. The hygro- 
metric state of the atmosphere in London is generally fairly high, and 
thus the whole conditions favour the formation of dense fogs. The 
still condition of the atmosphere which usually accompanies a high 
barometer is favourable to foggy weather ; a strong wind causing the 
fog to disperse by absorbing the condensed moisture. 

Various attempts have been made to devise a method for dissi- 
pating fogs, so as to obtain clear spaces in localities where traffic is 
otherwise practically suspended, as, for example, the mouths of 
harbours, railway stations, and busy street crossings. Amongst the 
methods tried mention may be made of the blowing of warm, dry air 
through trumpet-shaped openings, over the locality, so as to evaporate 
the moisture ; and of the electrical method, in which the air and 
spheres of water are electrified by proximity to wires carrying a 
current at high potential, when the small spheres cohere, forming 
drops which rapidly fall to the ground. None of the methods pro- 
posed have yet passed the experimental stage. 

The intensity, and probably the number, of fogs occurring in large 
centres of population would undoubtedly be lessened if the smoke in 
the atmosphere were reduced to a minimum, either by the perfecting 
of smoke-prevention appliances for industrial and domestic fires, or by 
the general use of smokeless fuel. The inconvenience and financial 
loss entailed by a dense fog, render persistent efforts in this direction 
highly desirable. 

Clouds and Rain. Clouds represent masses of condensed water 
vapour, floating in the atmosphere at a height varying from 10 miles 
downwards. As in the case of mists and fogs, the individual globules 
of water composing the cloud are formed round dust-centres. The 
condensation originates in a cooling effect produced by currents of 



Rain. 261 

cold air mingling with warmer and moister air. As clouds are denser 
than the atmosphere a continuous sinking takes place, and if a dry 
region of the atmosphere be entered, the condensed water will again 
become vapour, and the cloud disappear. If a cloud enters a moister 
region, or if the initial cooling be great, larger spheres of water form, 
which are not able to float in the air, and fall as rain. The size of 
the water globules is the only distinction between a Scotch mist, in 
which the particles are small and sink slowly, and a heavy rain, which 
is due to large particles falling rapidly. The freezing of the smaller 
type of spheres produces snow, whilst hail represents large globules 
which have solidified after formation. 

The amount of rain which falls in a district during a given time is 
measured by means of the rain-gauge, which is a cylindrical vessel into 
which a funnel is placed. The diameter of the funnel-top is accurately 
known, and the rain falling within it runs into the cylinder, from which 
it is transferred to a measuring vessel. The result is expressed in 
inches of rainfall, that is, the depth to which water would have formed 
from the rain on a non-porous surface. By employing a narrow 
measuring-cylinder, fractions may be obtained ; thus if the area of the 
top of the funnel were ten times that of the bore of the measure, an 
actual fall of T ^th of an inch would fill the measure to a height of 
i inch, and a very small fall could thus be measured. The rainfall of 
a district depends upon the nature of the prevailing winds, the presence 
of elevated masses of land, and other causes. A knowledge of the 
average annual rainfall of a district is essential to the engineer when 
deciding upon a locality for a surface water-supply ; and is of the 
highest importance from an agricultural standpoint. 



262 Heat for Engineers. 



CHAPTER XV. 

THE PRODUCTION OF LOW TEMPERATURES. LIQUEFACTION OF GASES. 

Methods by which Low Temperatures may be Obtained. A reduc- 
tion of temperature may be obtained by means of the following 
processes : 

1. The solution of a solid in a liquid, or the mutual liquefaction 
of two solids. This method has been dealt with in Chapter IX. 
under the head of freezing mixtures. 

2. The evaporation of a liquid, when conducted without the 
application of external heat. 

3. The expansion of a compressed gas, when work is done during 
the expansion. 

4. The escape of a compressed gas through a fine opening or jet. 
All these methods have been usefully applied, and those not 

hitherto described will furnish the subject matter of the present 
chapter. 

Production of Low Temperatures by the Evaporation of Liquids. 
The rapid evaporation of a liquid is usually procured by applying 
heat, in which case the latent heat of vaporisation is furnished by the 
flame or other source of heat. If, however, the liquid be made to 
evaporate rapidly by mechanical means, such as the reduction of the 
pressure on its surface, the latent heat will be extracted from the 
liquid itself, and to some extent from the containing vessel, the 
result being a fall of temperature. Rapid evaporation is necessary to 
obtain a considerable lowering of temperature, as the latent heat ex- 
tracted in a given time then greatly exceeds the heat received by the 
liquid from surrounding objects. A vessel of water, exposed to air, 
shows practically no fall in temperature, because the evaporation 
proceeds so slowly that the latent heat absorbed is balanced by the 
gain from the atmosphere and surrounding objects. When allowed 
to evaporate under the receiver of an air-pump, however, the heat 
which enters the water from without is far less, in a given time, than 
that which disappears in the form of latent heat, and consequently a 
notable fall in temperature occurs. 



The Production of Low Temperatures. 263 

As in the case of freezing mixtures, a definite limit of low tem- 
perature exists for a given liquid undergoing evaporation. This limit 
is reached when the latent heat extracted from the liquid is equal to 
the heat entering from without. Even if it were possible perfectly to 
shield a liquid from external heat, a stage would be arrived at when 
the pump would fail to maintain a less pressure in the space than the 
existing vapour pressure, when evaporation would cease and no 
further fall in temperature could take place. The vapour pressure of 
liquids diminishes as the temperature falls, and finally obtains a value 
as low as the vacuum-producing power of the pump, which then ceases 
to be operative. As an example, the case of water in a flask, origin- 
ally at 20 C., and connected to an air-pump may be considered. On 
reducing the pressure to 17*4 mm. (which is the pressure of water 
vapour at 20 C.), the water will boil, and as every gram which 
evaporates at 20 C. absorbs 592*6 calories from the residual liquid 
and vessel, the temperature will fall, and the vapour pressure also. 
When o C. is reached, the vapour pressure is only 4* 6 mm., and as 
a less number of vapour molecules suffice to furnish the diminished 
pressure, the rate of evaporation falls off considerably. The rate of 
evaporation may be taken roughly as proportional to the pressure ; 

hence at o C. the vapour formed in a given time is , or roughly 

17 '4 

\ of that given off at 20 C. At o C. the water freezes, and any 
further cooling is due to vapour leaving the ice. At - 20 C. the 

pressure falls to '93 mm., and the rate of evaporation to ^-, or 

roughly -^ of the original rate. With the best available appliances 
a further reduction of temperature would not be found possible, as it 
would be necessary to maintain a higher degree of vacuum than 93 
mm., and to shield the vessel so perfectly that the minute extraction 
of latent heat resulting from the feeble evaporation would overcome 
the ingress of heat from surrounding objects. When these opposing 
tendencies are balanced, the limit of low temperature is reached. 

It is evident from the foregoing that a liquid capable of maintain- 
ing a high vapour pressure, even at low temperatures, or which gives 
rise to a solid possessing a high vapour pressure, is better suited than 
water for obtaining low temperatures. Ether, for example, has a 
vapour pressure of 69 mm. at - 20 C., and if the limit of the pump 
were i mm. internal pressure, it is evident that a much lower tempera- 
ture than - 20 C. could be obtained by the use of this liquid. In 
general the more volatile the liquid, the greater will be the reduction 
of temperature attainable. The most volatile liquids are those obtain- 



264 



Heat for Engineers. 



able by the condensation of gases, and consequently the study of 
methods for producing low temperatures is intimately associated with 
that of the liquefaction of gases, which will now be entered into. 

Liquefaction of Gases by Pressure. In 1806 Northmore discovered 
that chlorine gas on being subjected to pressure, undergoes liquefac- 
tion ; this being the first recorded instance of a gas being made to 
assume the liquid state. At 12-5 the pressure required is 8 5 atmo- 
spheres, and at o, 6 atmospheres. At - 34 C. chlorine liquefies 
under a pressure of i atmosphere. Some years later Faraday con- 
tinued the investigation, and showed that many gases could be lique- 
fied easily by combined cooling and pressure. Faraday took a stout 
glass tube, sealed at both ends, chemicals for the generation of the 
gas under experiment being placed in one end of the tube, whilst the 
free end was surrounded by a freezing-mixture. By liberating a large 
amount of gas in the closed tube, a high internal pressure was pro- 
duced, which, combined with the cooling, brought about liquefaction. 
In this way Faraday liquefied sulphur dioxide, carbon dioxide, nitrous 
oxide, cyanogen, ammonia, and hydrochloric acid ; and also investi- 
gated the properties of the liquids obtained. 

The pressure required to produce liquefaction is equal to the 
vapour pressure of the liquid at the existing temperature. Thus 
sulphur dioxide, which liquefies at - 8 C., under i atmosphere pres- 
sure, possesses a vapour pressure of i atmosphere or 760 mm. at this 
temperature, which is therefore the normal boiling-point of the liquid. 
At o C. the vapour pressure rises to 1165 mm., and if a closed bottle 
contain liquid sulphur dioxide at o C., the internal pressure will be 
1165 mm. Hence the reason why cooling facilitates liquefaction: 
the vapour pressure of the liquid, and consequently the pressure 
required to cause liquefaction, are lowered. 

The following table shows the vapour-pressures of a number of 
gases at o C. 



Name 


Vapour Pressure 
in Atmospheres 


Name 


Vapour Pressure 
in Atmospheres. 


Sulphur dioxide 


I'53 


(Sulphuretted hy-^l 
\ drogen j 


IO*OO 


Cyanogen 


2'37 


Hydrochloric acid. 


26'2O 


Ammonia 


4-40 


Nitrous oxide 


32'OO 


Chlorine 


5'95 


Carbon dioxide . 3^'5O 



The superiority of any of these liquids over water or ether in 
respect to the production of low temperatures by evaporation is made 



Liquefaction of Gases. 265 

evident by the above figures. Under the receiver of an air-pump a 
temperature below 50 C. can easily be obtained with liquid sul- 
phur dioxide, as the amount of evaporation is still considerable. 
When the pressure on any liquefied gas is liberated, boiling com- 
mences, and as the latent heat of vaporisation is extracted from the 
liquid itself, the temperature falls to the boiling point of the liquid at 
the reduced pressure. Thus when exposed to the atmosphere, liquid 
sulphur dioxide acquires a temperature of 8 C. ; ammonia, 
- 33 7 C.; and carbon dioxide 78 * 2 C. This fall of temperature 
to the normal boiling point is identical with the case of water under 
pressure in a steam boiler, which falls in temperature to 100 C. when 
the boiler is fully opened to the atmosphere. 

Most liquid gases can be caused to solidify by placing under the 
receiver of an air-pump, and rapidly exhausting the contents. The 
solidification of carbon dioxide may be easily brought about by filling 
a steel cylinder, tubed after the manner of a soda-water syphon, with 
the liquid ; when, on opening the valve, the liquid is driven by the 
internal pressure through the tube, escaping into the atmosphere in 
the form of a spray. The rapid evaporation of the globules com- 
posing the spray, combined with the cooling effect due to the escaping 
gas doing work in overcoming the atmospheric pressure, causes so 
low a temperature that the inner portions of the globules solidify, 
forming a finely-divided white powder. By tying a flannel bag, two 
or three layers thick, over the exit-tube, the solid may be collected 
and its properties examined. The solid evaporates in air without 
previous liquefaction, its temperature being about - 90 C. Rapid 
evaporation of the solid in a vacuum causes the temperature to fall 
to - i20C., or even lower, the vapour pressure of the solid being 
noticeable even at this temperature. 

The gases hydrogen, nitrogen, oxygen, air, and carbon monoxide 
baffled all the attempts of the early experimenters to reduce these 
substances to the liquid state, in spite of the application of enormous 
pressures and the best available means of cooling. The term " per- 
manent gases" was applied to distinguish these gases from others 
which could be liquefied, and it was thought by some investigate rs 
that a distinction existed between the so-called " permanent " gases 
and others, which rendered the liquefaction of the former class 
impossible. The researches of Andrews, however (published in 1869) 
threw a new light on the problem, and by indicating the conditions 
necessary to produce liquefaction, ultimately led to the condensation 
of all the " permanent " gases. Andrews discovered that a tempera- 
ture exists for every gas below which no amount of pressure will cause 



266 Heat for Engineers. 

liquefaction, to which the term " critical " temperature was applied. 
Above 31 C., for example, carbon dioxide cannot be obtained in the 
liquid state, no matter what pressure be exerted. The explanation of 
the failure to liquefy hydrogen, oxygen, and other gases was that the 
critical temperatures were so low that ordinary cooling failed to reach 
them, and consequently the application of high pressures was of no 
avail. Later work has completely demonstrated the truth of this 
proposition ; but before describing the means adopted for the con- 
densation of the gases difficult to liquefy, it will be advantageous to 
consider the important conclusions to which the researches of Andrews 
lead. 

Critical Temperature. Continuity of Liquid and Gaseous States. 
Assuming that a liquid differs from a gas in the respect that the 
molecules tend to cohere, owing to a lessened velocity and closer 
proximity, the existence of a critical temperature indicates that 
nearness alone, as produced by pressure, does not give rise to 
sufficient cohesive power to enable the properties of a liquid to be 
manifested. In addition to being closer together, the speed at which 
the molecules move must not exceed a definite rate, and the critical 
temperature is that at which the molecular velocity is just small 
enough to permit of the necessary cohesion. It might be inferred 
from this that the liquid and gaseous states are not abruptly sepa- 
rated, but that every intermediate state between liquid and gas may 
exist. Andrews showed that this actually was the case, and that 
these two conditions of matter liquid and gaseous merge insensibly 
into one another. 

A well-defined liquid differs from a gas or vapour physically in 
that it possesses a greater density, a higher refractive index, a less 
amount of internal energy shown by the absorption of heat on 
vaporising and in possessing a boundary surface or meniscus. The 
consideration of the case of water, heated in a closed boiler, will 
serve to show that these distinctions are only relative. As the tem- 
perature rises, the number of vapour molecules in the space above 
the water increases rapidly, and therefore the density of the steam 
becomes greater. At 100 C. the density of the steam is only T7 -\j 7) - 
of that of the water, but at 230" the value has risen to -^ anci above 
this temperature shows a rapidly augmented increase. At the same 
time the density of the water diminishes, owing to expansion ; and 
evidently a stage will be reached at w r hich liquid and vapour possess 
the same density. The same reasoning applies to the index of 
refraction ; and as the temperature rises the energy absorbed in the 
act of evaporation becomes less and less, finally becoming zero when 



Liquefaction of Gases. 



267 



the molecules of the liquid attain the same velocity as those of the 
vapour. The boundary surface, or meniscus, possessed by a liquid 
is due to surface tension, which causes the surface to assume a 
curved shape. The value of the surface tension falls as the tem- 
perature rises, the meniscus becoming flatter or less curved, and 
finally becomes zero, at which stage the bounding surface disappears, 
and the liquid becomes vapour. All the distinctions enumerated 
between a liquid and its 
vapour cease to hold at a 
certain temperature, which 
is the critical temperature of 
the substance. This tem- 
perature for water is 365 C., 
at which steam and water 
have the same density and 
refractive index; and at which 
temperature also the latent 
heat of vaporisation and sur- 
face tension have zero values. 
As all these properties change 
gradually, it follows that the 
transition from liquid to 
vapour, and vice versa, is 
continuous, and not abrupt. 

The behaviour of a gas at 
different temperatures, rang- 
ing on either side of the 
critical temperature, may be 
studied with advantage by 
reference to the isothermals 




FIG. 



71. ISOTHERMALS OF CARBON 
DIOXIDE (Andrews). 



in Fig. 71, which represent 
the results obtained by 
Andrews for carbon dioxide. 

Starting with the lowest isothermal (the temperature being steady at 
13 'i throughout, whilst the pressure was varied), and proceeding 
from the right-hand side, it will be observed that at first the volume 
diminishes and the pressure rises. At about 50 atmospheres, however, 
the pressure remains steady, whilst the volume diminishes, the iso- 
thermal becoming parallel to the axis of volumes. During the stage 
represented by the horizontal line, liquefaction has taken place, and 
as the pressure of a vapour in contact with its liquid is constant for a 
given temperature, a further diminution in volume merely causes more 



268 



Heat for Engineers. 



vapour to liquefy, without altering the pressure. When the whole of 
the gas has been liquefied, the pressure is applied to the liquid only, and 
as liquids in general are only slightly compressible, a rise in pressure 
to 90 atmospheres or more causes little decrease in volume, as shown 
by the vertical part of the isothermal. The next isothermal, for 
2i'5C., shows the same general features; no liquefaction com- 
mencing, however, until a pressure of 60 atmospheres has been 
applied. The third isothermal, representing pressure and volume 
changes at 31 i C., has no horizontal portion, although a flexure in 
the curve occurs at 75 atmospheres; and the absence of the hori- 
zontal part implies that the vapour was not in contact with its liquid, 
or, in other words, no liquid was formed which in the experiment 
was observed to be the case. In the isothermals for 32 5 and 35*5 
the flexure is still present, but less marked, and at 48*1 has entirely 
disappeared, when the shape approximates to that of the rectangular 
hyperbola which represents Boyle's law. The limiting case, when 
the isothermal just ceases to show a horizontal part, occurs at 
30*92 C., which is the critical temperature of carbon dioxide. 

Critical Pressure. The pressure required to produce liquefaction 
at the critical temperature is known as the critical pressure. In a 
diagram such as Fig. 71, the critical pressure would be represented 
by the mark opposite the horizontal portion of the critical tempera- 
ture isothermal. The term does not apply to any other isothermal ; 
and if that for carbon dioxide at 30-92 were drawn, the horizontal 
part would be opposite 73 atmospheres on the pressure scale. 
Hence 73 atmospheres is the critical pressure of carbon dioxide. A 
table of critical temperatures and pressures is appended : 



Name 


Critical Temperature, 
Degrees C. 


Critical Pressure, 
Atmospheres 


Carbon dioxide 


3 0- 9 2 


73 


Sulphur dioxide 


I 5 6 


79 


Alcohol . . . . . 243 


63 


Ether ..... 194 


' 35-6 


Ammonia . . . . 130 


H5 


Water 365 


196 


Oxygen -118 


So 


Nitrogen .... 146 


34 


Hydrogen .... 240 


i5'4 



Liquefaction of Gases. 269 

Pictd's Liquefaction of Oxygen. In 1877, Pictet, of Geneva, suc- 
ceeded in liquefying oxygen by cooling the gas, under a high pressure, 
to a temperature which proved to be below the critical temperature, 
now known to be n8C. The oxygen was compressed into a 
steel tube, furnished with a tap, and cooled by means of a jacket of 
liquid carbon dioxide, which was exhausted by a pump. Finally, on 
opening the tap, a pale blue liquid was seen to escape, which evapo- 
rated almost instantaneously. It was thus demonstrated that the 
possibility of reducing gases such as oxygen to the liquid state 
depended, as predicted by Andrews, upon the production of a tem- 
perature below the critical temperature of the gas. 

Caillctd 's Liquefaction of Oxygen. By an independent method, 
Cailletet succeeded in liquefying oxygen in the same year as Pictet. 
The principle adopted was the cooling effect obtained when a gas is 
allowed to expand suddenly from a high pressure, doing work during 
the expansion. The gas was compressed into a thick-walled glass 
tube by means of a hydraulic press, and cooled by means of solid 
carbon dioxide or a liquefied gas. On opening a valve connected to 
the press, an outlet was afforded for the contents ; the gas therefore 
expanded suddenly, driving out the water, and consequently falling 
in temperature. By employing high pressures it was found that the 
cooling effect was sufficient to cause liquefaction, the liquid being 
visible in the form of globules on the sides of the tube. In order to 
prevent the gas becoming wet, mercury was used in the lower half of 
the cylinder of the press, the result of the pumping being to drive the 
mercury up the tube containing the gas, and so to reduce the volume 
to any desired extent. 

Siemens' Regenerative System for Producing Low Temperatures. 
About the year 1862 Sir William Siemens devised a method for 
obtaining low temperatures, based on the cooling effect observed 
when a gas at high pressure escapes through a jet into the atmosphere. 
The actual fall of temperature noted by Joule and Kelvin for air (see 
Chapter VI.) was 29 C. per atmosphere difference of pressure on 
the two sides of the jet, hence air at o C. and 101 atmospheres pres- 
sure, escaping through a jet into a space at i atmosphere pressure, 
would fall in temperature by 29 C. Siemens proposed to utilise uiis 
effect for producing indefinitely low temperatures, by allowing the 
gas escaping through the jet to play upon a metal spiral through which 
the gas passed before reaching the jet. The principle of the method 
is illustrated in Fig. 72, which shows a metal spiral terminating in a 
fine jet, and connected at the other end to a supply of gas at high 
pressure. The gas on leaving the jet is cooled, and by impinging on 



270 



Heat for Engineers. 



the spiral lowers the temperature of the interior gas which is about to 
escape. Each portion leaving the jet is consequently cooler than the 
preceding portion, and if the apparatus could be well shielded from 
external heat, it would appear that the temperature would continue to 
fall indefinitely The principle involved is the exact converse of that 
utilised for the production of high temperatures in the Siemens' re- 
generative furnace. Although the process is in reality continuous, it 
may perhaps be simpler to understand by considering different stages. 
Thus if at the commencement the air were at 10 C., and the pres- 
sure such as to cause a fall of 10 in the escaping gas, the latter would 




FIG. 72. PRINCIPLE OF SIEMENS' REGENERATIVE METHOD FOR 
PRODUCING Low TEMPERATURES. 

be at o C. on leaving the jet. By circulating round the spiral the 
cold air would eventually reduce the temperature of the gas about to 
escape to o C., and if the same pressure were maintained, the tem- 
perature after escape would be 10 C., and so on. Siemens does 
not appear to have applied the system practically, but its revival by 
Linde, Dewar, and others has resulted in the liquefaction of all known 
gases, with the single exception of helium, and has enabled large 
quantities of liquid air, oxygen, nitrogen, hydrogen, etc. to be obtained 
readily. It is found that at low temperatures the cooling effect is 
much greater, for the same difference of pressure, than at atmospheric 
temperatures, which adds further to the efficiency of the process. 



Liquefaction of Gases. 



271 



Linde' s Apparatus for Liquefying Air. The liquefaction of air 
was accomplished by Dr. Linde in 1895 by means of the regenerative 
system, the method of cooling the gas approaching the outlet being 
more effectual, however, than that suggested by Siemens. The 
arrangement employed is shown in Fig. 73, and consisted of a com- 
pressor C, by means of which air was driven through a cooling-tank 
T, the heat of compression being removed by circulating water round 
the pipe through which the air passed. After leaving the cooler, the 
air was passed through the inner tube of a double spiral S, into a 
vessel V through a small valve A, which could be regulated to produce 
any desired size of opening. After undergoing cooling by expanding 




FIG. 73. LINDE'S APPARATUS FOR LIQUEFYING AIR (early form). 

from the valve, the air escaped from the vessel V through the outer 
tube C, thus completely surrounding the oncoming gas contained in 
the inner tube, and effectively reducing its temperature. Finally, the 
air again entered the compressor, and was again forced round the 
circuit. After the lapse of 15 hours liquid air began to collect in tho 
vessel. 

In the modern forms of machines for the production of liquid air 
the same principle is applied, but by improvements in the working 
parts the liquefaction can be accomplished in a much shorter time. 
Machines of this type have been devised by Linde, Hampson, and 
others. In Dewar's apparatus for the rapid production of liquid air 



272 



Heat for Engineers. 



a steel cylinder containing air at 200 atmospheres pressure is con- 
nected to a copper coil which is surrounded by solid carbon dioxide, 
which serves to cool the air to about - 80 C. The air, after travers- 
ing this coil, passes on to a second coil, furnished with a pin-hole 
outlet, and surrounded by a vacuum vessel. After a few minutes 
liquid air escapes through the pin-hole, and collects in the vessel. 

Liquefaction of Hydrogen. Prof. Dewar was the first to accom- 
plish the liquefaction of hydrogen in 1898, although Olszewski and 
others had previously obtained a froth partly composed of the liquid. 
The hydrogen, at a pressure of 180 atmospheres, was passed through 
a spiral surrounded by liquid air, and afterwards expanded through 
a spiral terminating in a fine jet, and con- 
tained in a vacuum vessel. Considerable 
quantities of the liquid were thus collected ; 
and by connecting the vessel to an air- 
pump and exhausting, the solid was readily 
obtained. Solid air and nitrogen may also 
be obtained by exhausting the respective 
liquids ; but owing to possessing a low 
vapour pressure, liquid oxygen fails to 
solidify when treated in this manner. 

Collection of Liquid Gases. Dewar' s 
Vacuum Vessel. The preservation of 
liquefied gases at very low temperatures 
presented considerable difficulties to the 
early investigators, it being found impos- 
sible to insulate the collecting vessel so 

perfectly as to prevent rapid evaporation. An arrangement of three 
glass vessels, separated by air spaces resembling a nest of three 
beakers was the appliance commonly used until Dewar introduced 
the vacuum vessel. This consists of two separate glass vessels, 
sealed together at the neck, and separated by a vacuum. Fig. 74 
shows a section of Dewar's vessel, which is remarkable from the 
perfection with which a substance placed in the inner compartment 
is shielded from the ingress of heat. The complete removal of the 
air forms a space almost entirely free from conduction and convec- 
tion, and by silvering the interior of the outer vessel, radiant heat is 
almost entirely prevented from entering. Any external heat reaching 
the contents must pass by conduction down the sides of the inner 
vessel, and as glass is a bad conductor of heat, the amount entering 
in a given time is extremely small. The superiority of the vacuum 
over any other form of insulation is so marked, however, that the 




FIG. 74. DEWAR'S VACUUM 
VESSEL. 



Liquefaction of Gases. 

absence of gaseous conduction and convection would not appeal 
to furnish a complete explanation. One litre of liquid air, for 
example, may be kept in a vacuum vessel for 24 hours without 
entirely evaporating, although the atmospheric temperature would* 
be 200 C. higher than that of the liquid air. If boiling water b& 
poured into a Dewar vessel of about i pint capacity, and the neck 
be closed by a cork, a temperature of about 90 C. will be indicated 
after the lapse of 12 hours. A protected Dewar vessel is now sold 
for the use of travellers and sportsmen under the name of the 
" Thermos " bottle, by the aid of which food may be kept hot for a 
long period. When used to store liquefied gases, the neck is plugged 
with cotton wool, so as to permit of the free escape of the gas given 
off by the liquid. 

Low Temperature Data. The following figures have been deter- 
mined for liquefied gases, the temperatures being measured by a gas 
thermometer, a thermal junction, or a platinum resistance thermo- 
meter : 



Substance 


Boiling Point, 
Degrees C. 


Freezing Point, 
Degrees C. 


Nitrous oxide .... 


-143 


-ISO'S 


Oxygen ..... 


182-5 


-2 3 8 


Nitrogen 


-193 


-214 


Hydrogen .... 


-252-5 


-257 



Lowest Temperature yet Attained. If solid hydrogen be caused to 
evaporate under the receiver of an air-pump, a temperature of 

- 262 C., or even lower may be attained. The limit of cooling is 
reached when the vapour pressure of the hydrogen becomes com- 
paratively small. It is possible, however, to attain a still lower 
temperature by the use of the rare gas helium, which up to the 
present has not been liquefied. Dewar, and more recently Olszewski, 
have attempted to liquefy helium by compressing the gas in a gl?ss 
tube, and afterwards allowing it to expand suddenly, the apparatus 
devised by Cailletet for the liquefaction of oxygen being used. 
Before expansion the helium was cooled with solid hydrogen to below 

- 250 C, and on expanding from 180 atmospheres to i the tem- 
perature fell to 271*3 C. This is the lowest temperature yet 
attained, being only i 7 C. removed from absolute zero; but is still 
insufficient to cause helium to liquefy. If sufficient helium could be 

T 



274 Heat for Engineers. 

collected to use in a regenerative apparatus, after a preliminary- 
cooling with solid hydrogen, its liquefaction would no doubt be 
effected, and by the rapid evaporation of the liquid or solid, a closer 
approximation to absolute zero could be obtained. 

Properties of Matter at very low Temperatures. The properties of 
different kinds of matter are profoundly modified at very low tem- 
peratures, such as that of liquid air. Many organic substances, such 
as feathers, become phosphorescent when cooled in liquid air ; and 
substances normally soft become frozen into hard, brittle solids. A 
piece of beef or other flesh, and vegetable matters also, become so 
brittle that they may be ground up to powder in a mortar. Mercury 
freezes to a hard solid, which, if pointed, may be driven into wood 
with a hammer. Metals in general, when cooled to the temperature 
of liquid air, exhibit a great increase in tensile strength, which, in the 
case of steel, is to some extent permanent after the steel has regained 
the normal atmospheric temperature. The resistance offered to 
electricity by metals also shows a great diminution, so much so 
that the resistance would appear to vanish or nearly so at absolute 
zero. Substances in general offer an easier passage to heat at very 
low temperatures, this fact explaining, in part, the reason why a 
vacuum jacket is so immeasurably superior to a lagging for protecting 
liquid gases from external heat. Chemical actions which take place 
with violence at ordinary temperatures cannot be made to operate 
at the temperature of liquid air ; the combination of liquid hydrogen 
with fluorine being the solitary exception to the general suspension 
of chemical activity. These, and many other striking phenomena, 
serve to show the extent to which the properties of matter, as we 
know them, depend upon the heat energy present. 

Uses of Liquefied Gases. A number of liquefied gases are now 
used for commercial purposes, and may be obtained from the makers 
stored in steel cylinders, in which the substance retains the liquid 
form owing to its own vapour pressure. Amongst these may be 
mentioned nitrous oxide, or laughing gas, which is used in mild 
operations to produce unconsciousness ; chlorine, for use in certain 
metallurgical processes, such as the refining of gold ; and sulphur 
dioxide, used for disinfecting and other purposes. The advantage 
gained by storing these gases in the liquid form is that the inconveni- 
ence of preparation is avoided, and a large quantity is condensed 
into a small space. Liquid carbon dioxide is largely used in the 
manufacture of aerated waters ; and on the small scale water may be 
aerated in syphons by inserting a small steel cylinder, filled with 
liquid carbon dioxide, and known as a " Sparklet," in the neck of the 



Liquefaction of Gases. 275 

syphon, and liberating the contents by piercing the cylinder : when 
a large volume of gas is produced which saturates the water, and 
provides sufficient pressure. to discharge the contents when the tap 
is opened. Liquid carbon dioxide, ammonia, and sulphur dioxide 
are also used in refrigerating machinery. 

At present liquid air, although it may be manufactured fairly 
cheaply, has not been applied successfully to any industrial process. 
Attempts have been made to use this liquid for propelling the motor 
of a vehicle, but the cost of production is too great to enable a 
liquid air motor to compete with one in which fuel or electricity is 
employed. A possible future use for liquid air may be found in the 
treatment of steel, which has been found by Hadfield to be perma- 
nently improved by dipping in this liquid. As the cost of production 
becomes less, many uses for liquid air will no doubt be found. 

Many experiments have been made with a view to utilising 
liquefied gases as propelling agents in guns, whereby the corrosive 
action of the hot gases produced by an explosive would be avoided, 
and the propelling force generated less suddenly. In no case, how- 
ever, has complete success been attained. 

Liquefaction of Helium By passing helium through a spiral 
cooled with frozen hydrogen, and allowing the escaping gas to cool 
the spiral further, as described on page 270, Professor Onnes, of 
Leyden, has succeeded in liquefying helium. The solid was obtained 
by evaporating the liquid under reduced pressure. The liquefaction 
temperature was found to be about - 269 C., and the freezing-point 
a little lower; it is evident, therefore, that the figures given by 
Dewar and Olszewski (p. 273) to represent the temperatures obtained 
in their attempts to liquefy helium were incorrect. Every known gas 
has now been reduced to the liquid and solid condition. 



T 2 



276 Heat for Engineers, 



CHAPTER XVI. 

REFRIGERATING MACHINERY; ICE MANUFACTURE; 
AND COLD STORAGE. 

Objects of Commercial Refrigeration. In industrial processes 
involving refrigeration, such as the preservation of food and perishable 
articles, the cooling of liquids such as water and milk, the manufacture 
of ice, and the cooling of rooms, it is not desired to obtain an exces- 
sively low temperature, but rather to produce and maintain indefinitely 
a moderately low temperature. Many food-stuffs would be seriously 
damaged if made too cold, and the difference between successful and 
unsuccessful preservation frequently depends upon the maintenance 
of a temperature not varying by more than two or three degrees 
Centigrade. A refrigerating machine, therefore, should be capable 
not only of producing the low temperature desired, but should permit 
of complete regulation of the cooling action, in order that this tem- 
perature may be kept practically constant. Modern refrigerating 
machinery enables both these ends to be secured, and has rendered 
possible the safe transport of perishable foods from the most distant 
parts of the globe. It is probably correct to state that no invention, 
in so short a time, has proved of more general service to mankind 
than the refrigerating machine. 

Early Forms of Refrigerating Machines. Carre's Ice Machine. 
Mechanical refrigeration may be said to have originated in the experi- 
ments of Dr. William Cullen, who, about the year 1755, discovered 
that a compressed gas was cooled by expansion. Cullen also dis- 
covered that water could be frozen by evaporation in a vacuum, and 
constructed a machine which consisted of an air-pump and receiver, 
in which the water to be frozen was placed. The least leakage in the 
air-pump, however, caused the process to fail; and under the best 
conditions, the operation of freezing the water was tedious. No 
advance on the discoveries of Cullen was made until the year 1810, 
when Leslie showed that if a quantity of strong sulphuric acid were 
present in the receiver of the air-pump, the water could be frozen 
much more rapidly, as the water vapour was absorbed by the acid as 



Carres Ice Machine. 277 

quickly as it formed, thus maintaining a vacuum chemically, and not 
relying upon the mechanical removal of the vapour from the pump. 
For many years the attempts at mechanical refrigeration proceeded in 
the direction of producing ice by the evaporation of water, assisted by 
a chemical absorbent; and in 1850 E. Carre', of Paris, invented a 
machine which was capable of producing a small quantity of ice in a 
few minutes, and which was largely used in hotels and restaurants. 
Carre's machine, which is still used to some extent, consisted of an 
air-pump of special construction, worked by hand, to which a vessel 
containing the water to be frozen was attached. In the interior of 
the pump, a chamber was placed containing strong sulphuric acid 
which assisted the action of the pump by absorbing the water vapour. 
In order to prevent the formation of a water-saturated layer on the 
surface of the acid, a stirring device was arranged, so that at every 
stroke of the pump the acid was agitated, and a fresh surface exposed 
for absorption. The acid required frequent renewal, and could easily 
be removed from the machine for this purpose. 

The great drawback to the use of Carre's machine, and to the 
method in general, is the necessity of maintaining a vacuum of less 
pressure than 4 6 mm. of mercury, or about \ of a pound per square 
inch. This represents the vapour pressure of water at the freezing- 
point, and unless a pressure smaller than 4-6 mm. be maintained in 
the vessel, evaporation will cease, and with it the cooling effect. The 
least wear on the plunger of the pump will cause sufficient leakage 
to prevent this degree of vacuity being attained, and consequently no 
ice will be formed. The introduction of the Fleuss pump, with oil- 
sealed valves, has largely overcome this difficulty, and many types of 
machine for producing small quantities of ice on this principle are now 
on the market, in which the superior type of pump is used and which 
are consequently more certain in action than Carre's machine. An 
attempt to apply the method on a large scale was made by Windhausen 
in 1870, but the ice produced proved to be frothy in character, and 
as such commanded no market ; and in addition, the process gave 
trouble from the difficulty of maintaining a proper vacuum. The 
necessity of renewing the sulphuric acid is a further drawback to the 
use of these machines, which are now only used for the production of 
ice on the small scale. 

Principles of Modern Refrigerating Machinery. Three distinct 
systems are in use at the present time for producing a cooling effect 
by mechanical or other means, which may be classified as under. 

i. Air Expansion System. The principle of this system is the 
cooling-effect produced by the expansion of a compressed gas, dis- 



278 Heat for Engineers. 

covered by Cullen about the year 1755. As shown in Chapter VI., 
the extent of the cooling depends upon the work done during the 
expansion, and in machines of this type the expanding gas is allowed 
to do work usefully by helping to compress the next charge. Atmo- 
spheric air is employed in all machines working on this system, being 
cheaper than any other gas, and equally efficient. 

2. The Compression System. In this case a gas or vapour is 
liquefied by pressure in a coil of piping surrounded by cold water. 
It is then passed on to a second coil, surrounded by the medium it is 
desired to cool, and there allowed to evaporate. The latent heat of 
evaporation is extracted from the medium surrounding the coil, which 
thereby undergoes a lowering of temperature. 

3. The Absorption System. A strong solution of ammonia gas in 
water is heated, the gas being thereby expelled, and by conducting 
:he operation in a closed space, the pressure exerted by the liberated 
gas causes it to liquefy, and to collect in a cool receiver connected 
with the space. The liquefied gas is then allowed to evaporate, and 
thus to cool its surroundings; after which it is absorbed in cold water 
or weak solution of ammonia, thus forming a strong solution from 
which it is again expelled by heat, and the previous operations 
repeated. The absorption system differs from the compression 
system only in the manner in which the liquefaction of the gas is 
effected. 

The special features of machines based upon each system, together 
with the advantages and drawbacks, will now be entered into. 

Air-Expansion Machines. The first successful application of the 
cooling effect produced by the expansion of compressed air was made 
by Dr. Gorrie, of Florida, U.S.A., in 1845. Air was compressed in 
a cylinder, into which a jet of water was injected, which served to 
absorb most of the heat of compression. After being further cooled 
by passing through a chamber surrounded by cold water, the com- 
pressed air was allowed to expand in a cylinder into which a jet of 
salt water was forced. The cooling due to the expansion caused the 
salt water to fall considerably in temperature, and the cold brine thus 
obtained was drawn off and circulated round vessels containing water, 
which ultimately froze. Improvements on this machine were made 
by Windhausen, Kirk, Bell, Coleman and others, resulting in the 
standard types of machine now manufactured. 

Air-expansion machines are now made to work on the " open 
cycle," in which case the expanded and cooled air is discharged 
directly into a cold store ; or on the " closed cycle," in which the 
cooled air is allowed to circulate round coils or vessels containing the 



Refrigerating Machines. 



279 



liquid to be cooled, and afterwards returned to the compressor. The 
general arrangement is shown in Fig. 75, in which C represents the 
compression cylinder, E the expansion cylinder, and D the cooler. 
The charge of air is compressed in C to a pressure sufficient to lift the 
valve communicating with D. The hot compressed air then passes 
through the cooler D, which consists of a series of tubes over which 




AIR COMPRESSOR 
AIR EXPANDER 

FIG. 75. PRINCIPLE OF AIR-EXPANSION REFRIGERATING MACHINE. 

cold water is caused to flow continuously. The cooled charge, still 
under high pressure, passes into the expansion cylinder E, the piston 
of which is connected to the same shaft as that of the compressor. 
The compressed air, by driving down the piston of E, does work in 
assisting to turn the shaft, thus compressing another charge in C ; hence 
the expansion is accompanied by a considerable reduction in tem- 
perature. On the return stroke of the piston in E, the cold air is dis- 



280 Heat for Engineers. 

charged through a pipe into the cold store or other space. When the 
piston in C is on the down stroke, a valve communicating with the 
opposite side of the cold store opens downwards, thus allowing a 
partly-cooled charge to enter, which is again compressed, cooled, ex- 
panded, and delivered into the cold chamber. By this means, the 
whole of the air in the chamber is cooled down to the desired tem- 
perature. It is evident that the pistons of C and E must be coupled 
to the shaft in such a manner that compression in the former and 
expansion in the latter occur simultaneously; that is, the up stroke in 
C corresponds to the down stroke in E, and vice versa. The delivery 
of cold air from E to the chamber will then correspond to the entrance 
of a fresh charge from the chamber into C. 

Air-expansion machines may be driven by a steam engine or 
motor coupled directly on to the sh:xft of the machine, or by means 
of a belt from independent shafting. Fig. 76 represents an air ex- 
pansion machine manufactured by the Haslam Foundry and Engi- 
neering Company, of Derby, driven by steam. The steam engine is 
compound, with the two cylinders arranged tandem, and is shown to 
the right in the illustration. The compressor is worked by the middle 
crank, and the expander coupled to the crank to the left. The cooler 
is placed at the back of the machine, which is thus compact and self- 
contained. Where vertical space is a consideration, a horizontal type 
of machine is used. 

Advantages and Drawbacks of Air- Expansion Machines. The 
chief point in favour of air-expansion machines is the cheapness and 
accessibility of the medium, no re-charging being necessary after 
repairs as in the case of machines of other types. There is no danger 
to the attendant, moreover, in case of leakage, whereas such media 
as ammonia and sulphur dioxide are highly dangerous. The extent 
of the cooling can be regulated by slowing down the engine, or 
by controlling the amount of the compression by means of the 
valves. 

A great drawback is the amount of space occupied, for a given 
refrigerating capacity, compared with machines of the compression 
type. Trouble also arises from the accumulation of snow, due to the 
freezing of water vapour in the air, in the expander. A snow-box is 
placed in the pipe communicating with the cold chamber in which the 
snow so formed collects, and is removed periodically, failing which 
the pipe might become choked. Another device is to cool the com- 
pressed air, before admission to the expander, by circulating round 
it cold air from the chamber on its way to the compressor, whereby 
most of the moisture is deposited as liquid, and may be drained off. 



Refrigerating Machi* 



nes. 281 

In either case the necessity of removing the moisture entails a com- 
plication of the machinery. 




FIG. 76. STEAM-DRIVEN ATR-EXPANSION REFRIGERATING MACHINE. 

Another serious drawback is the low efficiency of air-expansion 
machines compared with those of other types, due in large measure to 



282 Heat Jor Engineers. 

the low temperature attained by the expanded air. It will be shown 
later that the highest efficiency of any type of machine is secured 
when the medium is cooled to the minimum extent consistent with 
proper refrigeration. It is far more economical, for example, to 
circulate 100 cubic feet of air cooled by 50, than 50 cubic feet of air 
cooled 100. Limitations of size in the machines render it necessary 
to circulate a comparatively small volume of air, intensely cooled, in 
order to secure the desired reduction in temperature, and as a result 
the efficiency is low. For a given expenditure of horse-power in 
driving the machines, a compression machine will give 4 or 5 times 
the refrigerating effect of an air-expansion machine. For this reason 
the compression type of machine has now almost entirely superseded 
the air-expansion machine, even on boats carrying large cargoes of 
perishable food, the difficulty of renewal of the medium being over- 
come by carrying reserve supplies in the liquid form, stored in 
cylinders. 

The principles governing the efficiency of refrigerating machines 
in general are dealt with in detail in Chapter XX., and may with 
advantage be studied in connection with the present chapter. 

The Compression System. The first attempt to apply the lique- 
faction and subsequent evaporation of a substance to practical 
refrigeration was made in 1834 by Jacob Perkins, who experimented 
with a volatile liquid derived from the distillation of rubber. The 
vapour produced by subjecting this liquid to a reduced pressure was 
compressed, re-forming the liquid, which was then allowed to evaporate 
in a space surrounded by the substance to be cooled, from which the 
latent heat of vaporisation of the liquid was extracted. The resulting 
vapour returned to the compressor, to be again liquefied and sent to 
the evaporator ; the heat produced by the liquefaction in the com- 
pressor being removed by cooling-water. Perkins did not succeed 
in producing a commercial machine, but his experiments demonstrated 
the possibility of obtaining a continuous refrigerating effect by sub- 
jecting a condensable vapour to a proper cycle of operations. It was 
not until 1860, however, that the process was employed for industrial 
purposes, when James Harrison, of New South Wales, revived the 
project, and by using ether as medium succeeded in constructing a 
machine which at once came into use for ice manufacture and other 
purposes. The introduction of ammonia as the medium by Linde in 
1873 marked the next great step in the development of compression 
machines, and was followed in 1876 by the employment of sulphur- 
dioxide by Pictet, and of carbon-dioxide by Raydt in 1881. Since 
the last date great improvements in the design and details of com- 



Refrigerating Machines. 28 



pression machines have been made by various inventors, with the 
result that, except for special purposes, other types are now seldom 
constructed. 

The cycle of operations in a modern compression machine may 
be understood by reference to Fig. 77. Assuming the interior of 
the machine to be fully charged with the medium, the upward 
stroke of the piston compresses the gas in the cylinder, and, at a 
given pressure, causes a valve connected with the condenser to open. 
The condenser consists of a coil of piping round which cold 
water is circulated, the heat produced by the compression being thus 
removed. The pressure employed suffices to liquefy the gas, which 
condenses in the coils, and is pushed forward through a regulating 
valve into a second set of coils, surrounded by the liquid to be 
cooled. The downward stroke of the piston causes a diminution of 
pressure in the cylinder, when the valve connected with the refrigerator 
or evaporator coils opens, the liquid in these coils then evaporating 
and entering the cylinder; the valve communicating with the con- 
denser being closed meanwhile owing to the superior pressure behind 
it. The cooling effect is due to the latent heat of vaporisation of the 
liquid, which is extracted from the evaporator coil and its surroundings 
A separator is interposed between the cylinder and condenser coil, 
which serves to intercept any lubricating oil which may be carried 
over from the cylinder, and which, if not removed, would finally choke 
up the coils. 

It is evident that the foregoing set of operations is repeated at 
every double stroke of the piston, and hence the cooling effect is con- 
tinuous. The act of compression represents the conversion of work 
into heat, which is removed by the cooling-water ; the act of expan- 
sion represents the conversion of heat derived from the substance to 
be cooled into work, which is utilised in the back stroke of the 
piston in helping to drive the machine. Heat is taken in at one side 
and rejected at the other, but, in direct opposition to the action of a 
heat engine, the heat is rejected at the higher temperature and taken in 
at the lower. A refrigerating machine in reality is the converse of a 
heat engine in respect to the cycle of operations. In a refrigerating 
machine the medium enters the cylinder at the lower temperature 
and leaves at a higher, work being absorbed in the process, whilst in 
a heat engine the medium enters at the higher temperature and leaves 
at the lower, work being given out as the result. 

The general arrangement of parts in an actual machine is shown 
in Fig. 78, which is self-explanatory. A point which calls for com- 
ment is the different readings of pressure recorded on the two gauges, 



28 4 



Heat for Engineers. 



one of which is connected to the condenser and the other to the 
evaporator coils, in spite of the fact that both coils communicate. 
The explanation is to be found in the small size of the opening 




Refrigerating Machines. 



285 



connecting the two sets of coils, which can be varied in dimensions by 
the regulator. If a wide opening connect two vessels containing a 
gas, the pressure in both vessels will be the same ; but if only a tiny 
orifice be provided it is possible to maintain widely different pressures 
in the two vessels. Hence, owing to the small opening connecting 
the two sets of coils, a higher pressure may exist in the condenser 
than in the evaporator. 

Evaporator Gauge 



Condenser Gauge 



Regulator 



Evaporator 

coi'i 



Condenser 
coil 



Condenser. 
casing 



Insujated division 
b/ween Condenser 
& Evaporator 




Patent Safety Valve 
' inhere 



Separator 



Compressoi 



Parent hol/ow 
Oil Gland 



Connecting Rod 



" Driving 
pufley 

Crank 
Shaft 



Brine, circulating 
pump 

FIG. 78. ARRANGEMENT OF PARTS IN COMPRESSION MACHINE. 

Choice of Medium. Theoretically, as the medium used serves 
merely to carry the heat, any gas or vapour fulfilling the conditions 
imposed should be as efficient as any other. In practice, however, 
the chemical and physical peculiarities of the gas or vapour selected 
must be taken into account. Obviously, a gas which corrodes the 
working parts would be inadmissible, and it is further desirable to use 
a non-inflammable medium, in order that leakage may not be accom- 



286 Heat for Engineers. 

parried by the danger of explosion. General use has only been made 
up to the present of ammonia, carbon-dioxide and sulphur-dioxide ; 
ether being more rarely used on account of its extreme inflammability. 
The relative fitness of the three gases named will now be separately 
considered. 

Ammonia gas (NH 3 ) is extremely cheap, and may be liquefied by 
the application of moderate pressures at ordinary atmospheric tem- 
peratures. It possesses a high critical temperature, viz. 130 C. or 
266 F.,and may therefore be liquefied by pressure under any existing 
atmospheric conditions. The liquid has a high latent heat of vapor- 
isation, and both gas and liquid have no chemical action on iron or 
steel. On the other hand, copper and its alloys (brass, bronze, etc.) 
are seriously corroded by ammonia, and cannot be employed in any 
part of the machine to which the gas has access. Further, ammonia 
gas is extremely poisonous, and a considerable leakage may prove fatal 
to the operator. A small leakage is readily detected by the pungent 
odour of the gas. In modern machines a dangerous leakage is a 
somewhat remote contingency, and the favourable properties of the 
gas in other respects have caused ammonia to be extensively used in 
compression machines. A table is appended showing the constants 
of ammonia at different temperatures. 

In connection with the table on p. 287, it should be remembered 
that gauge pressure is less than absolute pressure by 14 7 Ib. per square 
inch. The pressure required to ensure liquefaction at any given 
temperature may be obtained from the table thus at 100 F. the 
absolute pressure requisite is 215*12 Ib. per square inch, or 14' 6 
atmospheres. This pressure would therefore exist in the condenser 
coils when the temperature inside always higher than that of the 
cooling-water outside is 100 F. The diminishing value of the latent 
heat of vaporisation as the temperature rises is common to all liquids, 
the value becoming zero, as has previously been pointed out, at the 
critical temperature. 

Carbon-dioxide (CO 2 ) is cheaper even than ammonia, and has the 
valuable property, both in the gaseous and liquid states, of being 
chemically inert towards all ordinary metals, thus affording a wider 
choice in materials for constructing the machine than when ammonia 
is used. Carbon-dioxide is not specifically poisonous, although an 
atmosphere of the gas will n' v t sustain animal life. The escape of an 
entire charge from a machine into the engine room is unaccompanied 
by any dangerous results, the percentage of oxygen in the atmosphere 
not being reduced sufficiently to give rise to risk of suffocation. In 
these respects carbon-dioxide is superior to ammonia as a refrigerating 



Refrigerating Mac/lines. 



287 



CONSTANTS OF AMMONIA (NH 3 ). 

Specific heat of ammonia vapour Constant pressure . . = 0*508 
,, ,, ,, Constant voiums . . = 0-3913 

,, ammonia liquid ... i '01235 + 0-008378 1- 



Temperature 
Degrees F. 


Gauge 
Pressure. 

Ib. per sq. in. 


Latent Heat 
of Evaporation. 
B.Th.U. 
per Ib. 


Volume of i Ib. in 
Cubic Feet 


Weight of i cubic 
foot in Pounds 


Vapour 


Liquid 


Vapour 


Liquid 


30 


-o'57 573"69 


18-69 


0237 


0535 


42-123 


-25 


+ 1-47 570-68 


16-44 


0238 


0608 


4I-858 


2O 


3'75 567-67 


T 4'5i 


"0240 


"0690 


4I-6I5 


-15 


6*29 


564-64 


12-83 


0241 


0779 


41-374 


10 9'io 


56l-6l 


11-38 


0243 


0878 


4I-I35 


5 I2'22 


558-56 


JO' 12 


0244 


0988 


40*900 


zero 


15-67 


555'50 


9-03 


0246 


' IIO7 


40 ' 650 


-t- s 


19-46 


552-43 


8-07 


0247 


1240 


40-404 


10 


23-64 


549*35 


7-23 


0249 


1383 


40-160 


15 


28-24 


546-26 


6-49 


0250 


1541 


39-920 


20 


33-25 


543' i5 


5-84 


0252 


I7II 


39-682 


25 


38-73 


540-03 


5-27 


0253 


1897 


39-432 


30 


44-72 


536-91 


4-76 


0255 


2099 


39-200 


35 


51-22 


533-78 


4-3I 


0256 


2 3 l8 


38-940 


40 


58-29 


53^63 


3-9I 


0258 


2554 


38-684 














45 


65-96 


527-47 


3-56 


O26O 


2809 


38-461 


5o 


74-26 


524-30 


3-24 


-O26l 


3084 


38-226 


55 


83-22 


521' 12 


2- 9 6 


0263 


3380 


37-994 


60 


92-89 


5J7-93 


2-70 


0265 


-3697 


37-736 


65 


103-33 


5I4-73 


2- 4 8 


0266 


4039 


37-48I 


70 


114-49 


5ii-52 


2-27 


0268 


4401 


37-230 


75 


126-52 


508 29 


2-O9 


0270 


4791 


36-995 


80 


139-40 


505'05 


I-92 


0272 


5205 


36-75I 


85 


I53-I8 


501-81 


1-77 


0273 


-5649 


36-509 


90 


167-92 


498-55 


1-64 


0275 


6l2O 


36'258 


95 


183-65 


495-29 


i'5 r 


0277 


6622 


36-023 


IOO 


200*42 


492-01 


i-39 


0279 


7153 


35-778 


!05 


218-28 


488-72 


1-29 


0281 


'7757 




no 


237-27 


485-42 


I'20 


0283 


8312 




115 


258-70 


482-41 


I'I2 


0285 


8912 


.- 



288 Heat for Engineers. 

medium, but on the other hand it is impossible to liquefy the gas at 
temperatures above 31 C. or 88 F., which is the critical temperature, 
and may frequently be exceeded in the condenser coils when the 
machine is used in hot climates. Failure to liquefy, however, does 
not entail a cessation of refrigerating action : what happens is that 
compressed gas is delivered into the evaporator coils instead of liquid, 
and by expanding into the cylinder causes a lowering of temperature. 
As the design of the machine is not suited to a cooling action of 
this character, the efficiency is slightly lowered when the condenser 
temperature exceeds 88 F. A further drawback to the use of carbon- 
dioxide is the extremely high working pressure, which at 50 F. is 
46 J atmospheres or 680 Ib. per square inch (absolute) and 1080 lb. 
per square inch at 86 F. This high pressure necessitates stronger 
working parts than are necessary for an ammonia machine / and makes 
the prevention of leakage a difficult matter. At the same time, the 
existence of the higher pressure enables the desired cooling effect to 
be obtained with a smaller compressor, and consequently, for a given 
power, a carbon dioxide machine is less in size than an ammonia 
machine. Further, if any gas escaping from the machine should come 
into contact with stored food-stuffs, no taint is produced by carbon 
dioxide, whereas both ammonia and sulphur dioxide impart a most 
objectionable flavour to meat, etc. Taking all the factors into con- 
sideration, the choice between ammonia and carbon dioxide becomes, 
difficult; the modern tendency, however, is to prefer the latter, except 
for the largest installations, influenced largely, no doubt, by considera- 
tions of space and the non-poisonous and inert character of carbon- 
dioxide. A table of constants of carbon dioxide is given on p. 289. 

A comparison of the table on p. 289 with that given for ammonia 
shows that whilst liquid CO., has a much lower latent heat of vaporisa- 
tion, a far greater weight of refrigerant is present in a given volume, 
which more than outweighs the inferiority in latent heat. For a given 
effect an ammonia compressor must possess seven times the volume 
required for a carbon-dioxide machine. 

Sulphur-dioxide (SO 2 ) is also a cheap gas, and was first used by 
Pictet, of Geneva, in refrigerating machines. It is capable of easy 
liquefaction, has a fairly high latent heat of vaporisation, and does 
not attack metals if free from moisture. It is very poisonous, how- 
ever, and owing to the low pressure at which it liquefies a relatively 
large compressor is necessary. One advantage of liquid sulphur- 
dioxide is that it acts as a lubricant to the moving parts, consequently 
no oil is necessary and the need for a separator obviated. In modern, 
practice the use of sulphur-dioxide is restricted to minor refrigerating 



Refrigerating Machines. 



289 



CONSTANTS OF CARBON DIOXIDE (CO 2 ).* 



Boiling 
Temperature 

Degrees F. 


Gauge 
Pressure 
Atmospheres. 
= 14-7. lb; 
per sq. inch 


Total Heat 
reckoned 
from 32 F. 


Latent Heat 
of 
Evaporation. 
B.Th.U. 
per Lb. 


Increase of 
Volume 
during 
Evaporation 


Weight of 
i cubic foot 
of Vapour 

Lb. 


-22 


13-28 


98*35 


I36*I5 


4138 


2\32I 


-13 


15-27 


99*14 


I3I*65 


'3459 


2-759 


~ 4 


I8'86 


99'88 


126-79 


2901 


3-265 


+ 5 


22-26 


100-58 


121-50 


2438 


3*853 


14 


25*93 


101-21 


II5-70 


2042 


4*535 


23 


30-08 


lOI'Sl 


IC9'37 


I7II 


5*33i 


32 


34'76 


102-35 


102-35 


1426 


6-265 


4i 


39*74 


I02-84 


94'52 


1177 


7*374 


5o 


45'2S 


103-34 


85-64 


0960 


8-708 


59 


51*24 


I03-59 


75-37 


0763 


10-356 


68 


57*75 


103-84 


62-98 


0577 


12*480 


77 


64-85 


103*95 


46-89 


0391 


15*475 


86 


72-47 


103-72 


19-28 


0147 


21-519 



* According to some makers of refrigerating machinery, this table stands in need 
of revision, as the figures in some cases do not agree with those obtained in practice. 

operations, such as the cooling of dairy produce, or small-size cold 
stores. A sulphur-dioxide machine intended for working on the 
large scale would require a far larger compressor than an ammonia 
machine, and consequently considerations of space and material lead 
to the selection of other media. The chief constants of sulphur 
dioxide will be found in the following table : 

CONSTANTS OF SULPHUR DIOXIDE (SO 2 ). 



Temperature, 
Degrees F. 


Absolute Pressure 
in lb. per sq. inch 


Latent Heat of 
Vaporisation, 
B.Th.U. per lb. 


Volume of i lb. 
of Vapour in 
Cubic Feet 


- 4 


9*27 


171-0 


8-06 


+ 14 


I4'75 


168-2 


5*27 


32 


22-53 


164-2 


3*59 


50 


33-26 


158*9 


2-44 


68 


47-6I 


152-5 


I-7I 


86 


66-36 


144-8 


I '22 


104 


90-30 


i35*9 


0-88 



2 go Heat for Engineers. 

It will be observed that the pressure required to liquefy the gas 
at a given temperature is much less than in the case of ammonia ; at 
50 F., for example, the values are 33*26 and 88-96 Ib. per square 
inch (absolute) respectively. This means that a less weight of the 
sulphur-dioxide is contained in a given space, and consequently that 
a larger compressor is necessary for a given cooling effect. 

Other Media. Apart from the three substances named, ether is 
the only other medium at present employed to any extent, and this 
only in cases where it is difficult to obtain fresh supplies of liquefied 
gases. Ether boils at 35 C., and may therefore be kept in ordinary 
bottles at most atmospheric temperatures. 

Use of Brine in Cooling. Two methods are available for 
removing the heat from a cold store or other place when the com- 
pression system is used. One is to allow the liquefied gas to 
evaporate in coils of piping distributed through the space to be 
cooled, and the other to circulate brine from a tank surrounding the 
evaporator coils through a system of pipes suitably placed in the cold 
store. The latter system is generally preferred, and possesses the 
advantage of acting as a storage of " cold " ; as when once the pipes 
are filled with cold brine the machine may be stopped without risk 
of an undue rise in temperature, even for several hours. Brine is 
selected as the cheapest liquid that will not freeze at the temperatures 
employed. For moderately low temperatures a brine made by dis- 
solving common salt in water may be used ; for lower temperatures 
calcium chloride, which, being more soluble, forms a solution of 
lower freezing-point, is substituted for common salt. The properties 
of solutions of these salts are appended in tabular form (see p. 291). 

The freezing-point of a saturated solution of calcium chloride is 
- 40 C. ( - 40 F.), and of common salt - 23 C. ( - 9 4 F.). 

Types of Compression Machines. Compression machines are 
made in a great variety of patterns, being procurable either combined 
with a steam engine or motor for driving purposes, or made so as to 
be belt-driven. Three types are selected for illustration, of which 
Fig. 79 represents a carbon-dioxide machine, horizontal land type,, 
manufactured by Messrs. J. E. Hall, Ltd., of Dartford. The driving 
power is furnished by a compound steam engine, the cylinders being 
arranged tandem ; the compressor being driven by a tail rod. The 
condenser and evaporator are separate from the machine, and may 
be fixed in any adjacent spot. Machines of this type are made 
capable of producing from 8 to 45 tons of ice in 24 hours, according 
to size. 

Fig. 80 shows a steam-driven ammonia machine, of the vertical 



Refrigerating Machines. 



291 



<u 


4> 

T3 




vo vO vo CO i* 




u 


1 


f O rl- GO 


smperatu 


U 

.? 

'c 
U 


N vo ON 3- , 
1 1 1 1 1 




a 


J 


i i T T T 


H 
bo 




vo O O O O 




H 
bo 




o 




(4 


fM l_T* l/"i CiT) 




*N 


r- 




1 


1 


M N "- 

1 




ta 





^> GO W vo o 


&** 


| 


rh vo O ^ O 

vo ON vO co ON 
ON OO 00 00 t>. 




li 


3 


O M VO ON CO 

VO ON vo M 00 
ON OO GO 00 *-. 


"* 


* 




H 

hJ 


Wl 


CO 






3 


CO t-^ Tf N Tj- 

T}- 00 CO OO CO 


< 
CO 

S5 

o 




"(3 


r^ co vo O 1-1 
co f^ -, vo ON 


fl 


g 


O b M H* N 


s 




1 


- g M M M 


J3 






S 


L^ 


3 

r 


H 




allon of 5 


U 


M GO O VO OO 

i-o O ^>* ^^ O 


s 

& 

Q 
O 


allon of S 




00 CO J^ g !>. 

^ vo O vo co ON 


O 


u 


b - M i, 


CO 

b 
O 


O 
"o 




O M HI M C4 


to 


a 

rt 


OO to ON vO xn 

O OO f*O 1 -O ^-O 


Q 

s 


I 
H 


5 


tH t^>. VO O CO 

. 10 vo t^ O C>1 

.a oo vo -^ M ON 




& 


ON ON ON ON ON 


u 

b 




^ 


ON ON ON ON 00 


^ 
wt 




vo O vo O vo 


SOLUTION c 


Percentage 

of Salf 


by Weight 


vo O vo O vo 

*i >i CS CS 


it 


if H 


co r^ rf M Tf 
T}~ CO CO OO co 
O O n >-i N 


fe 
o 

8 


|| 


-'! 


r-^ co vo o "- 1 
co r~ >-i vo ON 

O o i-i - 


" 


** 


M IH HI M M 


r 1 
ce) 
W 
cu 


" 


SS 




1 

. 


Twaddell 


- rr & ft ^ 


O 

C^ 

PH 


J 
rt 

,y 


"T3 

H 


t^' vo co O oo 
1-1 N CO co 


ss on various S 


Beaume 


vo M r^ co co 




es on various S 


Beaume 


vo O vo ON rt- 



& 

Q 


Salometer 


Tf t^ CXD N N 

N ij- O ON 




i 

Q 


Salometer 


8 3- 3 3 8 



U 2 



Refrigerating Machines. 



293 



type, made by the Haslum Foundry and Engineering Company, of 
Derby. The condenser coils are placed in the bed-plate, and a 




FIG. 80. STEAM-DRIVEN AMMONIA MACHINE, VERTICAL TYPE. 

water-pump is connected to the shaft for the purpose of circulating 
water round the condenser. A receiver for the liquefied ammonia is 
also provided. The steam engine and compressor are fixed side by 



294 



Heat for Engineers. 



side, and the oil separator and gauges are placed at one side of the 
machine. This forms a convenient and compact machine for > small 
cooling operations, particularly where space is a consideration. 




FIG. 81. BELT-DRIVEN SULPHUR-DIOXIDE MACHINE. 

The machine illustrated in Fig. 81 is a sulphur-dioxide refrige- 
rator made by William Douglas and Sons, Ltd., of Putney, intended 
specially for dairies and small cold stores. It is driven by means of 
a belt, and by passing the shaft to which the compressor crank is 



Refrigerating Machines. 295 

connected through the condenser tank, great steadiness is secured. 
The evaporator coils, surrounded by brine, are contained in a lagged 
tank on the base-plate, and pumps are provided for circulating the 
brine and cooling-water. The regulating valve is situated above the 
condenser tank. This machine is largely used in minor refrigerating 
operations ; and may suitably be driven by a small suction-gas or 
other gas engine. 

Description of Parts of Compression Machines, i. The Compressor. 
The piston, and in larger machines the cylinder also, are best 
made from steel forgings, the piston being fitted with rings. The 
valves are made of tempered steel, and the seats of phosphor bronze 
or steel, bronze being inadmissible in ammonia machines. The 
piston rod moves in a gland filled with oil under pressure, which 
causes two cup-leathers to be squeezed against the piston rod, and 
thus prevents leakage. By maintaining the oil at a higher pressure 
than the enclosed gas which is effected by a small pump all 
possibility of leakage is prevented, and sufficient oil is taken by the 
rod into the cylinder to ensure proper lubrication of the piston. 
This oil is afterwards carried to the separator, and run out when 
necessary. Compressors are made either single or double-acting. 

2. The Condenser. Two types of condenser are used, viz., the 
submerged condenser, in which the coils are immersed in water in a 
tank through which a circulation is maintained; and the surface 
condenser, in which the pipes are exposed to the air, and water from 
a trough placed above allowed to trickle over. The submerged type 
is generally used for small machines, and in cases where the cost of 
water is not of moment ; the surface type is more economical so far 
as cooling-water is concerned, as the latent heat of evaporation of 
the water is utilised in the cooling process. The tubes are made of 
wrought iron or mild steel, welded into continuous lengths. The 
condenser may be placed in any convenient position, and may be 
located at a considerable distance from the compressor. 

3. The Evaporator. This consists of coils of iron piping, which 
is surrounded by the medium to be cooled. In case of brine-cooling, 
the coils are placed in a tank through which the brine is circulated 
by a pump ; when used without brine the coils are placed in the cold 
store, and the heat absorbed by the evaporating liquid extracted 
directly from the air. 

4. The Oil-Separator. In order to remove any oil carried over 
by the compressed gas in the form of spray, a chamber furnished 
with a baffle-plate is provided, situated between the compressor and 
condenser. The oil adheres to the baffle-plate, and gradually trickles 



296 Heat for Engineers. 

down to the bottom of the vessel, from which it may be withdrawn 
by opening a suitable cock. 

5. The Safety-Valve. The high pressures prevailing in com- 
pression machines render a safety-valve desirable, and these, when 
used, consist of a conical valve held on to its seat by a strong spring, 
which must be overcome before the valve lifts. Messrs. Hall, of 
Dartford, interpose a copper disc between the interior of the machine 
and the valve, which would burst under an undue rise of pressure, 
and allow the valve to come into action. Any loss of gas in ordinary 
working, due to a leaky valve, is thus avoided. 

6. The Expansion Valve. The essential feature of this valve is 
that the size of the opening between the condenser and evaporator 
must be capable of a very fine adjustment, as the quantity of liquid 
passing through determines the amount of evaporation which ensues 
in the coils, and hence the extent of the cooling. Numerous forms 
are made, some of which are elaborate in structure. A simple and 
effective valve is made by constructing a conical opening between the 
two sets of coils, which may be closed, either wholly or partially, by 
means of a conical plug, the extension of which is screwed and passes 
through a nut to the handle. Every gradation from fully open to 
completely closed is thus made possible. 

Advantages of Compression Machines. Compared with air-expan- 
sion machines, the greater efficiency, smaller size, and easier regula- 
tion of compressing machines confer upon the latter a great superiority. 
Not only can a far larger refrigerating effect be obtained for the 
expenditure of a given amount of energy, but the space occupied a 
great consideration in many cases and the prime cost of the smaller 
machine are much less than when the air-expansion system is 
employed. By the use of circulating brine the temperature of a cold 
store may be adjusted with greater precision than is attained by the 
ingress of cold air. In consequence of the advantages enumerated, 
compression machines are rapidly superseding those of the air-expan- 
sion type, both for use on land and sea. 

2 he Absorption System. Ferdinand Carre, of Paris, was the first 
to invent a machine working on the absorption system. It consisted 
of a boiler, containing a saturated solution of ammonia in water, and 
connected by a pipe to a chamber surrounding a vessel in which water 
was placed to be frozen. On heating the solution in the boiler, large 
quantities of the gas are expelled, and sufficient pressure is thereby 
generated to cause the gas to liquefy in the chamber, which, during 
this part of the part of the operation, is placed in a tank of water to 
assist the condensation. The boiler is now removed from the fire 
or source of heat; and on cooling the solution re-absorbs the 



Refrigerating Machines. 



297 



ammonia gas above it, causing a partial vacuum in the chamber sur- 
rounding the water. Rapid evaporation of the liquefied ammonia 
ensues in consequence, and by extracting the latent heat of evapora- 
tion from its surroundings, causes the water to freeze. The solution 
in the boiler is now strong, and the operations may be repeated 
indefinite]}. 

The step from the intermittent action of F. Carre's machine to a 
continuous action was made soon after by many inventors, and in 
Britain Messrs. Pontifex and Wood took up the manufacture of absorp- 
tion machines with considerable success, introducing many improve- 
ments which led to a widespread adoption in breweries and elsewhere. 
No other gas than ammonia has been used, as the combined properties 
of extreme solubility in cold water and almost complete expulsion on 
boiling, and the absence of corrosive action on iron, are not possessed 




FIG. 82. PRINCIPLE OF ABSORPTION REFRIGERATING MACHINE. 

by other gases. At 16 C., or 61 F., water will absorb 760 times its 
volume of ammonia gas, which is almost entirely expelled on boiling. 
The points in favour of and against ammonia as a medium, already 
enumerated in connection with compression machines, apply to 
absorption machines also. 

Principle of Modern Absorption Machines. Modern machines 
working on the absorption system take many forms, but the general 
principle may be understood from Fig. 82, which represents the 
method adopted in the machines manufactured by Messrs. Ransom^s 
and Rapier, Ltd., of Ipswich. A strong solution of ammonia in water 
is heated by steam-pipes passing through the generator, the gas being 
thereby expelled and driven over into the condenser. The large 
mass of gas driven off generates a pressure of 1 20 Ib. in the condenser, 
which consists of a series of pipes surrounded by cold water. The 
gas liquefies under this pressure, and passes in the liquid state through 
an expansion valve of the same type as those employed in compression 
machines, into the cooler or evaporator, which also resembles the 



298 Heat for Engineers. 

corresponding part of a compression machine. From the cooler the 
gas passes into the absorber, which contains a cold, weak solution of 
ammonia, in which the gas re-dissolves, strengthening the solution, 
which is then pumped back again into the generator. The solution 
in the generator, as fast as it is deprived of gas by the heat of the 
steam coils, is allowed to trickle through a regulating valve into the 
absorber, through a cooling arrangement not indicated in the diagram, 
and, after absorbing a fresh quantity of gas, returns to the generator. 
The whole arrangement is such as to secure a continuous disengage- 
ment of ammonia gas, and consequently a continuous refrigerating 
effect. In order to prevent moisture being carried over by the 
ammonia gas, a water-separator or purifier is inserted between the 
generator and condenser. 

It will be observed that the absorption system differs from the 
compression process only in the method employed to secure a con- 
tinuous supply of liquefied gas, heat compression taking the place of 
mechanical compression. The appearance of the actual machine is 
depicted in Fig. 83, the various parts being constructed in the form 
of wrought iron cylinders which contain the coils of piping common 
to the generator, evaporator, condenser, and weak ammonia cooler; 
the whole being mounted so as to give compactness and easy access 
to the regulators. 

Advantages and Drawbacks of Absorption Machines. The chief 
points in favour of the absorption system are the almost entire 
absence of moving mechanism, and the ease with which the machine 
may be operated, even by unskilled labour. The upkeep of the plant 
is consequently less costly than in the case of compression or air- 
expansion machines, as there are fewer repairs and less labour re- 
quired. Against this must be recorded the drawback of the necessity 
of a steam boiler as adjunct, whereas machines of the other types 
can be worked by motors, or a small oil or gas engine, in cases where 
steam is not available. The efficiency is about equal to that of the 
compression machine. On the whole, the absorption machine is well 
adapted for cooling operations in dairies, etc., where a skilled atten- 
dant is not at hand ; and in making clear ice an economy can be 
effected by using the steam condensed in the process as the supply of 
distilled water for conversion into ice. 

11 Capacity" of Refrigerating Machines. The capacity of a refrigera- 
ting machine may be expressed by the number of heat units extracted 
per hour from the evaporator* (or the ice-making equivalent of the heat 

* The extraction of 12,000 B.Th.U. per hour from water at o C. or 32 F. is 
frequently taken as a unit of capacity, and is called " I ton." It is equivalent to 
the production of 2000 Ib. of ice in 24 hours from water at the freezing point. 



Refrigerating Machines. 



299 



extracted) ; or by the actual quantity of ice manufactured in a given 
time. In each case] the temperature of the cooling-water and atmo- 
sphere must be specified. It is customary to take each of these 
temperatures as 55 F., and the time in the case of ice-making capacity 




FIG. 83. ABSORPTION MACHINE. 

as 24 hours. Thus a machine capable of making 10 tons of ice in 
24 hours is said to have an " actual " capacity of 10 tons. Owing to 
considerable losses in the ice-making plant itself, the capacity as 
measured by the heat extracted from the surroundings of the evapo- 
rator coils, will exceed the " actual " capacity. The former, which is, 



-oo Heat for Engineers. 

designated the " refrigerating " capacity, depends, as shown below, on 
the working temperature, but in ordinary working is usually about 
twice as large as the " actual " capacity. 

"Energy-Ratio" of Refrigerating Machines. In a heat-engine 
work is given out by taking in heat at a high temperature and rejecting 
heat at a lower temperature, the difference between the entering and 
leaving quantities being the equivalent of the work done by the engine. 
The " efficiency," or proportion of heat converted into work, is there- 
fore expressed by the ratio 

Heat entering - heat rejected 
Heat entering 

In a refrigerating machine matters are reversed ; the heat enters at the 
lower temperature (from the evaporator coils) and is rejected at a 
higher temperature (in the condenser). To make this possible, work 
must be furnished from an external source ; and the ratio of the 
cooling effect to the work expended in driving evidently decides the 
capability of the machine. This ratio is given by the expression 

Heat extracted 



Heat expelled - heat extracted 
or 

Heat extracted 
Heat equivalent of work furnished 

the work entering the machine being converted into heat, and 
being equivalent to the net amount of heat rejected. Various terms 
such as " coefficient of duty," etc., have been proposed for this ratio, 
which appears, however, to be best expressed by the designation 
" energy ratio" as suggested by the author. It will be shown later 
(Chapter XX.) that the quantities of heat expelled and taken in by an 
ordinary heat engine, or an inverse heat engine (refrigerating machine) 
are proportional to the absolute temperatures at which the heat 
leaves and enters. Applying this to a refrigerating machine, 
Energy ratio = 

_^\bsolute temp, at which heat is extracted (T ? ) 
Absolute temp, at which expelled - absolute temp, at which extracted 

TO (T 2 ) 

or, expressed in symbols, 

Energy ratio = Ta 



Refrigerating Machines. 301 

It is evident that the practical energy ratio will be less than the calcu- 
lated, owing to the losses by friction, etc.; and the ingress of external 
heat. A fuller discussion of these points will be entered into in con- 
nection with the subject of thermodynamics ; a few examples, how- 
ever, will now be given to illustrate the use of the formula obtained. 

Example i. The temperature of the cooling water supplied to the 
condenser of a refrigerating machine (and assumed to be equal to that 
of the contained medium) is 20 C., whilst that in the interior of the 
evaporator is - 6oC. To find the energy ratio. 

Converting into absolute degrees, T 2 = 213, and 1\ = 293 ; 

hence energy ratio = - - - = 2 '66. 
293 - 213 

This means that the heat extracted from the surroundings of the 
evaporator coils would be 2 '66 times as great as the heat equivalent 
of the work done in driving the machine, neglecting losses. 

Example 2. To compare the economy of an air-expansion 
machine which delivers i Ib. of air at - 4oC. with that of another 
machine which delivers 2 Ib. at - 20 C. into a similar store. Con- 
denser temperature in each case = 25 C. 

The amount of cooling due to the entry of i Ib. of air at - 40 C. 
is the same as that caused by 2 Ib. at - 20. The energy, ratio, 

however, differs in the two cases, being -^^ - = 3*59 and 

298 - 233 



= 5 "63 respectively. 



Hence for a given cooling effect, the machine working at the 
higher temperature would require less driving-power, in the ratio 

3-59 _ _J_. or ! H.P. in the second case would be equal in 

5-63 i-57 

cooling effect to i '57 in the first. 

Example 3. A carbon dioxide machine works at gauge-pressures 
of i8'86ats. and 51 "24 ats. in evaporator and condenser respectively. 
10 H.P. are required to drive the machine, and the losses from various 
causes are 50 per cent. To find the capacity of the machine, i,e. 
number of tons of ice made in 24 hours from water at 15 C. 

Reference to the table of constants of carbon dioxide f shows that 
the temperatures corresponding to 18*86 and 51*24 ats. are -4 F. 
and 59 F., or - 20 C. and + 15 C. Hence the energy ratio, or 

heat extracted _ . g , tQ _^53__ = J . 

heat equiv. of work provided 288 - 253 



302 Heat for Engineers. 

Allowing for 50 per cent, losses, the figure becomes -^ = 3-62 

(approx.). This means that every horse-power expended on the 
machine will extract rnat equivalent to 3*62 H.P. from the water to 
be frozen. Hence 10 H.P. in 24 hours will extract 

ip_x_3_ 3 ooo_x 60 x 24 x 3^62 = Ij229>000 lb _o c units (approx-) . 
1400 

since 1400 ft.-lb. = i lb-C. unit. To convert i Ib. of water at 15 C. 
into ice requires 95 lb.-C. units; hence weight of ice made = 

_I229000_ = 8tons 

95 x 2240 

The examples given are intended to illustrate the general prin- 
ciples governing the working of the machines, and are not to be 
taken as applying to actual working conditions, which are influenced 
by many factors such as atmospheric temperature, temperature of 
cooling water, internal friction of machine, etc. It is evident that 
economic working is secured by (a) keeping the condenser as cool 
as possible, and (b) working at as high a temperature as possible in 
the evaporator, consistent with obtaining the desired cooling effect. 

T. 
If in the formula 2 - - , T : and T 2 be equal, the energy ratio = 

A l " *2 

infinity. The meaning of this is that when the condenser and 
evaporator are at the same temperature, no work is being done ; and 
it will also be seen that the nearer T l and T 2 approximate, the 
greater will be the energy ratio and consequently the economy of 
working of the machine. If the evaporator temperature = o 
(absolute) in the formula, then the energy ratio = o ; which means 
that no amount of work can extract heat from a body at absolute 
zero. Other things being equal, the less the value of T 2 the less will 
be the energy ratio ; that is, it becomes increasingly more difficult 
to extract heat from a substance as its temperature falls. The bear- 
ing of these points on the practical working of a machine of any type 
is obvious. 

Working Data. The results obtained in practice with a standard 
type of compression machine are given in tabular form on p. 303. 

Taking the figures for the last machine in the list on p. 303, it 
will be observed that for an expenditure of 8 H.P. for 24 hours, 
40 cwt. of ice are actually obtained. The work represented by 
8 H.P. for 24 hours is 

8 x 33000 x 60 x 24 ft.-lb. 



Refrigerating Machines. 303 

CARBON-DIOXIDE MACHINES (H. J. West and Co., Southwark). 



Brake 
Horse- 
Power 
Required 


Ice-Making 
Capacity in 
24 Hours 


Heat Extracted in B.Th.U. 
per Hour, from Brine at 


Capacity of 
Cold Store 
Reduced to 
35 F.in 
Cubic Feet 


Condensing 
Water at 
55 F., 
Gallons pet 
Hour 


25 F. 


35 F. 


45 F. 


If 


cvvt. 
3 


4,000 


5,000 


7,000 


3 00 


48 


2* 


6 


8,000 


10,000 


14,000 


600 


90 


3 


12 


15,000 


21,000 


27,000 


1300 


150 


4 


20 


25,000 


35>ooo 


45,000 


2500 


250 


6 


30 


38,000 


52,000 


68,000 


4000 


3 20 


8 


40 


50,000 


70,000 


90,000 


5OOO 


4OO 



and the work equivalent of the heat required to freeze i Ib. of water, 
originally at 56 F., is 

778 x 1 68 ft.-lb. 

since 24 B.Th.U. are required to cool the water to 32 F., and 144 
B.Th.U. to freeze it. If the heat extracted were equal to the work 
done, the ice made in 24 hours would be 

8 x -33000 x 60 x 24 ., 

- - 22 -- ? = 2927 Ib. 
778 x 168 

Actually, however, 40 cwt. or 4480 Ib. are made, hence every H.P. 
of work done in driving the machine extracts from the ice plant heat 
equivalent to 



2927 

The heat extracted from brine at 25 F. is 50,000 B.Th.U. per hour, 
or 50,000 x 24 B.Th.U. in 24 hours. If no losses occurred in the 
ice-making plant, the weight produced would be 



50000 x 24 _ 50000 
~~~ 7 



7143 Ib. in 24 hours 



from water at 56 F. The radiation and other losses in the process 
are, therefore, equivalent to (7 1 43 - 44 8 ) x l68 = 447,5 B.Th.U. 
approximately, or nearly 37-5 per cent, of the total heat extracted. 

Ice Manufacture. Artificial ice is made by conducting cold brine 
from a refrigerating machine to a receptacle in which vessels con- 



304 Heat for Engineers. 

taining the water to be frozen are placed. After circulating round 
the vessels, the brine returns to the refrigerator, where it is again 
cooled and circulated. A small pump attached to the machine is 
employed to force the brine round the circuit. Occasionally the 
medium used in the machine is allowed to evaporate (or expand) 
round the ice-vessels, in which case brine circulation is dispensed 
with. Three chief systems are in vogue for producing' artificial ice, 
known as the can, cell, and plate systems, and differing from one 
another in the details of procedure. A brief description of each 
system will now be given. 

The Can System. In this method the water to be frozen is placed 
in a galvanized iron vessel, rectangular in section, and tapering from 
the top downwards to facilitate the removal of the ice. A number 
of these cans are placed in a wooden trough, through which cold 
brine is circulated at a temperature of about 18 F. or - 8 C. Ice 
forms first on the sides of the cans, and spreads gradually towards 
the centre, until the whole is frozen. The cans are then removed 
and inverted, and a jet of warm water made to play over the outside, 
which melts the layer of ice in contact with the can and so loosens 
the block, over which the can will now slide. This process is cheap 
and comparatively rapid, but the quality of the ice made is not of 
the highest. 

The Cell System. This differs from the foregoing in the respect 
that the water-vessels are fixed, and furnished with hollow walls 
between which the cold brine or medium circulates. These cells 
are generally cubical in shape, and consequently the block of ice 
produced will take longer to melt than that obtained from a can, as 
a cube possesses less surface in proportion to its mass than the 
truncated prism obtained in the can system. In order to remove 
the blocks of ice from the cells, a piece of rope is inserted in the top 
of the cell, round which the water freezes. Warm brine is then 
circulated round the cells to loosen the ice, which may then be hauled 
out by means of the piece of rope. Cell ice takes longer to form 
than can ice, but, generally speaking, is more compact. 

The Plate System. The mode of procedure adopted in this 
system is to freeze from one side only, to which end a hollow plate, 
through which brine or the medium may be circulated, is placed in 
a large tank containing the water to be frozen. Ice forms on the 
plate, and spreads outwards, being removed when the block has 
attained the desired thickness. This process is very slow, but the ice 
produced is of superior quality, being compact and durable. A 
number of such plates may be placed in the tank, and the ice removed 



Ice Manufacture. 305 

before the blocks spreading out from the opposite faces of adjacent 
plates are allowed to meet. Slow freezing always produces the most 
compact ice. 

Different Kinds of Artificial Ice. When ordinary drinking water, 
containing salts of calcium, etc., and dissolved gases, is frozen, an 
opaque ice results, which is soft and lacks durability, especially when 
quickly formed, as in the can system. The opaque character of the 
ice is mainly due to the liberation of the dissolved gases at the 
moment freezing occurs, the gas bubbles becoming entangled amongst 
the ice. The salts in solution are only set free to a slight extent in 
the layer of ice which first forms ; thus in a can or cell the layers 
next to the walls are practically free from these salts. The chief 
separation of mineral matter occurs when the centre or core freezes, 
and hence this portion is generally more opaque than the rest of the 
block. In the plate system this drawback does not exist, as only a 
portion of the water in the tank is frozen, and the residue, rich in 
salts, may be removed and replaced by other water. 

A much superior class of ice, both with regard to appearance 
and durability, can be secured by continuously agitating the water 
during the freezing process. The dissolved gases then escape, and a 
much clearer and more compact ice is obtained. Various kinds of 
mechanical agitators have been devised for this purpose ; and the 
difficulty of the opaque core due to the salts present may be over- 
come by siphoning out the water in the centre, and replacing it by 
distilled water, when a block clear throughout can be obtained from 
either cans or cells. 

The best form of ice, however, from every standpoint, is that 
made from freshly-distilled water. The waste steam from a steam 
plant may be utilised as the source of supply ; and if recently con- 
densed, it will be free from dissolved gases, and produce ice of great 
transparency and solidity. Care must be taken, however, not to use 
steam which is contaminated with the vapour of oil, derived from 
the engine in which it has been used. 

The chief uses to which opaque ice is applied are the making of 
freezing-mixtures, the preservation of fish on fishing-boats, and the 
cooling of the small rooms used by butchers, etc., to store perishable 
articles of food in hot weather. For table use, or for addition to 
liquids for consumption, clear ice is employed. Such ice should be 
made from water of the highest degree of organic purity, and should 
be carefully protected from contamination during the manufacture. 
Many tradesmen still prefer natural ice (obtained chiefly from 
Norway) to refrigerator ice, claiming that the latter discolours and 



306 



Heat for Engineers. 



imparts a taint to foods with which it is brought into contact. Such 
a result would be due to the use of impure water, or to carelessness 
during manufacture or subsequent storage. 

Working Data for Can Ice. The following data have been 
arrived at by Messrs. H. J. West and Co., for the ice-making plant 
manufactured by them : 



Weight 
of Ice Block 


Size of Can 


Time of Freezing 
in Temperate 
Climate 


Number of Cans 
Required per Ton of 
Daily Output 


Ib. 


in. 


hours 




56 


4 x 13 X 33 


12 


20 


84 


6 x 15 X 33 


22 


24 


112 


8 x 16 x 33 


36 


30 


224 


10 x 24 x 36 


60 


25 


336 


12 X 26 X 36 


72 


20 



A rough guide as to the number of hours required to freeze a 
given block of ice of thickness S, in temperate climates, can be 
obtained by the use of the formula 

7 S 2 
Time in hours = + i 

32 - / 

where / is the temperature of the brine in degrees Fahrenheit, and S 
the thickness in inches of ice made in cans of dimensions similar to 
those given in the preceding table. Applying values in the formula, 
a block 6 inches thick would require 15 hours to freeze with brine 
at 14 F. ; and 19 hours with brine at 18 F. The formula assumes 
favourable working conditions all round, and gives a value less than 
that usually realised. Plate ice takes four times as long to make. 

Cost of Ice-Making. Taking into account labour, fuel, depre- 
ciation of machinery, lubricants, cost of water, etc., the cost of 
making ice should not exceed 3^. per ton. The larger the plant, the 
cheaper will be the ice, as the large machine is not only relatively 
more efficient than the smaller one, but requires practically the same 
amount of labour. Machines of actual ice-making capacity of 
200 tons per 24 hours have been constructed, the cost per ton in 
such cases being considerably below the figure named. 

Cold Storage. As the successful preservation of food-stuffs and 
other perishable articles depends upon the maintenance of a low 
temperature, which must not be subject to wide fluctuations, it follows 



Cold Storage. 



307 



that suitable arrangements for cooling continuously the room in 
which the articles are stored must be made. When the initial cooling 
has been effected, it is then only necessary to remove the heat which 
inevitably leaks in from the surrounding atmosphere through the 
walls of the store. It will be observed from the following table that 
the temperature to be attained is seldom more than a few degrees 
below freezing-point. 

SUITABLE TEMPERATURES FOR STORING VARIOUS ARTICLES. 



Name 


Temperature in F. 


Temperature in C. 


Beef and mutton (fresh) . 


33 to 40 


i to 5 


(frozen) . 


16 ,, 25 


-9 -4 


Veal 


35 


i'5 


Pork j 35 


i*5 


Poultry and game . . . . 3 to 35 


-i to 1-5 


Fish (fresh) 25 ,, 32 


-4 o 


(frozen) . 16 25 


-9 > -4 


Milk 


35 


1*5 


Cream ...... 


35 


1 '5 


Butter 


25 to 30 


4 to i 


Eggs . . 33 35 


o*5 i*5 


Cheese 32 33 


o 0-5 


Fruits ...... 


32 40 


o ,, 5 


Beer (in barrel) .... 


33 40 


o'5 5 


,, (bottled) 


45 


7'5 


Vegetables 35 


i*5 


Furs 


30 to 40 


i to 5 



The necessary reduction of temperature is achieved by one of 
the three following methods : 

1. Circulation of cold brine from the refrigerator through a 
system of pipes, or through hollow walls, or a combination of both. 

2. Circulation of cold air by means of fans, or, in the case of 
air-expansion machines, delivering the cold air direct from the 
machine. 

3. Circulation of the medium (ammonia, carbon-dioxide, or 
sulphur-dioxide) through pipes in the cold store. 

Each of these methods will be considered in turn. 
Cooling by Brine Circulation. This method is most commonly 

x 2 



3o8 Heat for Engineers. 

employed in cold stores, as it is not only capable of nice regulation, 
but enables the low temperature to be maintained for long periods, 
after the initial cooling of the articles, without working the machine. 
The large mass of brine in the pipes, with its high specific heat 
(o 9 or more), suffices to absorb all heat entering the store for long 
periods, before its temperature rises to a sufficient extent to endanger 
the articles stored. A much greater cumulative effect is thus obtained 
with brine than by either of the alternative methods of cool ng. 

The pipes containing the brine are located on the ceiling of the 
store, and consequently the air in contact with them becomes cooled 
and sinks downwards amongst the articles, warmer air from below 
rising to replace that which has fallen. This in turn is cooled by 
contact with the pipes, and thus a circulation of cold air is established. 
The cold pipes also absorb the heat radiated from the various objects, 
and finally the temperature of the store is reduced to the desired 
degree. Iron pipes are generally employed, and are not corroded 
to any great extent by solutions of common salt or calcium chloride, 
provided air be expelled. It is not advisable to galvanize the pipes, 
as corrosion then occurs to a marked extent. 

In some cases the walls of the cold store are made hollow, and 
brine circulated through the space. This procedure greatly facilitates 
the cooling or freezing of articles hung on or near the walls, and also 
provides a large reserve of "cold" to maintain the low temperature 
when the machine is resting. 

When the articles are to be frozen, and not merely chilled, a brine 
of low freezing point is requisite, and for this reason a solution of 
calcium chloride is preferable to one of common salt, which might 
freeze and choke the pipes. When a less intense degree of cooling 
is desired, a solution of common salt may be safely employed. The 
circulation of brine is maintained by means of a small pump coupled 
with the machine. 

Fig, 84 illustrates the application of the brine system of cooling 
as applied in a vessel conveying a cargo of frozen meat. The brine 
is passed through a continuous length of piping, bent into parallel 
branches, and fastened to the ceiling of the cold chambers. 

Cooling by Cold Air Circulation. This system was originally 
employed in air-expansion machines, the cold air from the expander 
being delivered through suitable trunks into the cold chambers. Now 
that this type of machine has been almost entirely superseded by 
compression machines, cold air circulation, when adopted, is carried 
out by forcing air, cooled by contact with cold brine, into the chamber 
by means of fans. The procedure adopted at some of the London 



Cold Storage. 



309 



docks is to allow the entering air to pass through a cascade of cold 
brine, falling over corrugated plates to give a large surface for cooling 
the air. Control of the temperature of the store is secured by regu- 
lating the quantity of cold air admitted, and the temperature of the 
brine from the refrigerator. The advantage secured by the method 
is the absence of fog in the store, as the entering air is deprived of its 
surplus moisture by the cold brine, and contains only the amount of 
moisture necessary to cause saturation at the entering temperature. 
A further advantage is that a better circulation of air amongst the 




FIG. 84. BRINE COOLING AS APPLIED TO A VESSEL. 

articles stored is secured than in the case of cooling by brine pipes, 
as the existence of stagnant layers is not possible. On the contrary, 
the reserve of cold material is smaller, and consequently the periods 
during which the machine may be rested shorter, than when trine 
circulation is used ; and the stored articles tend to become dry. 

Cooling by Circulation of the Medium. In this method the evapo- 
rator coils are continued into the cold store, and the liquid produced 
by the compression allowed to evaporate throughout the whole length, 
and thus cool the chamber. This procedure enables the use of brine 
to be dispensed with, and is in this respect more economical. A 



310 Heat for Engineers. 

drawback to its use is the leakage which almost invariably occurs, 
resulting, in the cases of ammonia and sulphur dioxide, in the tainting 
of stored food-stuffs. In addition, the control of temperature cannot 
be secured with the same degree of precision as in the case of brine 
or air circulation, and the reserve of cold material is small. This 
method is not employed to any great extent at the present time. 

Insulation of Cold Stores. As the maintenance of a low tempera- 
ture in a cold store depends upon the removal of heat which enters 
through the walls from external surroundings, it is necessary to line 
the walls with materials which do not permit of the free transmission 
of heat. Any materials used, however, should not be liable to become 
damp by absorbing atmospheric moisture, as a large proportion of the 
cooling effect is then wasted in freezing this moisture. The insulating 
material, moreover, should not tend to become mouldy, as contami- 
nation of stored food-stuffs might result. The materials chiefly 
employed are cork, sawdust, charcoal, hair-felt, peat, and slag-wool, 
all of which are poor conductors of heat, and so largely prevent the 
ingress of heat from surroundings. The methods of applying these 
materials will be given in detail in the succeeding chapter. 

Other Applications of Refrigerating Machinery. Amongst the 
other uses to which refrigerating machinery has been applied, of 
which space does not permit of a detailed description, may be men- 
tioned the cooling of milk and other dairy produce ; the cooling of 
water in breweries; the cooling of chocolate; the freezing of the walls 
of borings in the earth to prevent ingress of water ; the cooling of 
buildings in hot weather ; and the production of ice for indoor skating- 
rinks. In the case of milk, cooling to below 10 C. immediately it is 
taken from the cow arrests the growth of germs almost entirely, and 
renders the milk much safer as an article of food. The cooling is 
effected by allowing the milk to trickle over the exterior of a 
corrugated drum, in the interior of which cold brine is circulated. 
The cooling of water and w r ort in breweries is usually effected by 
allowing the liquid to fall over a series of pipes containing cold brine. 



II 



CHAPTER XVII. 

THE TRANSFER OF HEAT. CONDUCTION. 

Methods by which heat may pass from one place to another* If a 
piece of hot iron be placed on a slab of metal, its temperature will 
fall until it attains that of its surroundings. One portion of the heat 
lost has passed into the slab on which it rests by the process known 
as " conduction " ; a second portion has been removed by the air in 
contact with the iron becoming hot and rising, colder air taking the 
place of that which has risen, and in turn removing another portion of 
the heat, the circulation thus set up being termed " convection " ; 
whilst another part of the heat has escaped in the form of energy 
waves from the surface, to which method of heat transfer the term 
" radiation " is applied. If the hot iron were suspended in air by a 
non-conducting thread, the heat would escape entirely by convection 
and radiation ; whilst if similarly suspended in a vacuum, the cooling 
would be due entirely to radiation. The first of these three methods, 
viz. conduction, forms the subject of the present chapter. 

Conduction. When one end of a bar of metal is placed in a fire, 
a rise in temperature may be observed in the portions outside the fire. 
The molecules of the metal in the fire, as the temperature rises, are 
set into a more rapid state of vibration, and communicate this enhanced 
movement to adjacent molecules, which, in turn, affect the molecules 
in their own vicinity, and thus an increased rate of movement is con- 
veyed to the molecules in the remote portions of the bar. This 
increased speed is identical with a rise in temperature, and conse- 
quently the process of conduction is in reality a mechanical transfer 
of heat energy. 

Good and Bad Conductors. Conduction takes place with greater 
facility in metals than in any other substances. For this reason a 
piece of metal feels colder to the touch than wood or felt, although 
the actual temperature is the same in each case ; the reason being 
that the metal conducts away the heat of the hand more rapidly, and 
thus gives rise to the sensation of cold. Non-metallic solids, liquids 
and gases are, in general, feeble conductors of heat. 



3 I2 



Heal for Engineers. 



Coefficient of Conductivity. -The rate at which the temperature 
rises in a given part of a substance, remote from the heated part, 
depends not only on the freedom with which heat energy is conducted 
but also on the specific heat of the material. Thus i calorie imparted 
to i gram of lead would cause a rise in temperature of about 32 C., 
whilst if imparted to i gram of aluminium the rise w r ould be only 
4'5C. Hence it cannot be inferred that, if two bars of metal be 
placed with one end exposed to the same source of heat, the bar 
which most quickly attains a given temperature at a point away from 
the source of heat is the better conductor. If judged in this manner, 
as Tyndall showed, bismuth would appear to be a superior conductor 
to iron, whereas the actual quantity of heat passing along the bismuth 
is much less than in the case of iron. The coefficient of conductivity, 
which refers to the quantity of heat energy passing through a sub- 
stance, is defined as follows : 

The coefficient of conductivity is the number of heat units trans- 
mitted in one second from one face of a cube of unit side to the 
opposite face, when the difference of temperature between the opposite 
faces is i degree. 

The units may be chosen in any given system. It is evident that 
in any actual case of conduction, the heat passing will vary directly 
as the time and area of section, and it is customary to assume that 
the heat passing varies directly as the difference of temperature 
between opposite ends, and inversely as the thickness, which is prac- 
tically correct within certain limits. The heat units passing are 
evidently directly proportional to the coefficient of conductivity of 
the material. Expressing this in algebraic form : 

Heat units transmitted = 

K x area of section x time in sees, x diff. of temp, between faces 
thickness or distance between faces 

where K = coefficient of conductivity. Examples illustrating the use 
of this equation will be given later. 

Determination of Coefficients of Conductivity. Several methods 
have been employed to determine the coefficients of conductivity of 
various substances. The method adopted by Forbes for metals is 
shown in Fig. 85, and consisted in maintaining one end of the bar at 
a constant high temperature, and noting the steady reading of a series 
of thermometers inserted in holes drilled in the bar, in which mercury 
was placed to secure a metallic contact with the thermometer bulbs. 
A considerable time is required to attain a steady condition, but this 



The Transfer of Heat. Conduction. 3 1 3 

is finally reached when the heat passing along the bar in a given time 
is exactly equal to that lost by radiation and convection from its 
surface. If the quantity conducted should exceed that which escapes, 
the temperature will rise, and conversely, if the heat lost were greater 
than that arriving from the source, the temperature would fall. Evi- 
dently, therefore, the two quantities are equal when steady readings 
are furnished by the thermometers. 

A second experiment with the bar was then performed, indicated 
to the right of the figure. The bar was heated to the same tempera- 




AB 




FIG. 85. FORBES' CONDUCTIVITY EXPERIMENT. 

ture throughout in a bath, and cooling readings taken at definite 
intervals of time over a range compassed by the highest and lowest 
temperatures indicated by the thermometers in the previous experi- 
ment. As the bar was at the same temperature throughout, one 
thermometer in the centre sufficed for the readings. The object of 
the second experiment was to determine the actual quantity of heat lost 
by the bar per second at any given temperature, and, from the data 
furnished by the two experiments, the coefficient of conductivity was 
calculated. 

The exact calculation is somewhat complicated, but the principles 
involved may be understood by reference to the following example. 
Imagine a portion of the bar, A B, i centimetre long. The difference 
in temperature between A and B can be obtained by drawing pro- 



314 Heat for Engineers. 

jectors on to the curve formed by joining the readings of the thermo- 
meters, and the area of section may be obtained by measurement. 
All the heat passing from A to B goes on to the rest of the bar and 
is lost by radiation and convection from the portion B C when the 
steady state has been reached. It remains to be found how many 
heat units per second escape from the part B C under the existing 
conditions, and this figure is obtained from the second experiment. 
If the whole bar weigh W grams, and has a specific heat S. and if it 
be observed that C calories per second are radiated at the average 
temperature existing between B and C in the first experiment, the 
heat escaping from the whole bar would be (W x S x C) calories per 
minute, and from the portion B C the number escaping would be 
/W x S x C x length of B C\ calories per second Thig ig equal to 
\ total length of bar 

the number of calories passing from A to B in the steady state, and 
as all the above values are known, the coefficient may be obtained 
from the equation : 

Calories passing from A to B 

K x area of section x i second x diff. of temp, between A and B 
distance between A and B 

all of the quantities being known except K, the coefficient, which in 
this case would be expressed in C.G.S. units. 

This method cannot well be employed in the case of badly- 
conducting materials, as a thermometer placed a few inches from the 
hot end would scarcely be affected by the small amount of heat 
reaching it. The successful carrying out of the experiment involves 
the provision of a steady temperature at the hot end, a constant 
atmospheric temperature, and prolonged observation to ensure that 
the steady condition has actually been reached. 

Amongst other methods which have been used for determining 
the coefficient of conductivity of solids, mention may be made of the 
following : A plate of the solid is placed between the ends of two 
thin copper cylinders, so as to make a good contact with each. 
Steam is passed through one cylinder, whilst the other is filled with 
ice. After a given time the water resulting from the melting of the 
ice is tapped off and weighed, and by multiplying the weight of ice 
melted in grams by 80, the number of calories passing in the given 
time is determined. The area, thickness, and difference of tempera- 
ture between the faces being known, the value of K may be obtained 
as in the previous equation. This method may be applied to bad 



The Transfer of Heat. Conduction. 315 

conductors as well as metals ; but many precautions are necessary to 
ensure concordant results. 

The coefficient of conductivity of liquids has been determined 
by placing the liquid under experiment in a thin, wooden cylinder, 
and floating a quantity of hot liquid on the cold. Horizontal thermo- 
meters were placed at different levels, and from the readings of a 
consecutive pair the difference between the upper and lower levels 
of a given stratum were known. The heat passing through this 
stratum in a given time was determined by multiplying the weight of 
the liquid below the stratum by its specific heat and average rise in 
temperature, the remaining data being the thickness of the stratum 
and the area of section of the cylinder. The calculation is the same 
as in the previous cases. A small quantity of heat is conducted along 
the wooden cylinder, but in most cases this is small in comparison 
with that transmitted down the column of liquid. 

No satisfactory method has yet been devised for determining the 
conductivity of gases, as it is practically impossible to obtain two 
perfectly steady layers at different temperatures, owing to convection 
and diffusion. 

Numerical Values of Coefficients of Conductivity. The follpwing 
table gives the numerical values of the coefficients of conductivity 
of a number of substances, the figures chosen being the average 
of several determinations made by different methods. In some 
instances considerable differences exist between the figures obtained 
by different observers for the same substance. The heat unit em- 
ployed is the calorie, the area of section i square centimetre, distance 
between faces i centimetre, time i second. 

It is only in very special cases that the figures (page 316) can be 
applied to calculate the quantity of heat transmitted through a 
material under working conditions. In the first place, the value of 
the coefficient varies greatly with the temperature. With metals, 
the conductivity decreases with the temperature ; the figure for iron, 
for example, diminishing from '16 at o C. to '13 at iooC., and 
ii at 300 C. With badly conducting materials, or insulators, the 
conductivity increases with the temperature in some cases, but 
diminishes in others. A further drawback, from the standpoint of 
practical utility, is that the figures hold true for an arbitrary condition 
seldom realised in practice that of two surfaces kept at a uniform 
temperature and shielded from radiation losses and air convection. 
As an example, the coefficient for air under these ideal conditions is 
given as "000051 ; but if an air-space be employed over a hot 
surface to prevent escape of heat, the effective value, owing to con- 



i6 



Heat for Engineers. 

COEFFICIENTS OF CONDUCTIVITY. 



Substance 


Range of Temperature 


Coefficient of 
Conductivity, C.G.S. units 


Metals 


c. 




Silver . . . ' 


7 to 15 


1*096 


Copper 


51 


I'OO 


Aluminium 


,, 


o'345 


Zinc .... 


, , 


0-295 


Brass 


5 ? 


0-265 


Iron . . 


, , 


o" 160 


Tin 




O'i53 


Lead 


> 


0*084 


Non- Metallic Solids 






Sandstone 





0*0107 


Ice ... 




0-0023 


Glass (crown) 


7 to 15 


O'OO2I 


,, (Jena), various . 


,, 


O'OOII to 0-0020 


Sand .... 


, 


0-00074 


Oak, across fibres 


, 


0-00059 


Fir, along fibres. 
,, across fibres 


' 


0-00047 
O-OOO26 


Cork .... 


, 


O-OOO4O 


Pine sawdust 


% 


o * 00024 


,, shavings 


i 


0*000l6 


Dry asbestos 


,, 


o 00030 


Silicate cotton (slag-wool) . 




0*00015 


\\ool 


5 } 


O'OOOI2 


Hair-felt, sheets. 





O'OOOII 


Liquids 






Water .... 


10 to 20 


0-00140 


Glycerine .... 





0*00064 


Alcohol (ethyl) . 


,, 


0-00055 


Ether .... 


,, 


0-00034 


Benzene .... 




0*00033 


Paraffin oil 


, , 


0*00045 


Turpentine 


> 


0*00031 


Gases 






Hydrogen .... 


7 to 10 


0*00033 


Marsh gas 


9 9 


0*000065 


Carbon monoxide 


> 1 


0*000050 


Air 


1 


0*000051 


Carbon dioxide . . . 





0*000027 



vection, is 0*0002, or 4 times as great. Any figure for practical use 
must be obtained from tests carried out under working conditions, 
and it frequently arises that a material inferior for a given purpose 
from the standpoint of absolute conductivity, proves superior in 
practice, owing to the difference between working and ideal con- 



The Transfer of Heat. Conduction. 317 

ditions. Examples of such practical tests are given later in the 
chapter. 

It is interesting to note, in the case of metals, that the numerical 
order for heat conductivity is the same as that for electrical conduc- 
tivity. The figures for consecutive metals, however, do not bear 
the same ratio to one another in the two cases. Water is the best 
liquid conductor (except mercury) ; and taking the figures for gases 
as reliable, it would appear that the conductivities are in the inverse 
order of the densities, that is, the lighter the gas the better it will 
conduct heat. 

A few examples will now be given to illustrate the use of the 
coefficients in calculating the heat transmitted through materials. 

Example i. The walls of a cold store are 20 cm. thick, and 
have a total area of 100 square metres. If the external temperature 
be 25 C., the internal temperature - 5 C., and the coefficient of con- 
ductivity of the material of the wall '0003, find the number of heat 
units which must be removed in i hour to prevent a rise in tem- 
perature. From equation on page 312, 

, 'ooo'* x 3600 x 1000000 x 70 

Calories passing through = 2 ^_ 

20 

= 1,620,000 calories; the time being reduced to seconds and the 
area of surface to square centimetres. Dividing by 252, the answer 

in B.Th.U.is I -^^ = 6 43 o. 
252 

This result would assist in deciding the size of the refrigerating 
machine required. 

Example 2. To compare the quantities of heat transmitted 
through a copper plate i inch thick, and an iron plate of the same 
area, but J inch thick. For equal thicknesses, under the same tem- 
perature conditions, the quantities would be directly as the con- 
ductivities viz. i to 'i 6. As the iron plate is only one-half as 
thick, the ratio will be i to '32, or about 3 to i in favour of the 
copper. 

Uses of Good Conductors of Heat. The good conductivity of 
copper renders it the most serviceable metal to employ for the fire- 
boxes of locomotives, where it is necessary rapidly to generate a large 
quantity of steam. Although the copper firebox is thicker, to ensure 
mechanical strength, than would be necessary if steel were used, the 
vastly superior conducting power of copper enables a much greater 
quantity of steam to be raised in a given time. In stationary boilers, 
where space is not so great a consideration, an increased heating 
surface enables iron to take the place of copper, thus effecting a great 



318 Heat for Engineers. 

saving in the prime cost. The actual surface temperature of the 
metal in the firebox or flue is much less than that of the flames, owing 
to the rapid conduction of the heat impinging upon it through the 
material to the water, and also to the existence of a layer of gas, 
cooled by contact with the plates, on the surface. 

The good conductivity of copper explains the efficiency of this 
metal in the construction of soldering-" irons." When the tip of 
the soldering-iron or bit is laid on the work, the surface of the metal 
operated on abstracts heat from the bit, and lowers the temperature 
of the point. Heat flows rapidly from the main portion of the bit to 
the cooled tip, and thus maintains the temperature necessary to effect 
the operation. 

The safety-lamp, invented by Sir Humphry Davy, is a further 
example of the utilisation of good conductors. If a piece of wire 
gauze be held over a gas-burner, and the gas be turned on, it may be 
ignited above the gauze and burn on the upper surface, without the 
flame striking through to the jet. The heat of combustion is rapidly 
conducted to the remote portions of the gauze, so that for a consider- 
able time no part of the metal is raised to the temperature of ignition 
of the gas. Hence, if a lamp be surrounded by gauze, explosive 
gases in a mine may find a way through the meshes and burn in the 
interior of the lamp thus warning the miner of the danger existing 
but the gases cannot burn externally until the gauze is raised to 
the temperature of ignition. 

Uses of Bad Conductors, or Heat Insulators. The various kinds 
of clothing which serve to protect the body from cold, are examples 
of heat insulators. Obviously, the thicker the material the less will 
be the heat escaping from the surface of the body to the surrounding 
air. Woollen materials, furs and silks are superior in this respect to 
cotton fabrics. Other examples are found in the use of wooden 
handles for smiths' tools, which prevent the heat of the tool from 
reaching the hand; and the superiority of stone, brick or wooden 
houses over corrugated iron structures, which are notoriously hot in 
summer and cold in winter. One of the most useful applications of 
heat insulators, from an engineering standpoint, is the protection 
of boilers, steam- pipes, etc., from loss of heat to the atmosphere, and 
of cold stores from ingress of heat. This application will now be 
specially dealt with. 

Heat Insulation. If a boiler or steam-pipe be exposed to air, a 
serious loss of heat is occasioned, and a further drawback arises, in 
the case of a steam-pipe or the exposed cylinder of a steam-engine, 
owing to the condensation of the steam in considerable quantities. 



Heat- Insulating Materials. 319 

This condensation, in a long bare steam-pipe, causes a considerable 
fall in pressure, and the accumulation of water in the cylinder of an 
engine is dangerous, as the end might be forced off. Again, a low 
temperature in a cold store would be very difficult to maintain unless 
the walls were properly insulated, and consequently a larger refrigera- 
tor would be necessary. In all such cases, it is customary to protect 
the surfaces with heat -insulating materials, which are commercially 
known as " laggings" Materials suitable for boilers and steam-pipes 
are not of necessity advantageous to employ for cold stores, and vice 
versa', and it will therefore be convenient to treat the two cases 
separately. 

Heat-Insulating Materials for Hot Surfaces. The properties 
desirable in a lagging for hot surfaces may be enumerated as 
follows : 

1. It should possess a low heat conductivity. 

2. It should be non-inflammable, as it may frequently be exposed 
to sparks from furnaces. 

3. It should not tend to crack when subjected to fluctuations of 
temperature, as otherwise it would in time become detached. 

4. The mechanical strength should be sufficient to enable it to 
resist vibrations and accidental blows. 

5. It should be capable of resisting the action of water or steam. 

6. The specific gravity, especially when a thick coating is used, 
should not be so high as to place an undue weight on steam-pipes. 

7. It should not cause corrosion of the lagged surface. 

8. As a minor qualification, the specific heat should be as low as 
possible, as this means a less absorption of heat by the lagging when 
starting from the cold. 

No single substance posseses all these features in a marked 
degree, and in choosing a lagging for a given purpose due regard 
should be paid to the properties which are of the greatest importance 
in the particular case. Many substances which are excellent non- 
conductors, cannot be used on account of failure to subscribe to the 
other conditions. A vacuum jacket should be an ideal lagging, but 
is not practicable. 

Superiority of Porous Materials. Experiment and practical use 
show conclusively that porous materials, or those which contain 
cavities enclosing air, are by far the most efficient non-conductors of 
heat. The pores should be sufficiently small to prevent convection 
currents in the enclosed air, but not so small as to cause too numerous 
lines of solid contact through the mass. The author has found, in 
the case of lagging made up in porous form, differences of 15 per 



320 Heat for Engineers. 

cent, in the conductivities of samples which were supposed to be 
identical, caused by variation in the size of the pores. 

Tests for Thermal Efficiency of Laggings for Hot Surfaces. The 
heat passing from a hot surface through a lagging is disposed of 
partly by radiation from the exterior, and partly by convection 
currents set up in the air in the vicinity. As the radiating powers 
of the surfaces of different laggings vary considerably, tests for absolute 
conductivity only, in which the surface is shielded from radiation, 
do not suffice to settle the question of practical efficiency. Moreover, 
it is frequently desirable to know the number of heat units escaping 
under working conditions, and in order to obtain this figure it is 
necessary to perform the test in a manner which realises these con- 
ditions. Two chief methods are employed for this purpose, which 
will be described separately. 

Condensed Steam Test for Laggings. A 4-inch or 6-inch steam- 
pipe is coated with the material to a definite thickness, and dry steam 
at constant pressure admitted. After the pipe has become thoroughly 
heated, the water condensed in the warming-up process is allowed 
to drain off, and the steam allowed to pass through the pipe for a 
definite time say two hours. At the end of this time the water con- 
densed is drained off and weighed, and represents the weight of 
steam which would condense under the given conditions. Knowing 
the latent heat of steam at the temperature employed, the number of 
heat units escaping may be calculated. 

There are several objections to this process. Firstly, it is difficult 
to procure perfectly dry steam, and it is doubtful whether the water- 
separators fixed at the entrance and exit of the pipe secure complete 
dryness. Secondly, it is necessary that the steam should be kept at 
a steady pressure (and temperature) during the whole of the experi- 
ment, which involves a special boiler, an elaborate outfit and great 
care. Thirdly, as the result of a test of many hours' duration, only 
one result is obtained, viz., that for a given thickness at a given tem- 
perature. To obtain a variety of results for different thicknesses at 
different temperatures would extend the duration of the experiments 
over some months. 

The table opposite, which represents the results of a test carried 
out by this method at the National Physical Laboratory, serves to 
show the nature of the observations and the manner of expressing 
the results. 

The Electrical Heat Test for Laggings. In this test the uncertainty 
arising from the use of steam of doubtful dryness is avoided by 
heating a steam-pipe internally by means of an electric current. In 



Heat-Insulating Materials. 

RESULTS OF TESTS ON COVERING \\ IN. THICK. 



,21 






Lagged Pipe 


Bare Pipe 


Steam pressure (gauge) .... 


219 Ib. per sq. in. 


ditto 


Steam temperature .... 
Temperature of air 


395 F. 
70 F. 


395 F. 
70 F. 


Steam condensed per hour 


5'22lb. 


23-6510. 


Latent heat of steam at 395 F. in B.Th.U.\ 
per Ib. / 


838 


838 


Difference between steam and air tem-1 
peratures / 


325 F. 


325 F. 


Loss of heat per hour in B.Th.U. 


4375 


19,820 


Loss from bare flanges, ditto . 


2165 


2,165 


Net loss from pipe per hour, ditto . 


2210 


17,655 


Steam condensed by pipe only (effect of \ 
flanges eliminated), Ib. per hour / 


2'64 


21-06 


Area of pipe surface, sq. ft. 


16-81 


16-81 


Steam condensed per sq. ft. per hour 


0-157 


1-25 


B.Th.U. escaping per sq. ft. per hour 


131 


1048 


ditto ditto ditto for) 
each degree F. excess temperature of> 
steam over air J 


0-40 


3*23 



Percentage of saving effected by lagged pipe over bare pipe 

_ f 1048 - 131 X ioo\ _ g 

1048 / ' ' 



a series of tests carried out by Professors S. P. Thompson and Dalby, 
a 6-inch steam-pipe, about 5 feet long, was covered to a known 
thickness with the material, and heated internally by passing a 
current through a length of " eureka " wire in the interior. An 
external resistance was placed in the circuit, and served to control 
the temperature of the pipe, which was read off from a series of 
thermometers which passed into the interior. An ammeter in the 
circuit, and a voltmeter across the terminals of the heater, served 13 
indicate the rate at which energy entered, as i volt x i ampere 
= o 24 calorie per second, or o 057 B.Th.U. per minute. The 
external resistance was regulated until a steady internal temperature 
was attained, when the heat escaping through the covering would of 
necessity be equal to that entering. This quantity was found by 
multiplying the readings of the voltmeter and ammeter to obtain the 



322 



Heat for Engineers. 



watts entering the pipe, and (watts x -o57) = B.Th.U. escaping per 
minute. The results could then be expressed in the usual manner as 
B.Th.U. escaping per square foot of lagged surface per hour; and, 
by adjusting the resistance, the escape of heat at several different 
temperatures was obtained. 

The electrical heat test, conducted in the manner described, 
is more reliable than the steam test, but still suffers from the dis- 
advantage that a long time is required to obtain a steady temperature, 
owing to the large amount of material employed. In order to 
overcome this drawback, the author made a number of experiments 




FIG. 86. ELECTRICAL CONNECTIONS OF TEST FOR HEAT-INSULATING 
MATERIALS. 

on a smaller scale, and found that it was possible to obtain results 
of equal accuracy in a much shorter time by the uses of the apparatus 
illustrated in Figs. 86 and 87. A piece of steam pipe, approximately 
8 inches long and 6 inches diameter, and possessing 1-5 sq. ft. of 
external surface, is coated with the material under test. Passing 
into the interior is a 32-candle-power lamp, with carbon filament, 
which serves as the source of heat. The electrical connections are 
shown in Fig. 86, where A is the ammeter, V the voltmeter, and 
R the adjustable resistance. Fig. 87 is reproduced from a photo- 
graph of the apparatus, and shows the various parts. The voltmeter 



Heat- Insulating Materials. 



323 



should be capable of being read to i volt, and the ammeter to 
0*1 ampere. A continuous wire resistance of 250 ohms enables 
a very fine adjustment to be obtained, and suffices for either a 
zoo-no or 200-220 volt circuit. Moving coil ammeters and 
voltmeters are best for direct current, and hot-wire instruments for 
an alternating current. The temperature is registered by means of 
a thermometer passing into the interior, the bulb of which is located 
about half-way down the cylinder, and mid-way between the lamp 
and inner wall. The bulb is shielded from the direct rays of the 
lamp by means of a piece of thin brass tubing, and under these 




FIG. 87. TEST FOR HEAT-INSULATING MATERIALS. 

circumstances gives a true reading of the average internal tempera- 
ture. If necessary, the cylinder may be made gas-tight, and the 
interior connected to a mercury column, when the exact internal 
temperature may be calculated from the increase of pressure, as in 
the constant volume air thermometer.* This refinement, however, 
is hardly necessary for commercial tests, and gives readings not 
differing greatly from those of a thermometer inserted in the manner 
described. 

Before commencing readings, the lagging must be thoroughly 
dried, either by placing on the top of a furnace, or in situ round the 
test-pipe. The ammeter and voltmeter arc then kept at a steady 

* See description by the Author in "Engineering," Dec. 6, 1907. 

Y 2 



324 Heat for Engineers. 

reading by means of the resistance until the thermometer remains 
stationary for 15 minutes, when each is read. The current is then 
reduced by about * 05 ampere, and a second stationary temperature 
obtained, and so on over the range of temperature desired. The 
product (watts x -057), as before, gives the B.Th.U. escaping per 
minute, and as the external surface is i 5 sq. ft., |- of the product 
gives the B.Th.U. escaping per sq. ft. per minute. The test may 
then be applied to other thicknesses of material, and complete data 
respecting the heat losses at all working temperatures obtained 
for all thicknesses in a far shorter time than is possible with large- 
scale tests. 

Many interesting points concerning the thermal efficiency of 
laggings may be noted in the results obtained by the author during 
a long series of tests conducted by this method on different laggings. 
As an example, the data furnished by a covering material composed 
of 85 per cent, of light magnesium carbonate and 15 per cent, 
asbestos fibre, known as Newall's Magnesia Covering, are appended 
in graphic form. Fig. 88 is a curve obtained by plotting B.Th.U. 
lost per sq. ft. per hour against corresponding thickness of lagging, 
the internal temperature of the pipe being 400 F. } and the outside 
temperature 68 F. It will be seen that the saving effected by the 
first \ inch is 815 B.Th.U., by the second J inch 900 B.Th.U., and 
by the succeeding | inch layers 930, 950 and 960 B.TtuU. respect- 
ively. The curve is approximately hyperbolic, and an infinite 
thickness would be requisite to prevent any loss whatever. The 
noteworthy feature of the curve is the marked decrease in steepness 
beyond the ordinate representing ij inches, indicating a rapidly 
diminishing saving power on the part of material added beyond 
this thickness. The curve corresponding to an internal temperature 
of 550 F. does not show such a marked falling-off until near the 
2-inch ordinate ; and hence the general practice of using a lagging 
i \ inch thick for temperatures up to 400 F., and 2 inches for 
higher temperatures, has a sound scientific basis. For inferior 
materials, a greater thickness is necessary to secure an equivalent 
result. 

The actual thickness to which a pipe should be lagged, in a 
given case, to secure maximum economy, can be obtained by 
considering the circumstances in conjunction with a curve of the 
type shown in Fig. 88. Experience must dictate the probable time 
that will elapse before the lagging must be renewed, and the price 
of fuel and number of working hours must also be taken into 
account. The number of B.Th.U. furnished by one pennyworth 



Heat-Insulating Materials. 



325 



of average coal, taking into account flue losses, etc., is, roughly, 
100,000. Hence if the estimated life of the lagging in hours be 
multiplied by the B.Th.U. escaping per sq. ft. per hour, and the 
product be divided by 100,000, the answer will be the value in 



j 














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s 


















































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V* 




















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s 






















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I 

\ 

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s 
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o 
































\ 




















































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^>v 






















































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>> 




















































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Y^ 
' f, 


T7< 


tJf 


rri 


rt ( 


/f 


ra 




^ 


r^?i 


77 


-? 


r?(< 


^ 


r 






















% 


f 


7= 


{/"I 




'r?- 


,r 




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in inches 

FIG. 88. CURVE SHOWING HEAT ESCAPING FROM A PIPE CONVEYING 
STEAM AT 400 F., WHEN LAGGED WITH DIFFERENT THICKNESSES 
OF MAGNESIA. 

pence of the escaping heat. If this calculation be performed for 
several thicknesses, it will be found that beyond a certain pc'nt 
a further thickness of lagging will cost more than the monetary 
equivalent of the additional heat saved. An example is appended, 
derived from the results obtained with the material under notice. 

Example. A pipe is to convey steam at 550 F. To find the 
most economic thickness to use of a lagging for which the following 



326 



Heat for Engineers. 



data were obtained, the duration of the cover being estimated at 
30,000 working hours : 

MONEY EQUIVALENT or HEAT LOST IN 30,000 HOURS. 



Bare pipe, per sq. ft. 
With -inch 



490 pence 
1 10 
70 



40 
33 



From the above figures it will be seen that the saving effected by 
successive layers of inch over that of the underlying thickness is 
380, 40, 15, 9, and 6 pence respectively, a further ij inch only 
effecting an additional saving of *]d. per square foot of lagged surface 
in the time named. If 2 -J- inch covering were 6d. per foot dearer 
than 2-inch, the limit of economy would be i\ inches; if more than 
6d. per foot dearer, a less thickness than 2\ inches would be more 
economical for the estimated period. It should be remembered that 
each additional layer has a greater diameter, and therefore contains 
more material than the one beneath. The cost of material therefore 
increases progressively with the thickness ; on the other hand, the 
labour charges for fixing are much the same, whatever the thickness. 

The effect of temperature on the heat escaping through a lagging 
is indicated in Fig. 89, for different thicknesses, the temperature of 
the surrounding air being 68 F. The curves show a gradually 
diminishing steepness as the temperature rises, indicating an improve- 
ment in insulating power at higher temperatures. This improvement 
is often manifested by very porous materials, and may be due to the 
expulsion of excess of air as the temperature rises. As this expulsion 
is gradual, it is necessary, in making a test, to heat the material to a 
high temperature for some time before commencing readings. 

It will be noticed that the curves diverge as the temperature rises, 
all having an origin at a point on the axis of temperature represented 
by 68 F. Hence the saving effected by the thicker coating becomes 
proportionately greater as the temperature rises. By taking the units 
represented by the distance between the two curves at any given 
temperature, and proceeding as in the foregoing example, the tem- 
perature limit above which the thicker lagging would be cheaper may 
be determined. 

The temperature gradient through a magnesia lagging is depicted 
graphically in Fig. 90, and was obtained by inserting thermal junc- 
tions at different depths. The normal prolongation of the curve 



Heat- Insulating Materials. 



327 



would indicate a surface temperature of 96 F., whereas the applica- 
tion of a junction to the surface showed 80 F. only. The former 
is probably correct, the latter being too low owing to radiation from 
the junction itself. For lower pipe temperatures a less steep gradient 
is obtained, the surface temperature being little altered. Too much 
reliance, therefore, cannot be placed on conclusions drawn from 



2<JQ 



250 



300 



350 



400 



+5O 



FIG. 89. CURVES SHOWING Loss OF HEAT THROUGH PIPES LAGGED WITH 
MAGNESIA AT DIFFERENT TEMPERATURES. 

the observation of surface temperature, as the actual quantity of heat 
escaping is not indicated by this alone. 

Effect of Surface on Insulating Power. A rough surface radiates 
heat more freely than a smooth one, and all lagging should therefore 
be finished smooth. This is generally done by applying paint or 
varnish. Colour is of little moment, as for non-luminous radiations 



328 



Heat for Engineers. 



all cblours are practically identical in radiating power. A coating of 
metallic paint such as aluminium is best of all, owing to its smooth- 
ness, and reduces the heat escaping from an ordinary surface of 
lagging by about 7 percent. This means that for every 100 B.Th.U. 
escaping from each square foot of lagged surface per hour in the 



4CO 






200 



K 



/CO 



FIG. 90. TEMPERATURE GRADIENT THROUGH MAGNESIA LAGGING. 

ordinary way, only 93 would escape if a coating of aluminium paint 
were used. Whether the 7 units saved would ultimately repay the 
extra cost of the paint, depends upon the life of the lagging and cost 
of ordinary and metallic paint. A smooth surface, owing to its 
retention of heat, feels warmer to the touch than would a rough 



Heat- Insulating Materials. 



329 



surface under the same conditions of internal temperature. Hence 
the test often applied to form an idea of the efficiency of a lagging 
that of feeling with the hand may give an entirely erroneous indica- 
tion unless the nature of the surface be taken into account. 

Insulating Values of Materials in Common Use. The following 
table shows the insulating value of a number of the best types of 
lagging at present in use. In modern engineering practice, such 
materials as dung, plaster-of- Paris, etc., are seldom used, the extra 
expenditure on a better lagging being justified by the diminished 
condensation of steam in the pipes, greater durability, and a lower 
atmospheric temperature in a closed engine-room. A good lagging 
is essential also in cases where it is desired to convey steam to a con- 
siderable distance without a notable fall in pressure. In locomotive 
work, also, the present tendency is to use a better-class insulator, such 
as magnesia, to cover the boiler, instead of the layer of felt and air- 
space formerly employed. 

TABLE OF INSULATING VALUES OF LAGGINGS, EACH i INCHES THICK. 



Name 


B.Th.U. escaping 
per sq. ft. per Hour, 
at Steam Temperature 
of 400 F., External 
Temperature = 68 F. 


B.Th.U. escaping 
per sq. ft. per Hour, 
for each Degree F. 
excess Temperature 
of Steam at 400 F. 
over External Air 


Xewall's Magnesia Covering 


118 


0-36 


Blue asbestos ..... 


121 


0-365 


Mica (best form only; 


123 


0'37 


White asbestos sectional covering, in- 1 
ferior types of mica ami magnesia J 


126 


0- 3 8 


Plastics, best make (salamander com- \ 
position, Kieselguhr, Leroy's f 
plastics, etc.), and inferior asbes- j 
tos sectional 


133 


0-40 


Plastics, cheaper and inferior varieties 


H3 


o-43 


Bare pipe 


1070 


3-3 



Fall of Pressure along a Steam Pipe. The temperature, and con- 
sequently the pressure, of steam in a pipe falls along its length, owing 
to the escape of heat from the surface. The extent of this fall 
may be calculated, for a given case, as indicated in the following 
example : 

Example. Steam enters a 4-inch steam pipe at 400 F. = 245 Ib. 



330 Heat for Engineers. 

(absolute) pressure per square inch. It is conveyed at the rate of 
8000 Ib. per hour ; to find the temperature and pressure at the end of 
100 feet (a) when lagged so that the average loss of heat per sq. ft. 
per hour is 120 B.Th.U.; (b) when unlagged, with an average loss of 
850 B.Th.U. per sq. ft. per hour. 

The total surface of the pipe = TT/// = x ~ x 100 = 105 

sq. ft. Hence the heat escaping in one hour from the lagged pipe 
= (105 x 120) = 12,600 B.Th.U., and from the bare pipe = (105 
x 850) = 89,250 B.Th.U. The total heat of i Ib. of steam at 400 F. 

(from tables) = 1233 B.Th.U., hence the total heat of 8000 Ib. at 

400 F. is 9,624,000. The total heat of the steam at the end of the 

pipe will be (9,624,000 - heat lost) = 

9,611,400 B.Th.U. in the lagged pipe, and 
9.534,75 m the bare pipe. 

Dividing each of these numbers by 8000, to obtain the residual 
total heat per pound of steam, the figures are 1201 '4 and 1191*8 
respectively. 

From tables, the temperature and pressure corresponding to a 
total heat of 1201-4 B.Th.U. per Ib. are 393*8 F. and 230 Ib. 
per sq. in. absolute pressure, which will be the values at the end of 
the lagged pipe ; and similarly the figures for the bare pipe will be 
found to be 362 F. and 157 Ib. absolute pressure. 

Hence the fall in temperature in the lagged pipe is 6*2 F., and 
in pressure 20 Ib. per sq. in.; whilst in the bare pipes the corresponding 
figures are 38 F., and 93 Ib. per sq. in. 

Descriptions of Laggings in Practical Use. A material may be 
made up in the form of "sectional" covering, in which case it is 
shaped beforehand to fit the object to be lagged, and applied in 
sections bound together by strips of metal, the advantage gained 
being easy application and removal. For large surfaces such as the 
exterior of boilers, the " mattress " form is frequently adopted, the 
material being contained in loose form in a cover woven from asbestos 
or other material so as to secure pliability. The third form is known 
as "plastic" the material being mixed with ingredients such as clay, 
etc., which impart adhesive properties, and applied to the surface 
with a trowel. In this case, the removal is difficult, and entails the 
destruction of the covering ; hence this method is only adopted where 
the lagging is expected to be permanent. Many varieties of each 
type are sold, some of which, together with their chief features, are 
indicated below. 



Heat- Insulating Materials. 331 

Newalfs Magnesia Covering. This consists of 85 per cent, of 
light magnesium carbonate, intimately mixed with 15 per cent, of as- 
bestos fibre, pressed into the desired shape when moist. On drying, 
the mixture adheres sufficiently to permit of use without crumbling. 
Asa heat insulator it is unsurpassed, being extremely porous ; it will 
not stand rough usage, however, and does not resist the continued 
action of water or steam. It is very light, and does not exert 
any corrosive action on metallic surfaces. This material is largely 
employed in the British Navy, the lagging being protected by thin 
plates of planished iron from accidental damage. It may also be 
used in mattress form, and is made by the Magnesia Coverings 
Company. 

Mica. This lagging is composed of flakes of mica bound together 
by wire netting, or enclosed in covers to form a mattress ; or better 
still, as made by the Mica Boiler Covering Company, the flakes may 
be cemented together by silicate of soda. The thermal efficiency of 
this material depends greatly on the quantity of air enclosed between 
the mica flakes, and in the best specimens is nearly equal to magnesia ; 
but if carelessly made the covering is much less efficient. It is liable 
to peel if subjected to rough usage, but can be protected by thin sheet- 
iron. It is uninjured by water or steam, and the sectional material 
made by moulding the mica with silicate of soda, and afterwards 
baking, is particularly serviceable in damp places. 

Asbestos Coverings. Of the different varieties of asbestos, the 
white and blue are used for lagging purposes, either in sectional or 
mattress form. White asbestos laggings are much used, and although 
inferior to magnesia or mica as heat insulators, are less expensive. 
In the " Viceroy " covering, made by the United Asbestos Company, 
the efficiency is increased by building up the cover from corrugated 
strips, thus enclosing more air spaces. As asbestos is capable of 
being woven, it forms a suitable material for making insulating ropes, 
which may be wound round small steam-pipes used for temporary 
purposes, and many firms supply such ropes in different thicknesses. 
The fibres of blue asbestos are more tenacious than those of the 
white variety, and in the mattress coverings made by the Cape 
Asbestos Company the cover is woven of blue asbestos, and is filled 
with thin fibres of the same material. These coverings will stand a 
considerable amount of rough usage without injury, and may be 
saturated with water without deterioration ; but are more expensive 
than the white asbestos laggings. Blue asbestos is also superior in 
insulating power to white. 

Slag- Wool or Silicate Cotton. This material is produced by 



332 Heat for Engineers. 

blowing steam through molten slag, and consists of fine fibres com- 
posed of silicates of lime and iron, resembling wool. It is enclosed 
in a suitable cover, and applied in mattress form to the hot surface. 
It is one of the best heat insulators known, but when subjected to 
vibration tends to crumble into powder, and thus to leave portions of 
the surface unprotected. It is also said to produce corrosion and 
pitting of iron surfaces, especially when moisture is present, and these 
two drawbacks have prevented its extensive use for hot surfaces. 
These objections do not apply to cold stores, for which it is largely 
used. 

Plastics. The expenses incidental to the manufacture of sectional 
or mattress coverings are obviated in this class of coverings, and 
cheaper materials may be used. A common substance used in the 
making of plastics is Kieselguhr or fossil meal, which is a highly porous 
form of silica of organic origin. This is made into cement by the 
admixture of sufficient binding material, and applied with a trowel, 
forming one of the best laggings of this type from the standpoint of 
thermal efficiency, but lacking in mechanical strength. Greater 
durability is secured at the expense of insulating power by the 
introduction of other materials ; some of the compositions on the 
market containing asbestos, magnesia, mica, etc. Amongst plastics 
which enjoy a well-deserved reputation amongst engineers may be 
mentioned the " Kieselguhr " laggings made by Messrs. A. Haacke 
and Co., The "Salamander" covering made by the United Asbestos 
Company, the various compositions made by Messrs. F. Leroy and Co. 
and the " Eagle " cement of Dick's Asbestos Company. Although 
inferior, as a class, in heat-insulating value to sectional coverings,, 
plastics are cheaper and often mechanically stronger. 

Choice of a Lagging. In selecting a lagging for a given purpose 
several points must be considered. If liable to rough treatment, 
mechanical strength is of primary importance; whilst to convey 
steam long distances with a minimum fall of pressure, high insulating 
power is the first consideration. In a closed engine-room it is 
advisable to employ a lagging with a surface temperature as low as 
possible. Other points to be rioted are liability or otherwise to- 
dampness, and the probable time which will elapse before renewal 
becomes necessary. The last-named is of importance, as in a short 
period the superior efficiency of an expensive material does not cover 
its extra cost over a less efficient, but cheaper, covering. It is 
obviously impossible to prescribe a lagging which will be the most 
economical under all conditions, and the choice must be guided by 
existing circumstances. Having decided on a material, the correct 



Insulation of Cold Stores. 333 

thickness to employ may be determined from the thermal constants 
of the substance, as indicated on page 326. 

Heat- Insulating Materials for Cold Surfaces. The fact that the 
temperature of a substance used to insulate a cold store never rises 
above that of the surrounding atmosphere or water, in the case of 
a ship enables many materials to be used which could not with 
safety be applied to hot surfaces. The essential features of a good 
material for lagging a cold surface are : 

1. Good insulating power. 

2. No tendency to absorb atmospheric moisture. 

3. Not liable to become mouldy, or to attract vermin. 

4. Low specific gravity, particularly when used to insulate a ship. 

5. Low cost. 

The substances most used are silicate cotton, cork, charcoal, 
peat, sawdust and hair, the first-named being the most extensively 
used, as, in addition to its excellent insulating qualities, it is prac- 
tically vermin-proof. Charcoal, owing to its lightness and cheapness, 
is much used to insulate the sides of the vessel from the chambers 
containing the frozen cargo. Powdered cork is good for the same 
purpose, but is more expensive. Peat and sawdust are frequently 
used on the score of cheapness, but are inferior in insulating power. 
Hair is a cheap and good insulator, but by no means vermin-proof, 
and lacks the cleanliness of other materials. 

The most reliable tests of the insulating value of the substances 
enumerated have been made by lagging a box to a given thickness, 
and placing a block of ice in the interior, which has been carefully 
weighed before placing in the box. After the lapse of a definite 
time, the ice is taken out and re-weighed, and from the loss in weight 
the escaping heat may be calculated. An equal thickness of another 
material is then placed round the box, and a similar block of ice 
inserted. The substance which shows the least ingress of heat, as 
judged by the ice melted, is the best insulator. The results, how- 
ever, may be varied to such a large extent by altering the density by 
close or tight packing, that it is difficult to state which is the best 
material. Beyond a marked inferiority in the cases of peat and saw- 
dust, no statement as to the efficiency of the remainder may be made 
without prescribing the degree of compactness preferably as so many 
pounds per cubic foot. Even if such data were available, however, 
no conclusions of great value could be drawn from them, as the 
material only forms a portion of the complete insulation, as will be 
seen later. A series of experiments performed with the completed 



334 Heat for Engineers. 

lagging would be necessary to furnish reliable data to guide in calcu- 
lating the ingress of heat under given conditions. At present only 
a few such experiments have been recorded ; but a fairly safe guide 
to the heat passing into the store may be obtained by assuming the 
coefficient of conductivity to be 0-00025 to o 0003 calories per 
second per square centimetre of surface, for each centimetre of 
thickness of a well-made partition or wall. 

Construction of Insulating Walls of a Cold Store. In general, the 
insulating wall of a cold store is constructed of wood, so as to enclose 
air spaces, damp-proof courses, and spaces filled with insulating- 
material. Of the large number of patterns existent, one will be 
selected to indicate the general principle of construction, and is 
shown in section in Fig. 91. The brick wall is coated with tar to 
render it damp-proof, and batons of wood, 2 inches by 4 inches in 
section, are nailed on at intervals. Over these is fastened a double 




"C\v^ 
FIG. 91. METHOD OF INSULATING A COLD STORE. 

layer of matchboarding, i inch thick, a layer of impregnated paper 
being placed between the boards as a damp-proof course. Then 
follow a second set of batons, a second double layer of matchboard- 
ing also with damp-proof paper between a third set of batons, and 
finally a double layer of matchboarding, the inner layer laid horizon- 
tally and the outer layer vertically the total thickness being 12 inches. 
The space nearest the walls is an air space, made so that any mois- 
ture penetrating the wall will have difficulty in passing through the 
structure. If this space were filled with insulating material the water 
would readily creep through to the layer of matchboarding. The 
two remaining spaces are filled with silicate cotton or other insulator. 
The prepared papers known as "Ruberoid" make an excellent 
damp-proof course between the boards. In American practice the 
filling of the air spaces with insulating material is not adopted to the 
same extent as in this country, ordinary air spaces only being 
frequently employed. 



Diffusivily. 335 

On vessels carrying a frozen cargo, the space between the outer 
shell and the store rooms is filled with charcoal or other insulating 
material, the heat of the sea-water and atmosphere thus being largely 
prevented from entering. 

The domestic ice-safe consists of a metal chamber separated by 
an air-space from the wooden exterior. The saving effected by this 
air space, as common experience shows, is considerable. 

Diffusivity. This term was applied by Lord Kelvin to the quo- 
tient coefficient of conductivity _ I{ ^ numerical , the 

specific heat of unit volume 

thickness of a plate of a substance which would be raised i by the 
heat conducted through a plate of unit thickness in i second, when 
the difference of temperature between opposite faces is i. For 
example, if a plate of aluminium i cm. thick, of area x square centi- 
metres be kept with opposite faces i C. different, the calories trans- 
mitted in i second will be (x x K) = -345 x, the coefficient of con- 
ductivity being 345. The specific heat of unit volume of aluminium 
that is, the number of calories required to raise i cubic centimetre 
by i C. is *6i. Hence the number of cubic centimetres raised i 

* ^ A C ^C 

by '345 x calories is _^_t5 = -565 x. The thickness of a plate of 
6i 

area x square centimetres, and volume -565 x is "565 cm., and the 
same result will evidently be obtained whatever be the value of x. 
The diffusivity of aluminium, therefore, is expressed by the number 
565. For other metals the diffusivities are as under : 

Copper . . . . . . . i 205 

Silver 1-86 

Zinc ....... o - 435 

Iron ....... o'iS4 

Tin 0-374 

Lead . . . . . . . 0*24 

The significance of these figures will be understood by consider- 
ing the case of two bars of different metals, of equal section, placed 
with one end in a hot space, a thermometer being inserted in each 
case near the hot end. The increase of temperature indicated by the 
thermometers will be most rapid in the bar possessing the greater 
diffusivity, and hence bars of tin and lead would show a more rapid 
rise in temperature than iron, because the quantity conducted by 
these metals in one second although less than that conducted by 
the iron operates on materials of low specific heat, and thus pro- 
duces a greater rise in temperature. As the bars become heated along 



Heat for Engineers. 



their length, however, the heat passing through is no longer expended 
in causing a rise in temperature, and proceeds onwards to the rest of 
the har ; hence, when the steady state is reached the highest tem- 
peratures are observed in the materials possessing the greatest con- 
ductivities. 

The diffusivities of different kinds of rocks have been determined 
by Lord Kelvin and others, and the results applied in observations 
of the fluctuations of temperature in the earth's crust in different 
localities. 

Heating of Masses of Metals in furnaces. The time required for 
the complete heating of a mass of metal when placed in a furnace 
evidently depends upon the diffusivity of the metal. In many 
instances, such as the annealing of large masses of steel, it is essential 
that the centre of the mass shall attain a sufficiently high temperature, 
if the operation is to be successful. At present, manufacturers are 
largely guided by experience as to the time a block of steel or other 
material is allowed to remain in the furnace, but reliable data on the 
point would be of the highest value. Such data could be obtained 
by noting the temperature indicated by a thermo-electric pyrometer 
inserted in blocks of different sizes, under given conditions of furnace 
temperature. The following results were obtained in this manner for 
steel billets of circular section, which were placed when cold in a 
furnace at 1300 F. The temperature of the furnace was then raised 
to 2000 F., and the time required for the centre of each billet to 
reach 1900 F. noted. 



Diameter in Inches 


Time in Hours 


Diameter in Inches 


Time in Hours 


18 


3i 


32 


10 


20 


4 


40 


154 


24 


5* 


41 


i6J 


28 


7! 


4 2 


17 


30 


Sf 


45 


19* 



From the above figures it will be seen that the time required 
varies directly as the area of section, and this would probably apply 
to all cases. 



337 



CHAPTER XVIII. 

THE TRANSFER OF HEAT. CONVECTION, 

Nature of Convection. The molecules of a liquid are capable of 
moving amongst each other with a certain degree of freedom, whilst 
those of a gas are almost perfectly free to move. A disturbance of 
equilibrium in either liquids or gases is consequently followed by a 
movement tending to restore equilibrium, and when heat is the 
disturbing cause this movement constitutes what is termed con- 
vection. 

If a vessel of water be heated from below, the lower portions, 
owing to expansion, become less dense than those above, and rise in 
consequence, being replaced by colder water from above. This 
continues until the temperature of the whole mass has been brought 
to the boiling point, and hence the transfer of heat from the source 
has been effected by convection. If the heat be applied at the upper 
surface, the less dense liquid remains floating on the top, and does 
not mix to any extent with the colder liquid below. Any heat com- 
municated downwards will be due to conduction, and as liquids are 
bad conductors the process is extremely slow. Conversely, the tem- 
perature of a mass of liquid may be cooled throughout by reducing 
the temperature of the upper portion as occurs in the freezing of a 
pond of water whilst if the lower portion only be cooled the upper 
layers are practically unaffected. The same reasoning applies to 
gases, in which case, however, a mixing of hot and cold gas may 
occur to some extent in opposition to gravitation, owing to the 
property of diffusion. The phenomena connected with the transfer 
of heat by convection are of the greatest importance in many engi- 
neering problems, and will be studied in this connection in the present 
chapter. 

Circulation of Water in Boilers. The two objects to be secured 
in a boiler of any type are (i) to obtain as large a heating surface as 
possible, consistent with strength, and (2) to ensure that all the water 
in turn shall come into contact with the heated surface. The latter 

z 



338 Heat for Engineer s> 

condition involves placing the fire at the lowest practicable level, so 
that the effect of convection may be as great as possible. 

In the locomotive boiler the firebox is separated from its casing 
at the sides by a space of about 2 inches, which space is occupied 
by water. The crown of the firebox is covered to a varying depth 
with water ; and a series of brass tubes pass longitudinally from the 
firebox through the barrel to the smoke-box and chimney. Heated 
water is therefore arising by convection from the sides and crown 
of the firebox, and from the tubes. All the water above the tubes 
and top of the firebox is therefore set into circulation and heated 
just in the same manner as water is boiled on a fire, but the water 
in the lowest part of the barrel would remain practically stagnant 
were it not for the fact that a large portion of the firebox is at a 
lower level than the barrel ; hence convection from the sides of the 
firebox establishes the necessary circulation in the water beneath 
the tubes, and circulation is secured in every part of the boiler. 
When once the water is boiling, the steam generated maintains an 
efficient circulation by rising to the top of the boiler from all the 
heated parts. 

In stationary boilers of the horizontal type the flues are placed 
as low as possible in the casing, so that the bulk of the water is 
above the hot surface. By the use of cross-tubes in the flue, placed 
at various angles, the lowest portions of the water are enabled to 
circulate, and the additional advantages of increased heating-surface 
and strength are secured. In the vertical type the main mass of 
water is above the flue, and the fire at the bottom ; hence the water 
in the space between the flue and casing can rise freely, being 
replaced by colder water from above. Cross-tubes are sometimes 
used to ensure greater strength and increased heating-surface. 

In water-tube boilers the tubes are filled with water and heated 
externally, as distinct from the tubes in a locomotive boiler, which 
are heated internally and surrounded by water. The tubes con- 
taining the water pass from the furnace to the barrel containing the 
main supply, and from which the steam is drawn off, this barrel 
resting on the top of the furnace. The heated portions of the tubes 
are inclined, so that as the hot water rises by convection into the 
barrel a fresh supply of cold water passes in at the other end. A 
rapid circulation is thus maintained, and is greatly augmented when 
the water entering the tubes is so hot as to be converted into steam 
in the tubes. In a well-designed water-tube boiler a more efficient 
circulation is secured than in boilers of any other type hence a 
reason why a more rapid supply of steam is procurable. 



Hot Water Circulation. 



339 



It is evident from all these examples that the property of 
convection in water is one of primary importance in the design of 
any type of boiler, and that, for a given heating-surface, the boiler 
in which circulation is best provided for will be the most efficient 
in practice. One of the chief drawbacks of defective circulation is 
the existence of different temperatures at different parts of the boiler, 
which is weakened by the strains thus caused ; whereas if heated 
equally throughout strains are avoided. 

Heating by Hot Water Circulation. One of the commonest 
methods of warming a building is by the circulation of hot water 
from a boiler through pipes and special radiators. For domestic 




FIG. 92. PRINCIPLE OF HOT-WATER CIRCULATION. 



purposes a supply of hot water in various rooms is obtained by a 
similar system of circulation. The principle involved in each case 
may be understood by reference to Fig. 92, where A represents 
a boiler heated from below, from which convection currents of hot 
water rise through the pipe B, which enters the boiler at the top. 
After passing through the system of pipes, in the circuit of which 
radiators such as R may be placed, the water returns to the boiler 
through the pipe C, inserted at the lower end. The open pipe E 
serves to allow for the expansion of the water, and hence is termed 
.an expansion-pipe. 

The general arrangement of a hot-water system is shown in 

z 2 



340 



Heat for Engineers. 



Fig. 93- The hot water from the boiler B passes to a cylinder A, 
which serves to store a supply for tapping off. From the cylinder 
the circulation is continued by a pipe fixed to the top, from which 
side-branches are taken to radiators. At the highest part of the 
flow-pipe an expansion-tube E is fitted as a T-piece, so that the 




FIG. 93. GENERAL ARRANGEMENT OF HOT-WATER APPARATUS 
IN A BUILDING. 

system may be kept full of water without danger of rupture owing ta 
expansion. The return-pipe is fitted at intervals with taps T, T, 
from which the hot water may be drawn off as desired for baths, 
lavatory-basins, etc. A better circulation is secured by drawing off 
from the return pipe than would obtain by using the flow-pipe for 
this purpose The water from the return-pipe passes into the cylinder 



Plot Water Circulation. 341 

A, and is discharged at the lower end, from whence it passes to the 
bottom of the boiler. The supply of water to the system is furnished 
by means of a cistern C, connected to the cold water supply, and 
furnished with a ball-cock. The lower end of this cistern is connected 
by a pipe to the bottom of the cylinder A, and when water is drawn 
off at any part an equal quantity enters from the cistern. When 
cold, the water will stand at the same level in the expansion pipe as 
in the cistern. An auxiliary flow-pipe F, connected as a branch to 
the hot-water entrance and exit of the cylinder A, serves to promote 
the circulation, and enables a more rapid supply of hot water to be 
available for the radiators, etc., than would be the case if the whole 
of the circulating water had to pass upwards through the cylinder, 
and heat up the large mass contained therein. The real function of 
the cylinder is to secure a reserve of hot water, which, on opening 
one of the taps, is driven into the pipes by the cold water entering 
at its lower end. For convenience in executing repairs, a stop-cock 
is placed near the cold-water entrance to the cylinder, which enables 
the supply to be cut off; and a drain-pipe D, communicating with 
the bottom of the cylinder, permits of the complete withdrawal of 
the water from the system. 

Many modifications of the system described are in use ; the 
differences, however, are in detail rather than principle. Any hot- 
water apparatus furnished with an expansion pipe open to the atmo- 
sphere is said to work on the " low-pressure " system, as distinct from 
the " high-pressure." In the latter case a continuous length of piping 
is used, bent into a coil at the fireplace, this coil serving as the boiler. 
At the highest level is placed an expansion chamber, having a 
capacity of about -fa that of the entire system ; and after the pipes 
have been completely filled with water the expansion chamber is 
hermetically sealed. The pressure in the interior may then rise to 
several atmospheres, with a consequent increase of temperature, as 
in the case of a steam-engine boiler. This system is sometimes 
used for heating rooms ; being a closed system it cannot be used 
for furnishing a supply of hot water in addition. In some large 
hospitals the water is heated by exhaust steam from the engines 
used in connection with the electric lighting installation, and the 
hot water pumped through pipes and radiators placed in the various 
wards. 

Length of Pipe required to Heat a Building. The following 
formula, derived from practice, may be used to calculate the length 
of pipe, of given diameter, required to produce an assigned tem- 
perature under given conditions : 



342 Heat for Engineers. 

Let P = temperature of pipes in degrees F. 

T = required in building, degrees F. 

/ = of outside air, degrees F. 

C = cubic feet of air to be warmed per minute 
D = diameter of pipe in inches 
L = length of pipe in feet 

Then 

T = ' l8C (P ~ t) (T - t) 
D (P - T) 

An example illustrating the use of this formula is appended. 

Example. To find the length of piping necessary to heat a room 
of 10,000 cubic feet capacity, the air of which is renewed 3 times 
per hour. Temperature of pipes = 150 F. ; air in room, 65 F. ; 
external air, 40 F. ; diameter of pipes = 4 inches. 

Applying values in formula 



L = (' l8 x 5) x ( I 5 ~ 4) x (65 - 4) 

4 x (150 - 65) 
= 73 feet. 

(The air to be warmed = 30,000 cubic feet per hour = 500 per 
min.) 

A few simple rules which lead to results not differing greatly from 
those obtained by the use of the formula are given below : 

1. To find the length of 4-inch pipe necessary to warm a room to 
60 F., divide the cubic contents in feet by 150, when the quotient 
will give the length of pipe in feet. Thus, for a room of 10,000 cubic 

feet capacity, the length required is I0?00 = 66| feet. If calculated 

J 5 

by the previous formula, the length indicated is 62 feet a discrepancy 
less than that which might be caused by variations in the temperature 
of the outside air. 

2. Three-inch pipes should be one-third longer, and 2-inch pipes 
twice as long as 4-inch pipes to heat the same space by the same 
amount. Or, generally, the length varies inversely as the diameter, 
as shown by the formula. 

3. To secure an internal temperature of 65 F. in a dwelling- 
house, consisting of two or more storeys, allow 1 2 ft. of 4-111. pipe for 
each 1000 cub. ft. of space. This is in excess of that required for a 
single room. 



Hot Water Circulation. 343 

4. In workshops 6 to 10 ft. of 4-in. pipe should be allowed for 
each 1000 cub. ft. of space. 

All the above rules allow for the customary renewal of air by 
ventilation. 

Calciilation of Radiating Surfaces in Heating Biiildings. If the 
length of pipe obtained in the previous formula be multiplied by 2 TT r, 
where r is the radius of the pipe in feet, the radiating surface neces- 
sary is obtained. Thus, in the foregoing example, where the length 
of 4-in. pipe necessary was found to be 73 ft., the radiating surface 
would be 

73 x 2 x x I = 76-5 sq. fl 
7 o 

Another method of arriving at the result is as follows : Measure up 
the surface of the walls and ceiling in square feet, exclusive of the glass 
of the windows, which is measured separately. Owing to its thinness, 
the glass allows of the greatest escape of heat by conduction, the loss 
through i sq. ft. being, on the average, equal to that escaping in this 
way through 10 sq. ft. of the remaining surface. Let T = tempera- 
ture at which the room is to be maintained, P = temperature of pipes 
and t = temperature of outside air, all in Fahrenheit degrees, then 

/'p t\ 
the fraction W r- = sq. ft. of radiating surface per sq. ft. of glass 

or its equivalent. 

Example. The dimensions of the room of a dwelling-house are 
20 x 15 x 12 ft., the window surface being 40 sq. ft. To find the 
area of radiating surface necessary to maintain a temperature of 65 F. 
when the temperature of the pipes is 150 F., and the outside air 
40 F. The total area of the walls and ceiling is 1140 sq. ft., or, 
deducting that of the glass, noo sq. ft. Dividing by TO the glass 
equivalent of the walls and ceiling = no sq. ft., and the total surface 

(T - /) 
in terms of glass, = 150 sq. ft. From the formula j L the 

amount of radiating surface per sq. ft. of glass or equivalent surface 

= V_5 ~ 4) = JL S q t f t . an( j t h e tota i sur f ace required = 150 x 5 
(150 - 65) 17 17 

= 44 sq. ft. This would be furnished by 42 ft. of 4-in. pipe. From 
Rule 3, for dwelling-houses, viz., 12 ft. of 4-in. pipe per 1000 cub. ft., 
the length calculated would be (12 x 3*6) = 43- 2 ft. length, as 
the contents = 3600 cub. ft. This is a practically identical result. 

It is evident that any rule relating to pipe length or surface can 
only be approximate, as the heating effect is modified by the amount 



344 Heat for Engineers. 

of fresh air admitted, thickness of walls, extent of window surface, etc. 
When the installation is made by any of the foregoing rules, how- 
ever, any deficiency or excess of heat can be remedied by increasing 
or diminishing the consumption of fuel in the furnace, thus raising or 
lowering the temperature of the pipes until the room is at the required 
temperature. 

For the high-pressure system, the length or surface of pipes used 
may be approximated by taking f of any of the results obtained as 
above. 

Fire-Grate Area for Hot-water Circulation. For a coal fire, with 
a good draught, 30 to 50 sq. in. of fire-grate area are required for 
every 100 sq. ft. of pipe surface. The larger figure leaves a safe 
margin for such contingencies as excessively low external temperature 
and frequent renewal of air. 

Construction of Hot- Water Radiators. In order to increase the 
area of the heated surface, radiators are interposed in the pipes con- 
veying the hot water. They consist of a number of flat pipes placed 
side by side, and thus present a large surface to the room. The 
exterior should be coated with paint which presents a rough surface, 
colour being of no importance for heat waves of the non-luminous 
type. The radiating power is diminished considerably, however, if 
a metallic paint, giving a smooth surface, be used ; hence the cover- 
ing of radiators with aluminium paint as is sometimes done for the 
sake of appearance is a mistake. 

Convection in Air. Winds. When a mass of air is heated by 
contact with the warm surface of the earth, it rises, and is replaced 
by colder air, which, entering the vacated region with a noticeable 
velocity, gives rise to a wind. The velocity of the wind depends 
upon the difference of temperature of the heated air and that 
surrounding the heated zone, and in some cases may equal 100 miles 
per hour. Such a velocity, however, is rarely attained, and is nearly 
i of the velocity with which air at o C. would rush into a vacuous 
space, viz., 743 miles per hour, or 1090 feet per second a figure 
identical with the velocity of sound in air. In general, there is a 
tendency for air in the equatorial regions to rise, causing a flow from 
the poles towards the equator. This tendency is greatly modified 
by local circumstances, such as the distribution of land and water, 
many special winds such as monsoons, the sirocco, the mistral, etc., 
having a more or less local origin. It should be remembered that 
the rays of the sun do not heat the air in passing through, but 
warm the earth's surface on striking, so that any increase in atmo- 
spheric temperature arises from contact with the surface. 



Draught of Chimneys. 345 

Draught of a Chimney. The velocity with which a column 
of hot air will rise through a chimney may be calculated from 
Torricelli's theorem regarding the escape of fluids from an opening. 
According to this theorem, the velocity is given by the expression 
V 2 = zgh, where h = head of fluid, and g the acceleration due to 
gravitation. The head of fluid giving rise to the upward pressure 
in this case is the difference between the height of the chimney, and 
the height to which a column of gas of the same section would 
extend when heated to the temperature existing in the chimney. 
Let H = height of chimney ; T = temperature of air before heating, 
= atmospheric temperature, in absolute degrees ; HJ = height of 
column at the higher absolute temperature ; T 1 = absolute tempera- 
ture of hot gas in chimney, then 



- 1 = , by Charles' law, and H, = 



The head of pressure is therefore 

HT! _ H __ HO^ 
~T " T 

and the velocity, 



v - 



This formula is of little service in practice, as the friction on the 
sides, and varying temperatures at different heights of the chimney, 
alter the velocity greatly. It serves to show, however, that the 
velocity increases with the height, and also directly as the difference 
between the external and internal temperatures, and inversely as the 
external temperature. 

A number of formulae derived from practice are appended, 
which give results much nearer the truth than those derived from 
the above formula. 

Let E = effective area = (actual area allowance for friction), 

in square feet 

H = horse-power generated 
A = actual area in square feet 
S = side of square chimney in inches 
D = diameter of round chimney in inches 
h = height of chimney in feet 



346 Heat for Engineers. 

Then 



H = 3'33E x I. . 2 

S = 12 VE + 4 ..... 3 
D = i3'54 VE + 4 4 



Before proceeding to examples involving these formulae, it may 
be stated that it is assumed in them that each horse-power involves 
the consumption of 5 Ib. of coal per hour, and that frictional losses 
are equivalent to the existence of a still layer of air 2 inches thick 
on each wall. 

Example i. A circular chimney has a diameter of 5 feet = 60 
inches. What height should it be made if used with a plant generat- 
ing 500 horse-power? 

Actual area in square feet = x (2'$)' 2 == 19*65. 

Effective ditto from (i) = 19-65 - (o'6 x v /I 9' 6 5) =I 7- 



From (5) h = ^ 3 ^ = ( ' 3 X ^ = 7* feet nearly. 
E J 17- 

Or, approximately, 80 feet. 

Example 2. To find the horse-power which could be generated 
by a plant furnished with a square chimney, of 6 feet side, and 120 
feet high. 

Actual area = 36 square feet. 

Effective area = 36 - ('6 x /36) = 32*4. 
From (2) H = (3-33 E x ,Jli) = 3-33 x 32*4 x ^120 
= 1182, or roughly 1200. 

In determining the dimensions of a chimney, due regard must be 
paid to the locality in which it is erected. If on a hill, open to winds, 
a less height will be necessary than when in a sheltered situation. 
The following table shows the heights given to chimneys under 
average circumstances, when intended for the consumption of a given 
quantity of good coal. The horse-power may be determined by 
dividing the coal burnt by 5. If inferior fuel be used, a greater 
height is requisite, and to burn anthracite slack to advantage a 
minimum height of 175 feet is necessary. 



Draught of Chimneys. 



347 



HEIGHT OF CHIMNEYS. 



Height 
in 
Feet 



Pounds of Coal Burnt per Hour in Chimney of Actual Diameter (feet) 
i ft. 1 1*5 2*0 a*5 3*0 3*5 4*0 4*5 . 5*0 5*5 j 6'o 7-0 8 - o 



So 

IOO 

125 
150 
175 

2OO 



9-0 



60 46 141 287 485 ' 735 10401390 1800 2250*2760 3320 4610 6080 



.. 331 561 85o|ii90i6oo207o;26oo l 3i8o38305320 6990 
.. j .. 950 1 1 340! 1 7 90' 2320 2810 3550)4290 5940 7810 



7700 
8900 

9950 
2000 258o j3 25o'396o|479o 6640 8730 

28301^3560143501524017290, 9570 ! 12150 
.. 138601472015690790010490 | 13200 

.. ! .. 150106050841011100 I 14100 



Draught of a Chimney in Terms of a Water- Column. A water- 
column furnishes a convenient means of expressing the draught of a 
chimney. If the end of one limb of a glass U-tube be bent so as to 
pass into the chimney, and water be poured into the tube, it will rise 
to a higher level in the limb connected with the chimney, owing to 
the diminished pressure caused by the upward rush of gases. The 
difference of level observed in the two branches expresses the draught 
in terms of a column of water. This is a convenient method of test- 
ing the efficiency of a chimney under working conditions. The 
following formula is useful for calculating the draught that should be 
given by a chimney of given height : 



where D = draught in inches of water 
H = height of chimney in feet 

T = absolute temperature of air in degrees Centigrade 
T! = absolute temperature of gases in chimney in degrees 
Centigrade. 

If temperatures on the Fahrenheit scale be used, the formula is 



the symbols T and IL\ representing absolute degrees, which on the 
Fahrenheit scale = (ordinary degrees + 460). 

Example. To find the draught, in inches of water, given by a 



34 8 Heat for Engineers. 

chimney 100 feet high, when the temperature of the air is 10 C. or 
50 F., and the temperature of the gases in the chimney is 160 C. 
or 32cT F. 

Applying in formula 

D _ I00 (4-"_0 

V 283 433 

or, in deg. F, D -100 (^- -^3,0) = ' 48 

In a practical determination the temperature of the furnace gases 
can be obtained from the readings of a pyrometer placed in the 
chimney. 

Another simple rule is as follows: "To find the maximum 
draught for a chimney when the temperature of the air is 62 F., and 
of the hot gases 600 F., multiply the height of the chimney above 
the grate by '007.'' The answer is given in inches of water, and 
in the case of a chimney 100 feet high would therefore be "j inch. 

Weight of Gases Ascending Chimney. The gases escaping from a 
chimney consist of carbon dioxide, carbon monoxide, steam, nitrogen, 
and unused oxygen. As these gases have different densities, it is 
evident that the weight escaping in a given case depends upon the 
relative amount of each present. For chimneys over 3 feet in 
diameter, under normal conditions, the weight is given approximately 
bv the formula 



Weight in Ib. per second = 85 x ^ x / h ( T i " T ) 

J-i \/ T 

where A = actual area in square feet, h = height of chimney in 
feet, Tj = absolute temperature of hot gases in degrees F., and 
T = absolute temperature of air in degrees F. 

Example. The weight of escaping gases for a chimney of area 
1 6 square feet, height TOO feet, with hot gases at 300 F. and air at 
60 F., would be 12-12 Ib. per second, as calculated by the above 
formula. 

If a series of weights be calculated for a chimney of given dimen- 
sions from the above formula, taking the temperature T of the outside 
air as constant, and varying T 15 it will be found that the weights 
increase rapidly up to a point where T T exceeds T by 200 F., after 
which the increase is slower, and finally a maximum is reached beyond 
which a further increase in Tj shows a diminishing weight of gases 
escaping. This is shown graphically in Fig. 94, in which pounds per 



Draught of Chimneys. 



349 



second are plotted against the difference of temperature between 
the hot gases and surrounding air, or (Tj T), in a chimney of 
given dimensions. It will be seen that the maximum occurs when 
(Tj T) is equal to about 550 F., so that if the air were at 60 F., 
any increase in temperature in the chimney above 6ioF. would re- 
sult in a less weight of escaping gases. The maximum, moreover, is 
only slightly in excess of the weight corresponding to (Tj_ - T) 
= 300 F., and hence it is desirable to reduce the temperature of the 
escaping gases to a point where (T x - T) = about 300 F., to ensure 
economic working. In this connection it should be remembered that 
the rate of combustion is determined by the weight of air passing 



K /./; 






















s" 

1 

r 

j> .^ 





2 


^^ 











__ 








' '* -^ 


& -A- 


/ 




















*' 
i* 


i/ 




















I 

i? , 























SCO 



8QO 



fOCO 



FIG. 94. CURVE SHOWING WEIGHT OF AIR PASSING UP A CHIMNEY 
AT DIFFERENT TEMPERATURES. 

through the fuel, and that the hotter the escaping gases, the greater 
will be the loss of heat in the chimney. The reason why a point of 
maximum efficiency is reached will be understood from the fact that 
the weight of one cubic foot of gases diminishes directly as the abso- 
lute temperature, whilst the velocity increases only in the ratio 
(approximately) of the square root of the absolute temperature, and 
hence fails, after a certain point, to compensate for the diminished 
density. 

Ventilation. The problem of renewing the air in rooms, embraced 
by the term " ventilation," involves in most cases the property of 
convection in air. Successful ventilation, however, is by no means 
a simple matter, and a system satisfactory for one building may prove 



35O Heat for Engineer . 

a failure for another differently constructed and situated. The sub- 
ject covers a wide ground, and it will only be possible to deal with 
the general principles involved, within the limits of the present 
treatise. 

Ordinary fresh air contains 4 parts in 10,000 of carbon dioxide, 
and in a room occupied by human beings, each exhaling o 6 cubic 
feet per hour, the proportion of CO 2 rises considerably unless the air 
be frequently renewed. Ideally, the proportion of CO 2 should never 
exceed 6 parts in 10,000, which means that every adult should have 
.a breathing space of 3000 cubic feet per hour, or 1000 cubic feet 
renewed three times per hour. The carbon dioxide itself is not 
injurious, but serves by its amount to furnish a clue to the quantity 
of organic matter present, which gives rise to " stuffiness " in a room, 
this effect being enhanced by the excess of moisture resulting from 
exhalation. In practice this ideal cannot, for various reasons, be 
attained, as to secure 3000 cubic feet of space per adult would 
involve buildings of absurdly excessive size, and to renew the air of 
a room in this country more frequently than three times per hour 
involves the creation of draughts, which, besides being uncomfortable, 
may cause more injury than slightly-vitiated air. No harm results 
in most cases from remaining for short periods in a room containing 
far more than 6 parts in 10,000 of CO 2 ; but ill-effects are noticeable 
in all cases where a stuffy atmosphere is persistently breathed. 

A general idea of the space allowed per head may be obtained 
from the following selected examples, the minimum usually being 
prescribed by Government regulations : 

Cubic Feet per Head 

Dwelling-houses ..... 1000 

Common lodging-houses .... 300 (minimum) 

Poor Law Boards ..... 300 ,, 

,, sick persons .... 850 to 1200 

Factories and workshops . . . 250 (minimum) 

,, overtime . . 400 ,, 

Army, regulation space .... 600 

London schools (County Council) . . 130 (minimum) 

Hospitals, ward space .... 2000 ,, 

In addition to cubic contents, it is necessary to prescribe a 
minimum for floor space. A room 20 feet long by 15 feet wide and 
10 feet high, would possess the same cubic contents as another 
15 x 10 x 20 feet high, but the latter would be much inferior in 
respect to an easy renewal of air. The minimum allowance for floor 
space is expressed in square feet by dividing the contents in cubic 
feet by 12. Thus a room of 1200 cubic feet capacity should have a 



Ventilation. 351 

minimum floor space of 100 square feet, and would be better, foi 
ventilating purposes, with a floor space of 120 square feet. 

The rate at which the air in a room may permissibly be, removed 
depends upon the sensitiveness of the occupants to draughts. The 
incoming air, when cold, should not on this account exceed 2^ feet 
per second in velocity, or 3 feet per second when warm. It is this 
factor which places a limit on efficient ventilation. 

"Natural" Ventilation. This term is intended to include all 
systems of ventilation in which the renewal of air is effected without 
the aid of mechanical appliances, such as exhaust-fans, etc. The 
expired air from individuals is at the temperature of the human body 
98 F. or 36-5 C. which is greater than the temperature existing 
in a room in this country, even in the hottest weather. Consequently 
the warm gases exhaled rise through the colder air of the room, and 
if an outlet be provided at a high level, together with an inlet for 
cold air at a lower level, the expired gases will escape above and be 
replaced by an equivalent quantity of pure air below. If an outlet 
only is provided, no circulation is set up, as this would entail the 
cold air entering at the same time and place as that at which the 
warm air escapes, one tendency counteracting the other. It is evident 
that the rate at which the air is renewed in this way depends upon 
the speed at which the warm gases rise and escape, and this in turn 
is determined by the difference of temperature between the warm 
gases and the air of the room. Hence a low temperature in the air 
of a room favours an efficient renewal of the air; but to secure 
comfort to the occupants this temperature should not fall below 65 F. 
The velocity with which the gases commence to ascend is conse- 
quently that due to a difference in temperature of about 35 F., or 
about 5 feet per second ; but as the warm gases rise diffusion takes 
place with the colder air of the room, and the velocity falls off con- 
siderably. In a lofty room this diffusion is complete before the 
upper portion is reached, the result being to establish a stagnant 
layer of warm air in this region. It is evident, therefore, that the 
automatic tendency to renew the air is considerably hampered, and 
cannot in itself be relied upon to secure efficient ventilation except 
under very favourable circumstances. 

Gas-jets burning in a room produce carbon dioxide and water, 
each jet consuming as much oxygen as three adults. The products 
of combustion are non-injurious when mixed with sufficient air, and 
with a properly arranged outlet and inlet the burning of gas-jets 
assists greatly in renewing the air of the room. The products rise 
from the jet at an extremely high temperature and consequent high 



5 - 2 Heat for Engineers. 

velocity, and reach the outlet before diffusion has taken place to any 
great extent. A strong escaping current is thus established, and a 
renewal of the air of the room results in consequence. In many 
cases the improved ventilation thus obtained more than compensates 
for the impurities introduced by the combustion of the gas, owing to 
the non-existence of a stagnant upper layer of air. For this reason 
the air of rooms illuminated by gas is frequently less vitiated than is 
the case when electric lighting is adopted, especially when occupied 
by a number of people. 

The renewal of air effected by opening the windows of a room 
takes place in different ways, according to circumstances. If there 
be no fireplace in the room, and a window be opened at the top, the 
warmer portions of the air will escape through the window, and be 
replaced by air entering under the door, or through any other inlet 
at a lower level. If, however, the room be furnished with a fireplace, 
the air of the room tends to rise up the chimney, owing to the wind 
blowing across the exit at the roof; and in this case the open window 
will serve as an inlet. This effect is greatly increased when a fire is 
burning in the grate, the hot gases rising up the chimney causing a 
rush of air from all inlets towards the fireplace. Experience shows 
that a room in which a bright fire is burning is generally well venti- 
lated. In warm weather the renewal of air is best effected by 
throwing open the windows and doors, and allowing a current of air 
to blow through the rooms. If the current be too strong for comfort, 
closing the door of a room, and opening the windows both at the top 
and bottom, will enable ventilation to take place. 

In many cases it is not found possible to secure the desired 
renewal of air by means of windows, etc., and recourse must then be 
had to special fittings for this purpose, some of which will now be 
described. 

The Sherringham. Valve. This arrangement, as shown in Fig. 95, 
consists of a V-shaped iron box, hinged at its lower edge, which is 
let into the wall to serve as an inlet. It can be opened to any 
desired extent by means of a cord passing over pulleys, and furnished 
with a counter-weight. The incoming air is directed upwards, so as 
to avoid creating a draught in the occupied part of the room. 

Tobiris Ttibe. In this method of air admission (Fig. 96), a tube 
running parallel with the wall is furnished with a right-angle bend 
which passes through the brickwork to the exterior, the entrance 
being guarded by an iron grating. As in the previous device, the 
entering air is directed upwards. 

Air Bricks. Entrance of air is sometimes obtained by the use 



Ventilation. 



353 



of perforated bricks, the holes through which the air enters the room 
being inclined upwards to avoid draughts. 

Chimney Breast Valves. The chimney of a room furnishes a 
convenient exit for vitiated air, and many arrangements are in use 
to permit of this method of escape. An opening is made in the flue 
near the ceiling, in which is placed a hinged valve of metal or mica, 
which lifts sufficiently to permit of the passage of the gases at 
the top of the room, owing to the diminished pressure generally 
existing in the air of a flue. Back action, caused by the air in the 
flue for some reason attaining a superior pressure, is prevented by 



FIG. 95. SHERRINGHAM VALVE. 

means of a stop, against which the hinged valve is urged, thus closing 
the opening. A grid-iron front to the valve-box enables the extent 
to which the gases escape to be controlled. 

Arrangements for Heating entering Air. Many arrangements 
are in existence for the purpose of warming the entering air by 
means of the heat generated by the fire in the room. The duct 
conveying the incoming air is made to pass in the vicinity of the 
fireplace, thus causing the air to be warmed before delivery into 
the room, the temperature of which is thus maintained with a 
smaller consumption of fuel than would otherwise be the case. 

" Artificial" Ventilation. The utilisation of the ordinary fixtures 
of a building, even when assisted by the addition of special outlets 
and inlets, frequently fails to secure an adequate supply of fresh air 
to the various rooms. In such cases it is customary to remove the 
air by exhaust-fans or by propulsion, the supply of fresh air being 
admitted by suitable inlets. As the quantity of air admitted may be 
regulated at will, and also purified or moistened if requisite, this 
would appear to be a more certain way of renewing the air of a 

2 A 



354 



Heat for Engineers. 



room than by employing "natural" methods only. In practice, 
however, the results anticipated are seldom realised, and in some 
cases costly installations have been abandoned as useless. The 
reasons for the failures experienced are somewhat obscure, but 
may probably be summed up by the statement 
that except in rare cases the whole of the air 
of a room cannot be continuously driven towards 
an exit without creating unpleasant draughts. 
In the case where an exhaust-fan is used to 
remove the vitiated air, for example, there is a 
tendency for a direct current to set up between 
the fan and the inlet, leaving the air in other 
localities practically stagnant. A judicious 
arrangement of a number of inlets at different 
parts of the room will minimise this difficulty, 
but even then it is necessary that the currents 
should continually pass amongst the occupants 
of the room, who, in most cases, object to the 
draught created, and close the offending inlet. 

In some cases the vitiated air is extracted 
by steam-jets, water-jets, or by a fire burning in a 
specially-constructed shaft. Generally speaking^ 
the impure air of a building can be removed 
better by extraction than by methods in which 
propulsion is used, where the fresh air forced 
in is relied upon to expel that already present 
in the room. 

The difficulties attendant on the ventilation 
of large buildings successfully are illustrated in 
the many attempts made in connection with the 
Houses of Parliament. The debating chamber 
in the House of Commons has been made 
the subject of many experiments in ventila- 
tion, but none have proved quite satisfactory. As arranged at 
present, the air is extracted by means of a ventilating shaft, at 
the bottom of which a coke fire is kept burning. The incoming 
air is driven in by means of a fan, which supplies the air at a 
somewhat greater rate than would compensate for the exhaustion 
caused by the fire in the shaft, and consequently the air in the 
chamber is at a slightly higher pressure than that existing in the 
corridors. In summer the fresh air supply is washed and cooled 
before admission, in winter it is warmed by passing over steam-heated 




FIG. 96. TOBIN'S 
TUBE. 



Ventilation. 355 

surfaces. Inlets for the fresh air are provided on the floor of the 
chamber and elsewhere, but all these elaborate arrangements do 
not succeed in continuously renewing the air at all parts of the 
chamber, and when crowded with members the inadequacy of the 
installation in this respect is manifest. The various schemes applied 
to hospitals, etc., in which artificial ventilation has been adopted, 
have generally fallen below expectations owing to the inherent 
difficulty of completely renewing the air without creating objection- 
able draughts. 

Size and Arrangement of Inlets. When the velocity of the 
entering air is known, the size of opening requisite to secure a 
complete renewal of the air in the room may easily be calculated. 
If, for example, the air in a room of 1000 cubic feet capacity requires 
to be changed 3 times per hour, it will be necessary to admit at least 
3000 cubic feet per hour to effect this renewal. If the velocity of 
the incoming air be 3 feet per second, and the size of the opening 
be x square feet, the quantity of air entering per second will be 
$x cubic feet, and per hour 3 x 3600.3: = 10800.3; cubic feet. 
Hence the area of the inlet necessary to admit 3000 cubic feet per 

hour = 3 = JL square feet = 40 square inches. 
10,800 3-6 

In practice it is necessary to make a greater allowance than is 
indicated by the calculation, as the velocity of the entering air may 
vary considerably, being greater when the outside temperature is 
relatively low, and when assisted by winds, and less with a high 
external temperature and in the absence of wind. The quantity 
admitted is also influenced by the nature of the inlet, owing to 
friction in the entrance-pipe or grating. It is therefore advantageous 
to allow a liberal margin above the calculated size, and to control 
the quantity admitted by altering the size of the inlet, which should 
be constructed so as to permit of regulation. 

In ventilating mines, and in all cases where the air is forced 
through pipes or ducts, the head of pressure necessary to generate 
by means of the fan or blower may be obtained from Morrison's 
formula, which is as follows : 

K V 2 P L 
~A~ 

where K = Coefficient of friction = 03 

V = Velocity of air in thousands of feet per minute 
P = Perimeter of cross-section in feet 
L = Length of duct in feet 

2 A 2 



356 Heat for Engineers. 

A = Area of duct in square feet 

H = Head in feet of pressure of air of same density as 
entering air. 

For a circular section, of diameter D, the perimeter P = TT D, 

TrD 2 

and the area A = . 

4 
Hence 

P = ?rD = 4 

A TrD 2 D 
4 

and hence the formula, for a duct of circular section, becomes 



Example. The head of air pressure necessary to deliver air at 
5 feet per second = 6 of a thousand feet per minute, through a duct 
of square section, i foot side and 200 feet long, is 

03 x *6 2 x 4 x 200 _ o. r 

i 

In arranging inlets, due regard to position in the room must be 
observed, so that the incoming air is breathed by the occupants 
before mixing with vitiated air, and draughts avoided. A better 
distribution is secured by the use of a number of small inlets in 
preference to one or two large ones. 

Use of Electric Heaters in Rooms. Many types of stoves are now 
in use in which the heat is furnished by electricity : a favourite form 
consisting of a number of glow-lamps placed in front of a metallic 
reflector, so as to imitate the brightness of a coal fire. It is claimed 
for these that the extra cost of the electricity is compensated for by 
the fact that all the heat generated is utilised in warming the room, 
whereas in the case of a coal fire the major portion of the heat 60 
to 80 per cent. escapes through the chimney. This claim cannot 
be substantiated, as 6 pounds of coal, costing i penny, will furnish 
80,000 B.Th.U., and if the chimney loss be 80 per cent., 16,000 
B.Th.U. are still available for warming the room. The heat equiva- 
lent of i Board of Trade unit of electricity is 3400 B.Th.U. and 
hence at the low price of i penny per unit electric heaters are far 
more costly than a coal fire. Even if the contrary were true, the 



Ventilation. 357 

ventilating effect of a coal or gas fire would still render this mode of 
heating preferable to electricity for domestic use. as from this stand- 
point the heat escaping up the flue is not lost, but fulfils a function 
as useful as the actual warming of the room. The real points in 
favour of electric heaters are cleanliness, and the ease with which 
the supply of heat may be switched on and off, and regulated as 
desired. 



Heat for Engineers. 



CHAPTER XIX. 

THE TRANSFER OF HEAT. RADIATION. 

Heat Waves. Any objects placed in the vicinity of a body at a 
higher temperature will be found to undergo a rise in temperature, 
even though a vacuum should separate them from the source of 
heat. The energy transferred in this manner through an intervening 
space, without the aid of conduction or convection, is termed 
" radiant " heat, and represents energy transmitted by ether waves. 
It may be shown in many ways that heat waves possess properties 
identical with light waves ; thus, for example, heat waves are capable 
of reflection, refraction, and polarisation. Every substance at a 
temperature above absolute zero acts as a source of heat waves, that 
is, gives rise to undulations in the ether ; and the higher the tem- 
perature the greater is the disturbance created, and the greater also 
is the quantity of energy leaving the substance in a given time. 
Hence if a number of bodies at different temperatures be placed in a 
room, the tendency of radiation is to establish an equal temperature 
in all, as the hotter bodies lose heat energy more rapidly than the 
colder ones. All radiate heat to each other, with the result that the 
hotter bodies lose more heat than they receive, whilst the colder 
bodies gain more than is radiated by them. Finally, when each body 
receives from its surroundings just sufficient heat to balance that 
which is radiated from it, equality of temperature has been attained. 
For like reasons a block of ice apart from air convection cools 
everything in a room, as the heat radiated from the objects to the 
ice is not returned in equal amount by the ice. 

Absorption of Heat Waves. The heat waves which impinge on a 
given object are partly thrown back by reflection, and partly absorbed, 
that is, utilised in imparting an increased kinetic energy to the mole- 
cules, a rise in temperature occurring in consequence. The facility 
with which heat energy is thus absorbed, and also with which it is 
given off by a substance, depends upon the nature of the surface 
which receives or sends off the heat waves, as will now be shown. 

Effect of Surface on Radiation and Absorption. It is well known 



The Transfer of Heat. Radiation. 359 

that hot water will take longer to cool when stored in a vessel with a 
smooth, metallic surface than when contained in a receptacle with a 
rough surface. Conversely, if cold water be placed in a vessel with 
a polished surface in front of a fire, it will take longer to become 
heated than if the surface were rough. The retention of heat by a 
polished surface is due to the relatively small amount of radiation 
which takes place; and the slow heating, when placed near a source 
of heat, is due to the small absorbing power. In each instance the 
reflecting power of the surface is the determining factor; the heat 
passing from the hot water to the polished surface being reflected 
back to a large extent in the one case, and cooling thus delayed, 
whilst in the other case the heat waves falling externally on the sur- 
face are in the main reflected back, only a small portion being absorbed 
and a slow heating resulting in consequence. A good reflecting 
surface is therefore not capable of radiating or absorbing heat waves 
to any great extent, but a rough surface, which has little reflecting 
power, will radiate or absorb freely. A surface which possessed no 
reflecting power, and which was opaque to heat waves, would absorb 
the whole of the radiant heat it received externally, and, conversely, 
would radiate completely any heat reaching it from beneath. No such 
surface is known, the closest approximation being given by lamp-black, 
which is superior to any other surface both with respect to radiation 
and absorption of heat waves in general. It will be shown later that 
for non-luminous or dark heat waves, other rough surfaces are practi- 
cally equal in these respects to one of lamp-black, but are much 
inferior for luminous heat waves. 

It will be seen from the foregoing that the polished brass dome of 
a locomotive assists in the retention of heat, and is preferable to a 
rough surface ; and also that the polishing of the cranks, connecting- 
rods, etc., causes them to reflect radiant heat from the boiler and 
cylinders and so to remain cool. A silvered tea-pot or other vessel 
will keep a liquid hot for a longer time than one with a rough surface, 
and a steam-pipe lagging is more efficient when finished with a smooth 
varnished surface than if left rough. 

The Absolute ''Black Body" Although no known surface acts as 
a perfect radiator or absorber of heat, it is possible, as Kirchoff 
showed, to make an arrangement which will give radiations equivalent 
to those received from a perfect radiating surface. Such an arrange- 
ment is termed a " black body," and the radiations obtained from it 
are known as "black-body" radiations. The necessary conditions 
are fulfilled by the radiations received from the interior of an enclosure 
kept at a constant temperature in all its parts. Such an enclosure is 



360 



Heat for Engineers* 



represented in Fig. 97, and if the temperature be equal throughout, the 
radiations received through a small opening in the side from the sur- 
face of A will be independent of the nature of the surface. For if A 
possess a perfect radiating surface, rays falling upon it from the 
enclosure will be entirely absorbed, and hence, as its temperature 
remains constant, the surface will radiate an amount equal to that 
received. If, on the other hand, the surface of A be not perfect, 
some of the heat rays falling upon it from the enclosure will be 
reflected, and the remainder absorbed. Equality of temperature, 
however, involves the condition that the heat leaving the surface is 
equal to the amount received, and as the heat incident upon A from 
the enclosure will be the same, whatever the nature of the surface, it 
follows that the heat leaving A is constant under the given conditions. 
Hence the amount of heat received from A through a small opening 




FIG. 97. "BLACK-BODY" RADIATIONS. 

in the side will be independent of the surface, as the constant tem- 
perature condition ensures that the heat leaving the surface is a fixed 
amount. Further, this amount is equal to the total radiations received 
by A from the enclosure, and hence the surface of A is equivalent to 
a perfect radiating surface, which would absorb all heat falling upon 
it and radiate an equal amount if its temperature were unchanged. 

In practice, a black body may be obtained in the manner indicated 
in Fig. 97, the box being packed in ice, or kept in a bath at constant 
temperature. A body placed in the interior of a tube heated extern- 
ally will similarly give black-body radiations through the open end 
when the temperature is constant. A block of steel in a furnace, the 
temperature of which is steady, also gives black-body radiations 
through a hole in the side of the furnace. In each case the imperfec- 
tion of the surface as a radiator is counterbalanced by the reflection 
of rays received from the enclosure, which pass through the opening 



The Transfer of Heat. Radiation. 361 

and make good any deficiency in the radiant heat proper. If outside 
the enclosure, the heat received from the surface would be less by the 
amount of these reflected rays. A lamp-black surface in the open 
radiates nearly as well as a black body, whilst smooth surfaces are 
greatly inferior. 

Connection between Quantity of Heat Radiated and Temperature. 
Newton, who was the first to investigate this subject, came to the 
conclusion that the heat lost by a body, when cooling under uniform 
conditions, was proportional to the difference between the temperature 
of the body and that of its surroundings. Thus, for a given substance 
at 210 C. and 110 C. respectively, cooling in surroundings at 10 C., 
the rates of cooling would be as (210 - 10) : (no - 10) = 2:1. 
Although this law is approximately true for small differences of tem- 
perature say 20 C. it is greatly in error when the differences are 
large. Dulong and Petit, and others, arrived at formulae from ex- 
periments conducted under known conditions, and by the use of these 
formulae a more correct result than that derived from Newton's law 
could be obtained. The correct law was announced by Stefan in 
1879, an d was later confirmed theoretically by Boltzmann. The 
Stefan-Boltzmann law states that the energy radiated by a given body 
is proportional to the fourth power of its absolute temperature, and 
expressed in symbols takes the form 

E = K (Tj 4 - T 2 4 ) 

where E = total energy radiated ; T : and T.> the absolute tempe~a- 
tures of the body and its surroundings respectively, and K = a constant. 
The law is only strictly true for black-body radiations, for which the 
constant K will depend upon the units chosen. For an ordinary 
body radiating heat, the constant K will depend also on the radiating 
surface; thus a lamp-black surface, at the same temperature, would 
radiate more energy than one of silver. Under black -body conditions 
the nature of the surface makes no difference, as previously shown. 

The application of the above law to pyrometry will be found in 
Chapter VIII. 

The rate at which a body cools in air depends not only upon the 
nature of the surface and the temperature, but also upon the specific 
heat. If, for example, i calorie be extracted from i gram of alu- 
minium (specific heat '23) the fall in temperature occasioned will be 

or 4 '4 C., whilst i calorie taken from i gram of iron (specific 
heat -n) will lower the temperature by - - or9C. If two surfaces 



362 Heat for Engineers. 

of different metals possess the same radiating power and area, the 
rates of cooling will be proportional to the specific heats of the metals 
compared by volume, when both are cooled from the same tempera- 
ture. In the case of a single substance, the rate at which the tem- 
perature falls depends upon the mass, the nature of the surface, and 
the absolute temperature the energy radiated, even for an imperfect 
surface, being nearly proportional to the fourth power of the absolute 
temperature. A mass of hot substance, cooling in air, also loses heat 
by convection, hence the fall in temperature will be more rapid than 
that calculated from the radiation constants only. In a large mass of 
material, the rate of cooling is influenced by the conductivity, which 
determines the rapidity with which heat from the interior reaches the 
surface. The rate of cooling will evidently be more rapid when the 
temperature of the surrounding atmosphere is low, as may be seen 
from the symbolic expression of the Stefan-Boltzmann law, which 
indicates that a diminution in T 2 causes an increase in the energy 
lost by radiation. 

Instruments for Detecting Radiant Heat. In radiant heat investiga- 
tions it frequently occurs that small differences or alterations in tem- 
perature, not detectable by an ordinary thermometer, require to be 
noted. The employment of a large-bulb mercury thermometer with 
a narrow bore is in general unsuitable in these cases, as the incident 
heat is usually small in quantity, and would not suffice to heat up a 
large mass of mercury. Any instrument, therefore, to be of service in 
this respect, must possess a low thermal capacity; that is, a slight 
quantity of heat energy must be capable of producing a rise of tem- 
perature sufficient to be indicated by the instrument. The methods 
available at present comprise (i) differential air thermoscopes, used for 
comparatively rough indications ; (2) thermopiles, for more delicate 
observations; and (3) the bolometer, (4) the radio -micrometer, 
and (5) the suspended-vane radiometer, for detecting excessively 
minute temperature changes. Each method will now be described 
in turn. 

The Differential Air Thermoscope (sometimes called Thermometer). 
This instrument, invented by Leslie, is shown in Fig. 98. It consists 
of a tube with a bulb at each end, bent so as to form two parallel 
branches. The bore of the tube contains a quantity of coloured 
liquid which serves as an index, and in good forms of the instrument 
the parallel branches are connected by a cross tube, furnished with a 
tap, which, on being opened, equalises the air-pressure in the bulbs, 
and causes the index-liquid to stand at the same level in both branches 
of the tube. On closing the tap, and subjecting one of the bulbs to 



The Transfer of Heat. Radiation. 363 

a slight rise in temperature, the index liquid will be forced down in 
the branch of the tube connected to the heated bulb, and will rise in 
the other. As air has a high coefficient of expansion, a slight rise in 
temperature will produce a marked depression of the liquid. The 
thermal capacity of the air-bulb, moreover, is small, hence the appli- 
cation of a small quantity of heat will cause a notable rise in tempera- 
ture. This instrument was used by Leslie in studying the phenomena 
of radiant heat. 

In more modern forms of the instrument, the buibs are connected 
to the index by flexible tubing, and hence may be placed in baths or 
any desired place. Bulbs with re-entrant portions are also made, so 
as to contain a liquid ; and thus such heat changes as that occasioned 





FIG. 98. DIFFERENTIAL FIG. 99. THERMOPILE. 

AIR THERMOSCOPE. 

by dissolving a small quantity of sal-ammoniac or other salt in water, 
may be readily detected. Many useful indications may be obtained 
with this improved form of thermoscope. 

The Thermopile. This instrument, due to Melloni, is a much more 
sensitive heat-detector than the air thermoscope. It consists of a 
number of junctions of antimony and bismuth, arranged in series, and 
collected together in a compact form so that all the junctions lie close 
together, as shown in Fig. 99. Melloni used this arrangement, in con- 
nection with an astatic galvanometer, for conducting his experiments 
on radiant heat. In conjunction with a mirror galvanometer, the 
thermopile is far more sensitive, and will indicate a very minute 
rise in temperature. Antimony and bismuth were chosen, as a 



364 Heat for Engineers. 

heated junction of these two metals gives a relatively large E.M.F., 
and when a number are placed in series, the total electromotive force 
is the sum of the E.M.F.'s generated at each junction. Hence a 
small rise of temperature is sufficient to give a marked indication on 
the galvanometer. 

The chief defect of the antimony-bismuth thermopile is that it 
possesses a high thermal capacity, and when once heated takes a long 
time to cool to its original temperature. This feature greatly impairs 
the sensitiveness of the thermopile, when used for detecting changes 
in which the quantity of heat is small. Both the metals are too brittle 
to be drawn into fine wires, and must possess considerable bulk in 
order to be worked satisfactorily. The so-called " linear " thermopile, 
devised by Rubens, is in this respect a great improvement on the old 
form. The junctions (of copper and constantan, or iron and constan- 
tan) are made of fine wire, and are hammered flat so as to present a 
large surface to the source of heat. A very large number of these 
junctions, joined in series, are brought close together, and it is thus 
possible, in a given size of thermopile, to obtain a higher E.M.F. than 
when a necessarily smaller number of antimony-bismuth junctions are 
used, whilst the thermal capacity is very small. The linear thermo- 
pile is well suited to such observations as the distribution of heat in 
the spectrum, and in all cases where the quantity of heat received by 
the instrument in a given time is small. The flattened junctions 
should be coated with lamp-black, in order that heat radiations falling 
on them may readily be absorbed. 

The Bolometer. The increase in the electrical resistance of 
platinum when heated has already been referred to in connection 
with the resistance pyrometer, and the same principle is applied in 
the delicate heat-detector devised by Langley, and known as the 
bolometer. A grating of thin platinum foil, each strip of which has 
dimensions about i cm. long, \ mm. wide, and -^ mm. thick, is 
blackened on its upper surface, and placed in one arm of a Wheat- 
stone bridge. This grating may be covered up or exposed to the 
heat source as required, and, in taking an observation, the adjustable 
arm of the bridge is altered until no deflection of the galvanometer 
occurs on depressing the keys, the grating meantime being shielded 
from the source of heat. The grating is now exposed, and if its 
temperature increases, its resistance also will increase, and on 
closing the circuit the galvanometer will show a deflection. With 
resistance coils of sufficient delicacy the increase may be measured, 
and the rise in temperature deduced. By using the most refined 
methods of measuring electrical resistance, Langley was able to 



The Transfer of Heat. Radiation. 365 

detect a difference of T^OUTT f a degree Centigrade in the tempera- 
ture of the grating. The chief advantage of the bolometer is the 
small quantity of heat required to raise the temperature of the grating, 
as the weight of the thin foil is extremely small, and the specific 
heat of platinum very low. The amount of heat required to raise 
the temperature of a grating composed of 10 strips, of the dimensions 
given, by i C., is less than '00007 of a calorie ; and in this respect 
the bolometer is greatly superior to the thermopile. In measuring 
the resistance, it is necessary to pass a current through the grating, 
which, although momentary, will cause its temperature to rise. By 
placing an exactly similar grating, constantly shielded, in another 
arm of the bridge, so as to counterbalance the other when both are 
at the same temperature, any discrepancy due to this cause is avoided, 
as the current will affect both equally. By the aid of the bolometer, 
Langley carried out a series of important investigations connected 
with the distribution of heat in the spectrum. 

The Radio- Micrometer. When a current of electricity is passed 
through a coil of wire suspended in a magnetic field, the coil turns 
either to the right or the left, according to the direction of the 
current. This principle is applied to the construction of sensitive 
galvanometers, and d'Arsonval constructed a detector of radiant 
heat in which the current through the coil was furnished by a small 
thermal-couple, on which the heat rays impinged, and which indi- 
cated any alteration in temperature sustained by the junction by the 
movement of the coil. Later, and independently, Professor Boys 
devised an extremely sensitive instrument, working on the same 
principle, to which the name of radio-micrometer was given. The 
working of the instrument may be understood by reference to 
Fig. 100. The coil consists of a thin loop of copper wire, suspended 
by a quartz fibre, and joined at one of its extremities to a thin piece 
of antimony, and at the other to a similar piece of bismuth. The 
antimony and bismuth are each soldered to a thin disc of copper, 
which has a blackened surface; and the coil hangs between the 
poles of a powerful magnet. A mirror is attached to the suspension, 
upon which a spot of light is thrown and reflected on to a scale, 
thus magnifying the movements of the coil. So long as the circuit 
formed by the loop and the thermal couple is at the same temperature 
throughout, no current will flow through it ; but the slighest alteration 
in the temperature of the copper disc, to which the antimony-bismuth 
couple are fastened, will give rise to a current in the circuit, and 
the loop will twist on its suspension owing to the mutual action 
between the current and magnetic field. 



3 66 



Heat for Engineers. 



In the actual instrument, the parts are covered in so as to be 
screened completely from radiations. Opposite the blackened 
copper disc is a metal tube furnished with a cap, which enables the 
heat received from any source to be tested by removing the cap, 

and allowing the radiations to 
impinge on the copper disc to 
which the thermal couple is 
attached. 

The radio-micrometer is 
one of the most sensitive in- 
struments for the detection of 
radiant heat, as it may be made 
of very low thermal capacity, 
and the quartz-fibre suspension 
enables the coil to move in 
response to the feeblest attrac- 
tion caused by the passing of 
very minute currents. A rise 
in temperature on the part of 
the disc of one millionth of a 
degree Centigrade causes a 
visible deflection, and the heat 
radiated by a burning candle 
may be detected at a distance 
greater than two miles. The 
chief drawback of the radio- 
micrometer in practical use is 
its lack of portability, as, like 
all delicately suspended galva- 
nometers, it must be fixed in 
position to take observations, 

whereas a thermopile or the grating of a bolometer may be moved 
to any desired spot to receive radiations. 

NichoVs Suspended- Vane Radiometer. The latest and most sen- 
sitive heat-detector is a modification of the radiometer of Crookes, 
which, as shown in Fig. 101, consists of a number of arms radiating 
from a central support in an exhausted globe. At the end of each 
arm is placed a mica vane, blackened on one side. Radiant energy, 
on striking the vanes, is absorbed to a greater extent by the blackened 
sides of the vanes than by the unblackened, and a repulsive motion of 
the vanes away from the source ensues, owing to the gaseous mole- 
cules in the tube being repelled from the hot side of the vanes. The 




FIG. loo. BOY'S RADIO-MICROMETER. 



The Transfer of Heat. Radiation. 367 

action resembles that of a lawn sprinkler, which revolves in the oppo- 
site direction to that at which the water shoots out. In Nichol's 
instrument the central arm, instead of being pivoted, is suspended by 
a quartz fibre to which a mirror is attached, from which a spot of 
light is reflected on to a scale. When a star of the first magnitude is 
focused on to one of the vanes by means of a concave mirror, a 
distinct movement of the spot of light 
along the scale is noted. A bolometer 
or radio-micrometer is not capable of 
detecting the radiant energy received 
from a star. 

Experiments on the Radiating Power 
of Surfaces. By the aid of a thermopile 
and astatic galvanometer Melloni investi- 
gated the relative quantities of heat 
radiated from different surfaces at dif- 
ferent temperatures, and also the quanti- 
ties absorbed. Four sources of heat 
were employed, as follows : 

1. A copper cube containing boiling 
water, the surfaces of which were coated 
with the substance investigated. 

2. A copper-plate, heated by a spirit- 
lamp to about 400 C., which could 
similarly be coated. 

3. A spiral of platinum wire, raised to incandescence in the flame 
of a spirit-lamp. Radiations from this were received on different 
surfaces, in order to compare the absorptive powers. 

4. A Locatelli oil-lamp, the flame of which was kept constant by 
an arrangement for maintaining the level of the oil. 

In expressing the results, the radiating . and absorbing power of 
lamp-black were taken as 100, and the values for other substances 
referred to this figure. Lamp-black, however, is not a perfect radiator, 
and consequently the figures must be regarded as comparative, and 
not expressing true percentages of energy radiated or absorbed. The 
following table shows the results obtained at 100 C. 




FIG. loi. CROOKES' 
RADIOMETER. 



Lamp-black 
White lead . 
Glass . 
Indian ink . 
Steel . 



RELATIVE RADIATING POWERS AT 100 C. 

Platinum . 
Polished brass 

copper . 

gold 



IOO 
100 

90 

85 
17 



silver 



;68 



Heat for Engineers. 



The above figures were obtained by receiving the radiations from 
the sides of a cube containing boiling water directly on the thermopile, 
one face of the cube being removable in order that plates with different 
surfaces might be inserted. In determining absorptive powers the 
radiations from various sources were received on a plate of copper 
coated with the substance under trial. The other side of this plate 
was coated with lamp-black, and presented to the thermopile. The 
heat absorbed caused the temperature of the plate to rise, and con- 
sequently the thermopile was affected by radiations from the lamp- 
blacked side. The greater the absorptive power, the higher was the 
temperature of the plate, and hence the greater the effect on the 
thermopile. The figures obtained for several surfaces are appended. 



Substances 


1 
Oil Lamp 


Incandescent Copper at 
Platinum 400 C. 


Hot Water, 
Cube at iooC. 


Lamp-black 
Indian ink 


100 

. ! 9 6 


100 

95 


IOO 

87 


IOO 

85 


White lead 


. ! 53 56 


89 


IOO 


Shellac . 


48 


47 70 


72 


Metallic surface . 


. ; 14 13-5 13 


13 



The above figures show that for most substances the absorptive 
power varies with the character of the incident radiations, and the 
same is true of the emissive power. Luminous waves possess a 
shorter wave-length than non-luminous waves, and a substance 
capable of absorbing or emitting the longer waves freely might have 
little power with respect to the shorter waves. Thus for the non- 
luminous waves from a substance at 100 C., white lead is equal to 
lamp-black in absorbing and radiating powers, but only about one- 
half as good for the radiations from a luminous source. The heat 
waves received by polished metals are largely reflected by the surface, 
whether incident upon the surface externally or internally, and hence 
such surfaces have little absorptive or emissive power. 

It may be seen from the above results that nothing is gained by 
painting a hot- water radiator black, as, at 100 C., white lead or any 
dull paint is equally good. If varnish or a metallic paint be used, 
however, the radiating power is considerably diminished. The supe- 
riority of a coal or coke fire for warming a room depends upon the 
high temperature and consequent large quantity of radiant energy, 
and also upon the black surface of the fuel, which radiates freely. 



The Transfer of Heat. Radiation. 369 

In both these respects a coal fire is superior to a gas fire, in which, 
owing to the small radiating power of a flame, balls of firebrick or 
pieces of asbestos are introduced to radiate tne heat. The tempera- 
ture in the gas fire does not rise so high, on the average, as the coal 
fire, and the heated materials have a smaller radiating power than 
coal. Much of the heat of a coal fire may be prevented from 
escaping up the chimney by making the back of the fireplace of fire- 
brick, bevelled so as to reflect heat into the room. Ultimately the 
firebrick becomes red-hot, and adds greatly to the radiations received 
from the fireplace. 

Other things being equal, dark-coloured substances in general 
possess a higher absorbing power for waves from a luminous source 
than those of a light colour. For this reason white or light-coloured 
clothing is cooler than dark-coloured in summer, inasmuch as less 
radiant heat from the sun is absorbed by the former. 

Actual Quantity of Energy Radiated by different Surfaces. The 
relative radiating powers as found by Melloni's experiments afford 
no clue to the actual quantity of energy radiated under different 
conditions. Later investigations by Lummer, Kurlbaum, Pringsheim, 
and others, have resulted in the determination of the energy constant 
for black-body and other radiations at different temperatures. In 
these experiments an enclosure similar to that illustrated in Fig. 97 
was employed to determine the quantity of radiant energy for a 
black body at low temperatures, whilst for higher temperatures a 
tube heated externally by electricity was employed. For exposed 
surfaces the substance was heated electrically or otherwise to definite 
temperatures ascertained by a pyrometer. Taking as a starting-point 
the Stefan-Boltzmann law 

E = K (TV - TV), 

the value for the constant K was found by Kurlbaum to be 
5-32 x io~ 12 , when the energy E is expressed as watts per square 
centimetre of surface, under black-body conditions. If the energy 
radiated be expressed as calories per square centimetre per second, 
the value of K is 1*28 x io~ ia . In the following table the energy 
radiated in calories per square centimetre per second is given fc: 
varying values of T p the temperature of the body receiving the 
radiations (T 2 ) being constant at 300 absolute, or 27 C. The 
values for a black body, oxide of iron, and platinum are given for the 
purpose of comparison. 

The superiority of a black body over other surfaces with respect 
to energy radiated is plainly indicated in the table (p. 370). It 

2 B 



370 



Heat for Engineers. 







Calories per Square Centimetre per 


Absolute Temperature 
of Hot Body (Ti) 


Absolute Temperature 
of Body receiving 
Radiations (T 2 ) 


second from 


Black Body Oxide of Iron 


Platinum 


I2OO 


300 


2-65 


I-2 3 


0'33 


1 100 





1-87 


0-79 


0-21 


1000 


n 


1-27 


0-50 


o - 128 


9 00 


,, 


0-83 


0-32 


0-075 


800 


,, 


0-52 


0-175 


0-039 


700 


,, 


0*30 


0-105 


0-019 


600 


,, 


0-155 


0-047 


0*007 


500 


,, 


0-070 


O'O2I 


O-OOI5 


4OO 


" 


O'O22 






will be noted, however, that this superiority becomes less marked 
as the temperature rises ; thus at 500 abs. the relative quantities 
radiated by a black body and oxide of iron are as 3 ' 32 to i, whereas 
at 1200 the ratio is 2*16 to i. A similar improvement in radiating 
power at higher temperatures is noticeable in the case of platinum 
also ; and it may be stated, in general, that the higher the temperature 
the nearer the radiations approximate to those of a black body. 

It will be seen that the radiations from an oxide of iron surface 
at 1200 abs. are slightly less than those obtained from a black body 
at 1000 abs. Hence a block of iron or steel, coated with oxide, 
which when under black-body conditions in a furnace shows a 
temperature of 1200 abs. or 927 C. on a heat radiation pyrometer, 
will only indicate 1000 abs. or 727 C. when sighted outside the 
furnace. It should be remembered that the figures given apply 
only to total energy radiated, and that the relative luminosities 
of a black body and a hot surface do not show the same propor- 
tion. A block of iron or steel, when sighted inside and outside 
the furnace with an optical pyrometer, will show a less apparent 
difference in temperature than is noticed with a Fe'ry heat-radiation 
pyrometer, which measures the total energy as distinct from the 
intensity of luminous rays. 

The radiations from a lamp-black surface, at temperatures below 
600 abs., approximate closely to those of a black body. 

Scattering, or Diffusion of Kadiant H<at. When radiant heat 
falls on a powder, a portion is absorbed, whilst the remainder is 
reflected in an irregular manner from granule to granule of the 
powder, ultimately escaping into the surrounding air in all directions. 



The Transfer of Heat. Radiation. 3 7 1 

This effect is specially noticeable with white powders, and resembles 
the scattering of light produced by the same means. To this action 
is due the great heat experienced in the vicinity of a white wall upon 
which the sun is shining. It is customary to whitewash the glass 
roof of a workshop in summer, as by doing so the heat rays from the 
-sun are largely scattered, and prevented from passing through the glass. 
The workshop is thus kept cool without entirely shutting out the light. 

Distribution of Energy in the Spectrum. The energy received 
from a luminous source consists of a mixture of ether waves of 
different wave-lengths, which may be separated by means of a prism 
or diffraction grating. The visible portion of the spectrum consists 
of waves which are capable of exciting the optic nerve, and so giving 
rise to the sensation of light. The violet rays, which are bent the 
most by a prism, have a shorter wave-length than the red rays, which 
are bent least ; whilst intermediate portions have intermediate wave- 
lengths. Beyond the visible spectrum, however, the existence of 
ether vibrations may be proved by various means. Thus beyond the 
violet end the waves are capable of exerting a chemical action on 
silver salts, and darken a photographic plate exposed in this region. 
Beyond the red end of the spectrum, waves of greater wave-length 
may be detected by means of a thermopile or other sensitive detector 
of radiant heat. The visible spectrum only constitutes a small por- 
tion of the total wave-lengths that may be traced by suitable detectors. 

When the waves existing in any portion of the spectrum whether 
visible or invisible are absorbed by the blackened surface of a 
thermopile or bolometer, the energy received is converted into heat ; 
and consequently the indications of these instruments afford a clue 
to the quantity of energy corresponding to different wave-lengths. 
Hence, if the heat-detector be placed successively in different parts of 
the spectrum, the distribution of energy in the various regions may be 
determined, as all the types of energy existing in different portions are 
converted into an equivalent quantity of heat when absorbed by the 
blackened surface of the instrument. Tyndall, who investigated the 
spectrum of an arc-lamp with a thermopile, obtained the results shown 
in graphic form in Fig. 102. No energy was detected beyond the 
violet end of the spectrum, but as the thermopile was moved towards 
the red end an increasing effect was obtained. Beyond the visible 
red a rapid increase in the energy received by the thermopile was 
noted, which attained a maximum and afterwards diminished as the 
instrument was moved further from the visible red. 

The later investigations of Langley and others confirm, in general, 
the results obtained by Tyndall. The sensitive indications of the 

2 B 2 



37 2 



Heat for Engineers. 



bolometer, as used by Langley, enabled the existence of radiant 
energy to be traced in portions of the spectrum where the quantity 
was too small to affect a thermopile. By the aid of this delicate 
instrument the distribution of energy in all parts of the spectrum was 
accurately measured, and the results obtained with spectra obtained 
from different sources were recorded. These investigations led to an 
important generalisation, which will now be considered. 

Wietts Laws. It was noticed by Langley and others that as the 
temperature of the luminous source increases, the position in the 
spectrum at which the maximum energy occurs moves towards the 
visible region. This is indicated in Fig. 103, in which it will be seen 
that the distribution curve for a spectrum from a source at 2000 
attains its maximum at some distance in the region beyond the red. 



100- 




FIG. 102. TYNDALL'S CURVE OF ENERGY DISTRIBUTION IN THE 
SPECTRUM OF AN ARC LAMP. 

At 3000 the maximum occurs nearer the red, but still in the invisible 
portion ; at 4000 the maximum is just in the visible part ; whilst at 
5000 and 6000 J the maximum position has shifted still further into 
the visible region. Hence, as the temperature rises, the wave-length 
corresponding to the position of maximum energy diminishes. 

The connection between temperature and wave-length is expressed 
by the following law, arrived at by Wien from theoretical considera- 
tions : " As the temperature increases, each wave-length in the 
spectrum diminishes in such a manner that the product of wave-length 
and absolute temperature is constant." Or, expressed in symbols, 

A T = a constant, 

where A = wave-length, and T the absolute temperature. As this 
law applies to each wave-length in the spectrum, the special wave- 



The Transfer of Heat. Radiation. 373 

length corresponding to the position of maximum energy is also 
governed by it, and hence 

'Vax. T = a constant. 

When the source is a black body, and the wave-lengths are measured 
in millionths of a centimetre, the value of the constant is 294,000. 



rkvisOkl 

Actuu&ty*. 




FIG. 103. ENERGY CURVES FOR SPECTRA OBTAINED FROM SOURCES 
AT DIFFERENT TEMPERATURES. 

Hence, by d ; viding 294,000 by the absolute temperature of the source, 
the wave-length of maximum energy is obtained. The figures for 
several temperatures are tabulated below : 





Absolute Temperature 


Wave-Length 
of Maximum Energy 






IOOO 


294 






2OOO 


H7 






3000 


9 8 






4OOO 


73 






5OOO 


59 






6000 


49 





374 Heat for Engineers. 

For radiations from other sources than a black body, the law still 
holds true, although the value of the constant is different. For 
polished platinum the constant is 262,600. 

By combining the above law with the Stefan-Boltzmann law, Wien 
obtained the following relation for a black body : 

E max . T~5 = a constant, 

where E is the energy corresponding to the wave-length of maximum 
energy, and T the absolute temperature. Both this and the pre- 
vious laws have been fully verified by the experiments of Lummer, 
Pringsheim, and others. The second law may be expressed as 
follows : The energy corresponding to the wave-length of the 
maximum energy varies directly as the fifth power of the absolute 
temperature of the source. When E is expressed in ergs per second, 
the value of the constant is 2188 x IQ-^, or 

E (max.) = 2188 x io-'7 x Ts. 

Hence, at 1000 abs., E (max.) will equal 21-88, the wave-length 
corresponding to E, from the first law, being 294 micro-centimetres. 
Effect of Temperature on Luminosity. It will be seen from the 
foregoing that a rise in temperature results in the shifting of the 
position of maximum energy towards the visible part of the spectrum. 
The result is that a greater proportion of the total energy appears 
as light at higher temperatures, and if the photometric intensity of 
the light received from a given body at different temperatures be 
measuied, the relation 

iJ ! . 

is found to hold good, where \ and I 2 are the intensities correspond- 
ing to absolute temperatures Tj and T 2 . The value of x varies 
considerably, being 30 when T : is 800 and T 2 900, but only 
12 when the absolute temperatures are 2000 and 2100. The value 



of the exponent x is approximately equal to ^^ at a given 
absolute temperature T. 

The great increase in luminosity observed in an incandescent 
electric lamp, as the temperature rises owing to an increase of voltage 
at the terminals, will be readily understood from the above relation. 
The first visible red corresponds to a temperature of 800 abs., and, 
on raising the temperature to 900 abs., the luminosity increases in 



The Transfer of Heat. Radiation. 375 



X^QQQ 

the ratio (^ ) , or 34*1. At higher temperatures the rate of 
\8co / 

.ncrease is less than this, but even at 2000 the value of x is 12. 
The limit of economic burning of a carbon filament lamp is reached 
at 2000 abs., any further increase in temperature resulting in a 
rapid blackening of the interior of the lamp, due to vaporisation 
of the carbon, which largely prevents the light from passing to the 
exterior. On the contrary, tantalum and tungsten filaments can be 
used with safety at 2100 or 2200 absolute, with a great gain in 
luminosity. Taking the former figure for comparison with a carbon 
filament at 2000, the relative intensities are expressed by the ratio 

( 2IO ) =1*8: and with the temperature at 2200 the ratio is 

V 20007 

/2j2oo\ _ ^ It is evident, therefore, that for a given candle- 



power much less energy will be required by the metallic filament 
lamp at the higher temperature, as the extra energy required to 
produce the higher temperature bears a much smaller proportion to 
the total energy than the proportionate gain in luminosity. Thus, 
if the loss of energy from the lamp be due to radiation only, the 
ratio of energy received at 2200 and 2000 which is equal to the 

energy radiated would be practically ( ) = i 46, according 

\2OOO/ 

to the Stefan-Boltzmann law ; whereas the luminosity is 3 i times 
as great. 

Example. A lamp giving 32 c.p. at 100 volts and i "28 amperes, 
at a temperature of 2000 C., would give (32 x 3-1) = approximately 
100 c.p. at 2200 C. The energy requisite to run the lamp at the 
higher temperature would be (roughly) i * 5 times as great ; hence 
if 100 volts were maintained at the terminals the current required 
would be 1*92 amperes. The relative cost per c.p. would be 

- = 2-1 nearly; that is, the cost of the light at the 

lower temperature would be more than twice as great as when the 
lamp is run at the higher temperature. 

At the present time, the extra cost of metal filament lamps must 
be placed against the saving effected in current ; but in spite of this 
it would appear that the carbon filament lamp will be superseded 
by the former class. 

Diathermancy , or Heat Transparency. As heat waves are identical 
with light waves, it might be expected that certain substances permit 
heat waves to pass through them, just as glass, quartz, etc., are trans- 
parent to light. This is found to be the case, although the proportion 



376 Heat for Engineers. 

of the incident heat transmitted through a medium may be different 
to the proportion of light which passes through. The relative heat- 
transmitting powers of substances can be determined by interpos- 
ing a layer between a source of heat and a thermopile, when the 
diminished deflection of the galvanometer indicates the amount shut 
off by the substance under trial. The radiant heat absorbed by air 
is extremely small, and may be neglected in the experiment. 

Tested in this manner, it is found that rock-salt is more transparent 
to heat waves than any other substance, and this superiority holds, 
whether the source of heat be luminous or non-luminous. Other 
substances, whilst permitting the passage of the heat from a luminous 
body freely, are practically opaque to radiations of longer wave-length 
such as are received from a non-luminous source. In the following 
table the percentage of heat transmitted by various materials from 
four different sources is given : 



Thickness =2*6 mm. 



Source of Heat 



Substance 


Flame of Oil 
Lamp 


White-hot 
Platinum 


Blackened 
Copper at 300 C. 


Blackened 
Copper at iooC. 


Rock-salt 


92 


9 2 


92 


9 2 




Fluorspar 


78 69 


42 


33 




Mirror glass . 


39 


2 4 


6 







Alum 


9 2 


o 







Ice ... 


6 


O 





o 




Solution of Alum 


Argand Burner 
12 









Salt 


12 


.. 


,, 


Distilled water 


II 


.. 


>t 


Carbon disulphide . 


63 








The foregoing table shows that different substances are more 
permeable to certain wave-lengths than to others, which is also true 
with respect to light. Glass transmits luminous waves of shorter wave- 
length with comparative freedom, but is almost entirely opaque to 
the non-luminous waves, which have a greater wave length. Hence, 
in a greenhouse the luminous waves from the sun enter freely through 
the glass, but, being absorbed by the various objects, the energy is 
expended in producing a rise of temperature, and the radiations from 
the objects are then of the non-luminous type, which cannot escape 



The Transfer of Heat. Radiation. 377 

through the glass. In consequence of this the temperature rises, the 
glass building acting as a trap for the heat received from the sun. 

A body which transmits light freely may be almost opaque to heat, 
and vice versa. Alum, ice and water, for example, are transparent to 
light, but do not readily transmit heat waves. On the other hand, a 
solution of iodine in carbon disulphide is practically opaque to light 
but extremely permeable to radiant heat. All the radiant heat 
absorbed is expended in raising the temperature of the absorbing 
substance. 

Gases, in general, permit of the passage of radiant heat with great 
freedom, the proportion absorbed being very small. Hence the sun's 
rays pass through the atmosphere without causing a sensible rise in 
temperature, but are absorbed by the surface of the earth. The 
atmosphere is heated by contact with the warm surface, and the rise 
in temperature is noted as far as the convection currents rising from 
the surface reach. For this reason, even on a hot day, the tempera- 
ture a few thousand feet above the earth's surface may be below 
freezing-point, as may be discovered by ascending in a balloon. 

Vapours, in distinction to gases, absorb a notable quantity of the 
total radiant heat received. Water vapour in the atmosphere thus 
exercises an effect in partially stopping the radiant heat received from 
the sun during the day, and in preventing the escape of radiant heat 
from the surface at night. Condensed water-vapour in the form of 
clouds, like ordinary water, is practically opaque to non-luminous 
radiations, and hence on a cloudy night the surface of the earth is 
seldom cooled sufficiently by radiation to permit of the formation of 
dew or hoar-frost. 

Selective Emission and Absorption. It is noticed, in general, that 
a substance absorbs almost entirely the rays it emits itself when 
heated, and in consequence is practically opaque to such rays. Thus 
rock-salt, although transparent to heat waves from most sources, is 
largely opaque to the radiations received from another piece of rock- 
salt. This is explained by assuming that radiant heat is emitted when 
the molecules of a body are in a state of vibration, which vibration 
is communicated to the ether in the form of waves ; and when these 
waves impinge on identical molecules to those producing the ether 
waves, the energy is expended in setting the molecules of the receiv- 
ing substance into vibration ; as, being identical, the molecules will 
respond to such waves sympathetically. If the receiving body differ 
from the radiating substance a partial response only will be obtained, 
and some of the waves will be transmitted. 

In this manner is explained the fact that glass, when heated, gives 



378 Heat for Engineers. 

out a large proportion of non-luminous heat, and little light ; for the 
vibrations of the molecules of glass are such as to respond to and 
absorb non-luminous radiations, and hence, when agitated by heat, 
the molecules will generate the same kind of waves that is, non- 
luminous. Viewed from this stand-point, the meaning of the fact 
that alum, for example, transmits 9 per cent, of the radiations of an 
oil-lamp, is that the molecules of alum respond to waves which convey 
91 per cent, of the total energy, but not to the waves which repre- 
sent the remaining 9 per cent. 



379 



CHAPTER XX. 

THE CONVERSION OF HEAT INTO WORK. LAWS OF 
THERMODYNAMICS. 

First Law of Thermodynamics. This law may be expressed as 
follows: "Heat and work are mutually convertible; a given quantity 
of heat being capable of performing a fixed amount of work, and 
conversely, a given amount of work is capable of producing a fixed 
quantity of heat." As the result of the work of many investigators, 
foremost of whom must be placed Dr. Joule, of Manchester, this 
law has been established on a secure experimental basis, and is the 
fundamental principle governing the action of all heat engines. One 
important conclusion derived from this law is that a limit exists to the 
amount of work obtainable from the consumption of a given weight 
of fuel, and when the work represented by i unit of heat termed 
the " mechanical equivalent " is known, the limit of the work that 
may be derived from i Ib. of fuel may be obtained numerically, and 
used to form a standard to which the actual performance of an engine 
may be compared. A brief description will now be given of the 
methods by which this important numerical relation has been ob 
tained. 

Joule's Experiments. The earliest form of apparatus used by Dr. 
Joule consisted of a vessel, containing water, in which paddles were 
caused to rotate by means of falling weights. The friction between 
the paddles and the water gave rise to heat, the quantity produced 
being determined by noting the rise in temperature, and knowing the 
weight of water used and the water equivalent of the vessel and 
paddles. The work done in producing this quantity of heat was 
obtained by multiplying the weights by the distance fallen. Allow- 
ance was made for radiation of heat by the vessel, and for the friction 
of the pulleys and other attachments by means of which the falling 
weights actuated the paddles. By equating the heat produced to the 
work done, the work equivalent of one heat unit was determined. In 
later experiments Joule employed iron paddles rotating in mercury, 
and also cast-iron rings rubbing against each other under mercury. 



380 Heat for Engineers. 

As a result of these experiments, Joule adopted 772 foot-pounds as 
the work equivalent of one British thermal unit. 

In still later experiments the paddles were caused to rotate con- 
tinuously, and the vessel supported on a hydraulic bearing. The 
friction between the moving liquid and the sides of the vessel tended 
to make the latter rotate. A cord was wound round a groove in the 
side of the vessel, and passed over pulleys to pans in which weights 
were placed. The rotation of the paddles was conducted at such a 
rate as to maintain the weights suspended in a fixed position, and the 
number of revolutions was recorded by a counter. The heat produced 
was measured as before; the work done was equal to that which 
would have been done had the weights been allowed to fall, and, by 
their falling, to rotate the calorimeter through the observed number of 
revolutions, that is, irdnw, d being the diameter of the vessel, n the 
number of revolutions, and w the sum of the suspended weights. 
This apparatus gave 772*55 foot-pounds as the equivalent of a 
British thermal unit. 

Hirris Experim(nts.\i\<t>\.Q.2,& of converting work into heat by 
friction, Him employed percussion. A large block of stone, faced 
with iron, was suspended by cords, and served as an anvil ; whilst 
a similarly suspended piece of steel served as a hammer. A piece of 
lead was placed between the two, and the hammer raised and allowed 
to fall so as to drive the lead on to the anvil. The work done was 
measured from the known weight of the hammer and the distance it 
had fallen, due allowance being made for recoil of the anvil, etc. 
The heat produced was determined by noting the rise in temperature 
of the known weight of lead, and equated to the work done. The 
figure obtained, in the units adopted above, was approximately 768. 

In further experiments Hirn compared the heat which disappeared 
in the cylinder of a steam engine with the output of work as obtained 
from the indicator diagram. After making due allowance for radia- 
tion and other losses, Hirn obtained results ranging between 750 
and 762. Considering the difficulties attendant in obtaining accurate 
results by this method, the figures afford a striking confirmation of 
the existence of a constant relation between heat and work, no 
matter how the one may be converted into the other. 

Rowland's Experiments. The apparatus used by Professor Row- 
land, of Baltimore, was the same in principle as that of Joule By 
using a more efficient form of paddle, and employing an engine 
to secure a rapid rotation, Rowland was able to obtain a rise in 
temperature of 40 C. per hour, or even more, whereas the rate in. 
Joule's apparatus was only at the rate of 62 C. per hour. Any 



Mechanical Equivalent of Heat. 381 

small error in the reading of the thermometer, therefore, influenced 
the result to a much less extent in the former case than in the latter ; 
thus an error of -r^V C. on a rise of 10 only causes an error of i in 
1000 ; whereas on a rise of '62 the error would be i in 62. More- 
over, the mercury thermometers used by Joule had not been com- 
pared with the gas scale, which is now adopted as the standard of 
temperature. 

Rowland used an accurate dynamometer to measure the work 
done by the engine in driving the paddles, and on equating this to 
the work done, obtained the figure 778 ft.-lb. as the equivalent of 
i British thermal unit. 

Determinations by Electrical Methods. The units employed in 
electrical measurements are based upon the C.G.S. system, and, 
assuming that such units are in strict accordance with the values 
intended to be assigned to them, it is possible to determine the 
mechanical equivalent of heat by electrical means. When a current 
of electricity is passed through a resistance, heat is produced, and 
if the work equivalent of the electricity expended be obtained by 
calculation, it may be equated to the heat generated, and the work 
equivalent of one heat unit deduced. From the manner in which 
the units of electricity have been chosen, a current of i ampere, 
maintained by a difference of potential of i volt between the ends 
of a resistance (which would therefore be equal to i ohm) does work 
at the rate of 10,000,000 (ten million) ergs per second ; that is, 
i watt represents work at the rate of 10,000,000 ergs per second. 
Hence, if a known current of electricity be passed through a wire 
for a given time, the work represented will be the product 

(volts x amperes x time in seconds x 10,000,000) ergs. 

As all the electrical energy is converted into heat, the work 
equivalent in ergs of the heat produced maybe equated to the above, 
from which 

J H = (C V/ x 10,000,000) ergs, 

where J = the mechanical equivalent of i heat unit, and H the 
number of heat units produced. By measuring the current passing, 
the voltage between the terminals of the resistance, and the heat 
produced, the value of J may be calculated from this equation. To 
perform the experiment, a wire resistance may be placed in a suitable 
calorimeter, and a current passed through it for a known time. By 
noting the rise in temperature, and accurately measuring the current 



382 Heat for Engineers. 

and voltage at the terminals of the resistance, the necessary data 
may be obtained. 

Determinations on the foregoing lines have been made by Griffiths, 
Callendar, and others, with the result that the figure obtained by 
Rowland 778 has been confirmed. It may therefore be assumed 
that this figure is a close approximation to the true value. 

Value of "J" in Terms of Different Units. The constant 
character of the relation between heat and work having thus been 
established, the first law of thermodynamics may be expressed 

symbolically as 

W = JH, 

where W = work done in producing a quantity of heat H, and J 
the mechanical equivalent of i heat unit. If H represent i British 
thermal unit, W = 778 ft.-lb. = J. If the heat unit chosen be i Ib. 
of water raised i C., the corresponding value of J will be 778 x 
= 1400 ft.-lb. If the work be expressed in centimetre-grams, and 
H = i calorie, J = 1400 x 30-54 = 42,750 cm. -grams, = 42,000,000- 
ergs (approx.). Tabulating these values, 

778 foot-pounds = i B.Th.U. 

1400 =i lb- C. unit 

42,750 centimetre-grams = i calorie 

42,000,000 ergs = i calorie 

The equivalent of i calorie in foot-pounds is 



Efficiency of an Engine. The efficiency of an engine is defined 
as the ratio of the work done by the engine to the energy provided. 
As heat may be expressed in work units, the ratio may be written 

Efficiency = work done by engine 

work equivalent of heat provided 

It is customary to multiply this ratio by 100, the efficiency then 
being expressed as a percentage. A few examples, illustrating the 
use of the mechanical equivalent of heat in calculating efficiencies, 
etc., will now be given. 

Example i. If all the heat obtained by burning i Ib. of coal, 
of calorific value 14.000 B.Th.U. per Ib., could be converted into 
work (14,000 x 778) = 10,892,000 ft.-lb. would result. For many 
reasons it is only possible, in the very best engines, to convert a 



Efficiency of Engines. 383 

comparatively small portion of the heat of the coal into work ; the 
above figure, however, represents the actual energy stored in i Ib. 
of the coal. 

Example 2. An engine works at the rate of 10 horse-power, 
and consumes 24 Ib. of coal, of calorific value 7500 calories per 
gram, in one hour. To find the efficiency of the engine. 

Efficiency work done 



work equivalent of heat provided 

= I0 x_33,ooo_x_6o = 

24 x 7,500 x 1400 
or 7 85 per cent. 

(Note that if i gram of coal raises i gram of water iC. in 
temperature, then i Ib. of coal raises i Ib. of water iC. in tempera- 
ture.) 

Example 3. A steam engine of 15,000 horse-power, working 
with an efficiency of 10 per cent., and using coal of calorific value 
8000 calories per gram (or lb.-C. units per Ib.), will consume 26,518 
Ib. or nearly 1 1 tons per hour, since 

x 33> 000 x 6o 



8000 x 1400 

where x = Ib. of coal burnt per hour. 

In the practical determination of the efficiency of an engine, 
the work done may be obtained from an indicator diagram, and 
expressed as indicated horse-power (I.H.P.) ; or may be measured 
by a brake-test on the engine, and stated as brake horse-power 
(B.H.P.). The work rate as recorded by an indicator diagram does 
not take into account frictional and other losses in the engine and 
its connections, and consequently the efficiency deduced by this 
means has a value higher than that calculated from the results of 
a brake-test, which measures the work available for external purposes. 
In obtaining the work equivalent of the heat provided, it is necessary 
to know the quantity and calorific value of the fuel used. In a steam- 
engine plant some of the heat of the fuel escapes up the chimney, 
and by radiation from the boiler surfaces, so that all/the heat of 
combustion does not enter the cylinder. If the efficiency of a 
steam-engine plant, however, is to be compared to than of an internal 
combustion engine, the furnace and boiler losses must be regarded 
as inseparable from the steam engine ; and a fair comparison would 
not be obtained if only the heat entering the cylinder were con- 



384 Heat for Engineers. 

sidered. The practical efficiency of any heat engine is therefore 
expressed by the ratio 

work available for external purposes 

work equivalent of heat furnished by the fuel used 

The theoretical efficiency of any heat engine will be shown later to 
depend upon the absolute temperatures at which heat is received 
and rejected. In this case a total absence of loss by radiation, 
friction of parts, or from any other cause, is assumed. 

The Second Law of Thermodynamics. This law, as stated by 
Clausius, is as follows : " It is impossible for a self-acting machine, 
unaided by any external agency, to convey heat from one body to 
another at a higher temperature ; or heat cannot of itself (that is, 
without compensation) pass from a colder to a warmer body." 

Lord Kelvin's statement of the same law is, that " It is impossible 
by means of inanimate material agency to derive mechanical effect 
from any portion of matter by cooling it below the temperature of 
the coldest of surrounding objects." 

This law, as expressed by either of the foregoing statements, 
applies only to cases in which the " body " or " portion of matter " 
is taken through a complete cycle of operations, so as to end in the 
name thermal condition as that which it possessed at the beginning. 
Thus by passing steam at 100 C. into a strong solution of calcium 
chloride, a higher temperature than 100 C. is reached, heat passing 
from the colder steam into the hotter solution ; but this is a single 
operation, and the steam does not end as it began. In like manner 
a compressed gas may do work on expansion, and, by expanding, 
cool itself below the temperature of surrounding objects; here again, 
however, the process is not cyclic, and the gas is left in a different 
thermal condition to that originally possessed. Broadly stated, the 
second law of thermodynamics expresses the fact that in all engines 
in which heat is converted into work, the process consists in extract- 
ing heat from a hot substance, some of which is converted into work, 
whilst the remainder is imparted to a colder substance. In no case 
can the converse process be performed, namely, to extract heat from 
the colder substance, a portion of which would become work and 
the residue go to the hot body. The law is thus founded upon 
universal experience. In a steam engine the hot steam enters the 
cylinder and gives up a part of its heat in driving the engine, and 
the remainder to the condenser; and by no possible device 
could the engine be made to give out work by taking in the colder 
steam from the condenser, using some of the heat possessed to 



Carnot's Ideal Engine. 385 

drive the engine and giving up the remainder to steam at a higher 
temperature. 

It should be remembered, however, that it is possible, by pro- 
viding work from an outside agency, to extract heat from the cold 
part of an engine and to impart a portion of the heat extracted to 
the warm part. This is what occurs in a refrigerating machine ; but, 
instead of deriving any mechanical effect from the cycle of operations, 
it is necessary to supply energy from without to make the process 
possible. For an engine to work in a manner contrary to the second 
law of thermodynamics, it would be necessary to construct a refriger- 
ating machine capable of working not only without external aid, but 
in such a manner as continuously to perform external work which 
is contrary to all experience. The truth of the law, and of deduc- 
tions made from it, may, therefore, be regarded as firmly established. 

The efficiency of an ideal heat engine will now be considered 
from the standpoint of the two fundamental laws of thermodynamics. 

Carnofs Ideal Engine. The conditions governing the action of 
heat engines in general were first brought to notice by Sadi Carnot 
in 1824. In his famous essay on "The Motive Power of Heat," 
Carnot introduced the conception of cycles of operation, and also 
the principle of reversibility; and thus laid the foundation of our 
modern knowledge concerning the conversion of heat into work in 
any type of engine. The ideal set of operations described by Carnot 
cannot be realised in practice ; but, just as in other connections a 
" perfect" gas and a " frictionless " surface serve as useful standards 
of comparison, so an ideal set of operations are of service in judging 
the actual performance of an engine. Moreover, a set of operations 
in which the maximum efficiency would be realised serve as a guide 
to follow, as far as practicable, in the design of an engine, and a 
study of these operations is therefore of the greatest utility. 

The action of Carnot's engine may be understood by reference to- 
Fig. 104. A cylinder, supposed to possess non-conducting sides and 
a perfectly-conducting end, is fitted with a non-conducting piston, 
and contains the working substance. A hot body and a cold body, 
each kept at a constant temperature, and a non-conducting stand, are 
also assumed to be available ; and the operations performed are as> 
follows : 

i. Starting with the working substance at the temperature (T x ) of 
the hot body, and the end of the piston in the position a 0, the 
cylinder is placed on the non-conducting stand, and the piston liber- 
ated, allowing the working substance to expand and drive a machine 
connected with the engine. In performing this work, the medium 

2 c 



3 86 



Heat for Engineers. 



parts with heat energy, and its temperature falls. This process is 
allowed to continue until the temperature of the cold body (T 2 ) has 
been reached, when the piston is at bb. 

2. The cylinder is now placed on the cold body, and the piston 
forced down to a position c c. External work is requisite to con- 



._ 


1 






^ 


...<5 




|V 


^sJvXs^^s^s: 


/^ 


--tf 


c 


1 




1 


d - 


1 





g 


d 




^ 




// 










FIG. 104. CARNOT'S IDEAL ENGINE. 

duct this process, and is converted into heat : but, as the end of the 
cylinder conducts perfectly, all the heat thus produced passes into 
the cold body, and hence the temperature of the medium remains 
at T 2 . 

3. The cylinder is again transferred to the insulating stand, and 
the piston further depressed. External work is again necessary, but 
the heat produced remains in the medium. This process is continued 
until the temperature rises to that of the hot body (TJ, the piston 
reaching a position d d. 

4. The cylinder is placed on the hot body, and the medium 
allowed to expand, doing work. The temperature is prevented from 
falling, owing to heat continuously passing into the cylinder from the 
hot body. This operation is allowed to go on until the piston arrives 
at the original position a a. The medium is now in the same con- 
dition as at the commencement, the temperature being T l and the 
volume identical with the starting volume. 

These four operations constitute a cycle which may be repeated 



Carnot's Ideal Engine. 387 

indefinitely. Moreover, as the working substance or medium is in 
exactly the same condition at the end of the cycle as at the com- 
mencement, it follows that the net output of work is not derived from 
the energy stored up in the medium, but from the heat furnished by 
the hot body. Consequently, the work done by an engine working 
with this cycle is independent of the medium used, which may be a 
gas such as air or hydrogen, or vapour such as steam or ether vapour. 
The working substance is only the instrument by means of which heat 
is converted into work ; and although its condition is altered during 
the several operations, the original state is regained at the end of the 
cycle. An analogy is furnished by the spring of a watch or clock, 
which acts as a medium for converting the energy expended in wind- 
ing it into the work necessary to actuate the mechanism, finally return- 
ing to its original condition. The work done does not depend upon 
whether the spring is made of steel or phosphor-bronze, but only upon 
the energy expended in winding it. 

Before considering further the cycle of operations in Carnot's 
engine, it may be of advantage to compare the action of a steam 
engine with the set of operations described. The hot body, or source 
of heat in the steam engine is the boiler, and the cold body the con- 
denser. The period during which steam enters the cylinder is the 
counterpart of operation (4) in Carnot's cycle, and the expansive 
working, after cut-off, corresponds to operation (i). After the 
exhaust is open, the conditions of operation (2) are partially realised ; 
but here the analogy ends, as it is not practicable to retain the steam 
in the cylinder and to re-heat it in situ to its original temperature. 

The study of Carnot's cycle of operations is much facilitated by 
reference to the indicator diagram that would be obtained from the 
ideal engine. Assuming, for the sake of simplicity, that the working 
substance is a perfect gas although the diagram could be worked 
out for any medium capable of going through the necessary changes 
of volume the starting pressure and volume may be represented by 
a A and O a in Fig. 105. The first operation is indicated by the line 
A B, and as this process consists of an expansion without heat enter- 
ing from without, the line AB will be an adiabatic (see Chapter VI. ^. 
The second operation is a compression at constant temperature, the 
heat produced by the compression escaping to the cold body ; hence 
the line B C, which represents this compression, is an isothermal. 
The third operation, shown graphically by C D, is an adiabatic 
compression, and the final operation, represented by DA, is an 
isothermal expansion. 

It has previously been shown that the work done in compressing 

2 C 2 



3 88 



Heat for Engineers. 



a gas, or by a gas in expanding, is given by the area bounded by the 
curve representing the pressure and volume changes, the perpen- 
diculars let fall from the extremity of the curve, and the axis of volume 
(p. 101). In the second and third operations in the cycle, work is 
done on the engine, the amount of which is represented by the areas 




V 

FIG. 105. GRAPHIC REPRESENTATION OF CARNOT'S CYCLE. 

B C cb and C D dc respectively, or taken together the area D C B b d. In 
operations (4) and (i) work is done by the engine, the quantity of 
which is indicated by the areas D A#^and A B/#, which together equal 
the area D A B b d. Hence the net work done by the engine, available 
for external purposes, is the difference between D A B bd and D C B</,. 
that is, the closed figure A B C D. 

The efficiency of the engine being defined as 

work done externally 
work (or work equivalent of heat) provided 

is represented by the ratio of the areas A B C D and D A B b d, or 

Area A B C D 



efficiency = 



Area DA 



Carnofs Ideal Engine. 389 

But as the working substance does not furnish any of the heat 
which is converted into work in the cycle, it is evident that the work 
done is the equivalent of the difference between the amount taken in 
from the hot body and the quantity rejected, which enters the cold 
body. Hence, if Q T = heat received from hot body, and Q 2 heat 
-entering cold body, the difference Q 1 - Q 2 = heat converted into work. 
Also the total quantity of heat taken in is Q I} therefore the efficiency 

is also expressed by the ratio .vi ".V-', this expression being the same 

Qi 

.as that previously obtained, except that it is expressed in heat units 
instead of work. 

Reversibility of Carnofs Engine. Referring to Fig. 105, it will be 
noted that the operations of Carnot's engine are represented graphic- 
ally by two adiabatics and two isothermals : and in following out the 
processes on the diagram, the closed figure A B C D is traversed in a 
clockwise direction. It is possible, however, to perform the set of 
operations in the converse manner, in which case the closed figure 
would be traversed in a contra-clockwise direction. Starting at the 
point A, the medium could be compressed isothermally at the higher 
temperature T T , the heat of compression being rejected and driven 
into the hot body. Arriving at D the medium could be allowed to 
expand adiabatically, doing external work; and from C to B iso- 
thermally, also doing external work, the heat necessary being derived 
from the cold body at the lower temperature T 2 . Finally the medium 
could be compressed adiabatically from B to A, and the cycle com- 
pleted. In this case, however, the work done on the engine in the 
two compressions is greater than that performed by the engine during 
the two expansions. It is this surplus work which makes it possible 
to extract heat from the cold body, and the process is evidently one 
of mechanical refrigeration. 

Comparing the action of a refrigerating machine with a reversed 
Carnot's engine, the compression of the gas in the cylinder corresponds 
(approximately) to operation (4) as described above, or from B to A 
in Fig. 105. When the valve opens to the condenser coils the tem- 
perature remains practically steady, any heat generated by further 
compression being removed by the cooling-water; hence the con- 
ditions are isothermal, and maybe represented by AD (unless the gas 
liquefies, in which case A D would be a horizontal straight line). On 
the return stroke the gas expands adiabatically (approximately), as 
shown by D C, until, on the evaporator valve opening into the cylinder, 
an isothermal expansion C B results, the heat necessary being extracted 
from the refrigerator coils. Hence a refrigerating machine is correctly 



3 go Heat for Engineers. 

described as a reversed heat engine, or as a "heat-pump," which 
pumps heat from a cold body into a warm one. 

The energy ratio of a refrigerating machine has been previously 
denned (p. 300) as 

work equivalent of heat extracted 

work done in driving the machine 

In a Carnot engine working backwards, this ratio would be 



expressed by area , as the work done at the expense of the 

area A B C D 

heat possessed by the medium is represented by the two expansions 
D C and C B, or, taken together, by the area D C B b d. The com- 
pressions B A and A D, conducted by means of external work, are 
similarly equal to the area B A D db, and the net work expended by 
(B A D db - D C B bd\ or the closed figure A B C D. Or, expressed in 

heat units, the energy ratio of the machine is equal to _ ^ 2 -, in 

Nil ~~ Q'2 

which Qo = quantity of heat extracted from the cold body, and Qj 
the heat equivalent of the work provided during the two compressions. 

Reversibility as a Condition of Maximum Efficiency. No engine 
can possess a greater efficiency than one which works on a reversible 
cycle. The condition of reversibility is that all the operations may 
be conducted in reverse manner by providing the engine with an 
amount of work equal to that performed by the engine when working 
directly. This condition is evidently fulfilled by Carnot's engine. 

The proof of this proposition is based on the second law of 
thermodynamics, and is as follows. Imagine an engine B to be more 
efficient than a reversible engine A. This means that, of a given 
quantity of heat received, B would convert a larger portion into work 
than A. If it be so arranged that B drive A backwards, B will be 
taking heat from the hot body and rejecting it to the cold body, whilst 
A will act in the converse manner. If the size of the engine B be 
regulated so that it takes in from the hot body the same quantity of 
heat as A gives up, no heat will, on the whole, be obtained from the 
hot body. But if B be more efficient than A it will convert a greater 
portion of the heat it takes in into work, and will therefore return to 
the cold body less heat than A takes from it. The compound engine 
formed by the two, would therefore be capable of doing outside work 
although heat only enters the system from the cold body which 
directly violates the second law of thermodynamics. Hence B cannot 
be more efficient than A, and also the efficiency of all reversible 
engines, working under the same conditions, is the same. 



Carnot's Ideal Engine. 391 

Another method of expressing this proof is as under. Let the 
engine A be made to pass through a refrigerating cycle by B, and 
let the heat given out by A during the cycle act as the motive power 
of B. Since A is reversible, the work done in driving it backwards 
is equal to its output when working forwards, and the heat given out 
when working as a refrigerator would, if taken in when working 
forwards, secure an output of work equal to the intake when working 
backwards. But this same amount of heat is taken in by B, which 
is assumed to be capable of converting a greater portion of it into 
heat than A. Hence B would give up less heat to the cold part than 
A extracts from it, and would be driving A with a quantity of work 
to spare, due to its superior utilisation of the heat. The combination 
would, therefore, be acting as a heat engine and refrigerating machine 
at the same time ; or, in other words, producing work continuously 
by utilising heat from the coldest part. This, as previously shown, 
is contrary to all experience. 

Efficiency of a Reversible Engine in Relation to Temperatures. 
Since the efficiency of a reversible engine is independent of the 
medium, and the work done is the mechanical equivalent of the 
difference between the quantity Q T taken in at the higher temperature, 
and the quantity Q 2 rejected at the lower, it follows that the ratio 

-^i depends upon the temperatures of the hot and cold bodies. 

This does not mean that ^1 depends upon the temperatures as 

Q-2 
expressed by the mercury or platinum scales, or upon any scale 

dependent on the physical properties of matter. Temperature in 
this connection would be defined as follows : " If an engine, working 
on a reversible cycle, take in a quantity of heat Q x at a temperature 
T 1} and reject a quantity Q 2 at a temperature T 2 , the ratio of the 
temperatures shall be equal to the ratio of the quantities, or 

T O 

1 = ^1." This is the basis of the thermodynamic scale proposed 

*2 Q2 

by Lord Kelvin, and a temperature scale thus founded is independent 
of any property of matter. 

The zero of such a scale would be reached when the quantity 
Q , rejected at the lower temperature, is nil, since in this case 

^l = :^l = oo = -J, whence T 2 = o. This leads to the conception 

of an absolute zero as determined by a substance being entirely void 
of heat. Further the efficiency under these circumstances would be 



unity or 100 per cent, since efficiency 



Heat for Engineers. 

Hence to secure an engine of efficiency 100 per cent, it would be 
necessary to have a cold body or condenser kept absolutely void of 
heat, or at the absolute zero thus defined. 

The choice of degrees on this scale is optional. If it be decided 
to take the melting-point of ice and steam at 760 mm. pressure as 
standards, then a reversible engine taking in a quantity of heat Q x 
from the steam, and rejecting Q 2 to the ice, would by these quantities 
determine the ratio of the absolute temperatures of steam and ice on 
this scale. Or, 

Q! _ absolute^tjienojyjTajr^)j^mperature of steam ^ 
Q : "absolute7thermodynamic) temperature of ice 

If it be agreed to call the temperature interval between ice and 
steam on this scale 100, the ratio will become 

T + 



where T is the absolute (thermodynamic) temperature of ice. To 
find the figure representing T in thermodynamic degrees, the value 

of the ratio *- 1 must be determined. It can be shown, by methods 

which do not come within the scope of the present treatise, that 
if a perfect gas be used as the working substance in Carnot's engine, 
working between the boiling-point and freezing-point of water, the 

value of the ratio ^ = $-?-? (nearly) and hence 



-- 

273 T 273 

and T, the temperature of melting ice, is 273 thermodynamic degrees. 
Hence the thermodynamic scale is practically identical with the gas 
scale, the deviation being very small when hydrogen gas is used 
as the thermometric substance. Accurately, absolute zero on the 
thermodynamic scale is - 273- 13 ; and this would be identical with 
the Centigrade scale if a perfect gas were available for constructing 
a gas thermometer. For most purposes it is sufficiently accurate to 
assume equality between the hydrogen and thermodynamic scales. 

In terms of temperature, therefore, the efficiency of a reversible 
engine is given by the expiession 



where r \\ is the absolute temperature at which heat is received, and 



Efficiency in Relation to Temperatures. 393 

T 2 the absolute temperature at which heat is rejected. This follows 
from the equality 

2i = Ti 

Q 2 T 2 
whence 

QI-OJ.-TI -T, 
Qi T I 

Examples will now be given in which the efficiency formula thus 
derived is utilised. 

Example i. To find the efficiency of a perfect engine which 
takes in heat at 200 C., and rejects it at 110 C. 

From the formula 



the efficiency is 

473 -383 = _9 = . 

473 473 

or 19 per cent. 

Example 2. To find the temperature at which a perfect engine 
must take in heat in order to possess an efficiency of '25, or 25 per 
cent, when heat is rejected at 80 C. 

. 2 -T!-T 2 _T 1 -(2 73 + 80) 

2 5 - ^ rp - 

1 1 X l 

' 75^ = 353 

.and Tj = 470-7 (absolute) or 197*7 C. 

Example 3. To compare the efficiencies of two engines, one 
working between 300 C. and 200 C., and the other between 200 C. 
and 100 C. 

The respective efficiencies are 511__473 an( ^ 473 ~373 

573 473 

or 17 ' 5 and 21*2 per cent. 

Note that the difference between the working temperatures is the 
same in each case, viz. 100 C., but as the quantity of heat taken in 
in the second case is less, the efficiency is greater than that of the fir^t 
engine. 

Energy Ratio of a Refrigerating Machine in Relation to Tempera- 
tures. Taken with respect to the energy received and rejected, the 
ratio in the case of a refrigerating machine, working on a reversible 
cycle, has been shown to be 

Qs 
Qi-Q, 



394 Heat for Engineers. 

where Q 2 is the energy received from the evaporator coils, and Q x the 

O T 
energy rejected in the condenser. Hence, as ^ L = i, the energy 

v-2 A a 

ratio in terms of temperature is 

T 



the temperatures being in absolute degrees. Examples of the use of 
this formula are given in Chapter XVI. 

Entropy. A substance undergoing an isothermal compression or 
expansion alters in volume and pressure, but the temperature remains 
constant. Hence, if A, B and C (Fig. 106) represent the isothermals 
of a given mass of a substance, they may be distinguished from each 
other by reference to the existing temperature. Thus A might be the 
isothermal for 10, B for 20, and C for 30, thus furnishing a constant 
distinction. If now we take the adiabatics dfh, egk, cutting these 
isothermals, a constant distinction may be found between these also. 
As volume, pressure and temperature all alter during an adiabatic 
change, the constant difference referred to must relate to some other 
fundamental property of the substance, or be derived from two or 
more of the three properties named. 

The characteristic feature of an adiabatic process is that heat is 
not permitted either to enter or leave the substance, whereas in an 
isothermal operation heat is allowed to enter or escape in such 
quantity as to prevent an alteration of temperature. If now we con- 
sider the cycle of operations in a Carnot's engine, represented by two 
isothermals and two adiabatics, such as de^Jg, and df, eg- (Fig. 106) 
a quantity of heat Q x is taken in during the isothermal expansion de 
at a temperature T : (absolute), and a quantity Q 2 is rejected during 
the isothermal compression gf at a temperature T. 2 (absolute). The 
relation existing between these quantities has been shown to be 

^ = 1, and hence j^l = ^. 

Similarly, fgk h might represent the cycle of the engine when 
heat enters at T 2 , and is rejected in the isothermal compression kh 
at a temperature T s , when as before -2~ 2 = % Accordingly, any 

2 3 

number of isothermals might be drawn intersecting the adiabatics 
tfaegk, and in each case the quantity of heat taken in (or given out), 
divided by the absolute temperature corresponding to the isothermals 
- that is Jjp would have the same value for the portions dejg.hk, 



Entropy. 



395 



etc., bounded by the two adiabatics. Hence the substance, when 
taken through the adiabatic process egk, differs in condition from that 
which obtains for the process dfh by a constant value represented by 

^. The difference of condition thus expressed is termed " difference 
of entropy" During an isothermal expansion, such as de, heat enters 



A? 9 




FlG. IO6. ISOTHERMALS AND ADIABATICS. 

the substance ; and the difference in condition between e and d is 
expressed by saying that the substance has undergone an increase 

of entropy represented by -2- 1 ; whereas in the isothermal compression 

A i 
gf heat escapes, and the substance suffers a decrease of entropy 

expressed by ~j? = J^-l. Hence the increase in the former equals 

2 Ji 

the decrease in the latter, and the condition of the substance at d, 
from this standpoint, is identical with that at f or any other part of the 
adiabatic dfk. Evidently, therefore, a substance passing through an 
adiabatic change possesses a definite thermal property or condition 
which remains constant, and differs from the constant property exist- 



Heat jor Engineers. 



ing in another acliabatic operation by the relation ^. To this con- 
stant thermal property the name of " entropy " is given. Although, 
at first sight, this property might appear to be a mere abstraction, it 
will be found on reflection to rank with the ordinary properties of 
matter, such as density and thermal capacity. 

The zero of entropy, for convenience, is taken to correspond 
to the condition of water at o C. This zero, like that of the 
thermometric scales, is arbitrary, but serves as a starting point for 
entropy calculations. The entropy of a substance is usually sig- 
nified by the letter <, and much useful information may be gained 
from diagrams obtained by plotting entropy (</>) against abso- 
lute temperature, which in this connection is generally signified by 
the letter 6. Fig. 107, which represents the temperature-entropy 



*TO 


































j 




' 


^ 














2SS 

2STO 

t 








* 


C 












3 3T /O /f 20 S 



FIG. 107. TEMPERATURE-ENTROPY DIAGRAM OF CARNOT'S ENGINE. 

diagram of Carnot's cycle, will serve to indicate the usefulness of 
this method of representation. Assuming that 2700 units of heat 
are taken in at the higher temperature 15 which is taken as 270 

(abs.), the increase of entropy will be - 7 = 10 units. Taking 

270 
A as the starting-point of the diagram, the line A B is drawn equal 



Entropy. 397 

to 10 entropy units on the scale chosen along the horizontal line 
through 270, and represents the isothermal expansion in Carnot's 
cycle. The succeeding adiabatic expansion, during which the tem- 
perature falls from 270 to that of the cold body here taken as 
260 is represented by the vertical line B C, as the entropy is 
constant during an adiabatic change. In the isothermal compression 
which follows, heat leaves the substance, going into the cold body ; 

hence the entropy falls by an amount ^-i = -^1 = -L = 10 units. 

<9 2 O l 270 

Hence the line CD, 10 units long, drawn along the horizontal 
through 260, represents the third operation. Finally, in the 
adiabatic compression, the temperature rises to 270, whilst the 
entropy remains the same. Hence the figure A B C D represents 
the <f> diagram of an engine working on Carnot's cycle. The work 
done during the cycle is J(Qj Q 2 ). But the difference of entropy 

between the two adiabatics (< 2 - X ) = -j = -J. Hence Qj = 0, 
fo 2 - ^) ; and Q 2 = 2 (0 2 - <k). 

Hence (Q x - Q 2 ) = (^ - 2 ) (< 2 -- ^) 

and the work done during the cycle is J x (6^ - $ 2 ) (< 2 - 4>i) = J 
x area of square ABCD = iooJ. If the 2700 heat units 
assumed to enter be taken as calories, the work done will be 
(100 x 42,750) cm.-grms. ; if B.Th.U., the work becomes (100 x 778} 
ft.-lb. This result agrees with that obtained from the efficiency 

formula l ? = : that is, of the total enemy provided 

T l 270' '270 

will be converted into work. As the work provided is 2700 J, the 

portion utilised as work is x 2700} = 100 J. 

270 

The temperature-entropy diagram for i Ib. of water or other 
substance may be constructed as follows. Let the entropy at o 
be called o. Then on raising the temperature to iC, the heat 
entering is i lb-C. unit, and the average temperature at which this 
heat enters is 273 '5 absolute. Hence the entropy of i Ib. of water 

at i C. is - - = '003656. If the temperature be now raised 

to 2 C., the entropy will increase by = '003643 ; and con- 

274 5 

sequently the entropy of i Ib. of water at 2C. will be (-003656 + 
003643) = '007299. In this manner the entropy corresponding 
to each degree can be calculated, and a 0<f> diagram constructed 



398 Heat for Engineers. 

from the figures. The entropy of i Ib. of water at any temperature 
T (abs.) is given by the formula 

4 = 2-30 (log 10 T - Iog 10 273). 

In obtaining the diagram for saturated steam, it is necessary to 
take into account the latent heat of vaporisation, which enters 
without change of temperature. If, for example, the entropy of 
saturated steam at 175 C. be required (water at at o C. being taken 
as o), the entropy of water at 175 must be added to the increase 
of entropy which occurs during the change of state. The entropy 
of i Ib. of water at 175 is o' 5 ; and the latent heat of i Ib. of steam 
at 17 5 C. is 482-7 lb.-C. units. The increase of entropy due to 

change of state is therefore 7 ^ Z l = i 08 ; and hence the 

(i75+ 273) 
entropy of i Ib. of steam at 175 is (i 08 + 0-5) = 1*58. 

Temperature-entropy diagrams are frequently of service in eluci- 
dating problems arising in connection with the working of heat engines 
and refrigerating machines. 



399 



CHAPTER XXI. 

THE CONVERSION OF HEAT INTO WORK. PRACTICAL 
HEAT ENGINES. 

General Remarks. In the foregoing chapter the principles ot 
thermodynamics have been considered in relation to an ideal engine, 
which cannot in practice be realised. The performance of any exist- 
ing engine must of necessity fall short of the ideal, as losses must 
occur owing to the friction of parts, the escape of heat by radiation, 
and other causes. The main principles established, however, are 
applicable to all engines, and serve to show not only the limitations of 
any appliance for converting heat into work continuously, but also 
the best possible way in which such conversion could ever be con- 
ducted. The engineer must choose, from the fuels and materials at 
his disposal, those which can be utilised in such a manner as to pro- 
duce the greatest amount of work at the minimum of cost; and 
although in doing this deviations may be made from what would 
appear to be the correct procedure theoretically, yet he must ever be 
guided in the main by the fundamental laws of thermodynamics. The 
extent to which actual engines may be made to approach the ideal, 
and the application of thermodynamic principles to problems con- 
nected with actual engines will form the substance of the present 
chapter. 

Disposal of Heat in a Steam Engine. As a starting-point for the 
consideration of the conversion of heat into work with practical appli- 
ances, the results of the trials made with a steam engine, fitted with 
all the modern apparatus available for securing economic working, 
will first be given. The engine under test was a Louisville-Leavitt 
pumping engine, and the figures given are taken from the Report of 
the Committee on the Thermal Efficiency of Steam Engines, published 
by the Institution of Civil Engineers in 1898. The heat entering or 
leaving each portion is given separately. 

The most striking fact exhibited by the figures is that only a 
small proportion of the heat generated is converted into work, viz. 
27,260 out of 183,600 B.Th.U. furnished by the fuel, or 14*85 per 



4oo Heat J or Engineers. 



DISPOSAL OF HEAT IN A STEAM-ENGINE PLANT. 

Fire-grate. B.Th.U. per minuto 

Heat generated 183,600 

Lost by radiation ....... 10,000 

Entering flue gases 41,900 

Heat entering boiler directly . (183,600 51,900) = 131,700 

Flue. 

Total heat entering 41 , 900 

Taken up by economiser (afterwards returned to boiler) 15,750 

Radiation losses on the way to, and in economiser . 6,000 
Heat escaping up the chimney . . (41,900 21,750) = 20, 150 

Boiler. 

Received directly from firegrate .... 131,700 

,, from economiser ..... 15,750 

,, from feed-water ..... 5>45 

,, from jackets ...... 6,600 

Less radiation losses in connections of economiser, etc. 250 

Total Heat received by boiler ..... 159,250 

Cylinders. 

Total heat leaving boiler . ..... 159,250 

Radiation loss from connecting pipes, etc. . . . 3, 100 

Heat entering cylinders . . . . . . 156,150 

Utilised as work ....... 27 , 260 

Entering condenser ...... 117,640 

,, jackets 6,750 

Radiation from engine ...... 4,500 

Temperature of entering steam .... 359 F. 

,, escaping steam .... iooF. 

Condenser. 

Total heat entering ...... 117,640 

Removed by cooling-water ..... 110,240 

Leaving in feed-water ...... 5 , 700 

Lost by radiation ....... i } 700 

Feed- Water. 

Received from condenser ..... 5>7o 

Radiation loss in connections to boiler . . . 250 

Entering boiler ..... 545o 

Jacket- Water. 

Heat entering from cylinders ..... 6,750 

Loss in connections to boiler ..... 150 

Returned to boiler .... 5 ^QQ, 



Disposal of Heat in Steam Engines. 401 

cent. A portion of the loss is due to the boiler ; but even if the engine 
itself be taken, the ratio of heat converted into work to that entering 

the cylinders is L?~ ; or deducting from the heat received the 
156150 

quantity returned to the boiler by the jacket and feed-water, the ratio 

becomes - , or 10*2 per cent. Even if radiation losses, and 

142150 

other means of escape of heat due to imperfect materials or appliances, 
could be entirely obviated, 104,200 B.Th.U. would still be required 
in the fire-grate to convert the same quantity as before 27,260 
into work, or the ideal steam-plant would only possess an efficiency 
of 26*2 per cent. If, as in the previous case, only that por- 
tion of the heat which reaches the cylinders less the quantity 
returned by the feed-water be taken as the heat received, the 

efficiency of the idealised engine becomes --- = 28 '6 per cent. 

953oo 

Before proceeding to discuss the losses in detail, other methods 
of expressing the performance of this and other engines will be noticed. 
The indicated horse-power (I.H.P.) of the engine was 643, and the 
net heat supplied per minute 142,150 B.Th.U. Hence 



heat supplied per I.H.P. per minute = T 4 2I 5g = 221 B.Th.U. 

^43 

The brake horse-power of the engine was 599, therefore 

heat supplied per B.H.P. per minute = I- 4 $ = 237 B.Th.U. 

599 

Both the above are useful methods of stating the thermal economy 
of an engine. The actual economy of the plant as a whole, however, 
is expressed by 

actual output of work brake horse-power x / 

work equivalent of heat of fuel (heat produced by fuel in time /) x J 

The sources of loss will now be considered separately, and the 
extent to which each may be avoided or minimised discussed. 

Radiation Losses from Steam-Pipe and other Surfaces. Radiation 
from hot surfaces can never be prevented completely, but can be 
reduced to a minimum by the use of good lagging. The extent of the 
saving thus effected has already been indicated in Chapter XVII. 
Some heat will escape, no matter how well the hot surfaces are lagged, 
and beyond a certain thickness the lagging material costs more than 

2 D 



4O2 Heat for Engineers. 

it saves. Direct radiation from the firebars into the ash-pit cannot be 
avoided ; and the radiant heat escaping from the brickwork of the 
flue is also a source of unavoidable loss, which might, however, be 
minimised, if bricks of higher insulating power could be obtained. 
On the whole, there is practically no prospect of radiation losses being 
minimised to any greater extent than at present. In the plant under 
notice the total radiation losses amounted to 25,950 B.Th.U. per 
minute, or 14-1 per cent, of the total heat yielded by the fuel. 

Flue-Gas Losses. In order that combustion may be maintained 
in the furnace, it is necessary to create a sufficient draught in the 
chimney, to provide which the gases resulting from the combustion 
must be allowed to escape at a higher temperature than that of the 
atmosphere. Hence the loss of a quantity of heat in the flue-gases is 
unavoidable. Usually, in actual working, the loss on this account is 
in excess of the amount required to create the draught, and hence a 
saving is effected by allowing the hot gases, before escaping, to play 
on a series of pipes which contain feed-water for the boiler, the arrange- 
ment being known as an " economises" Allowing for this saving, 
the heat escaping into the chimney in the test described was 20,150 
B.Th.U. per minute, or 10-9 per cent, of the total heat of the fuel. 
It would be difficult to minimise this loss under normal working 
conditions. 

Condenser Losses. By far the greater portion of the heat of the 
fuel amounting in the present case to 110,240 B.Th.U. per minute, 
or 60 -i per cent, of the whole escapes by the condenser, and is 
lost to the plant. It is essential that the entering steam, after per- 
forming its work, shall escape in the form of vapour ; and hence the 
large quantity of heat required to convert the water in the boiler into 
steam is inevitably lost. By keeping the condenser as cool as- 
possible the steam may be made to work expansively to a pressure 
equal to, or below that of the atmosphere, but the latent heat of 
vaporisation, given out when the steam condenses, is carried away 
by the cooling-water. A small fraction only is returned to the boiler 
in the feed-water derived from the condensation, which is warmer 
than water at atmospheric temperature. When a condenser is not 
used, the escaping steam may be employed to warm up the feed- 
water for the boiler, the arrangement for this purpose being termed 
a "feed- water heater." In this case also only a small portion of the 
heat is saved, as every pound of escaping steam is replaced by 
i pound of feed-water ; and at the best the heat utilised from each 
pound of steam is that required to raise i Ib. of water from atmo- 
spheric temperature to the boiling-point. Thus if the escaping steam 



Disposal of Heat in Steam Engines. 403 

beat 100 C. or 212 F., the heat evolved by the condensation of 

i Ib. would be capable of raising the temperature of ^- = 5*97, 

90 

or nearly 6 Ib, of water from 10 C. to 100 C., or 50 F. to 212 F. ; 
whereas only i Ib. of water is required to replace i Ib. of steam. 
Hence in a feed-water heater utilising the heat of condensation in 
this manner, a waste of |ths of the total is unavoidable. Any ap- 
parent superiority over a condenser in this respect is nullified by 
the fact that in a condensing engine more work is taken out of the 
steam before it is permitted to escape. 

Working in the usual manner, there appears no possibility of 
minimising the condenser losses. Whether a saving can be effected 
by radical alterations in the plant, or by using some medium other 
than steam, will be considered subsequently. 

Frictional Losses. After deducting the various losses enumerated, 
only 27,260 B.Th.U. per minute, or 14-9 per cent, of the heat of the 
fuel, remain to represent the thermal efficiency, or proportion of the 
total heat converted into work in the cylinders. The whole of this 
however, is not available for external work, as some is lost in the 
friction of the moving parts of the engine, which causes a waste 
equivalent to 1870 B.Th.U. per minute. Hence the external useful 
work is represented by 25,390 B.Th.U. per minute, or 599 horse- 
power. The indicated horse-power would be the equivalent of 
27,260 B.Th.U. per minute, or 643. The frictional losses might be 
minimised if ball-bearings could be employed throughout, but this 
is not feasible in practice, and hence the loss on this account is 
unavoidable also. 

In the steam plant under notice, therefore, which possesses no 
obvious defects, and when worked with the utmost care, it is im- 
possible to obtain a better output from 183,600 B.Th.U. per minute 
than 599 H.P., or 13*83 per cent, of the energy supplied. This 
proportion is so small that is desirable to discuss the possibilities 
of increasing the efficiency of such an engine, either by a different 
method of procedure or other alterations. The points arising in this 
connection will now be noticed. 

Availability of Heat. After putting aside the radiation and fric- 
tional losses in a steam engine as incurable, owing to the imperfection 
of the materials at our disposal, the question of the utilisation of the 
heat lost in the condenser remains for consideration. Although the 
heat entering the condenser is great in quantity, it is useless to the 
engine, from a work standpoint, owing to the low temperature exist- 
ing in the condenser. The second law of thermodynamics expresses 

2 D 2 



404 Heat for Engineers. 

the impossibility of continuously performing work by transferring heat 
from the condenser to the boiler ; and hence the usefulness of heat, 
in respect to its capability of being converted into work, depends 
upon temperature. The heat possessed by a body may be very 
great in quantity, but unless the body is at a sufficiently high tem- 
perature the heat is not available for the production of work. 

The proportion of heat which may be converted into work in an 

T T 

ideal engine has been shown to be 1 2 , and hence, unless heat 

M 

is furnished at a higher temperature than that of the condenser (T 2 ), 

no work can be obtained from it. The availability of heat, therefore, 
is dependent on the absolute temperature, and not on the quantity. 
For example, to convert i Ib. of water at o C. into steam at 120 C. 
requires 643 lb-C. units, and to raise the temperature of i Ib. of air 
from o C. to 3800 C. (at constant volume) requires 643 lb-C. units 
also. A perfect engine taking in steam at i20C. and rejecting it 
at 100 C. would possess an efficiency of 393___3>73 _ 051 or 5 per 
cent, only ; whereas if an engine could take in a gas at 3800 C., 

and reject it at 100 C , its efficiency would be ^ '^ ^? '91 

4 7 3 
or 91 per cent., although the heat quantity involved is the same as 

in the case of Ihe steam. It is evident, therefore, that the higher 
the entering temperature, and the lower the temperature of exit, the 
greater will be the proportion of heat energy available for producing 
work. 

The increase of the temperature, in the case of steam, cannot 
be continued beyond the point at which the resulting pressure 
becomes too high to enable tight joints to be made, as the resultant 
leakage would counterbalance the advantage gained. In addition, 
the boiler and working parts would have to be made stronger, thus 
increasing the prime cost. Hence, however desirable from the 
standpoint of increased efficiency, a limit to working at high tempera- 
tures with steam is soon reached owing to mechanical considerations. 
At 200 C., for example, the pressure of saturated steam is 225 Ib. 
(absolute) per square inch, and small successive rises in tempera- 
ture beyond 200 produce a constantly increasing rise in pressure. 
There is little chance, therefore, of increasing the upper temperature 
of the steam beyond the limits at present in use, with the present 
methods of construction of the engine. 

The custom of superheating the steam before admission to the 
cylinder results in economy, chiefly from the fact that condensation 
in the passages and cylinder is largely prevented. At first sight it 



Superheated Steam. 405 

might appear that by taking steam at say 150 C., and super- 
heating it to 200 C., the advantage of working at a considerably 
higher temperature would result in a large increase of efficiency, 
compared with that obtained by working at 150 with saturated 
steam. The superheated steam, however, is essentially a different 

T 1 _ T 1 

medium to saturated steam, and the efficiency formula ~ r , - 

* i 
does not apply to a case in which the medium is changed during the 

cycle. Saturated steam at 150 C. has a pressure of 69*5 Ib. 
(absolute) per square inch, and if heated out of contact with the 
water in the boiler the pressure rises in practically the same ratio 
as in the case of a gas. Calculated in this way, the pressure of the 



superheated steam at 200 C. would be 60 q x y + 20 /) _ 

(273 + 150) 

77 '5 Ib. per square inch; whereas saturated steam at 200 C. has a 
pressure of 225 Ib., or nearly three times as great, and is evidently 
capable of performing far more work than steam which has been 
generated at 150 and superheated to 200. Or, to view the question 
from another standpoint, the heat taken up by i Ib. of steam when 
superheated from 150 to 200 will be the product 

(weight x specific heat x rise in temperature) 

or (i x "48 x 50) = 24 lb- C. units. After admission to the 
cylinder, each pound of steam admitted will do work equivalent to 
24 lb-C. units in cooling to 150 C., after which the work performed 
will be that due to saturated steam cooling from 150 to the tem- 
perature of the conden:er. If, instead of superheating, the steam 
in the boiler were heated to 200 C., a far greater quantity of work 
would be performed owing to the superior pressure of the saturated 
steam. Hence the work-producing power of steam generated at a 
low temperature and superheated to a higher, should not be confused 
with that of saturated steam at the higher temperature ; nor must it 
be imagined that the efficiency of an engine using superheated 
steam can be expressed in terms of the temperatures of superheat 
and rejection, as the character of the medium changes fundamer tally 
during the cycle. The chief advantages of superheating are due to 
the possibility of raising the temperature of the steam without 
greatly increasing its pressure ; the heat necessary for this process 
being afterwards converted into work, and the resultant steam 
rendered unsaturated and therefore not liable to condense. The 
limit of superheating is reached when the temperature of the steam 
is such that the materials of the cylinder are corroded. 



4o6 Heat for Engineers. 

The extent to which the temperature of the condenser may 
be lowered is restricted in practice by the supply and temperature 
of the cooling-water. In the steam-test previously described, the 
condenser was kept at 100 F. (38 C), and to secure so low a 
temperature as this entails the use of a most efficient condenser and 
a plentiful supply of cold water. Sulphur dioxide in the liquid 
form, which may be produced by little expenditure of energy from 
the gas, has been used in Germany to maintain a lower condenser 
temperature than is possible with water-cooling. In the best case, 
however, a limit would be reached at 32 F. or o C., at which 
temperature the water would freeze. Hence, owing to practical 
difficulties, the availability of energy imparted to steam is restricted 
by an upper temperature limit lying between 200 C. and 300 C., 
and a lower limit of 32 F. or o C. Any improvement on existing 
steam-engines, in respect to efficiency, will be such as to permit of 
a greater range of working temperatures by raising the upper limit, 
or which reduce losses at present unavoidable. 

Mention may be made here of the use of exhaust steam from 
a non-condensing engine for the purpose of working a second or 
supplementary engine, in which the medium is a more volatile 
liquid than water. Ether, for example, boils at 35 C., and at 9OC. 
exerts in a closed space a pressure of 70 Ib. per square inch (abs.). 
Exhaust steam might thus be used to heat a boiler containing ether, 
and an engine might be driven by the ether vapour. This method 
has occasionally been tried, but although a considerable saving ot 
heat results, the cost of the engine and its upkeep are such as to 
reduce in a large measure the net financial saving ; and from this 
standpoint a feed-water heater is generally preferred. Methylated 
spirits has been used as the medium for these supplementary 
engines. 

Steam compared with other Media. In an ideal engine, working 
between limits of temperature T l and T 2 , the efficiency would be 
the same, no matter what medium were used. It does not follow, 
however, that all media would be equally suitable in practice. If 
steam and air be compared as media, working between limits of 
200^ C. (473 abs.) and 40 C. (313 abs.), there would be no choice 
so far as the proportion of heat converted into work was concerned. 
Saturated steam at 200 C., however, has a pressure of 225 Ib. per 
square inch (abs.), whereas air, taken as being at atmospheric 
pressure at 40 J C., would only possess a pressure of 22-2 Ib. (abs.). 
It is evident, therefore, that in order to furnish the same horse-power 
the area of the piston of the air engine would have to be many times 



Steam Compared ^v^th other Media. 407 

as great as that of the steam engine, and this unwieldy size would 
not only entail greater prime cost, but also larger expenses in 
upkeep. Even if the temperature of the air were 1000 C., the 
pressure would only be 60 Ib. (abs.> per square inch, and if such a 
working temperature were possible the size of the engine would still 
be a fatal drawback. The use of gases is further discounted by the 
fact that the supply of hot gas from a boiler would be difficult to 
maintain ; whereas water represents concentrated steam, i cubic inch 
producing nearly a cubic foot of steam. Hence, using a boiler, 
practical difficulties prevent the use of gases as a substitute for 
steam. The internal combustion engine, however, enables gases to 
be used to advantage, as will be shown later. 

The vapours of other liquids, such as ether, alcohol, petroleum, 
etc., cannot be substituted for steam, for various reasons, and no 
advantage would accrue from their use unless they could be made 
to work between wider limits of temperature than steam. All these 
liquids are costly compared with \vater, and the three named are 
highly inflammable, so that a leakage would be a source of danger. 
Water, by its abundance, non-inflammability, and comparatively 
small chemical action on metals, is preferable to any other liquid at 
present known ; and to justify the substitution of another liquid it 
would be necessary that such liquid should possess, in large degree, 
the advantages enumerated, and should be capable in addition of 
being worked between wider limits of temperature than water, so as 
to procure an increase of efficiency. 

Cycle of Operations in a Steam Engine. It now remains to be 
considered whether it is practically possible to modify the cycle of 
operations in a steam engine so as to secure a greater efficiency. 
Referring to the indicator diagram (Fig. 108) the nearly vertical 



B 




FIG. 108. INDICATOR DIAGRAM OF CONDENSING STEAM ENGINE. 

line A B represents the rise of pressure due to the admission of steam 
to the cylinder. Whilst the valve remains open, this pressure will 
remain constant, as shown by the line B C, which represents the 



408 Heat for Engineers. 

isothermal of saturated steam at the boiler temperature, and is 
therefore horizontal. The curved line C D represents the fall of 
pressure due to the work done by the expansion of the steam, and 
is approximately an adiabatic, not quite fulfilling this condition 
owing to the escape of heat through the walls of the cylinder. At 
D the cylinder is made to communicate with the condenser, and the 
piston moving backward drives out the steam at the pressure and 
temperature existing in the condenser. Hence the line D A is the 
isothermal of water vapour at the temperature of the condenser, and 
is horizontal. The area of the closed figure A B C D represents the 
work done during the cycle, when the units taken correspond to the 
actual volume of the cylinder, and the actual pressures. 

An important difference between this cycle and that of Carnot's 
engine is at once apparent. Whereas, in an ideal engine, the 
working substance remains in the cylinder and is not renewed, the 
steam after expanding is expelled, and replaced by fresh steam. 
If it were possible to compress and re-heat the expanded steam in 
situ, a boiler would no longer be necessary. No arrangement has 
yet been devised, however, which would make such operations 
possible, and even if such arrangement were forthcoming, it would 
suffer from similar heat losses by radiation, etc., as the boiler itself. 
Moreover, in compressing the expanded steam isothermally, con- 
densation would ensue, and the water produced would have to be 
converted into steam again by the heat applied to the cylinder. 
The rapid application of heat to the cylinder at one part of the 
stroke, and the almost instantaneous extraction of heat which would 
be requisite at another part, are not practically possible ; and hence 
the replacement of the working substance once per cycle is a 
necessity in the steam engine and also in internal combustion 
engines. Comparing the indicator diagram under notice with that 
Df Carnot's engine on page 388, the line B C is the equivalent of 
the isothermal D A (although different in shape), the boiler being 
analagous to the hot body. The line C D is similarly equivalent te 
to the adiabatic A B, work being done in both cases by the expand- 
ing medium, which falls in temperature. Here the resemblance 
ceases, as no attempt is made in the steam engine, for the reasons 
stated, to bring the steam back to its original hot state by means of 
processes analagous to the isothermal and adiabatic compressions 
B C, C D. Any improvement in efficiency which might result from 
the alteration of the existing cycle so as to make it reversible, must 
be regarded as unattainable in practice. 

Conclusions Regarding Steam Engines. In the foregoing pages it 



Special Advantages of Steam Engines. 409 

has been shown that the low efficiency of steam engines arises from 
a variety of causes, and future improvements in this respect will 
depend upon the introduction of higher working pressures (and tem- 
peratures) and lower condenser temperatures, and in such minor 
savings as the lessening of radiation and condensation. Viewed from 
the standpoint of thermal efficiency, steam engines are greatly inferior 
to internal combustion engines, as will appear subsequently. Until 
quite recently, however, it has been found more economical to use 
steam engines for most purposes, as the inferior efficiency was more 
than counterbalanced by the cheapness of coal compared with gas. 
Since the introduction of cheap producer gas, however, this advantage 
on the part of the steam engine has ceased to exist, with the result that 
steam power has been in many cases supplanted by the cheaper gas 
power, particularly for generating horse-powers below 100. For 
power production on the largest scale, however, the steam engine 
possesses the advantage in respect to size, and where space is a con- 
sideration this fact is of importance. It cannot be predicted at 
present as to what is the upper practicable limit of power production 
by the internal combustion engine, but plant of 3000 H.P. has already 
been laid down. The reciprocating steam engine is reversible in 
direction, whereas the internal combustion engine is not; and this 
reversibility is essential in many engines, such as locomotives. For 
high-speed working the steam turbine is the best engine yet intro- 
duced, the vibration caused by reciprocating engines being largely 
obviated. The conversion of heat into work in the steam turbine is 
essentially the same as in the reciprocating engine, the steam being 
admitted at high pressure and allowed to work expansively to a low 
pressure, the work being applied to the rotation of the shaft instead 
of the longitudinal movement of a piston. This is the latest form of 
the steam engine, and there does not appear any immediate prospect 
of the general replacement of steam power for very large-scale 
purposes by any other type of engine. 

Disposal of Heat in Internal Combustion Engines. By generating 
the heat in the cylinder of the engine itself, instead of employing an 
intermediary such as steam, the losses inseparable from the use of a 
boiler are avoided. In gas engines a mixture of combustible gases 
with air is exploded, the resultant chemical action giving rise to the 
heat ; whilst in oil engines the vapour of the oil, mixed with air, is 
similarly used to produce heat. In each case work is done on the 
piston by the expansion of the hot gases resulting from the com- 
bustion. 

As the explosion of the mixtures gives rise to a high temperature 



4io Heat for Engineers. 

1500 C. or more it is evident that unless steps are taken to keep 
the cylinder cool the engine could not be worked, as the charge would 
ignite immediately on entering. Hence a circulation of water must 
be kept up round the cylinder, to ensure that the walls are kept well 
below the temperature of ignition of the explosive mixture. In 
practical working, therefore, a portion of the heat generated must of 
necessity be carried away by the cooling-water, and in consequence 
is not available for conversion into work. A further loss is caused 
by radiation from exposed parts, although this is relatively small ; 
and in addition the gases, after expanding, are expelled from the 
cylinder whilst still retaining a considerable portion of the heat 
generated. As the piston is urged forward against the pressure of 
the atmosphere, it is evident that the hot gases would cease to expand 
and do work when the pressure exerted was equal to that of the 
atmosphere, and in practice the expansion cannot be carried to this 
limit. Hence, in internal combustion engines, there are three unavoid- 
able sources of heat loss in practice, viz. in the cooling-water, by radia- 
tion, and in the escape-gases. 

In a well-designed internal combustion engine the disposal of 
heat is approximately as under : 

Per cent. 

Loss to cooling-water, and by radiation ... 25 
Loss in escape gases ...... 35 

Converted into work ...... 40 

The thermal efficiency 40 per cent. is therefore much higher 
than that obtainable with a steam engine, but whether any financial 
advantage is gained depends upon the relative costs of fuel, upkeep, 
and prime costs of the engines. All these points must be considered 
in deciding upon an engine to be used under given circumstances. 

The " mechanical " efficiency, or proportion of heat available for 
external work, is less than the thermal efficiency owing to frictional 
losses in the engine itself. These losses amount to about 3 per cent, 
of the total heat provided ; and hence the mechanical efficiency of a 
good internal combustion engine is about 37 per cent. 

The superior efficiency of these engines over the steam engine 
arises from the fact that the operations take place between wider 
limits of temperature. The absence of boiler losses is counter- 
balanced by the loss to the cooling-water ; and the greater efficiency 
results from the use of a higher working temperature, and consequent 
greater availability of the heat. The experimental difficulties of 
obtaining exact data relating to the working temperatures have not 
yet been overcome ; but assuming the temperature produced by the 



Internal Combustion Engines. 411 

explosion to be 1500 C., and that of the escape gases to be 500 C.. 
the efficiency of a perfect engine working between these temperatures 

would be T 773 ~ 773 or ^5.^ per cent Compared with this, a 

1773 

perfect engine taking in heat at 200 C., and rejecting it at 60 C. 
(the temperatures that might exist in a steam engine working with a 
condenser) would have an efficiency of only 29*6 per cent. 

It is evident that an increase in the temperature produced by 
the explosion, and a diminution of the temperature at which the hot 
gases are expelled, would raise the efficiency of an internal combus- 
tion engine. The possibility or advisability of modifying these 
temperatures is subject to practical limitations. The existence of a 
very high temperature on the inner surface of the cylinder, fluctua- 
ting at different parts of the cycle, and of a uniform low tem- 
perature on the exterior, subject the material to severe strains and 
stresses; and so far as the life of the engine is concerned, it is 
most economical to employ as low an explosion temperature as 
possible, and special means of reducing this temperature have been 
tried. The lowest temperature possible for escaping gases to possess 
would be that at which the pressure exerted would be equal to that 
of the atmosphere. To attain this temperature in practice it would 
be necessary to produce by the explosion just sufficient heat to enable 
the resulting gases to expand so as to fall to atmospheric pressure 
when the piston is at the end of its stroke. The difficulties arising 
in practice tend to make this desired end unattainable. The explo- 
sive mixture after ignition has a different composition to that possessed 
on entrance to the cylinder, and would occupy a different volume at 
the same temperature; and it would be necessary so to regulate the 
quantities of air and combustible matter drawn in that the resultant 
gases would just fill the cylinder at atmospheric pressure. Moreover, 
each explosion would have to be uniform in character which is not 
always the case in practice and hence the expansion of the gases 
down to atmospheric pressure cannot be ensured. The nearer this 
end is attained, by regulation of the charge and size of the com- 
bustion chamber, the greater will be the efficiency. 

Cycle of Operations in Internal Combustion Engines. Whereas 
in the steam engine the cycle is completed in one forward and one 
backward movement of the piston, all ordinary internal combustion 
engines require two complete forward and backward movements in 
passing through the cycle. The operations are as follows : 

i. Backward Stroke. Charge of air and combustible gas or 
vapour enters cylinder. 



412 



Heat for Engineers. 



2. Forward Stroke. The mixture is compressed, and fired 
at or near the end of the stroke, causing a great increase in pressure. 

3. Backward Stroke. The hot gases expand, doing work on the 
piston, and consequently falling in temperature. 

4. Forward Stroke. The expanded gases are removed from the 

cylinder. 

These operations are shown in the indicator diagram, Fig. 109. 
Starting at the point A, the charge is drawn in at atmospheric 

pressure, as indicated by the hori- 
zontal line A B. The next opera- 
tioncompression of the charge 
is shown by the curved line 
BC (approximately an adiabatic). 
The vertical line C D represents 
the rise of pressure due to the 
explosion of the charge ; and 
D E also approximately an 
adiabatic the expansion of the 
hot gases during the second back- 
ward stroke. At E the exhaust 
opens, and the pressure falls to 
atmospheric, as shown by the 
vertical line E B. Finally, on 
the forward stroke which follows, 
the expanded gases are expelled 
at atmospheric pressure, as indi- 
cated by the line B A. The closed 
figure B C D E represents the 
work done during the cycle. 

It will be noticed that this cycle, like that of the steam engine, 
is not reversible. Compared with Carnot's cycle, the adiabatic 
compression B C and the expansion D E correspond to C D and A B 
in Fig. 105. The heat is not taken in, however, from a body at 
constant temperature, but suddenly developed in the charge itself; 
and the isothermal compression in Carnot's engine (B C, Fig. 105) 
is also absent. Although falling short of the ideal cycle, however, 
the set of operations employed in internal combustion engines result 
in the utilisation of a relatively large proportion of the heat furnished 
by the explosion. Diagrams obtained in practice will differ from 
Fig. 109 according to the time at which the charge is fired ; the rate 
of burning of the charge ; and the amount of expansion permitted 
before the exhaust opens. Firing the charge before complete com- 




FIG. 109. INDICATOR DIAGRAM OF 
INTERNAL COMBUSTION ENGINE. 



Internal Combustion Engines. 413 

pression enables the pressure to rise to a maximum by the time the 
compression stroke is completed, the combustion not being instan- 
taneous ; and in this case the line D C will be curved, the position 
of C depending upon the part of the stroke at which firing takes 
place. Further expansive working would prolong the line D E and 
shorten E B, evidently demanding a longer stroke. 

Conclusions regarding Internal Combustion Engines. Compared 
with the steam engine, internal combustion engines as a class are 
capable of yielding a much higher thermal efficiency. Whether an 
actual financial saving results from the use of the latter class depends 
upon the cost of the fuel. Where blast-furnace gases are available, 
an extremely cheap source of power is obtained for the driving of 
machinery connected with the works. Mond's gas, made from coal 
slack, is also very cheap ; and suction gas taken directly into the 
engine is a further source of cheap fuel. In the vapour engines used 
for motor-cars, volatile fuels of the type of petrol, benzol and alcohol 
are used ; which are relatively costly compared with gas or coal. 
In oil engines, however, in which the cheaper varieties of oil can be 
used such as in the Diesel engine the cost per horse-power is less 
than with steam. The following figures are given by Mr. Swinburne 
as representing the brake horse-power hours obtainable with the 
various types of engine and fuels, for an expenditure in each case 
of ico/. this sum including the cost of labour, lubricants, cooling 
water, fuel, and any other details of upkeep : 

B.H.P. Hours per ^100. 

Gas engine using Mond's gas. . . . 235,000 

,, ,, suction gas . . . 202,500 

Diesel oil engine ..... 1*81,000 

Steam plant (condensing) .... 72,500 

Explosion oil engine ..... 68,500 

Gas engine with town gas .... 52,600 

As might be expected from the above figures, modern internal 
combustion engines are now formidable rivals to steam engines. The 
production of cheap gas has given a great impetus to the use of gas 
engines, and the tendency at the present time is to instal gas engines 
or a good form of oil engine in preference to steam plant, up to 
a certain horse-power. Large gas engines are now being introduced 
capable of producing 3000 H.P., on the multi-cylinder system; and 
single units of 1000 H.P. are in use. Such engines take up a larger 
space than steam engines of corresponding power ; but where space 
is not an important consideration it is probable that steam will largely 
be superseded in the future, even for large-scale power production. 



Heat for Engineers. 



At present the use of steam for generating 100 H.P. or more is general, 
and for the highest horse-powers such as those requisite in large 
steamers no rival to steam has yet been found. It may be confi- 
dently predicted, however, that the internal combustion engine, owing 
to its superior economy, will have its applications continuously 
extended. The drawback of lack of reversibility in these engines 
applies also to the steam turbine, and may probably be overcome. 

Refrigerating Machines. As a refrigerating machine is engaged 
in extracting heat, the losses, from a refrigerating standpoint, are due 
to the ingress of heat from surroundings. Thus the tanks containing 
the brine receive heat from without, as also do the various pipes con- 
veying the brine, and this results in a loss of efficiency. The same 
is true of a cold store or ice-making plant. As the difference between 
the atmospheric temperature and the cold parts is relatively small 
say 40 C. in a temperate climate the loss of efficiency is not of the 
same order of magnitude as that which obtains from similar causes in 
a heat engine. Friction of parts in the engine is a further source of 
loss ; but if the condenser water become heated above atmospheric 
temperature, radiation from it into the air is a gain to the machine. 
Evidently the efficiency will be less in a hot climate, and a good 
result for a compression machine, working under favourable conditions 
would be represented by a practical energy ratio of 3. As each plant 




FIG. no. INDICATOR DIAGRAM OF REFRIGERATING MACHINE 
(Compression System.) 

varies so much in the detail of the refrigeration performed, it is diffi- 
cult to procure general details of the losses, which in an average case 
amount to 50 per cent, of the heat- extracting power in the aggregate, 
Cycle of Operations in a Refrigerating Machine. Fig. no repre- 



Refrigerating Cycle of Operations. 415 

sents the general type of indicator diagram furnished by a compression 
machine. Starting at A, the gas is compressed adiabatically, as 
represented by the line A B. At B the valve opens, the prominence 
at this point being due to the lifting of the valve. The compressed 
gas now communicates with the condenser, which contains the liquid 
gas, and hence the pressure remains at that of the condenser for the 
rest of the stroke. This is shown by the horizontal part of B C, which 
is the isothermal of a vapour in contact with its own liquid. At C 
the piston commences the return stroke, and the pressure falls in the 
manner indicated by the adiabatic CD. At D the valve to the 
evaporator opens, causing the prominence at D, and the remainder of 
the stroke is accomplished at the pressure existing in the evaporator 
coils. As these contain the liquid, the line D A will be horizontal,, 
and represents the isothermal of the saturated vapour at the tempera- 
ture of the evaporator coils. 

It will be observed that this cycle is bounded by two isothermals 
and two adiabatics, and is in reality a reversed Carnot's cycle. As. 
such it is not susceptible of improvement, but in practice the com- 
pression A B and the expansion C D are not truly adiabatic. Other 
differences, such as fluctuations of pressure along B C and A D may 
also be noted frequently, but the cycle in general is such as to secure 
the best refrigerating effect from a given amount of work. 



INDEX 



FACE 

Abel, flash-point apparatus .. .. .. .. .. .. 227 

Absolute or real expansion of liquids .. .. .. .. 59)^3 

zero of temperature .. .. .. .. 104,135,391 

Absorption of gases by solids ... .. .. .. .. .. 116 

system of refrigeration .. .. .. .. .. 296 

Adiabatic compression and expansion .. .. .. .. 108, in 

Air-expansion refrigerating machines .. .. .. .. .. 278 

Air required for combustion of coal .. .. .. ,. .. 28 

Ammonia, constants of .. .. .. .. .. .. .. 287 

properties of .. .. .. .. .. .. .. 286 

A ndrews, researches on critical temperature .. .. .. .. 265 

Aneroid barometer .. .. .. .. .. .. .. 97 

Asbestos laggings 331 

Atmosphere .. .. .. .. .. .. .. .. 93 

Atmospheric moisture .. .. .. ... ... .. .. 247 

Automatic water-sprinklers .. .. .. .. .. 201-204 

Availability of heat for work .. .. .. .. .. .. 403 



B 

BALANCE-WHEEL of watch, compensated 85 

Barometer, aneroid .. .. .. .. .. .. .. 97 

corrections of readings .. .. .. .. .. 96 

Forties .. .. .. .. .. .. .. 95 

simple 94 

Barometric pressure, " normal ".. .. .. .. .. .. 96 

Beckmann, thermometers .. ., .. .. .. ..126 

"Black body" 169,359 

Boilers, circulation in .. .. .. .. .. .. .. 337 

expansion of .. .. .. .. .. .. .. 74 

loss of heat in .. .. .. .. .. .. 400 

Boiling, normal and abnormal .. .. .. ..' .. .. 233 

Boiling point, definition of .. .. .. .. .. ..212 

2 E 



4 i 8 Heat for Engineers. 



Boiling point, determination of .. .. .. 229 

,, effect of dissolved solids on .. .. .. 233 

of pressure on .. .. ..231 

use in determining altitudes .. .. 232 

Bolometer .. .. 3 6 4 

Bomb calorimeters .... .. 14 

Boyle, law of gases . . . . . . . . 99 

Breguet, metallic thermometer .. .. .. .-87 

Brine, properties of ..291 

use of in cooling .. .. .. .. .. .. 290,307 

"Bumping" 234 

Bunsen, ice calorimeter .. .. .. .. .. .. .. 4 1 



Cailletet, liquefaction of oxygen .. .. .. .. .. .. 269 

Callendar, compensated gas thermometer .. .. .. ..129 

experiments on mechanical equivalent of heat .. .. 382 

platinum resistance pyrometer .. .. .. .. 143 

recorder .. -.153 
and Griffiths, formulae for electrical resistance of plati- 
num .. .. .. .. .. .. .. 144 

Can system of ice manufacture . . . . . . . . . . . . 304 

Carbon dioxide, constants of .. .. .. .. .. .. 289 

properties of .. .. .. .. .. .. 286 

solidification of .. .. .. .. .. 265 

Carborundum .. .. .. .. .. .. .. .. 206 

Carnot, ideal engine .. .. .. .. .. .. .. 385 

Carre, ice machine .. .. .. .. .. .. .. 276 

Cell system of ice manufacture .. .. .. .. .. .. 304 

Centigrade scale of temperature .. .. .. .. .. 119,125 

Charcoal, absorption of gases by .. .. .. .. .. 117 

Charles, law of gases .. .. .. .. .. .. 72, 103 

Chimneys, draught of .. .. .. .. .. .. .. 345 

height of 347 

weight of ascending gases in .. .. .. .. 348 

Circulation, hot-water .. .. .. .. .. .. .. 339 

in boilers .. .. .. .. .. .. .. 337 

Clement and Desorme, experiment with gases.. .. .. .. 109 

Clouds .. .. .. .. .. .. .. .. .. 260 

Coal gas 31 

Coals, British .. .. .. .. .. .. .. .. 27 

Coefficient of conductivity .. .. .. .. .. ..312 

,. of expansion of gases .. .. .. .. .. 69 

11 of liquids .. .. .. .. .. 58 

,, ofsolids .. .. .. .. .. 52 



Index. 4 1 9 



PAGE 



Cold storage .. .. .. .. .. .. .. .. 306 

stores, insulation of .. .. .. .. .. .. 310, 333 

methods of cooling .. .. .. .. .. .. 307 

Comparison of air and platinum temperature scales .. .. .. 145 

Compensated balance-wheels .. .. .. .. .. .. 85 

pendulums .. .. .. .. .. .. .. 91 

Compound strip, action of .. .. .. .. .. .. 85 

mechanisms .. .. .. .. .. ..85-87 

Compression system of refrigeration .. .. .. .. .. 282 

Condensers.. .. .. .. .. .. ., .. 246,295 

Conduction of heat .. ... .. .. .. .. .. 311 

Conductivity, coefficient of .. .. .. .. .. ..312 

Contraction, breakage due to .. .. .. .. .. .. 78 

of liquids on solidifying .. .. .. .. .. 191 

of metal castings .. .. .. .. .. .. 77 

Conservation of energy .. .. .. .. .. .. .. 2 

Constant pressure gas thermometer .. .. .. .. ..129 

volume gas thermometer .. .. .. .. .. 131 

Cooling-jets .. .. .. .. .. .. .. .. 246 

Convection .. .. .. .. .. .. .. .. 337 

Critical points of steel .. .. .. .. .. .. .. 183 

pressure of gases.. .. .. .. .. .. .. 268 

temperature of gases .. .. .. .. .. .. 266 

Cycle of operations in engines .. .. .. .. 385,407,411 

in refrigerating machines., .. 279,283,297,414 



D 

Dalton, laws of vapours .. .. .. .. .. .. .. 220 

Daniell^ hygrometer .. .. .. .. .. .. ..252 

Darling, apparatus for pressure of volatile liquids .. .. .. 222 

fuel calorimeter.. .. .. .. .. .. .. 19 

test for heat-insulating materials .. .. .. .. 322 

and Young, apparatus for expansion of liquids .. .. 60 

Dew 258 

Dewar, liquefaction of hydrogen .. .. .. .. .. 272 

liquid air apparatus .. .. .. .. .. .. 271 

vacuum vessel .. .. .. .. .. .. .. 272 

Dew point .. .. .. .. .. .. .. .. .. 248 

Diathermancy .. .. .. .. .. .. .. .. 375 

Differential air thermoscope .. .. .. .. .. .. 362 

method for determining recalescence points .. .. 183 

Diffusion 98 

Diffusivity .. .. .. .. .. .. .. .. .. 335 

Dines, hygrometer .. .. .. .. .. .. 250 

Distillation .. .. .. .. .. .. .. .. .. 245 

2 ]: 2 



420 Heat for Engineers. 



Dryness-fraction of steam .. -.244 

Dulong and Petit, hydrostatic method for expansion of liquids .. 63 

specific heat law .. .. ..49 



E 

EBULLITION 229 

Efficiency of engines .. .. 382,391,401 

Electric furnaces .. .. .. .. .. 33 

heaters for rooms .. .. .. 356 

lamps .. .. 375 

Endothermic compounds .. .. .. .. -- 13 

Energy, conservation of .. .. .. .. .. .. 2 

forms of .. .. .. .. .. .. .. 2 

radiated by different surfaces .. .. .. .. .. 369 

ratio of refrigerating machines .. .. 300,390,393 

Entropy .. .. .. .. .. .. .. .. .. 394 

Eutectics 189 

Exothermic compounds .. .. .. .. .. .. 13 

Expansion, force exerted in .. .. .. .. .. . 5 1 

of gases ..69 

of liquids .. .. .. .. .. .. .58,82 

of solids .. .. .. .. .. .. .. 52 

Explosives .. .. .. .. .. .. .. .. .. 116 



F 

Fahrenheit, scale of temperature .. .. .. .. 119,125 

Fery, heat-radiation pyrometers .. .. .. .. .. ..174 

optical pyrometer .. ... .. .. .. .. .. 176 

Fire-alarms.. ... .. .. .. .. .. .. 84, 86 

Fixed points, for pyrometers .. .. .. .. .. 138,160 

> 5) for thermometers .. .. .. .. .. ..123 

Flash-point.. .. .. .. .. .. .. .. .. 227 

Fogs .. 259 

Foot-warmers .. .. .. .. .. .. .. .. 206 

Forbes, conductivity experiment .. .. .. .. .. 312 

For tin, barometer . . . . . . . . . . . . . . . . 95 

Fourth-power radiation law .. .. .. .. .. 168,361 

Freezing mixtures .. .. .. .. .. .. 207 

point, determination of .. .. .. .. ..187 

effect of dissolved solids on .. .. .. ..199 

Fuel calorimeters .. .. .. .. .. 14-21; 

Fuels, gaseous .. .. .. .. .. , t 31 

heating power of .. .. .. .. .. .. _ n 

30 



Index. 421 



PAGE 



Fuels, solid .. .. .. .. .. .. .. .. 27 

Fundamental coefficient .. .. .. .. .. .. .. 146 

interval .. .. .. .. .. .. .. 146 

zero 146 

Furnace linings .. .. .. .. .- .. .. .. 205 

Furnaces, electric .. .. .. .. .. .. .. .. 33 

regenerative .. .. .. .. ... .. .. 33 

Fusible alloys .. .. .. .. .. .. .. .. 191 

Fusion method, for high temperatures .. .. .. .. ..178 



GALVANOMETERS, anti-vibration mounting for 167 

for use in pyrometry .. .. .. ..157 

Gas engines .. .. .. .. .. .. .. .. 409 

Gases, absorption of by solids .. .. .. .. .. .. 116 

distinguished from vapours .. .. .. .. .. 225 

general properties of .. .. .. .. .. 97-118 

laws of .. .. .. .. .. .. .. 99-105 

liquefaction of . . . . . . . . . . . . . . 264 

passage of through solids .. .. .. .. ..117 

pressure exerted by .. .. .. .. .. .. 99 

two specific heats of .. .. .. .. .. 109,114 

Girders, expansion of .. .. .. .. .. .. .. 78 

Griffiths, experiments on mechanical equivalent of heat . . . . 382 

Grinnell, automatic water-sprinklers .. .. .. .. .. 201 

Guillame, non-expansive alloys .. .. .. .. .. .. 56 



H 

HEAT as Energy I 

methods of producing .. .. .. .. .. .. 10 

molecular changes due to .. .. .. .. .. ..211 

physical effects on solids .. .. .. .. .. ..182 

resemblances to light .. .. .. .. .. ..2,358 

waves 358 

High temperatures, production of .. .. .. .. .. 32 

,, table of .. .. .. .. .. .. 181 

Him, experiments on mechanical equivalent of heat .. .. 380 

Holborn, optical pyrometer .. .. .. .. .. .. 176 

H olden and Brookes, steam-trap ... .. .. .. .. 89 

H olden (Col.) and Lambert, mounting for galvanometers .. .. 167 

Hope, apparatus for maximum density .. .. .. .. .. 68 

Hot-water circulation for heating buildings .. .. .. .. 339 

radiators .. .. .. .. .. .. .. 344 

Hydrocarbons, heating values of .. .. .. .. .. 13 



422 Heat for Engineers. 



Hygrometers .... .... 249-257 

Hygrometric state .. 2 49 

Hygroscopes .. .. 2 57 



I 

ICE, manufacture of .. .. .. 33 

physical properties of ..192 

properties of artificial .. .. .. .. 35 

"Imp" steam trap .. 9 

Indicator diagrams .. 3 88 > 47, 4 I2 > 4 J 4 

Indicators for platinum resistance pyrometers 149-1 5 1 

,, thermo-electric pyrometers 158 

Internal combustion engines .. .... 409 

Isothermals .. .. .. .. .. 100 

of carbon dioxide .. .. .. .. .. .. 267 

Insulating materials .. .. .. 319, 330 

tests for 320 



J 

Jolly, constant volume gas thermometer .. .. .. .. 131 

Joly, steam calorimeter .. .. .. .. .. .. .. 43 

Joule, experiments on gases .. .. .. .. .. .. 106 

on mechanical equivalent of heat .. ..2,379 

and Kelvin, porous plug experiment .. .. .. .. 107 

Junker, fuel calorimeter .. .. .. .. .. .. .. 23 



K 

Kelvin, thermodynamic scale of temperature.. .. .. 121, 391 

and Joule, porous plug experiment .. .. .. .. 107 

Kinetic theory of matter .. .. .. .. .. .. .. 97 

Kot tin, cooling-jets .. .. .. .. .. .. .. 246 

Krocker, bomb calorimeter .. .. .. .. ig 



L 

LAGGINGS, comparative values of .. .. .. .. .. 329 

for cold surfaces .. .. .. .. .. .. 333 

for hot surfaces .. .. .. .. .. .. 319 

tests for efficiency of .. .. .. .. .. .. 320 

Lambrccht) polymeter .. .. .. .. .. .. .. 257 

Laplace and Lavoisier , expansion apparatus .. .. .. .. 53 

ice calorimeter.. .. .. .. 41 



Index. 423 



Latent heat of fusion .. .. .. .. .. .. .. 196 

of vaporisation .. .. .. .. 236 

Le Chatelier, optical pyrometer.. .. .. 175 

thermo-electric pyrometer .. .. ..156 

Lewis Thompson, fuel calorimeter .... .25 

Linde, liquid air apparatus .. .. .. .. .. .271 

Linear-expansion pyrometers .. .. .. .. .. .. 178 

Liquefaction of gases .. .. .. .. .. .. .. 264 

Liquefied gases, uses of .. .. .. .. . .. .. 274 

Low temperatures, data .. .. .. .. .. .. . 273 

,, ,, production of .. .. .. .. .. 262 

Luminosity, as affected by temperature .. .. .. 175, 374 

M 

MAGNESIA lagging .. .. .. ... .. .. .. 324 

Magnesite, for furnace linings .. .. .. .. .. .. 206 

Mahler, bomb calorimeter .. .. .. .. .. .. 15 

,, formula for coal .. .. .. .. .. .. .. 13 

Marcet, steam boiler .. : .. .. .. 214 

Maximum and minimum thermometers .. .. .. .. 127 

., density of water .. .. .. .. .. .. 68 

Mayer, calculation of mechanical equivalent of heat .. .. .. 114 

Measurement of electrical resistance .. .. .. .. .. 147 

Measures of constant length .. .. .. .. .. .. 80 

of length and volume .. .. .. .. .. .. 8 

correction of .. .. .. 79, 81 

Mechanical equivalent of heat .. .. ... .. .. 2,379 

Melloni, experiments on radiant heat .. .. .. .. .. 367 

Melting points of solids .. .. .. .. .. .. .. 186 

Mercury, expansion of .. .. .. .. .. .. 65 

Mesure and Nouel, optical pyrometer .. .. .. .. ..177 

Method of condensation, for specific heats .. .. .. .. 43 

of cooling for specific heats .. .. .. .. .. 44 

of fusion for specific heats .. .. .. .. .. 40 

of mixtures for specific heats .. .. .. .. .. 37 

Mica lagging 331 

"Midget" steam-trap 88 

Mists .. .. .. .. .. .. . .. .. 259 

Mixed gases and vapours .. .. .. .. .. .. '.20 

Mond, gaseous fuel .. .. .. .. .. .. .. 31 

Morris, automatic water-sprinkler .. .. .. .. .. 203 

N 

Neivt^n, law of cooling .. .. .. .. .. .. 361 

Nickel-steel alloy, non-expansive .. .. ..56 



424 

OPTICAL pyrometers 



Heat for Engineers. 



PAGE 
I7A-I78 



Parr, fuel calorimeter .... 

" Partial" melting points .. .. 

Pearson, fire-alarm .... 

Pendulums, compensated 

" Perfect" gas, properties of .. 

Petrol 

Petroleum, use as fuel .. 

Pictet, liquefaction of oxygen . . 

Pistons, expansion of 

Plastic laggings .. 

Plate system, for ice manufacture 

Platinum, absorption of gases by 

alloys with rhodium and iridium 
melting point of 
resistance to electricity 
scale of temperature .. 

Porous plug experiment .. 

Pyrometers, calorimetric .. .. 

contraction (Wedgwoods] 
electrical resistance .. .. 
fixed points for graduation, of 



24 



heat radiation 
installation of 
linear-expansion 
miscellaneous 
optical .. 

thermo-electric 



5 

3 ' 
* 
* 
'* 

*3 8 
H3 



139 

.. H 2 
138, 1 60 

-- -4. 



178 
180 



QUARTZ, low expansion of 
vessels .. .. 



79 



RADIANT heat, application to pyrometry .. .. .. .. 168 

Radiation 358 

Radiometer .. .. .. .. .. .. .. .. 367 

Radio-micrometer.. .. .. .. .. .. .. .. 365 

Rails, expansion of .. .. .. .. .. .. .. 73 



Index. 425 

PAGE 

Rain 260 

Rain-gauge.. .. 261 

Reaumur, scale of temperature .. .. .. .. .. 119,125 

Recalescence of iron and steel .. .. .. .. .. 50, 183 

Recorder, Callendar's .. .. .. . .. .. ..153 

Roberts- Austen's .. .. .. .. .. ..162 

"Thread" 163 

Refractory materials .. .. .. .. .. .. .. 206 

Refrigerating machines .. .. .. .. .. .. .. 276 

capacity of .. .. .. .. .. 298 

energy ratio of 300, 390, 393 

indicator diagrams of .. .. .. 414 

Regelation .. .. .. .. .. .. .. .. .. 194 

IZegnault, hygrometer .. .. .. .. .. .. .. 253 

method of mixtures .. .. .. .. .. .. 37 

Relative humidity .. .. .. .. .. .. .. .. 249 

Resistance pyrometers .. .. .. .. .. .. .. 148 

Reversible cycles .. .. .. .. .. .. .. .. 389 

Roberts-Austen, recorder.. .. .. .. .. .. ..162 

Rowland, experiments on mechanical equivalent of heat .. 2, 380 

Rumford, experiments on heat .. .. .. .. .. .. I 



S 

SAFETY-PLUGS 205 

Saturated vapours.. .. .. .. .. .. .. 212,226 

" Scattering " of heat .. . . .. .. .. .. .. 370 

Sealing of platinum into glass .. .. .. .. .. .. 56 

Seger, fusible pyramids .. .. .. .. .. .. ..179 

" Sentinel " pyrometers .. .. .. .. .. .. .. i8c 

Separating calorimeter .. .. .. .. .. .. 243 

Sherringham, valve for ventilation . .. .. .. 352 

Shrinking of tires .. .. .. .. .. .. .. .. 75 

Siemens, calorimetric pyrometer .. .. .. .. .. 141 

indicator for pyrometers .. .. .. .. ..150 

method of producing low temperatures .. .. .. 269 

platinum resistance pyrometer .. .. .. .. 142 

regenerative furnace .. .. .. .. .. .. 32 

Silica, vitrified .. .. .. .. .. .. .. 79,142,165 

Siloxicon .. .. .. .. .. .. .. .. .. 206 

Slag-wool or silicate cotton, use for insulation .. .. .. 332 

Smoke prevention .. .. .. .. .. .. .. .. 29 

Soldering .. .. .. .. .. .. .. .. .. 200 

Specific gravity, altered by expansion .. .. .. .. .. 81 

heat .. .. .. .. .. 35-49 

effect of temperature on .. .. .. .. .. 48 







426 Pleat for Engineers. 



Specific gravity of gases .. 45> IO 9 

Spectrum, distribution of energy in .. 37 1 

Spheroidal state .. 

Sprinklers, automatic water- 

States of matter .. ' 97 

Stefan-Boltzmann, radiation law - 168,361 

Steam, latent heat of .. .. 2 37 

moisture in .. .. ..241 

properties of saturated .. .... 240 

superheated .. .. 241,405 

., use for heating .. .. 2 44 

Steam-engine, disposal of heat in 399 

t1 cycle of operations in .. .. .. 47 

Steam-pipe joints .. 

coverings . S^SS 

Steam-traps ...... 87-90 

Stills ........ 2 45 

Storage, cold ....... 3 c6 

of volatile liquids .. .. 221 

Suction gas .. .. .. 3 2 

Sulphur dioxide, constants of .. .. .. .. .. 289 

properties of .. .. .. -. .. .. 288 

Supersaturation .. .. .. .. .. 195 

Surfusion .. .. .. .. .. : 94 



T 

TABLES, see special index, p. 429. 

Tantalum, use in electric lamps .. .. .. .. 375 

Temperature, definition of .. .. .. .. .. .. 119 

,, effect on luminosity .. .. .. .. 175,374 

on specific heat .. .. .. .. .. 48 

principles of instruments for measuring .. .. 120 

standards of .. .. .. .. .. .. 119 

Temperature-entropy (6 </j) diagrams .. .. .. .. .. 396 

Thermal capacity .. .. .. .. .. .. .. .. 3; 

couples, for low temperatures .. .. .. .. .. 166 

properties of .. 155, 165 

Thermit 34 

Thermodynamic scale of temperature .. .. .. .. 121,391 

Thermodynamics, first law of .. .. .. .. .. 379 

second law of .. .. .. .. .. 384 

Thermo-electric pyrometers .. .. .. .. .. 155-168 

Thermometers, conversion of scales .. .. .. .. .. 125 

defects of .. .. .. .. .. ..124 

fixed points for .. .. .. .. .. .. 122 



Index. 427 



PACK 

Thermometers for high temperatures .. .. .. .. ..128- 

for special ranges .. .. .. .. ..125 

gas, constant pressure .. .. .. .. ..129 

volume 131 

liquid-in-bulb .. .. .. .. .. ..121 

maximum and minimum .. .. .. .. 127 

registering .. .. .. .. .. ..126 

Thermoregulators .. .. .. .. .. .. .. 83 

Thermopile.. .. .. .. .. .. .. .. .. 363 

" Thermos " bottle .. .. 273 

"Thread "recorder 163 

' Throttling" calorimeter .. .. .. .. .. .. 242. 

Tobin, ventilating tube .. .. .. .. .. .. .. 352. 

Total heat of vapours .. .. .. .. .. .. .. 239 

Tungsten, use in electric lamps .. .. .. .. .. .. 375. 

Tyndall, experiments on radiant heat .. .. .. .. ..371 



U 

UNITS .. .. .. .. .. .. .. .. .. 3-9 

Unsaturated vapours .. .. .. .. .. .. 212,226 



V 

VAPOUR density .. .. .. .. .. .. .. .. 227 

pressure .. .. .. .. .. .. ..213 

Vapours .. .. .. .. .. .. .. .. 211-228 

,, distinguished from gases .. .. .. .. .. 225 

Vatighan and Stubbs, steam-trap .. .. . .. .. 87 

Ventilation .. .. .. .. .. .. .. .. .. 349 

artificial .. .. .. .. 353 

,, natural .. .. .. .. .. .. .. 351 

size of inlets for .. .. .. .. .. 355 

Vitrified silica .. .. .. .. .. .. .. 79. 142,165 

Volatile liquids, storage of .. .. .. .. .. .. 221 



W 

Walworth, automatic water-sprinkler .. .. .. ..202 

Wanner, optical pyrometer . . . . . . . . . . ..176 

Water, anomalous expansion of .. .. .. .. .. 66 

equivalent of calorimeter .. .. .. .. .. 38 

gas .. .. .. 31 

., maximum density of .. .. .. . ..68' 

sprinklers, automatic .. .. .. .. .. 201-204 

,, vapour, pressure of .. .. .. .. .. .. 216 



428 Heat for Engineers. 



PAGE 



Watt, separate condenser for steam-engines .. .. .. .. 224 

Wedgwood, pyrometer .. .. .. .. .. .. .. 139 

Weight thermometer .. .. .. . .. .. .. 59 

Wein, energy laws .. .. .. .. .. .. .. 372 

Welding .. .. .. .. .. .. .. .. .. 200 

Wet and dry bulb hygrometer .. .. .. .. .. .. 254 

Wheatstone, bridge for measuring electrical resistance .. .. 147 

IVhipple, indicator for pyrometers .. .. .. .. .. 151 

Wiborght air pyrometer .. .. .. .. .. .. ..142 

Winds .. .. .. .. .. .. .. .. .. 344 



Y 

Young (y.) and Darling, apparatus for expansion of liquids .. 60 



INDEX TO TABLES. 



PAGR- 



Allowance for contraction of metal castings .. .. .. .. 77 

Alloys of very low melting-points .. .. .. .. .. 191 

Boiling-points of liquids .. .. .. .. .. .. .. 230 

British coals .. .. .. .. .. .. .. .. 28 

Calorific value of gaseous fuels .. .. .. .. .. .. 26 

of hydrocarbons .. .. .. .. .. 13 

Coefficients of conductivity .. .. .. .. .. ..316 

of expansion of liquids .. .. .. .. .. 66 

of expansion of solids .. .. .. .. .. 55 

Comparison of air and platinum temperature scales .. .. .. 145 

Composition of coals .. .. .. .. .. .. .. 27 

,, of gaseous fuels .. .. .. .. .. .. 31 

Connection between British and C.G.S. units.. .. .. .. 5 

various heat units 

Constants of ammonia .. .. .. .. .. .. .. 287 

of carbon dioxide .. .. .. .. .. .. 289 

of sulphur dioxide .. .. .. .. .. .. 289 

Critical temperatures and pressures . . . . . . . . . . 268 

Diathermancies .. .. .. .. .. .. .. .. 376 

Diffusivities .. .. .. .. .. .. .. .. 335 

Disposal of heat in steam engine .. .. .. .. .. 400 

of heat in internal combustion engine .. .. .. 410 

Energy radiated by different surfaces .. .. .. .. .. 370- 

Fixed points for graduation of pyrometers .. .. .. 138,160 

Freezing mixtures .. .. .. .. .. .. .. .. 208 

Height of chimneys .. .. .. .. .. .. .. 347 

High temperature data .. .. .. .. .. .. .. 181 

Insulating value of different laggings .. .. .. .. .. 329 

Latent heats of fusion .. .. .. .. .. .. .. 198 

of vaporisation .. .. .. .. .. .. 238 

Low temperature data .. .. .. .. .. .. .. 273 

Melting-points of solids .. .. .. .. .. .. .. 193, 

of mixtures of lead and tin .. .. .. ..190 

of salts .. .. 179 

Pressure of aqueous vapour 216 

Properties of brine solutions .. .. .. .. .. .. 291 

of saturated steam .. .. .. .. .. .. 240 



430 Heat for Engineers. 



PAGE 



Ratio of two specific heats of gases .. .. .. .. ..in 

Relation between cold and molten volume of metals .. .. .. 77 

Relative absorptive powers of surfaces . . . . . . . . . . 368 

radiating powers of surfaces .. .. .. .. .. 367 

Results of tests on a lagging .. ..321 

Space allowed per head in occupied rooms .. .. .. .. 350 

Specific heats .. .. 47 

Suitable temperatures for cold storage .. .. .. .. .. 307 

Temperatures corresponding to colour changes .. .. .. 175 

Time required to heat steel in a furnace .. .. .. .. 336 

Value of * J " in different units .. .. .. .. .. ..382 

Wet and dry bulb hygrometer .. .. .. .. .. .. 255 

\Vorkingdataofcarbondioxiderefrigeratingmachines .. .. 303 






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