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The Cambridge Technical Series 
General Editor: P. Abbott, B.A. 



ELEMENTARY PHYSICS 
FOR ENGINEERS 



CAMBRIDGE UNIVERSITY PRESS 

C. F. CLAY, Manager 

iLonHon: FETTER LANE, E.G. 

enmburgt): loo PRINCES STREET 




fitia lorfe: G. P. PUTNAM'S SONS 
Bombag. Calcutta anH fSaUraB: MACMILLAN AND CO., Ltd. 
Coronto: J. M. DENT AND SONS Ltd. 
ffokBo: THE MARUZEN-KABUSHIKI-KAISHA 



AH rights reserved 



-\4 



ELEMENTARY PHYSICS 
FOR ENGINEERS 



AN ELEMENTARY TEXT BOOK FOR FIRST 
YEAR STUDENTS TAKING AN ENGINEERING 
COURSE IN A TECHNICAL INSTITUTION 



BY 



J. PALEY YORKE 

Head of the Physics and Electrical Engineering Department 

at the London County Council School of Engineering 

Poplar, London 



Cambridge : 

at the University Press 

1916 




PREFACE 

THE importance of Physics to the engineer is in- 
estimable but the student of engineering does 
not often recognise the fact. 

This little volume is intended to appeal to him 
firstly because it is written specially for him and 
secondly because the author has attempted to present 
some essential facts of elementary physics as briefly 
and straightforwardly as possible without any pedantry 
or insistence upon details of no practical importance. 
He has also avoided all reference to historical deter- 
minations of physical constants and has described in 
all cases the simplest and most direct methods, merely 
indicating the directions in which refinements might 
be made. At the same time he has endeavoured to 
make no sacrifice of fundamental principle and no 
attempt has been made to advance with insufficient 
fines of communication. 

The author frankly admits that he has tried to be 
interesting and readable, and in case this should be 
regarded as a deplorable lapse from the more generally 
accepted standards he pleads the privilege of one who 
has had considerable experience with students of engi- 
neering in Technical Institutions. 

He hopes by this little volume to induce a greater 
number of engineering students to recognise that 
Physics is as essential to engineering as is Fuel to a 
Steam Engine. 

J. P. Y. 

London, 1916. 



CONTENTS 

CHAPTER I 

MATTER AND ITS GENERAL PROPERTIES 

Definition of matter. Weight. Force. Mass. Inertia. Theory 
of structure of matter. Indestructibility of matter. Classifi- 
calion of matter. Solids, liquids and gases. Density. Modes 
of determination. Elasticity. Strain and stress. Hooke's 
Law. Modulus of Elasticity . . . pages 1-14 

CHAPTER II 
PROPERTIES OF LIQUIDS 

Pressure produced by liquids. Pressure at different depths. Upward 
pressure. Pressure at a point. Pressure on sides of a vessel. 
Buoyancy. Floating bodies. Archimedes' principle. Specific 
gravity or Relative density and modes of determination. 
Hydrometer. Pumps. Capillarity. Surface Tension. Diffusion. 
Viscosity 15-36 

CHAPTER III 

PROPERTIES OF GASES 

Weight. Pressure exerted equally in all directions. Atmospheric 
pressure. The Barometer. The relationship between volume 
and pressure 37-47 

CHAPTER IV 

FORCE, WORK AND ENERGY 

Units of Length, Mass, Time and Volume on British and metric 
systems. Force. Units of Force. Work and its measurement. 
Examples on both systems. Energy. Potential and kinetic 
energy. Various forms of energy. Principle of conservation 
of energy. Power 48-56 



Contents vii 

CHAPTER V 
HEAT AND TEMPERATURE 

Production of heat. General effects. Distinction between Heat 
and Temperature. Measurement of Temperature. Fixed 
points. Construction and calibration of Mercury Ther- 
mometers. Scales of Temperature. Other Thermometers. 
Pyrometer. Self-registering Thermometers. Clinical Ther- 
mometer 57-71 

CHAPTER VI 
EXPANSION OF SOLIDS 

Laws of expansion. Coefficient of Unear expansion and mode of 
determination. Some advantages and disadvantages of the 
expansion of solids. Superficial expansion. Voluminal ex- 
pansion . "^ . . 72-80 

CHAPTER VII 
EXPANSION OF LIQUIDS 

Real and apparent expansion. Modes of determination of co- 
efficients. Peculiar behaviour of water. Temperature af 
maximum density 81-85 

CHAPTER VIII 
EXPANSION OF GASES 

Charles' law and mode of experimental verification. Variation of 
pressure with temperature. Absolute zero and absolute scale 
of temperature 86—94 

CHAPTER IX 
MEASUREMENT OF HEAT 

Units of heat on different systems and their relationship. Specific 
heat. Water equivalent. Measurement of specific heat. 
Calorific value of fuels. Mode of determination. Two values 
for the specific heat of a gas .... 95-106 



viii Contents 

CHAPTER X 
FUSION AND SOLIDIFICATION 
Change of physical state by application or withdrawal of heat. 
Melting and freezing point*'. Heat required to melt a solid. 
Latent heat of fusion. Melting points by cooling. Change of 
volume with change of state. Solution. Freezing mixtures. 
Effect of pressure on the melting point . 107-114 

CHAPTER XI 
VAPORISATION 
Vaporisation. Condensation. Evaporation. Ebullition. Boiling 
point. Effect of pressure on boiling point. Temperature of 
steam at different pressures. Heat necessary for vaporisation. 
Vapour pressure. Boyle's law and vapour pressure. Tem- 
perature and vapour pressure. Latent Heat of vaporisation. 
Sensible Heat and Total Heat. Variation 6f Latent Heat of 
steam with temperature. Pressure Volume and Temperature 
of saturated steam. Hygrometry. The dew-point . 115-132 

CHAPTER XII 

TRANSMISSION OF HEAT 

Conduction. Thermal conducti\'ity. Examples and appUcations 
of conductivity. The safety lamp. Conduction in Uquids. 
Convection in liquids. Hot water circulation. Convection in 
gases. Ventilation and heating by convection. Radiation. 
Reflexion and absorption of heat-energy. Transmission and 
absorption of heat-energy. Radiation from different surfaces 
at equal temperatures. Flame radiation. Dew formation. 

133-148 

CHAPTER Xm 
THERM9-DYNAMICS 
Mechanical equivalent of heat and mode of determination. Funda- 
mental principle of the heat engine. Effect of compression and 
expansion on saturated steam. Isothermal and adiabatic ex- 
pansion. The indicator diagram .... 149-162 

Index 163-165 



CHAPTER I 

MATTER AND ITS GENERAL PROPERTIES 

We all know that there are many different states or 
conditions of matter. Ice, water and steam are three 
different conditions of exactly the same kind of matter ; 
they differ only in having distinctive physical pro- 
perties, being constitutionally or chemically identical. 
Though they have certain distinctive characteristics — 
such for example as the definite shape of a piece of ice 
and the entire lack of shape of water or steam : the 
definite volume of a given weight of water and the 
indefiniteness of the volume of a given weight of steam 
which can be compressed or expanded with ease — they 
have nevertheless certain properties in common with 
all other forms of matter. 

Indeed it is common to define matter as that which 
occupies space or that which has weight. Each of these 
definitions names a property common to all matter. 
It seems rather unnecessary to try to define matter : 
we feel that everyone must know what matter is : and 
the definitions are likely to introduce ideas more diffi- 
cult to appreciate than the thing which is being defined. 
But we can see nevertheless that it may be useful and 
even necessary to have some definite dividing line 
between matter and the various sensations which can 
proceed from it. The colour of a rose is merely a 
sensation : its perfume is the same : but the rose 

p. Y. 1 



2 Matter and its General ProperticH [CH. 

itself is matter. Our distinction is that the rose lias 
weight and occupies space. Colour has no weight, nor 
does it occupy space. 

Again when a piece of coal is burning it is giving 
out Heat. Is that heat matter ? Well, if we ap})ly the 
test of weight to it we find that it is not. A hot object 
weighs neither more nor less than the same object 
cold. If we weigh the coal before it is ignited and 
then while it is burning if we collect all the products 
of the burning — that is to say all the gas and smoke 
and ash — we should find that there was no change in 
weight. This is a well-known experiment — though 
usually done with a piece of candle instead of coal — 
and it is being mentioned now to shew that though this 
burning matter is giving out heat, and also light, yet 
these things are weightless and are therefore outside 
our definition of matter. For if they had weight then 
the mere residue of the ash and the fumes would not 
have had the same weight as the original matter. We 
will return presently to the further question of how we 
shall classify Heat. 

The experiment quoted above is one of many which 
have led us to the firm belief that matter cannot be 
destroyed. We can change its form both physically 
and chemically but we cannot annihilate it. This is 
one of the fundamental law* of physical chemistry and 
one of the greatest importance and usefulness. 

Weight. All forms of matter possess weight. It is 
to be supposed that all readers know what is meant by 
the statement. In books of this kind much space and 
many words are used to convey to the readers' minds 
ideas with which they must already be sufficiently 
famiHar. W^e explain that Force is that which produces 



i] flatter and its General Properties 3 

or tends to produce motion : that it is also that which 
is necessary to destroy motion : that it is also necessary 
if the direction of motion of a body is to be changed. 
We then proceed to define motion as the change of 
position of a body with respect to some other body; 
and we may even devote some space to the explanation 
of what position is. It is extremely probable that 
everyone knows these things, though it is very likely 
that only a few could frame their knowledge in words. 

In the same way weight is the attraction between 
every portion of matter and the earth. This attraction 
tends to draw everything vertically downwards towards 
the earth. It is called the force of gravitation ; but 
nobody has the least idea why the earth attracts things 
or what this mysterious force is. We are so used to it, 
it is so continiially present that we take it quite as a 
matter of course, and never pause to consider that it 
is mysterious and inexplicable. The attraction of a 
needle to a magnet fills us with wonder or awe but the 
attraction of a stone to the earth seems to be inevitable 
and ordinary. 

Weight then is a/orce ; it is a particular force which 
acts only in one direction upon matter, and that 
direction is vertically downwards. Of course the force 
is also tending to pull the earth vertically upwards, 
but the reader will have no difficulty in appreciating 
the fact that no movement of the earth as a whole would 
be detected by us. We can think of every portion of 
matter being attached to the centre of the earth by 
imaginary stretched elastic threads. These threads 
will be in tension and will tend to shorten by pulling 
the object and the earth towards each other. The pull 
will be equal in both directions — but when we think 

1—2 



4 Matter and its (Sineral Properties [CH. 

of the enormous mass of the earth compared with the 
mass of the object we may be considering we can 
readily see that the object will go downwards much 
more than the earth will come up. At the same time 
we can see the tendency and in seeing that we are also 
seeing something of a very important mechanical law 
about the reaction which accompanies every action. 

We say then that matter is that which possesses 
weight. Air and all other gases can be weighed by 
taking a flask, exhausting the air from it by means of 
a vacuum pump, weighing it carefully, and then 
allowing either air or any other gas to enter it when 
it can be weighed again. The increase in weight will 
represent the weight of that flask of the gas at the 
particular pressure under which the flask was filled. 
If a higher pressure were used then, as more gas would 
be forced into the flask, the increase in the weight would 
be correspondingly greater. 

Mass. This leads us naturally to the meaning of 
the word mass. By the mass of a body we mean the 
quantity of matter in it. This is often confused with 
bulk or volume and of course the greater the volume 
of any one particular kind of matter the greater must 
be the quantity of that matter. But on the other 
hand is there the same quantity of stuff in a cubic 
foot of cork as there is in a cubic foot of lead ? Is there 
the same quantity of steam in a given boiler, with the 
water level at a certain point, whatever the steam 
pressure may be? The answers will suggest that we 
cannot compare the masses of different kinds of matter 
by comparing their volumes. 

It is usual to compare masses of matter by weighing 
them. A quantity of cork weighing 1 pound contains 



i] Matter and its General Properties 5 

the same quantity of matter as a piece of lead weighing 
1 pound. At the same time we must be careful to 
remember that weight is simply the force of attraction 
between the matter and the earth and that mass is the 
quantity of stuff in it. When we ask for a pound of 
sugar we want a mass of it which is attracted to the 
earth with a force of 1 lb. weight. 

It may help us to see this distinction if we remember 
— as most of us probably do — that a given object has 
slightly different weights or forces of attraction at 
different parts of the earth, owing to the shape of the 
earth and to the fact that at some places we are nearer 
to its centre than at others. Well, although an object 
may have different weights, yet we know that its mass 
must remain the same. This helps us to see the dis- 
tinction between the two — though it may suggest 
certain difficulties in buying by weight from different 
parts of the earth. As a matter of fact the difference 
is very slight — about two parts in a thousand at the 
outside — and if the substances be weighed with balances 
and "weights" we can see that the "weights" will be 
equally affected and that we should get equal masses 
from different places. But if spring balances be used 
then a pound weight of sugar sent from a place far 
north would be a smaller mass than a pound sent from 
a place near the equator. 

The reader will learn in the mechanics portion of 
his course of study how masses may be compared in 
other ways in which the weights are eliminated. 

Inertia. There is another property, called Inertia, 
which is common to all forms of matter. When we 
say that matter has inertia we mean {a) that it cannot 
start to move without the application of some force. 



() Matter and its General Properties [cH. 

(6) that, if moving, it cannot stop without the appli- 
cation of force, (c) that if moving in any particular 
direction it will continue to move in that direction 
unless some force or forces be applied to it to make 
it change its direction. That is to nay force is necessary 
to overcome inertia. 

Inertia is not a cause and it is not a reason. It is 
the name given to the fact that every object tends to 
remain in whatever condition of motion or rest it may 
be at any given moment. That tendency means that 
it is very difficult to start'anything suddenly/ or to stop 
it suddenly or to change its direction of motion suddenly. 
Experimental verification of these truths may be ob- 
tained by anyone during a short journey in a tramcar. 
If one is standing in a stationary car, scorning the 
friendly aid of "the strap," and the car starts abruptly 
one learns that matter (oneself in this case) tends to 
remain in its previous condition of rest, and that straps 
are really useful adjuncts of the car. 

If the motorman suddenly applies his brakes and 
reduces the speed of the car the passengers shew a 
unanimous tendency to continue their previous speed 
by side-slipping along their seats in the direction of 
the car's motion. If one is walking towards the con- 
ductor's end during this slowing down process one finds 
considerable difficulty in getting there, just as though 
one was climbing a very steep hill against a stiff breeze. 
If one is walking towards the motorman's end and he 
slows down one finds it difficult not to run . In rounding 
a sharp curve — that is'to say changing the direction of 
motion — there is always the tendency to be thrown 
towards the outside of the curve, shewing the tendency 
of moving matter to continue in its original direction. 



i] Matter and its General Properties 7 

There are countless examples of tljis property of 
matter. A hammer head reaches a nail, but it does not 
stop suddenly : the distance the nail is driven in depends 
on the kind of nail and the substance and the weight 
and the speed of the hammer. Chiselling, forging, 
pile-driving, wood-chopping, stone-breaking and cream- 
separating are amongst the many processes which 
depend upon the fact that matter possesses inertia. 
The "banking" of railway tracks at all curves so that 
the outer rail is higher than the inner is necessary to 
assist the train to change its direction of motion. 
When a motor car or a bicycle side-slips it is due to 
the tendency to continue in its original direction and 
if it is taken round the corner too sharply the result 
will be side-slipping or overturning to the outside of 
the curve. Most people fondly believe that if a cart 
is taken too suddenly round a bend it will fall inwards. 
Let the reader ask any half-dozen of his friends. 

Then we know how difficult it is to start moving on 
a very slippery floor, or on ice, and how equally difficult 
it is to stop again. It is not suggested here that one's 
inertia is any greater than it would be on a rough floor : 
the point is that one cannot get a "grip" and thus 
cannot exert such a large force either to start or to 
stop. The skidding of a locomotive when starting 
with a train of great mass is another example of this 
point. 

Theory of Structure of Matter. In order to explain 
and connect the many facts of nature it is necessary 
that we should have some idea of the structure of 
matter. The generally accepted theory is that known 
as the kinetic theory, a theory which assumes that all 
substances are composed of an enormous number of 



H M<itter and Its General Properties [ch. 

very small particles or grains called molecules. Further 
it assumes that these molecules are not generally in 
contact with their neighbours but are in a state of 
continued agitation and vibration ; that collisions 
between them are of frequent occurrence ; that even 
when any two or more are in contact with one another 
there are distinct interspaces between them called 
inter-molecular spaces. 

According to this theory a portion of matter is not 
continuous substance but a conglomeration of small 
particles which attract one another with a force called 
cohesion. 

The motion of the molecules in solid matter is very 
restricted : it is probably rather in the nature of 
vibration or oscillation than migration. In liquids 
the molecules are not supposed to be so close together 
and thus may thread their way through the mass like 
a person in a crowd. In the case of gases the spaces 
between the molecules are assumed to be still greater 
so that the molecules can move about with considerable 
freedom. 

It is also believed that the hotter a body is the 
greater does the movement and vibration of each 
molecule become. That is to say, the energy of move- 
ment of each molecule is increased as the temperature 
is increased. Indeed from this theory it is argued that 
if the temperature could be lowered until there was no 
molecular agitation there could be no heat in the body 
and such a temperature would be the absolute zero of 
temperature. 

Classification of matter. Apart from the properties 
which are common to all kinds of matter there are 
other properties which are peculiar to one form or 



i] Matter and its General Properties 9 

another. Such properties enable us to classify matter 
into different groups. In physics such classification is 
based solely upon physical properties and our groups 
are only three in number namely, solids, liquids and 
gases. Sometimes indeed it is said that there are only 
two groups, solids and fluids, the word fluid including 
liquid and gas. 

Solids are distinguished from fluids — that is from 
liquids and gases — in that each portion of a solid has 
a definite shape of its own. This property is termed 
rigidity. Liquids and gases have no rigidity : a portion 
of a hquid has no definite shape though it has a definite 
volume : a given weight of a gas has no definite shape, 
and its volume depends upon the pressure acting upon 
it. This latter fact helps us to distinguish between 
a liquid and a gas. A liquid is practically incom- 
pressible but a gas is readily compressed. 

A fluid cannot resist a stress unless it is supported 
on all sides. 

Density. Though all forms of matter have weight 
yet if we take the same bulk or volume of different 
forms such as cork, #ater, lead and marble we shall 
find that they have different weights. 

The mass of a unit volume of a substance is called 
the density of that substance. 

If we know the density of a substance we can 
calculate either the mass of any known volume or the 
volume of any known mass. 

On the British system of units density would be 
expressed in pounds per cubic foot. On the metric 
system it is expressed in grammes per cubic centimetre. 

Thus the density of pure water (at 4° C.) is 62-4 
approximately on the British system and 1 on the 



10 Matter and its General Properties [en. 

metric system. I^ead is 705-12 on the British and 11-3 
on the metric. Of course in both systems the lead 
is 11-3 times as heavy as the same bulk of water. 
(See Chapter II.) 

For the determination of the density of a substance 
it is only necessary to be able to weigh a portion of the 
substance and then to find its volume. If the substance 
has a regular form its volume can be calculated. If it 
be irregular it can be immersed in water and the volume 
of displaced water can then be measured. There are 
many simple methods of obtaining and measuring the 
displaced water. There is the obvious method of 
placing a label to mark the level of water in a vessel 
and then placing the substance in the vessel. The 
water above the label mark is now sucked out by means 
of a pipette until the level is restored. The volume of 
the water removed must of course be that of the sub- 
stance and it can be measured in a graduated vessel. 











tA^ 


n 




=^w 




— , , 


'" 






-1- 




==.=^— 




.-_— _ 


~-~ 


_-_— . 


— - 


(a) 






a 


W 


^ 



Fig. 1 
Fig. 1 illustrates special forms of vessels designed to 
facilitate the collection and measurement of the dis- 
placed water. In (a) the vessel i» filled up with water 
and allowed to adjust its level through the side spout. 



I] 



Matter and its General Properties 



11 



A dry measuring vessel is then placed under the spout 
and the substance whose volume is required is carefully 
lowered into the water. The other form (6) is called a 
volumenometer and it utilises a small siphon with the 
ends drawn out to fine points. This prevents the 
siphon from emptying itself. Its use is obvious. 

More refined methods depend upon weighing instead 
of measuring the displaced water (as with the specific 
gravity bottle) and upon the principle of Archimedes. 
The reader will be able to appreciate these after reading 
Chapter II. 

Densities of some common substances. 



Substance 


Density in lbs. per 
cubic foot (approx.) 


Density in grammes 
per cubic centimetre * 


Platinum 


1344 




21-522 


Gold 


1200 




19-245 


Lead 


712 




11-^ 


Silver 


655 




10-5 


Copper 


549-556 




8-8 -8-9 


Iron (wrought) 


466-487 




7-47-7-8 


Iron (cast) 


378-468 




6-9 -7-5 


Steel 


435-493 




7-73-7-9 


Brass 


505-527 




8-1 -8-45 


Oak 


43-2-61-9 




0-69 to 0-99 


Water 


62-4 




1 



* Since the mass of 1 cubic centimetre of water is 1 gramme it 
follows that the density of a substance in grammes per cubic centi- 
metre is numerically equal to its relative density or specific gravity 
with respect to water (see page 25). 

Properties of Solids. Different solids differ from 
one another not only in chemical composition but 
also in physical characteristics. Such properties of 
solids as porosity, hai-dness, malleability, ductility, 



12 Matter and its (itcueral Properties [CH. 

plasticity and elasticity are shewn in various degrees 
in different substances. The nature of the properties 
denoted by the words above is generally understood — 
with the exception, perhaps, of that property called 
elasticity. 

Elasticity. If the reader were asked to state what 
was the most highly elastic substance we know of he 
would probably give india-rubber without much 
hesitation. Now elasticity is measured by the mag- 
nitude of the force which is necessary to produce a 
given change in the shape of a substance : and for such 
comparison it is necessary that all the substances used 
be of the same original dimensions. If we were going to 
compare elasticity so far as stretching is concerned then 
we would use wires of equal length and equal diameter 
and we would find out what weights we should have to 
load on the bottom end in order to stretch them by 
the same amount. That substance which required the 
largest weight would have the gTesii^st elasticity. 

Of course it would be necessary to see that when 
the weiglits were removed again the wires returned to 
their original lengths. If they did not — that is if they 
were permanently stretched — then we must have loaded 
them beyond their limits of elasticity. Some substances 
can be temporarily stretched to a great extent and such 
are said to have wide limits of elasticity. Thus india- 
rubber has not a very high degree of elasticity — that is 
to say it is easily stretched — but it has very wide limits 
of elasticity. Steel has a high degree of elasticity but 
very narrow limits. 

The same statements apply to compression, to 
bending and to twisting. 

Stress and Strain. When the form or shape of a 



i] Matter and its General Properties 13 

body has been altered by the apphcation of a force the 
alteration is called a strain. If a piece of india-rubber 
is stretched (from 6 inches to 7 inches) the change is 
called a strain. The same term would be used if it 
was compressed to 5 inches, or twisted round through 
any number of degrees, or bent to form an arc. The 
force producing the strain is called a stress. In strict 
usage the word strain is used to denote the change 
produced per unit of length. In a case of stretching 
for example the extension per unit length of the sub- 
stance is the strain. If a wire be 60 inches long and it 
is extended by 1-5 inches then the strain is 

Similarly stress is used to denote the force per unit 
area of cross section. Thus if the wire quoted above 
has a diameter of 0-05 inch and the stretching force 
was 10 lbs. weight the stress would be 10 -^ area of 
cross section of the wire 

= 5095 lbs. per sq. inch. 



3-14 X (-025)2 

Hooke's Law. From a series of experiments Hooke 
deduced the law that within the limits of elasticity the 
extension of a substance is directly proportional to the 
stretching force. 

It may also be expressed that strain is directly 

proportional to stress. The ratio of - — ^ for any 

stram 

substance is called Young's modulus for that substance. 

This is an important quantity in that section of 

engineering work dealing with the strength of materials. 

Hooke's law also applies to twisting. If a wire be 



^ 



11 Mutter and its (Icneral Projtcrticn [CH. i 

rigidly fixed at one end and a twisting force applied 
to the other the angle of twist or torsion will be directly 
proportional to the twisting force. It also applies to 
bending. If a beam be laid horis^ontally with each end 
resting on a support and it be loaded with weights at 
the centre it will bend. The extent to which the centre 
of the beam is depressed vertically below its original 
position is called the deflexion of the beam. The 
deflexion is directly proportional to the bending force. 
It will be obvious that in all these cases — stretching, 
compressing, twisting or bending — the amount of change 
produced will depend not only upon the force applied 
but also upon the original length of the substance, 
upon its cross sectional area and upon the particular 
material used. 



EXAMPLES 
(See table above for densities) 

1. What is the weight of a cyUnder of copper (a) in lbs., (b) in 
grammes, if it is 6" high and 2" diameter and an inch is approxi- 
mately 2"54 cms. ? 

2. What would be the volume of a piece of gold which would 
have the same weight as 1 cubic foot of silver? 

3. If sheet lead costs £27 per ton, what will be the cost of a roll 
32 feet long, 3 feet wide and J" thick ? 

4. What is the density of the sphere which weighs 4 lbs. and has 
a diameter of 3 inches ? 

5. In what proportions should two liquids A and B be mixed so 
that the mixture shall have a density of 1-2, the density of A being 
0-8, that of 5 1-6. 

6. A wire of diameter 0-035 inch and 6 feet long is found to 
become longer by 0-25 inch when an extra weight of 14 lbs. is hung 
on to it. What is the stress and the strain and Young's modulus 
of elasticity ? 



CHAPTER II 

PROPERTIES OF LIQUIDS 

As we have seen liquids have no rigidity and there- 
fore have no definite shape. A given mass of Hquid 
will always assume the shape of the portion of a vessel 
which it occupies. Moreover a liquid is practically 
incompressible and in this respect it differs from those 
fluids which we call gases. 

If we place some water in a vessel we know that the 
weight of the water must be acting on the base of that 
vessel. But we also know that the water does not 




/ 

Fig. 2 

merely exert a downward pressure. If holes are 
pierced in the vessel at positions A and B — as shewn 
in Fig. 2 — we find that the water streams out through 



16 Properties of Llqukh [CH. 

thoni aiul that it comes out from B with a greater 
velocity than from A. This indicates firstly that the 
wat«r must be exerting horizontal pressure on the sides 
of the vessel : and secondly that the pressure at B is 
greater than that at A . 

Pressure at different depths. It does not require 
any deep reasoning to realise that as we pour more water 
into a given vessel the downward pressure upon its base 
must increase and that the greater the depth of liquid 
the greater will be this downward pressure. 

If we did not conduct any investigations we might 
be led to conclude that if we place a piece of cork 
sufficiently- far below the surface of water it would 
sink — forced downwards by the enormous pressure 
which would be exerted at a great depth. But our 
experiences — that is to say our investigations, whether 
they were deliberate or casual — tell us that this is not 
true. Our experiences tell us that when we put our 
hands under water we are not conscious of an extra 
weight upon them : that when w^e put them at greater 
depths we are not conscious of any greater weight than 
when they were near the surface : that, in fact, we are 
conscious that our hands seem to be altogether lighter 
^when held under the water and that different depths 
do not appear to make any difference at all upon the 
sensation of lightness. Our experiences teach us that 
when we dive into water, instead of being weighed down 
by the weight of water above us we are in fact buoyed 
up and we ultimately come — at any rate those of us 
who are reading must" always have come — to the 
surface. 

Well then, our experiences tell us that somehow or 
other there appears to be an upward pressure in a 



11] 



Properties of Liquids 



17 



liquid. One simple experiment to illustrate this is to 
take a piece of glass tube open at both ends ; close one 
end by placing a finger over it ; place the tube vertically 
in a tall jar of water with the open end downwards. 
A little water will be forced up the tube — compressing 
the air inside. As it is lowered further more water 
will be forced up the tube and the air inside will 
be more compressed. There must be some upward 
pressure to do this. Then remove the finger from the 
top : water will rush up the tube and may even be 
forced out through the top in the first rush. Ultimately 
it will settle down so that the water level inside the 
tube is the same as that outside — suggesting therefore 
that this upward pressure at the bottom of the tube is 
exactly equal to the downward pressure there. 



ILL 




(a) (h) 

Fig. 3 



A more convincing experiment is illustrated by 
Fig. 3. A fairly wide glass tube open at both ends 
has one end carefully ground flat and a circular disc 



1 }{ Properties of Liquids [CH. 

of aluminium is placed against this end. It is held 
tightly on by means of a piece of string passing up 
through the middle of the tube. It is then immersed 
in a tall jar of water — the disc-covered end downwards 
— and it is found that the string is no longer necessary 
to hold on the disc. The upward pressure on the bottom 
of the disc is sufficient to hold it on. 

If now some water be poured carefully into the tube 
it will be found that the disc will not fall off until the 
level of the water inside the tube is very nearly equal 
to that in the jar. If the disc were made of a substance 
of the same density as water it would hold on until the 
level was quite up to that in the jar. This experi- 
ment shews very clearly that the upward pressure on 
the bottom of the disc was equal to the downward 
pressure which would have been exerted on it if it had 
been immersed at the same depth — for when the tube 
was filled with water to the same depth as in the jar 
we found that the downward pressure of this depth 
just counter-balanced the upward pressure — making 
due allowances for the weight of the disc. 

In addition to this it can be shewn by a similar 
experiment that the liquid exerts a horizontal pres- 
sure and that the horizontal pressure is also equal 
to the downward and the upward pressures : that in 
fact at a given point in a liquid there is a pressure in 
every direction and that it is equal in every direction. 

Pressure at a point. It is necessary that we should 
have some clear idea of what is meant by the pressure 
at a given point in a Hjg[uid. If we consider the base 
of a vessel, for example, it is clear that the weight of 
water on the base depends not only upon the height of 
water above it but also on the area of the base. And 



ii] Prope7'ties of Liquids 19 

since different vessels may have different base areas it 
will be necessary for us in speaking of pressure at any 
point to speak of the pressure per unit area at that point. 
We may speak of the pressure per square foot or per 
square inch or per square centimetre, and the total 
pressure on any base will be the pressure per square 
unit multiplied by the number of square units contained 
in the base. 

Let us suppose that we have a rectangular vessel 
having a base area of 1 square foot and that it is filled 
with water to a height of 1 foot. There is therefore 
1 cubic foot of water weighing 1000 ozs. resting on a 
square foot of base. Since there are 144 square inches 
in the square foot the pressure per square inch must 
be ^fff- = 6' 94 ozs. (approx.). We can say therefore 
that the pressure at any point on that base area is 
6-94 ozs. per square inch. And further whatever the 
shape or size of the base may be if the water above it 
is 1 foot high the pressure per square inch on the base 
will be 6-94 ozs. 

Pressure at a point depends only on vertical depth 
and density. This last statement needs substantiation. 
An experiment may be performed with a special U-tube 
— shewn in Fig. 4 {a) — which is provided with a screw 
collar at sc on which different shaped and sized limbs 
may be screwed. Different limbs are shewn in (6), (c) 
and (d). It is found that if water be poured into the 
U-tube it will always rise to the same level on each side 
whatever the shape or size of the limbs may be. Since 
it follows that when the liquid comes to rest the pressure 
exerted by the water in the two limbs must be equal, 
therefore the pressure produced at a given point is 
not dependent on the size or shape or quantity of water 

2—2 



i}(» 



Properties of Li</ui{ls 



[ni. 



in I Ik- vrs.st'l hul only upon the verfical depth (see {(J)) 
of the point beh)\v the surface and u])on tlie density 
of the liquid. Aiid it follows that if we have a number 
of vessels having equal bases but having different shapes 
and volumes the pressure on the bases will be equal 
if they contain only the same vertical depth of the same 
liquid. The explanation of this fact may not be very 
obvious to the reader, but if he has any knowledge of 
elementary mechanics he will know that there will be 
"reaction^' at every point of the walls of the vessel. 
If these walls be quite vertical as in (a), then the re- 
actions will be horizontal and will balance one another, 




but in the case of inclined walls the reactions, which 
will be at right angles to the wall, will therefore add to 
the mere water weight on the base in (c) whilst they will 
counterbalance the extra water weight in the case (6). 

Therefore in speaking of the pressure at a point in 
a liquid we have only to think of the vertical depth of 
that point and the density of the liquid. At a point 
1 foot below the supface of water the pressure is 
6*94 ozs. per sq. inch in every direction: at a point 
L feet below it will be Z- x 6-94 ozs. per sq. inch. If 
the liquid be D times as heavy as water bulk for bulk 



II J Properties of Liquids 21 

then the pressure at any point L feet below the surface 
will be Z) X iy X 6-94 ozs. per square inch. 

On the metric system it is even simpler because 
1 cubic centimetre of water weighs 1 gramme. There- 
fore the pressure per square centimetre at any point 
below the surface will be D x L grammes, where 
L = depth of the point in centimetres and D = the 
number of times that the liquid is heavier than water. 
On the metric system this D will be the density in 
grammes per cubic centimetre. 

Pressure on the sides of a vessel. Since at any given 
point the pressure is equal in all directions it follows 
that the pressure on the sides or walls of a vessel at any 
point is determined in exactly the same way as it would 
be for a point on a horizontal surface at the same depth. 
But of course it will be seen that the pressure on the 
walls increases gradually with the depth and that the 
total pressure on the side can only be found by deter- 
mining the pressure on each unit area and adding them 
all together. 

If the vessel has rectangular sides then we can get 
the total pressure very simply by finding the pressure 
at a point half-way down from the surface of the liquid 
to the bottom and multiplying this by the total number 
of square inches (or cms., according to units used) which 
are under the water. 

For example, in the case of the tank shewn in Fig. 5, 
which is a cubical tank of 6 foot side filled to a depth 
of 5 feet with water, the average pressure on one 
side will be the pressure at a depth of 2-5 feet below 
the surface. This is 2-5 x 6-94 ozs. per square inch 
which is 17-35 ozs. per square inch. There are 
5 X 6 = 30 square feet below the water and since 



22 



Properties of Liquids 



[CH. 



there are 144 square inches to the square foot it follows 
that the total pressure on the side will be 

144 X 30 X 17-35 ozs. = 74952 ozs. = 40845 lbs. 

The total pressure on the base will be 

(5 X 6-94) X 6 X 6 X 144= 179,885 ozs. 




Fig. 6 

In the same way the total pressure on a lock gate 
would be calculated though in that case there would 
be some water on both sides of the gate at the lower 
portion. Further, though we get the total pressure in 
this way it is not of much use in designing a lock gate 
since it is necessary to design it to stand a much greater 
pressure at the bottom than at the top of the gate. 
The same applies to water tanks of any appreciable 
depth — such as a ship's ballast tanks which are strength- 
ened towards the bottom. 

Buoyancy. If we imagine that a substance is placed 
under water, as shewn in Fig. 6, we can see that the 
water will exert upon it pressure in every direction. 
But since the substance occupies space it is not a point 
and therefore the pressure in every direction will not 
be equal. On the upper surface A the downward 
pressure will be due to the vertical depth 8 A ; whilst 
on the lower surface the upward pressure will be due 



n] 



Properties of Liquids 



23 



to the vertical depth SB, and the side pressures will 
balance one another. Thus we find that the upward 
pressure is greater than the downward pressure. 

Whether it will sink or float depends now upon the 
weight of the substance. If this weight is greater than 
the difference of . the upward and downward water 
pressures then the substance will sink : but if its weight 
is less than the difference between the upward and 
downward pressures it will rise to the surface and float. 





D 








o 


' '/ " 


U 





*? — 












\' 


-A— 
B"- 


ifference 
UP 


\ 







'm 











/ 


^Bf 










- ~ - 


Is' 



Fig. 6 

This will be true whatever the liquid may be, but of 
course the difference between the upward and down- 
ward pressures will be different if we use liquids of 
different density, and thus substances which would 
sink in one liquid might float in another. 

Floating Bodies. When a body floats so that the 
top of it is above the surface then there is no down- 
ward liquid pressure upon it at all. Therefore it will 
float to such a depth that the upward liquid pressure 
upon it is just equal to its own weight. If, therefore. 



24 



Properties of I/iqukls 



[CH. 



we take some similarly shaped pieces of different sub- 
stances which will float, and put them on water the 
denser substances will sink deeper than the lighter, and 
the volumes of the submerged portions will be in pro- 
portion to the densities of the several substances. 

Archimedes' experiment. Figure 7 (a) represents a 
spring balance on the hook of which is suspended a 
hollow cyhnder or bucket. Under tliis is also suspended 
a soUd cylinder having the same external dimensions 




as the internal dimensions of the bucket and having 
therefore the same volume. It does not matter what 
this solid cyhnder is made of provided that it will sink 
in water. The reading of J;he spring balance is shewn. 
The solid cyhnder is then immersed in water — (6) — 
and of course the arrangement weighs less than before 
as shewn by the balance. The bucket is then gradually 



II ] - Properties of Liquids 25 

filled with water. When it is quite full (c) the balance is 
found to shew the same weight as it did originally. 

This is known as Archimedes' experiment and it 
shews that the cylinder weighed less in water than in 
air by the weight of its own volume of water. 

If the experiment be repeated using some other 
liquid it will be found that when the bucket is filled 
with that liquid the original weight will be registered 
on the balance. 

Thus it is said that when a body is immersed in any 
liquid its net weight is less than its weight in air by 
the weight of the liquid which it displaces. 

This is equivalent to saying that the difference 
between the downward and the upward pressures on 
an immersed body is equal to the weight of the liquid 
which the body displaces. When the body is wholly 
immersed the volume of displaced liquid is equal to 
the volume of the body. 

In speaking of a ship's weight it is customary to 
state that its "displacement" is so many tons — a state- 
ment which means that the volume of the water which 
is displaced by the vessel when floating to its "no cargo" 
line would weigh that number of tons. This, of course, 
means that the ship and its fittings also have that weight. 

Determination of Specific Gravity or Relative Density. 
The specific gravity of a substance — which is the ratio 
of the weight of any given volume of the substance to the 
weight of the same volume of water — may be determined 
in many ways. The direct methods consist simply in 
weighing the substance and then weighing an equal bulk 
of water. It is not always simple to find the volume of 
the substance — though this can always be done "by 
displacement," that is by immersing the substance in a 



20 Properties of Liquida [ch. 

graduated vessel ot water and noting the level of the 
water before and after the substance is immersed. The 
difference in the two volumes \v\\\ be the volume of the 
substance and such a volume of water can then be 
weighed. If the substance is one which dissolves in 
watesr — like copper sulphate crystals for example — then 
it can be placed in the graduated vessel containing some 
liquid in which it does not dissolve — such as alcohol in 
the case chosen. The difference in volume will give the 
volume of the crystals and an equal volume of water 
can then be weighed out. 

The specific gravity or relative density as it is often 
called is the ratio 

Weight of a given volume of the substance 
Weight of an equal volume of water 

The reader will doubtless have many opportunities 
of making this kind of measurement and it should be 
unnecessary to give any details in these pages. 

It should be pointed out however that these direct 
methods may not give very accurate results owing to 
the errors likely to arise in the volume measurements — 
especially when such volumes are small. Thus it is 
more usual to determine relative densities by utilising 
the principle of Archimedes. If a substance be weighed 
firstly in air and secondly suspended in a vessel of 
water — as shewn in Fig. 8 — the difference between 
these weights represents the weight of the same volume 
of water as the substance. Thus the specific gravity 
or relative density can be determined at once : and it 
will be recognised that the weighing can be done with 
great accuracy and that the w^hole measurement will 
take less time than a "direct" method. 



ii] Projyerties of Liquids 27 

If the substance is one which floats in water, then, 
after weighing it in air, a "sinker," of lead say, can be 
attached to it and a second weighing done with the 
sinker under water and the substance in air : then a 
third weighing with both sinker and substance under 
water. The difference between the second and third 
weighings will be the weight of a volume of water of 
the same bulk as the substance. 




Fig. 8 

The relative density of a Uquid is determined by 
weighing a solid in air, then in water and thirdly in the 
liquid. The difference between the first and second 
weighings is the weight of a volume of water equal to 
the volume of the substance ; and the difference be- 
tween the first and third weighings is the weight of the 
same volume of the liquid. 

The relative density of a sohd soluble in water is 
found by weighing in air and then in a liquid in which 
it is not soluble. The specific gravity or relative 
density of this liquid must be known or found. The 
difference between the weighings is the weight of a 
volume of liquid equal to the volume of the solid. 
The weight of the same volume of water may then be 



28 



Properties of Liquids 



[CH. 



calculated since the relative density of the li((uid is 
known. From this the relative density of the soluble 
substance is found. 

In the case of powdered substances like chalk or 
sand the "specific gravity bottle" is used. This is a 
bottle having a ground glass stopper through which 
a fine hole is bored. The bottle is filled with water. 
When the stopper is put in the excess is forced out 
through the hole and thus the bottle may be com- 
pletely filled. It is then weighed. The powdered 
substance is weighed and then put into the bottle. It 
displaces its own bulk of water. The bottle is weighed 
again. The specific gravity of the powder can readily 
be obtained from these weighings. 

The Hydrometer. The hydrometer is a simple 
device for measuring directly the specific gravity of 
a liquid. It is made of glass and usually in the form 
shcAvn in Fig. 9. It floats in an upright position and 






the thin neck has a scale on it which indicates the 
specific gravity of the fiquid in which it is floating. It 
will always float to such a depth that the weight of the 



ii] Properties of Liquids 29 

liquid which it displaces will be equal to its own weight. 
Thus in a lighter liquid it will sink further than in a 
heavier liquid. In the figure (a) represents the position 
in water, (6) in alcohol, and (c) in battery strength 
sulphuric acid. It is usual to have a set of hydrometers 
to cover a wide range of specific gravities. 

Hydrometers are used in many different branches of 
commerce and the "scales" are usually designed to 
meet the particular cases. They are not usually direct 
reading in terms of specific gravity but in terms which 
meet the needs of the persons who use them. The 
sailor's hydrometer for example simply indicates the 
number of ounces above 1000 which will be the weight- 
of 1 cubic foot of sea water. If the hydrometer sinks 
to 25 it means that 1 cubic foot of that water will weigh 
1025 ounces. The brewer's hydrometer has a scale 
which is used in conjunction with a specially compiled 
set of tables. And even some of the ordinary hydro- 
meters have scales which require the use of some 
constant or some empirical formula in order to obtain 
the specific gravity of the liquid in which they are 
immersed. Of such kinds perhaps Beaume's and 
Twaddell's are best known. 

Pumps. The action of the simple pumps should not 
require any detailed explanation after the foregoing 
discussions. The diagrams shewn should be nearly 
sufficient. 

Fig. 10 illustrates a simple lift pump. In the pump 
a piston B can be moved up and down in a cylinder. 
In the base of the cylinder is a valve — shewn in the 
diagram as a flap — which will open if the pressure below 
is greater than that above and shut if it is less. In the 
piston 5 is a similar valve which opens and shuts under 



;}() 



Properties of Liiiuuh 



[CH. 



similar conditions. The cylinder base is connected to 
the wat«r through a fall pipe. 

When the piston is raised the effect is to expand 
the air between A and B and so lower the pressure 
there. This shuts the valve in B and the water from 
the well is forced up the pipe P by the excess of the 
atmospheric pressure over the cylinder pressure. Thus 
the cyhnder becomes filled. The piston is then pushed 
down. This sliuts the valve A and opens B so that 





Fig. 10 



Fig. 11 



the water is forced to the top of the piston. The piston 
is raised again and with it, of course, the water above it 
which comes out of the outlet O. At the same time the 
previous action is going on below the piston. 

Fig. 1 1 illustrates a force pump in which the water is 
forced out of the outlet under pressure. This is the tj^pe 
of pump used for fire-engine work, garden pumps, etc. 



ii] Properties of Liquids 3 1 

The piston B has no valve. When it is Hfted valve 
A is opened and C is closed. Water enters the pump 
cylinder. On the downward stroke A is closed and the 
water is forced through C into the chamber F. As the 
water rises in this chamber above the lower level of the 
outlet pipe it will compress the air until ultimately the 
pressure will be sufficient to force the water through 
in a more or less continuous stream. 

It should be remembered that since pressure is dis- 
tributed equally in every direction in a liquid a force 
pump having a small cylinder can nevertheless be used 
to produce a total enormous pressure. For example if 
a steam boiler is to be tested for pressure, the test 
employed is a "water test" in which the boiler is filled 
completely with water. A hand pump capable of 
generating 300 lbs. per sq. inch pressure is then coupled 
to the boiler and the pump is operated. This pressure 
is communicated to the boiler and the water will exert 
an outward pressure of 300 lbs. per sq. inch on every 
square inch of the boiler. Any leak will shew itself: 
and in the event of the boiler breaking down no 
hurt is likely to be caused to those conducting the 
test. 

It is in the same way that the hydraulic press, 
the hydraulic ram and hydraulic jack are operated. 

The reader possibly knows that the feed water 
pump of a steam boiler pumps water into the boiler 
against the steam pressure. If the steam pressure is 
150 lbs. per sq. inch then the feed water must be 
pumped in at a greater pressure. This can be done 
with quite small pumps, for the pressure which can 
be generated and distributed does not depend upon 
the capacity of the cylinder. 



32 Properties of Lltjuids [cji. 

Capillarity. If we examine the surface of water in 
a glass vessel we notice that all round the edge next 
to the glass the water is curved upwards. If we dip 
a piece of clean glass tube into the water we notice 
the same curving against the wall of the tube both 
inside and outside. If the tube has a fine bore we also 
notice — perhaps to our surprise — that the water rises 
inside this tube to a greater height than the water 
outside. If we use tubes of different internal diameters 
we shall find that the water rises to a greater height in 
the fine bored tubes than in the large bores. Because 
of this fact — that the phenomenon is shewn best with 
tubes as fine as hairs — it is called capillarity. 

If we use mercury instead of water we observe a 
reversed formation of the surface, and the mercury in 
the tube will be depressed below the surface of that 
outside. Again as We use finer and finer tubes 
the depression wiU become correspondingly greater. 
Fig. 12 illustrates the surface formations in the two 
cases. Fig. 13 shews what happens when these liquids 
are poured into U -tubes having a thick and a thin 
limb — the thin limb being a capillary tube^. 

Mercury does not "wet" glass and if any hquid be 
placed in a vessel of material which it does not wet its 
surface would be formed similarly to the mercury in 
glass. If a pencil of paraffin wax be dipped into water 
it will be found that the edge of the water against the 
wax is turned down. If a piece of clean zinc be dipped 
into mercury the edge_of the mercury near to the zinc 
will be curved upwards — just like water against glass. 

There are many illustrations of capillary action. 

' The size of the capillary tube is exaggerated for the purpose of the 
diagram. 



ii] Properties of Liquids 33 

There is the feeding of a lamp -flame with oil : the 
wetting of a whole towel when one end is left in 




Water Mercury 

Fig. 12 



water : the absorption of ink by blotting paper : the 
absorption of water by wood and the consequent 
swelling of the wood. 




Water Mercury 

Fig. 13 

Surface Tension. The surface of any liquid acts 
more or less like a stretched membrane. A needle can 
be floated on water if it first be rested on a cigarette 

P.Y. 3 



34 Properties of Liquids [CH. 

paper which N\ill ultimately sink, leaving the needle 
resting in a little depression on the surface — but 
actually not making any contact with the water. 
Many insects walk on the surface of water. A camel- 
hair brush under water has its hairs projecting in all 
directions, but when it is withdrawn all the hairs are 
drawn together as though they were in a fine india- 
rubber sheath. The formation of a drop of water 
shews the same thing — how the water seems to be 
held in a flexible skin. This skin is under tension and 
endeavouring to contract. Hence we find rain drops 
are spherical : drops of water run off a duck's back 
like hailstones off an umbrella: lead shot is made by 
"raining" molten lead from the top of a tall tower into 
a water vat at the bottom. 

Different liquids have different surface tensions which 
can be determined or compared either by observing 
the heights to which they rise in capillary tubes of 
equal diameter, allowances being made for the different 
densities of the liquids, or by a direct weighing method. 
This consists in suspending a thin plate of glass vertically 
from one arm of a balance and adjusting the balance. 
A vessel of water is then placed beneath the glass and 
gradually raised until the water just touches the lower 
edge — when the surface tension pulls down the balance. 
Weights are placed on the other pan until the glass is 
brought up again so that its lower edge just touches the 
water or whatever Uquid is being tested. 

Diffusion. If we place some coloured salt solution 
at the bottom of a vessel of water — and we can do it 
very easily by means of a pipette — we shall find quite 
a sharp dividing line between the heavier salt solution 
and the lighter water. But if we leave them undisturbed 



ii] Properties of Liquids 35 

we shall find that very gradually some of the heavy 
liquid will have come to the top and some of the 
lighter water will have gone to the bottom and that 
eventually the Kquids will become mixed. This 
gradual intermingling — done apparently against the 
laws of gravity — is called dijfusion. 

Diffusion takes place more readily between gases 
than between liquids, and every gas can diffuse into 
every other gas : this cannot be said of Uquids. 

In the case of gases it is impossible to keep them 
separated one upon another — like oil upon water. This 
is fortunate for us, because if gases arranged themselves 
layer upon layer with the heaviest at the bottom and 
the lightest at the top our atmosphere would consist of 
successive layers of carbonic acid gas, oxygen, nitrogen, 
water vapour and ammonia. Animal life would be 
impossible. As it is however gases diffuse so readily 
that they are all intimately mixed — and even in the 
immediate neighbourhood of an oxygen manufactory 
which takes its oxygen from the atmosphere there is 
no sign of a scarcity of oxygen; this is due to the 
rapid diffusion which takes place. 

Viscosity. Some liquids are more viscous than 
others. It is easier to swallow water than castor oil, 
not so much because of any special or objectionable 
flavour but because of the slow dehberate manner in 
which the oil trickles down the gullet. The oil is said 
to be viscous ; and treacle, honey and thick oils have 
this property of viscosity to a great degree. It may 
be said to be due to frictional forces between adjacent 
layers. 

Liquids which flow readily — like water or alcohol or 
petrol — are called mobile liquids. 

3—2 



30 Proper ticK of Liquids [oh. ii 

The viscosity of a liquid is usually lowered by an 
increase in temperature : so much so that when super- 
heated steam is used in a steam engine the question 
of lubrication becomes more difficult. 

Viscosity of different liquids may be compared by 
finding the rate at which they may be discharged 
through equal tubes under equal pressures. 

EXAMPLES 

1. What is the total pressure on the base of a rectangular tank 
full of water, the internal dimensions being 6' deep, 8' long and 
4' wide? Also find the total pressure and the average pressure 
in lbs. per square inch on each side of the tank. 

2. A diver is at a mean depth of 30 feet below the surface of 
the sea. What must be the least pressure of the air supplied to him 
in lbs. per square inch so that he does not feel the pressure of the 
water upon his diving suit? The relative density of sea water is 
1025. 

3. A substance weighs 256 grammes in air and its relative 
density or specific gravity is 8-4. What would it weigh if immersed 
in water ? What would it weigh in a liquid of specific gravity 1-25 ? 

4. A substance weighs 7-6 ozs. in air and 6-95 ozs. in water. 
What is its specific gravity ? What is its volume in cubic inches ? 

5. A substance weighs 32-6 grammes in air and 26 grammes in 
a liquid whose specific gravity is 0-84. What is the specific gravity 
of the substance and what is its volume ? 

6. Four lbs. of cork of specific gravity 0-18 are securely fastened 
to 15 lbs. of lead of specific gravity 11-4. Will they sink or float 
when immersed in water ? 



CHAPTER III 

PROPERTIES OF GASES 

As we have already seen a gas is a portion of matter 
which has no rigidity and which is readily compressed. 
It has neither definite shape nor definite volume, for 
a given mass of it may be made to occupy various 
volumes at will by varying the pressure to which it is 
subjected. 

We have already seen that gases have weight and 
it is the weight of the air surrounding the earth which 
causes the pressure commonly called the atmospheric 
pressure. It is that same weight which causes the air 
to hang round the earth instead of distributing itself 
through the vast vacuous spaces which nature is said 
to abhor. As the reader probably knows, the belt of 
air about the earth does not extend to the moon — as 
was supposed to be the case in the early part of the 
seventeenth century— but is only a few miles deep. 
,The total weight of this belt of air on the earth's surface 
is enormous, and if the reader would like to know 
exactly how much it is he can calculate it from the fact 
that the pressure of the air is, on the average, 14* 7 lbs. 
to the square inch. He has therefore only to calculate 
the number of square inches on the surface of the earth 
and multiply this by 14-7 and he will have the total 
weight of the air in pounds. 

When a gas is enclosed in any space it exerts pressure 



iMi Properties of GascH [c'H. 

ill every direction. Moreover it exerts pressure equally 
in every direction. One of the simplest illustrations 
which can be offered of the truth of this stat-ement is 
that of the soap bubble. It matters not how we blow 
into the bubble, or what manner of pipe we use, the 
bubble is beautifully spherical. If the pressure of the 
gas both inside and outside the soap film were not equal 
in every direction then clearly the bubble' would not be 
spherical in form. 

If we construct a cylinder — as shewn diagiammati- 
cally in Fig. 14 — and provide it" with a number of 
pressure gauges, then when a piston is forced into the 




Fig. 14 

cylinder it will be seen that all the gauges indicate the 
same pressure at a given moment. On the other hand 
we know that if the cyhnder were filled with a solid — 
like steel for example — and pressure was applied to the 
piston there would be no pressure exerted on the sides 
of the cylinder: it would only be exerted on the end. 
If we filled the cylinder with water we should find that 
it exerted pressure in all directions equally. 

The fact that a gas exerts pressure equally in all 
directions accounts for our unconsciousness of the 
existence of atmospheric pressure. It would be im- 
possible for us to hold our arms out at length if the 



in] Properties of Gases 39 

atmospheric pressure of 14-7 lbs. per square inch were 
only acting downwards. The air would indeed be a 
burden to us. 

A simple experiment illustrating the magnitude of 
this pressure may be made by exhausting the air from 
the inside of a tin can. The surest and simplest way 
of doing this is to put a little water inside the can and 
boil it. When steam is coming freely from the opening 
remove the flame, cork up the can, and plunge it 
into a vessel of cold water. The can will immediately 
collapse. The explanation is that the air was driven 
out of the can by the steam, and that the cold water 
condensed the steam thus reducing the pressure inside 
the can to practically nothing. The pressure of the 
air outside acting in every direction upon the can is 
sufficient to crush it. It is probably known to many 
readers how in certain engineering operations — tunnel- 
ling under a river for example— the workmen work in 
a high pressure space in a special "shield." The 
pressure of the air in this shield is considerably higher 
than that of the atmosphere outside and the men have 
to pass through a sort of air lock in which the pressure 
is gradually raised to that inside the shield or gradually 
lowered to that of the atmosphere according to the 
direction in which the men are going. The change of 
pressure is decidedly unpleasant unless it is done very 
gradually so that the pressure inside the body may never 
differ sensibly from that outside. 

It is well known that if a piece of paper be placed 
over the top of a tumbler filled with water the whole 
may be held in an inverted position and the water will 
not force the paper away. In this case the downward 
pressure on the paper is represented by the weight of 



4() 



Properties of Gases 



[CH. 



the water iji the tumbler and the upward pressure is 
the atmospheric pressure of 14-7 lbs. to the square inch. 
There is no downward atmospheric pressure on the 
paper because there is no air in the tumbler. Unless 
the tumbler be 34 feet or more in length the upward 
atmospheric pressure will be greater than the downward 
pressure of the water in th(> tuniV)ler : hoiu-(^ it will not 
run out. 

If a glass tube of about 3G inches length be arranged 
as shewn in Fig. 15 so that one end dips under some 
mercury and the other end is connected to a vacuum 



To Vacuum pump 




Pig. 15 

pump the mercury will rise in the tube as the vacuum 
improves until finally it reaches about 30 inches above 
the mercury in the lower vessel. Beyond this it will 
not rise however good the vacuum may be. If the 
experiment be repeated with other liquids — and in 
such a case the tube should be 40 feet long — it will be 
found that water will rise to about 34 feet, glycerine to 
about 30 feet, and so on. But in every case the height 
to which the liquid rises will be such that it will produce 



IIIJ 



Properties of Gases 



41 



a pressure of about 14-7 lbs. per square inch at the 
bottom of the cohimn — which is to say that the Hquid 
will rise up to such a height that it produces a down- 
ward pressure equal to that of the atmosphere. 

The Barometer. It is on this principle that we 
usually measure atmospheric pressure, the instrument 
used being called a barometer. To construct a barometer 
a glass tube of 36 inches length having a fairly thick 
wall and a bore of about | inch is sealed at one end 
and filled with clean mercury. Care must be taken 
that no air bubbles or water vapour are left in ; and 
to this end the tube should be thoroughly cleaned and 
dried before filling. A finger is then placed over the 
end and the tube is inverted and its lower end placed 
in a dish or cistern of mercury. The finger is then 
removed and the mercury will fall a little in the tube — 
as shewn in Fig. 16 (a). Since there is no air in the 




Fig. 16 



tube the column of mercury will adjust itself to such a 
height that its downward pressure is the same as that 
of the atmosphere. The "height" of the barometer 



42 Properties of Gases [v\\. 

is the vertical difference of level between the mercury 
in the tube and the mercury in the cistern. If the 
tube be tilted as shewn in Fig. 16 (6) or made in the form 
shewn in Fig. 16 (c) the mercury will adjust itself so that 
the vertical difference of level is the same as in the 
straight vertical tube. 

Standard Barometer. In the usual standard pattern 
of mercury barometer the cistern is provided with a 
plunger, worked by means of a screw, which can be 
adjusted so that the level of the mercury in the cistern 
coincides with the zero mark of the scale of inches and 
centimetres. This adjustment must always be made 
before the height of the barometer is read. It will 
be clear that unless some arrangement of this kind 
is provided a rise in the barometer will draw some 
mercury out of the cistern and the level vdW be below 
the zero of the scale ; whilst a fall in the mercury will 
raise the cistern level above the zero of the scale. In 
the usual domestic pattern this is compensated for in 
the marking of the scale : and it will be found that the 
distances marked off are shghtly less than true inches. 
It is of course cheaper to do this than to provide a 
special cistern. 

Boyle's Law. The relationship between the volvmae 
which a given mass of a gas occupies and the pressure 
to which it is subjected is expressed in a law known as 
Boyle's law. This states that the volume of a given mass 
of a gas, kept at constant temperature, varies inversely as 
the pressure to which it is subjected. 

Most of us learned jgomething about this law when 
we played with popguns. We learned -that as we 
decreased the volume of the air in the barrel of the gun 
by pushing in the plunger we increased the pressure on 



Ill 



Properties of Gases 



43 



the cork and on the plunger until finally the cork was 
blown out. We found that the plunger was harder 
to push as it got further into the barrel and in learning 
this we had got the main idea of Boyle's law, that if 
we increase pressure we decrease volume. What we 
had not learnt was the exact relationship between the 
two, namely that the one varies inversely as the other. 
Thus if the pressure be doubled the volume will be 
halved : if the pressure be increased seven times the 
volume will be reduced to one-seventh and so on. 

This law may be experimentally verified by means 
of the apparatus shewn in Fig. 17, in which we have 





/\ 



I 



Fig. 17 

two tubes L and R connected by some rubber tubing. 
L is sealed at the top and is graduated in cubic centi- 
metres or inches or any other scale of volume. R is 



44 Proper tHx of Goscs [CH. 

open to the atmosphere and is arranged so that it can 
be raised or lowered. A certain volume of dry air (or 
any other dry gas) is enclosed in L by means of mercury 
and the volume can be read off on the scale. By 
raising or lowering R the pressure and volume of the 
gas in L can be changed. 

If the side R be adjusted so that the level of the 
mercury is the same in both tubes then it follows that 
the pressure is the same also. But the pressure on the 
surface of the mercury in R is the atmospheric pressure 
and therefore if we read the height of the barometer 
we know the pressure of the gas in L and we can read 
the volume on the volume scale. If R be now raised, 
as shewn in the top diagram on the right, so that the 
level of its mercury is above the level of the mercury 
in the tube L, then it follows that the pressure of the 
gas in L is greater than the atmospheric pressure by 
the pressure represented by a column of mercury of 
length AB — since it can support this column of mercury 
in addition to the atmospheric pressiire. Therefore the 
new pressure is the atmospheric pressure in inches or 
cms. plus the difference in the level of the mercury in the 
two limbs also in inches or cms. as the case may be. If, 
on the other hand, the limb R be lowered so that its 
mercury is below that in L it follows now that the 
atmospheric pressure is greater than that in L by an 
amount represented by the difference in level AB, so 
that the pressure of the gas in L is the atmospheric 
pressure minus the difference in level AB. 

The following are some results obtained with this 
apparatus : 



Ill] 



Properdes qf Gases 



45 



Volume 


Heiglit of 


Difference of 


1 Pressure of 


.Pres- 


of gas 


barometer 


level AB 


gas in L in cms. 


sure X 


in L 


in cms. 


in cms. 


of mercury 


Volume 


8 


75-8 


+ 53 


128-8 


1030 


11 


75-8 


+ 17-7 


93-5 


1028 


12 


75-8 


+ 9-6 


i 85-4 


1024 


15 


75-8 


- 71 


68-7 


1030 


16 


75-8 


- 11-4 


64-4 


1030 


17 


75-8 


- 15-2 


60-6 


1030 


18 


75-8 


- 18-4 


57-4 


1033 


24 


75-8 


- 32-8 


43 


1032 



In the last column of the tabulated results the 
product of the pressure and the volume is given and 
it is seen that this product is practically the same right 
down the column. When one quantity varies inversely 
as another and a number of results are taken under 
equal conditions then it will always be found that the 
product of the two quantities is constant. 

If Pj represents the pressure when the volume is 
Fi and P^ represents it when the volume is Fg then 
Boyle's law may be expressed 

V, Pi- 

That is to say the ratio of the volumes is equal to 
the inverse of the ratio of the pressures under equal 
circumstances. 

Therefore ^i^i==^2^2- 

Hence the fact that our last column is practically 
constant js an experimental verification of the law. 

The relationship between the volume and pressure 
may also be plotted as a graph. Fig. 18 shews the 
graph given by the results above. The form of 
this curve is known mathematically as a rectangular 
hyperbola. 



40 



Properties of Gases 



[CH. 



It will be seen later that Boyle's law is not universally 
true, though for dry gases it can be regarded as suffi- 
ciently true for all practical purposes. 



25 
20 

15 

10 

5 


1 




























X 













50 



150 



200 



Fig. 18. 



100 
Pressure 
Curve shewing relation of volume and pressure of air 
at constant temperature. 



Airships. The principle of Archimedes is as true 
for gases as it is for liquids. Any object weighs less 
in air than it would do in a vacuum by the weight of 
its own volume of air.' It also weighs less near to the 
ground where the air is dense than it would do at a 
higher level. 



Ill] Properties of Gases 47 

A balloon or any other lighter-than-air ship is filled 
with a gas lighter than air and is made of such a volume 
that the weight of air which it displaces is greater than 
its own weight. It is thus buoyed up and will rise to 
a height such that the weight of air displaced at that 
height is equal to weight of airship and contents. To 
ascend the volume of air displaced must either be in- 
creased (as in the Zeppelin type) or the weight must be 
decreased by dropping ballast. To descend the volume 
of air displaced must be decreased. 

EXAMPLES 

1. A certain mass of aii- has a volume of 12 cubic feet when 
there is a pressure of 14-7 lbs. per square inch (1 atmosphere) acting 
upon it: what will its volume be when the pressure is [a) 10 lbs., 
{h) 17-5 lbs. per square inch? 

2. A steel oxygen cylinder has an internal volume of 3 cubic 
feet. It is filled with oxygen at a pressure of 120 lbs. per square 
inch. What would be the volume of the gas at atmospheric pressure ? 

3. If a mercury barometer reading was 29-4 inches, what would 
be the reading of a glycerine barometer at the same time- — the 
specific gravity of glycerine being 1-21 and that of mercury 13-6? 

4. Plot the graph shewn in Fig. 18 and extend it on each side 
to shew the volume changes between the pressures of 20 and 200. 

5. A balloon on the ground where the atmospheric pressure is 
14-7 lbs. per square inch displaces 30,000 cubic feet of air. What 
volume will it displace when at such a height that the atmospheric 
pressure is 12 lbs. ? 

6. When a certain steam boiler is working at a pressure of 
120 lbs. per square inch it is capable of discharging 20 lbs. of steam 
per minute. If the pressure be worked up to 150 lbs. per square 
inch and maintained there what would be the possible discharge rate ? 

7. A cylindrical steel cylinder is 5 feet long and 8 inches in- 
ternal diameter and is filled with "Poison gas" at a pressure of 
100 lbs. per square inch. What space would this gas occupy when 
let out into the air when the barometer reads 30 inches of mercury ? 



CHAPTER IV 

FORCE, WORK AND ENERGY 

Work. We buy coal, not for its own sake, but for 
the heal which we can get out of it. We buy gas from 
the gas company for the light which we can get from it 
in burning. Neither heat nor light can be regarded as 
matter : they have no weight and no other property 
which we associate with matter. 

We classify them as forms of energy and we define 
energy as the capabiUty of doing work. 

For scientific purposes we have a definite meaning 
for the word work, and it is restricted to the production 
of motion of matter. We say that when a force acting 
upon a body produces motion then work has been done. 
Unless motion is produced however no work is done. 

Force. In order to produce motion we must apply 
force. We have seen already that weight is a force ; we 
possess a system for measuring weights and we can 
therefore measure our forces in terms of pounds weight, 
or grammes weight or any other units of weight that we 
care to use. We can also indicate these forces by means 
of spring balances so that we can be quite independent 
of the force of gravity. 

If we raise a bucket of water vertically upwards we 
shall have to apply a force which, it can be seen, will 
be equal to the total weight of the bucket and its 
contents. If we just haul it along the ground without 



CH. iv] Force, Work and Energy 49 

lifting it the force which we shall have to apply will 
depend entirely upon the surface of that ground. If 
this is very smooth — like ice — very little force will be 
needed to haul the bucket along ; but if the surface be 
rough and gritty then the force required might be 
considerable. 

We can take a better illustration from railway 
traction. If we have to raise a truck bodily off the 
rails then we must apply a force equal to the total 
weight : but if we have to move it along the rails then 
it is only necessary to apply a force sufficient to over- 
come the friction of the bearings and the rails, and that 
force is about 10 to 15 lbs. for every ton which the 
truck and its contents weigh. Thus if the truck and 
its contents weighed 10 tons then the force to lift it 
vertically upwards would be 10 tons or 22,400 lbs. : 
but the force necessary to move it along the rails would 
only be 100 — 150 lbs. according to the quality of the 
truck and the track. 

Now work is measured by the force required to 
produce the motion and by the amount of movement 
produced ; that is to say by the product of the force 
producing the motion and the distance through which 
the object moves in the direction in which the force is 
being applied. 

Units of Force and Work. Clearly a unit of work 
will be done when a unit of force produces motion 
through a unit of length in its own direction. It 
follows therefore that we may have many different 
units. On the British system the unit most commonly 
used is the Foot-Pound — namely the work done when 
a force of one pound produces motion to the extent of 
one foot in its own direction. 

p. Y. 4 



'){) Force, Woric and Energy [ch. 

In scientific work the units of force chiefly used differ 
from the *' weights" which have been given. A unit of 
force is defined as tliat force which acting for a unit of 
time upon a unit of mass produces a unit change of 
velocity. For example it is found that if a force of 
7|.V.j lbs. weight be apphed to a mass of 1 lb. mass which 
is free to move without friction, it will move and its 
velocity will increase by 1 foot per second every second. 
Therefore the unit of force according to this definition 
is ~~,, lbs. weight. This is called a Poundal. 

Similarly it is found that a force of tj^t gramme 
weight will cause the velocity of a mass of 1 gramme 
to increase by 1 centimetre per second every second. 
Thus the metric unit of force is y^y gramme weight. 
This is called a Dyne. 

Returning to our units of work again we see that 
the true unit of work on the British system would be a 
foot-pounial, which is ^^ of the foot-pound ; and on 
the metric system we have the centimetre-dyne which 
is called an erg. This is a very small quantity of 
work, and the practical unit of work on the c.G.s. 
system is a multiple of the erg, namely 10,000,000 ergs, 
and this unit is called a Joule. 

1 joule is equivalent to 0-737 foot-pound. This is 
the electrical engineer's unit of work. 

Mechanical engineers generally prefer to use one 
pound weight as a unit of force and one foot-pound as 
the unit of work. This means that the engineer's unit 
of mass must be correspondingly increased in order to 
meet the conceptionjaf a unit of force being that force 
which would produce a change of velocity of 1 foot 
per sec. in one second when acting on a U7iit mass. 
A force of 1 lb. weight would produce a change of 32-2 



iv] Force, Woric and Energy 51 

feet per sec. in one second on a mass of 1 lb. mass : 
but if the mass were increased to 32-2 lbs. mass the 
change of velocity per second produced by a force of 
1 lb. weight would only be 1 foot per sec. Therefore 
the engineer's unit of force is the pound weight and the 
unit of mass is 32-2 lbs. No name has been given to 
this although the remarkable word slug was once 
suggested. 

This Ust of units is very dull and uninteresting but 
of very great importance. A student who slurs these 
over is storing up trouble for himself, for there can 
be no doubt that the man who understands all his 
units will have little or no trouble with the various 
numerical problems of his subjects. 

Examples of work. We may briefly illustrate the 
use of these units. If a railway truck requires a force 
of 100 lbs. to pull it along so that it is just moving 
against the friction then the work required will be 
100 foot-lbs. for every foot along which it is moved. 
Let us find out how many ergs and joules this is equiva- 
lent to. Since there are 453-6 grammes to the pound, 
the force = 453-6 x 100 grammes weight; and since 
there are 981 dynes of force to the gramme weight the 
force in dynes = 453-6 x 100 x 981. 

Further since there are 30-48 centimetres to the foot 
the work done in centimetre -dynes, i.e. in ergs, will be 
453-6 X 100 X 981 x 30-48 or 1,356,303,916 ergs. And 
since there are 10' ergs to 1 joule the work done in 
joules will be 13 5* 63 joules. 

If work is done by a force which varies in magnitude, 
then the product of the average force and the distance 
through which it is applied will give the measure of that 
work. The measurement of the work done on the 

4—2 



52 ■ Force^ Work and Energy [ch. 

piston of a steam engine during its motion along the 
cylinder is an example of this kind, jand the indicator 
diagram represents how the force is changing for each 
position of the piston. From the diagram the average 
force can be determined (see Chapter XIII). 

Energy. We say that a body has energy when it 
is capable of doing work and therefore we measure its 
energy by the number of units of work it can do. 

For example, the weight of an eight-day clock when 
wound up to the top is capable of doing a certain amount 
of work in falling gradually to its lowest position. If 
the weight weighs 7 lbs. and the distance between its 
highest and lowest position is 4 feet then when wound 
it possesses 28 foot-lbs, of energy which it can give out 
to keep the clock going. When it has fallen half-way 
it only possesses 14 foot-lbs. of clock energy — the other 
14 having been given up. 

There are two general divisions of energy. Some 
bodies, hke the clock weight, possess energy on account 
of their position or state. A compressed spring, a 
coiled-up watch spring, a sprung bow, an elevated pile- 
driver, a stone on the edge of a cliff and some water 
in a high reservoir are examples of things possessing 
energy because of their condition, position or state. 
We say that these things have potential energy. 

Other bodies are capable of doing work because of 
their motion. A flying bullet, a falling stone, the water 
of a waterfall, the steam forced from a high pressure 
boiler, the wind, a hammer head just at the moment 
of impact, are examples of things possessing energy due 
to their motion. We say that these have kinetic energy. 

The energy of a body is capable of being changed 
from potential to kinetic and vice versa. Fig. 19 (a) 



IV] 



Force, Work and Energy 



53 



represents a pile driver: position A shews the driver 
at rest at its highest position where its energy is all 
potential : position B represents it moving downwards 
towards the pile, and though its potential energy must 
be less than it was at A yet it now has kinetic energy 
due to its motion : position G represents it at the 
moment of impact, and here its potential energy in 
relation to the pile is zero but its kinetic energy is 
greater than it was at B since it has gained speed. 



h 
II 

1 1 
I I 
I I 
I i 
I I 
I I 
I I 
I I 
I I 
I 



E F 



(a) (b) 

Fig. 19 

Fig. 19 (6) represents a pendulum swinging between 
extreme positions of D and G. At the positions 
D and G it is at rest at its highest position and its 
energy is all potential. At F it is at its lowest position 
and its pendulum energy is all kinetic. At E its energy 
is partly potential and partly kinetic. 

The reader will learn that in all these cases the sum 
of the potential and kinetic energies at any moment is 
a constant quantity; and that what a body loses in 
potential energy it gains in kinetic energy. 



.')4 rurct, WinL nuil Entiijij [cm. 

Principle of the Conservation of Energy. Many ex- 
periineiits liave heoii pcrlorinod in comparatively recent 
times which go to shew that though we can alter the 
jorm of the energy of a body yet we cannot destroy 
energy nor yet can we create it. We shall deal with 
some of these experiments at a later stage, but it should 
be made clear to the reader now that this is regarded as 
an estabHshed fact and that it is practically the funda- 
mental basis of modern science. It is known as the 
principle of the conservation of energy and it is exactly 
parallel to the principle that matter can neither be 
created nor destroyed though it can be changed in 
form and condition. 

The reader will ask what happens to the energy of the 
pile driver when the driver has come to rest on the pile 
head ? It is found that it has been changed into another 
form — a form which we call Hmi. With the aid of heat 
mechanical work can be done and it has been shewn 
that the amount of mechanical work which a given 
"quantity of heat" can do is such that if this same 
amount of mechanical work be converted into heat it 
will produce in turn the same "quantity of heat" as 
that with which we started. And further, in whatever 
way we do work which produces heat — whether by 
friction or by hammering or by boring or by percussion — 
we always get the same " quantity of heat" if we do the 
same amount of work. This is discussed in detail in 
Chapter XIII. 

In the same way^heat energy Qan be converted to 
light energy. Heat energy can also be converted to 
electrical energy, mechanical energy can be converted to 
electrical energy which in turn can be converted to 
heat or to light or to mechanical energy again. In fact 



Tv] Force, Woi'h and Energy 55 

it. is just that "flexibility" of electrical energy which 
makes it of such use to mankind, for it is so easy to 
transmit from one place to another and it is so easily 
changed to whatever form or forms we desire. Then 
in coal we have a store of chemical energy which changes 
to heat in burning ; the heat is given to water and pro- 
duces steam at a high pressure charged as it were with 
potential energy ; the steam is liberated and its kinetic 
energy is given up to the piston of an engine ; the kinetic 
energy of the engine is transmitted to the dynamo and 
converted to electrical energy ; the electrical energy is 
transmitted to where it is needed and there transformed 
to any form we wish — to heat, to light, to chemical 
energy in secondary cells and in chemical manufacturing 
process and to mechanical energy in motors. But all 
this energy has come from the boiler furnace ; we have 
not made any ; we have not destroyed any ; but we 
may possibly have wasted a considerable quantity. We 
have not used all the heat given by the coal — much has 
gone up the chimney so to speak ; we have produced 
heat at all our bearings because we cannot make them 
mechanically perfect and frictionless,'and so the energy 
necessary to overcome that friction has been changed 
to heat. 

We may sum up then by saying that energy like 
matter can neither be created nor destroyed but that 
it can be changed from any one form to any other form 
of which it is susceptible. 

Power. In scientific work this word has a very 
restricted meaning and one which differs considerably 
from its meaning in common usage. By power we 
mean the rate at which work is done. 20 foot-lbs. of 
work may be done in a second or in an hour and though 



.")G Force, Work and Energy [ch. iv 

the actual ^^'ork done \\ ill be the same in each case yet 
the rate of working will be very different. The unit of 
power would naturally be the rate of working when a 
unit of work is done in a unit of time. In practice, 
engineers take as a unit of power 550 foot-lbs. of work 
per second which is called 1 horse-power. This is 
equivalent to 33,000 foot-lbs. per minute. The elec- 
trical engineer's unit of power is 1 joule per second which 
is called a ivatt. 1000 watts or 1000 joules per second 
is called a Hlowatt and this is more generally used in 
heavy electrical engineering. 1 horse-power is equiva- 
lent to 746 watts. 

It might be well to point out here that a 1 horse- 
power motor might be constructed to work at high 
speed so that it could, for example, haul up a load 
of 1 lb. through 550 feet in a second, whilst another 
1 horse-power motor could haul up 550 lbs. through 
1 foot in a second. Thus a mere knowledge of the 
horse-power does not give ua any idea of the hauling 
capacity of the motor or engine and it is entirely wrong 
to imagine that a 1 horse -power motor can necessarily 
pull with the same puU us that which can be exerted by 
an average horse. 

The reader can ask himself what is the object of the 
gear box of a motor car. 

EXAMPLES 

1. How much work would be done in pumping 120,000 gallons 
of water from a depth of 22 feet ? If this work were done in 2 hours 
what would be the rate of working (a) in foot-lbs. per minute, (b) in 
horse- power? ^ 

2. How many ergs of work are equivalent to 1 foot-lb. ? (There 
are 45.3-6 grammes per lb. and 2-54 cms. to the inch.) 

How many joules of work is this equivalent to and if the work 
was done in l/5th sec. what would be the rate of working in watts? 



CHAPTER V 

HEAT AND TEMPERATURE 

It may be well to begin by saying that we do not 
know what heat really is. All we can say with any 
degree of definiteness is that heat is an agent which 
produces certain effects. We can study the nature of 
these effects and the conditions under which they may 
be produced and their application generally for the 
benefit of mankind. A moment's reflection will shew 
that we need not necessarily know the precise nature 
of this thing which we call heat, although, on the other 
hand, we can see that such knowledge might help us 
considerably both in the production and use of this 
most valuable agent. 

We know that heat can produce certain effects. 
Our first knowledge is of its comforting effects upon 
our person and of its chemical effects upon our food. 
And as our vision grows more extended we become 
conscious of its effects upon life in both the animal and 
vegetable worlds. Then we find how it can change the 
physical state of matter from solid to liquid and from 
liquid to gas. Then again we begin to realise that it 
is an agent which can do work for us. We think of the 
steam engine and reflect that after all it is the burning 
of the fuel which yields us all the energy ; and further 
knowledge shews us that in the gas engine, the oil 



i)H Hent nmf Temjterdtnrv [CH. 

engine and the petrol engine, combustion and the pro- 
duction of heat give us the source of all their energy of 
motion. How important then it is that we should 
know as much as possible about the various effects 
which heat can produce and the various methods of 
producing and using it. 

Production of Heat. We have already seen that 
energy can shew itself in many different forms, and 
that one of these forms is heat. We have reahsed that 
energy like matter can be changed from one form to 
another, and that it can neither be created not yet 
destroyed. It follows therefore that whenever we 
produce heat it is at the expense of an equivalent 
amount of energy which was previously existing in 
some other form. 

The chief method of production is by the expendi- 
ture of chemical energy. All forms of burning or com- 
bustion are examples of this, from the combustion of 
that great mass which we call the sun down to the 
burning of the humble match. If we bum a given 
mass of anything — coal or candle — and keep all the 
residue we shall find the mass of matter the 'same as 
before, but that mass has no longer the energy which 
it had before combustion. The heat was obtained not 
at the expense of any of the matter or stuff but at the 
expense of its chemical energy — that mysterious weight- 
less attribute of the coals or candles for which we 
really pay when we buy them. We do not really 
want the coal as such when we buy it: we want the 
chemical energy which it contains and which we can 
change to heat energy whenever we desire to do so. 
The same statement applies to any other kind of fuel 
and to all those fearsome mixtures termed explosives. 



v] Heat and Temperature 59 

Further it is probably known to most readers that 
heat can be produced by chemical changes without 
combustion. If some water be added to strong 
sulphuric acid heat will be produced at once, and con- 
sequently great care must be taken in the dilution of 
acids. Further everyone knows how heat is developed 
in a haystack if the hay be stacked before it is dry. 

The mechanical energy of motion may be changed 
into heat. Whenever there is any kind of resistance 
to motion — that is to say any kind of friction — heat 
is developed in direct proportion to the amount of 
energy necessary to overcome that friction. Such heat 
is, as a general rule, waste energy ; but as friction is 
always present the loss is unavoidable. An engine 
driver tests the bearings of his engine by feeling them. 
Bad bearings become unduly heated, and the increase 
in warmth serves as a danger signal. The striking of 
a match is an example of the useful conversion of 
mechanical to heat energy. The old flint and tinder, 
and the yet older rubbing of dry sticks together are 
similar examples. "Shooting stars" are examples of 
the heat produced by the resistance of the air to bodies 
falling through it at an enormous speed. The melting 
of a rifle bullet on striking a steel target affords another 
example of the changing of mechanical energy to heat. 

Electrical energy can also be converted to the form 
of heat and every reader knows something about electric 
lighting and heating. 

In short whenever work is done without producing 
its equivalent in some other form of energy the balance 
is shewn in the form of heat.. 

Temperature. We know that a reservoir of water 
is capable of doing work and that such work can only 



60 Heat and Temperature [ch. 

be done by the motion of some of the water. It can 
do work, for example, by a downflow to a water-turbine 
and we know that the amoimt of work which the 
reservoir can do depends upon the quantity of water 
it contains and the height of the reservoir above the 
ivater -turbine. That is to say the energy of the reservoir 
is measured by the product of the mass of water arid 
the height above the turbine, and we coukl get the 
same energy out of a reservoir at half the height if it 
held twice as much water. 

Let us imagine that any furnace or source of heat 
is a sort of reservoir of heat energy — the energy de- 
pending upon some quantity we will call heat and upon 
some kind of height which we will call temperature or 
heat-level. 

The analogy between this reservoir and the water 
reservoir will hold good for most things but it ought to 
be borne in mind that it is only an analogy and that we 
are taking a considerable licence in comparing heat to 
water. But just as we say that water will always flow 
from a reservoir at a higher level to one at a lower level 
quite irrespective of the size or shape or quantity of 
water or amount of energy in those reservoirs, so also 
may we say that heat is only transmitted from a body 
at a higher temperature to one at a lower temperature 
whatever may be the other differences between those 
bodies. 

We may thus take it that temperature is a sort of 
level of heat as different from the agent heat itself as 
height or level is different from water. Nobody would 
confuse a reservoir of water with its height, yet most 
people confuse heat and temperature. 

Measurement of Temperature. It will be necessary 



v] Heat and Temperature 61 

to measure temperatures or differences in temperature 
if we are going to make any really valuable investi- 
gations into the effects of heat upon bodies. Our 
senses enable -us to form a rough estimate of tempera- 
ture such as saying that this body is hotter (i.e. at a 
higher temperature and not necessarily containing more 
heat energy) than that. But our senses are not reliable, 
for they can lead us into the declaration that one thing 
is hotter than another when they are actually at the 
same temperature. An example of this may be fur- 
nished at any moment, for if we go into any room which 
has been without a fire for some time, having therefore 
a uniform temperature or heat level all over, and touch 
various articles such as the fender or curb, the hearth- 
rug and a table leg, we shall find that they all appear to 
have different temperatures. The explanation of this 
lies simply in the fact that the articles conduct heat 
to or from the body at different rates and so produce 
different sensations. 

Temperature is measured by means of a thermometer 
which depends for its action upon the fact that when 
heat is given to matter it generally produces an increase 
in volume. 

Let a glass flask be taken and filled with water (or any 
other liquid) and provided with a cork and tube so that 
the water rises to some height A in the tube, as shewn 
in Fig. 20. If now some hot water be poured over the 
flask it will be noticed that at first the water drops to 
a position such as B but soon rises again to such levels 
as C and D. We might perhaps imagine that water there- 
fore contracts for a moment when heated : but if we heat 
the water from within — by means of a small coil of wire 
through which a current of electricity can be passed — 



()2 



Heat and Temperature 



CH. 



we shall find that there is no initial dnj]). 11 we bend 
a piece of glass tube or rod into the fonn of a triangle 
and bring the two sides together at the apex so that 
they can just grip a coin — as shewn in Fig. 21 — and 
then heat the base we shall find that glass expands when 
heated ; this will be shewn by the coin dropping from 
the apex of the triangle. We therefore conclude that the 
dropping of the water in the first instance — when the 
hot water was poured over the fiask — ^was due to the 





Fig. 21 



Fig. 20 

glass receiving the heat first and expanding, thus having 
a larger volume. But when the heat got through to 
the water inside then that expanded too, and since it 
ultimately went above its original mark A we conclude 



v] Heat and Temperature 63 

that water expands more than glass does. As a matter 
of fact liquids in general expand more than solids. 

Now if we put this flask into vessels of water at 
different temperatures we shall find that the water in 
the tube will set at a different level for each tempera- 
ture. 

This furnishes us with the basis of temperature 
measurement. We could mark a scale off in any way 
we desired and it would be sufficient perhaps for our 
purpose — ^but if everybody had his own scale of tempera- 
ture we could hardly make any progress. What the 
scale is really does not matter ; but it is of first import- 
ance that we should all use the same. The well-known 
case of the bricklayer's labourer who was sent to make 
a certain measurement and came back with the result 
as three bricks and half a brick and a hand and two 
fingers, furnishes an example. His measurement could 
be reproduced by himself — but it was useless to others. 
The length of a foot is quite a detail : it is only 
important that we should agree to call a particular 
length one foot. And the same appHes to temperature 
measurement; it is unimportant what a degree of 
temperature is, but we must all understand it and agree 
to it and be able to reproduce it. 

The Fixed Points of Temperature. In making a 
scale of temperature it will be necessary to have two 
fixed points of temperature to which reference can be 
made at any time. One of these — the lower fixed 
point — is the temperature at which pure ice melts or 
pure water freezes. This is found to be a constant 
temperature. The other fixed point — the upper fixed 
point — is the temperature of steam over water which 
is boiling at standard atmospheric pressure. This is 



64 HeM and Temperature [CH. 

a rather complicated fixed point, and the reasons for 
its complexity lie in the following facts. Firstly the 
temperature at which water boils is largely affected by 
the presence of any impurities — such as dirt or salt — 
whilst the temperature of the steam above the water is 
not affected in any way by these. If we throw a few 
pinches of salt into a saucepan of boiling water we shall 
find that the temperature of the water will rise, but 
the temperature of the steam will remain as it was. 

Secondly the temperature at which water boils is 
slightly affected by the kind of vessel it is boiled in. 
Water boils at a slightly higher temperature in glass 
than in copper, but the steam temperature is the same 
in both. These two points account for the choice of 
steam. 

Thirdlj^ the temperature of steam depends upon 
the pressure to which it is subjected — rising with an 
increase of pressure and falling with a decrease. Daily 
changes of atmospheric pressure will affect the tem- 
perature of steam ; therefore in defining a fixed point 
of temperature we must clearly specify that the steam 
shall be under some definite pressure. Standard 
atmospheric pressure is defined as the pressure equiva- 
lent to 30 inches of mercury at sea level in latitude 45° 
at the temperature of the lower fixed point. 

These fixed points are called the freezing 'point and 
the boiling point respectively. 

Construction of Thermometer. The usual ther- 
mometer consists of a glass bulb and stem containing 
mercury or quicksilver. The flask shewn in Fig. 20 is not 
quite suitable for temperature measurements. It is too 
big : it will absorb a large quantity of heat itself : and 
it will need quite a long time to take up the temperature 



V] 



Heat and Tem2)erature 



65 



required. But the idea is sound enough and so we make 
a small bulb at the end of a tube of thick wall and 
very fine bore. That is to say we reduce the whole 
thing in proportion so that we get a reasonably small 
instrument which will- absorb very little heat. Then 
we use mercury instead of water because it conducts 
heat better ; it requires less heat to raise the tempera- 
ture of the same volume a given amount; it remains 
liquid over a wider range of temperature ; and it does 
not wet the glass, and therefore runs up and down the 
tube with greater ease. 





Fig. 22 



Fior. 23 



We need not discuss the details of filling, sealing and 
resting of the thermometer. We need hardly say any- 
thing about the marking of the fixed points except to 
state that the thermometer bulb and stem as far as 
possible should be immersed in steam or in melting ice 
under the conditions specified in our statements of the 

P.Y. 5 



66 Heat and Temperature [CH. 

fixed points of temperature. There is no doubt that 
every reader will be testing the fixed points of a 
thermometer in the laboratory and he can there study 
the arrangements which will ic^scinble those shewn in 
Figs. 22 and 23. 

Scales of Temperature. It is rather unfortunate 
that there are three scales of temperature in existence 
and use. These three are known as the Centigrade, the 
Fahrenheit and the Reaumur respectively. Fig. 24 
illustrates the essential features of these scales and 
their differences. Celsius, who gave us the Centigrade 
scale, called the freezing point — written 0° C. — and 
the boihng point 100, and he divided up the interval 
into 100 equal parts each of which he called 1° C. 

Fahrenheit originally took different fixed points : 
he took a mixture of ice and salt and he imagined that 
that was the lowest temperature which could be ob- 
tained and so called it 0° F. Then he took the tempera- 
ture of the human body as his upper fixed point and 
called it 100° F. The interval he divided up into 100 
equal parts so that his scale was a Centigrade scale, 
though different from Celsius' scale. On Fahrenheit's 
scale the temperature of pure melting ice was found to 
be 32° F., and the boiling point 212° F. Thus the 
interval between the freezing and boihng points is 180 
Fahrenheit degrees. 

Reaumur's scale differs from Celsius' in that the 
boiling point is called 80° — because 80 is an easier 
number to subdivide than 100 ! 

Conversion from one scale to another. In this 
country both the Fahrenheit and Centigrade scales are 
used. The scale in common use is the Fahrenheit, the 
Centigrade being used for scientific work and by 



V] 



H^at mid Temperature 



Q7 



electrical engineers. Mechanical engineers have gener- 
ally used the Fahrenheit but there are signs of the more 
general adoption of the Centigrade scale. Conversion 
from one scale to another is a simple matter and should 
not be beyond the powers of our readers without any 
further assistance in these pages. 



Upper Fixed Point 




Lower Fixed Point 



Fig. 24 

It need only be pointed out that since 100 Centigrade 
degrees cover the same temperature interval as 180 
Fahrenheit degrees and 80 Reaumur degrees therefore 
1 Centigrade degree = ^ Fahrenheit degree = | Reaumur 
degree. 

It must also be noted that since the scales start from 
different points the Fahrenheit temperature has a sort 
of handicap allowance of 32 above the other two. This 

5—2 



68 Heat and Tem))€ratkre [CH. 

allowanoe must be added or subtracted according to 
the direction of conversion. 

Thus 15°C. = 15C. degrees above the freezing 
point, 

and since 1 C. degree = f F. degree, 

.'. 15 C. degrees = 16 x § = 27 F. degrees, 

i.e. 27 F. degrees above the freezing point, 

.-. 15° C. = 27 + 32 = 59° F. 

Similarly 15° C. = 15 x f = 12° Reaumur. 

Again let us convert 113° F. to Centigrade and 
Reaumur. 

113° F. = 113-32 F. degrees above the freezing- 
point = 81 F. degrees, 

since 1 F. degree = f C. degree. 

.•. 81 F. degrees above the f.p. = --g— C. degrees 
above f.p. = 45° C. 

and 81 F. degrees above the f.p. = ~^ R. degrees 
above the f.p. = 36° R. 

All readings below 0° on any scale are called minus 
quantities. 

Other thermometers. The mercury-in -glass ther- 
mometer has a wide range of general usefulness but 
when temperatures below — 40° C. (which, by the way, 
is also — 40° F. as the reader should verify) are to be 
measured, some other form must be employed since 
mercury freezes at — 40° C. or F. Grenerally alcohol 
is used instead of mercury and it can be used down 
to — 1 10° C. For lower temperatures than this 
gaseous and electrical thermometers are generally 
used. These will be discussed later. 



v] Heat and Temperature 69 

For temperatures above 250° C. or 482° F. mercury 
thermometers must also be superseded. The boihng 
point of mercury is 350° C, but unless the upper part 
of the stem is filled with some inert gas it cannot be 
used beyond 250° C. 

For higher temperatures recourse is usually made 
to a class of instruments called pyrometers. Some of 
these depend upon the expansion of solids, but the 
majority in use in engineering practice at the present 
time are electrical and depend upon the fact that when 
a junction of two dissimilar metals is heated a current 
of electricity is generated which increases as the temper- 
ature of the junction increases. This current operates 
a delicate detector — really a voltmeter— the scale of 
which is marked off directly in degrees of temperature. 
These are very valuable instruments and are of great 
service in measuring any high temperatures such as 
superheated steam, flue temperatures, boiler-plate 
temperatures and so on. Fig. 25 is a diagram illus- 
trating the principle of a pyrometer as supplied by 




Fig. 25 

Messrs R. W. Paul. We cannot well discuss it in 
detail since it is possible that many readers have 
not progressed sufficiently into the study of the 
sister science of electricity to be able to appreciate 



70 Heat and Temperature [CH. 

it. Those who have will be able to understand it 
well enough from what has been said. 

Self-registering Thermometers. If it is desired to 
know the highest or lowest temperature reached during 
any particular interval of time a self-registering ther- 
mometer is used. A simple form (Rutherford's) of 
maximum thermometer is shewn in Fig. 26 (a), and (6) 
illustrates the thermometer for recording the minimum 
temperature. The maximum thermometer is just an 



I 



D 



(a) 



Yi.i.^^yyyy^^yyyy.-r^':^:^, 




(b) 
Pig. 26 



ordinary mercury thermometer provided with a little 
index I which can slide freely along the tube. As the 
mercury expands it pushes the index along and when 
it contracts the index will be left /'. The position of 
the left-hand end of the index will be the maximum 
temperature recorded since the index was last set in 
position against the thread of mercury. 

The minimum thermometer contains alcohol instead 
of mercury and the index is placed inside the alcohol in 
the tube. As the alcohol contracts this index will be 
drawn back, but when the temperature rises again it 
will remain at its lowest point. Of course the index 
must be small enough not to impede the flow of alcohol 
up the stem. The indexes are set in position by tilting 
the thermometer and tapping them gently. In some 
forms they are made of iron and are set in position by 
means of a small magnet. 



v] Heat and Temperahn'e 71 

Fig. 27 illustrates the doctor's or clinical thermo- 
meter. The bore of the tube is constricted at the 
point a. When the mercury is expanding the force 
of expansion is great enough to push the mercury 
through this narrow part of the tube ; but on con- 
tracting the thread of mercury breaks at the con- 



i""i'"'r"'i-F'i|""i"ii|""i""i""i""M"'i""i 



r) 



Fig. 27 

striction thus leaving the thread in the stem at the 
same position it occupied when in the patient's mouth. 
Before the thermometer can be used again the thread 
must be shaken down — an operation frequently re- 
sulting in disaster to the thermometer. 

EXAMPLES 

1 . Convert the following Centigrade temperatures to Fahrenheit : 
36°, 2000°, - 273°, - 40°. 

2. Convert the following Fahrenheit temperatures to Centigrade : 
10°, 0°, - 40°, - 400°, 98-4°, 2000°. 

3. Convert the followmg Reaumur temperatures to Fahrenheit 
and to Centigrade: 12°, - 32°, - 218-4°, 160°. 



CHAPTER VI 

EXPANSION OF SOLIDS 

One of the chief effects of heat upon matter is the 
change of volume which it produces. In the vast 
majority of cases an increase in the temperature of 
a body is accompanied by an increase in the volume, 
but there are cases in which the converse is true. 

In the case of sohds we may have expansion of 
length, breadth and thickness — and this is generally 
the case. India-j-ubber in a state of tension contracts 
in length when heated — but its volume increases. All 
metals however expand proportionately in all direc- 
tions. If a sphere of metal be heated it will expand 
but will still be a sphere. All metals expand with 
increase in temperature and contra<)t with decrease in 
temperature, and metals expand more than any other 
solids under the same conditions. Further, different 
metals expand differently under equal conditions. 

Laws of expansion. We will consider firstly the 
expansion of length or Hnear expansion of a substance. 
It has been shewn — and can be shewn again by the 
apparatus illustrated in Fig. 28 — that the length of a 
solid increases uniformly with the increase in tempera- 
ture. An increase of 20° of temperature will produce 
twenty times the increase in length which would be 
produced by a 1° increase in temperature. 



CH. vi] Expansion of Solids 73 

Secondly it can be shewn in the same way that the 
actual amount of expansion produced for a given in- 
crease in temperature depends upon the original length 
of the substance. That is to say a 10 foot length of 
metal would have a total expansion 10 times greater 
than a 1 foot length of the same metal for the same 
increase in temperature. 

Thirdly, the expansion produced depends upon the 
substance which is expanding. Obviously if we wish 
to compare the expansion of different substances we 
must take equal lengths and heat them through equal 
ranges of temperature. It is also obvious that it would 
be most convenient to take unit lengths and to heat 
them through 1° of temperature. 

Coefl&cient of linear expansion. The increase in 
the length of a unit length produced by increasing the 
temperature 1° is called the coefficient of linear expansion 
of a substance. 

Strictly, the definition given above is not true. It 
should be the increase in the length of a unit length at 
the freezing point when increased 1°. But the value of 
the coefficient is so small that for all practical purposes 
the definition with which we started is sufficiently 
accurate and is certainly simpler. 

A foot of brass when heated 1° C. becomes 1-0000188 
foot. Similarly 1 centimetre . of brass when heated 
1° C. becomes 1-0000188 centimetre. From our defini- 
tion it follows that the coefficient of linear expansion 
of brass is 0-0000188 per degree Centigrade, and we can 
readily see that if an increase of 1° C. produces an 
increase in length of 0-0000188 unit, then an increase 
of 1° F., which is only {}th of a degree Centigrade, will 
only produce an increase in length of {} x 0-0000188 or 



74 Expansion of Solids [ch. 

0-00001044 unit. That is to say the coefficient of 
expansion per degree Fahrenheit will only be fjths of 
that per degree Centigrade. 

Again though we have only spoken of exjjansion, 
the same laws exactly apply to contraction produced by 
a decrease in temperature, and we might even define 
the coefficient of expansion (or contraction) as the 
increase (or decrease) in the length of a unit length of 
a substance for an increase (or decrease) of 1° of tem- 
perature. 

Calculations. Calculations are obviously quite 
simple for we have only to remember that the increase 
(or decrease) in length is directly proportional to 

(tt) the increase (or decrease) in temperature, 

(b) the original length, 

(c) the coefficient of linear expansion of the sub- 

stance, 
and we can apply the simple rules of proportion. 
There is clearly no need to deduce any formula for such 
straightforward work. 

Example. A rod of copper is 33" long at 15° C. : 
what will be its length at 100° C, the coefficient of 
linear expansion of copper being 0-0000172 per degree C. 

It follows therefore that 

1 inch of copper heated through 1° C. expands by 
0-0000172 of an inch, . 

.'. 33 inches of copper heated through 1° C. will 
expand by 33 x -0000172", 

.*. 33 inches of copper heated through 85° (i.e. 
100-15) will expand by 33 x 85 x -0000172" 
- 0-048246". 

Therefore the length of the rod at 100° C. will be 
33-048246" or, as we should express it in practice, 33-048". 



VI] 



Expansion of Solids 



75 



Determination of coefficient of linear expansion. 

Fig. 28 illustrates a simple form of apparatus which 
can be used to determine the coefficient of expansion 
of a solid. The rod R to be tested is placed inside a 
jacket J which can be filled with steam or water at 
any desired temperature. The rod is fixed between 
two screws as shewn, AS being an adjusting screw and 
MS a micrometer screw. The micrometer is adjusted 
to zero and the rod is tightened up by means of the 
adjusting screw. This should be done at the higher 
temperature first. Then the temperature of J is 
lowered and the micrometer screw is turned until the 




Fig. 28 



rod is tight again. The decrease in the length of the 
rod is thus given by the micrometer screw : the original 
and final temperatures are given by the thermometer : 
and the original length of the bar is obtained by re- 
moving the rod and measuring it with a straight-edge. 
From these particulars the coefficient of linear expan- 
sion may be calculated. 

The above method is not very accurate, the chief 
source of error lying in the expansion and contraction 
of the screws. But it will serve to illustrate the general 
principle and the reader will be quite able to understand 



7(5 



Eaypaiision of Solids 



[CH. 



the many more refined arrangements for this measure- 
ment if he understands this one. 

Table shewing some coefficients of linear expansion 
per (legrec Ceriliijrade. 



Zinc 

Copper ... 
Iron, sof t . . . 
Steel, soft 

Nickel steel (^li^o nickel 
Nickel steel (45 % nickt 
Cast iron 
Tin 
Lead 
Silver 
Gold 

Platinum . 
Porcelain . 
Glass (soft) 
These numbers represent 



... 000(X)294 

0-()000172 

0(XX)0122 

0-0(XX)108 

) ... 0-00000087 

1) ... 0-0tKX)082 

... 0-0(X)011 

... 0-000025 

... 0-000028 

... 0-000021 

... 0-000015 

... 0-000009 

... 0-0000088 

... 0-000009 

average values only. 



Some advantages of expansion and contraction. Much 
practical advantage can be taken of the expansion and 
contraction of substances due to temperature changes. 
The forces exerted by the expansion or contraction may 
be very great and they are used to advantage in such 
operations as fixing iron tyres on wheels and other 
"shrinking" operations. The tyre is made of such a 
size that it will just fit on to the wheel when it is hot 
and the wheel is cold. When the tyre cools it grips the 
wheel tightly. Similarly one sleeve or cylinder may 
be shrunk on to a smaller cylinder. 

Then we have a very universal application in the 
case of hot ri vetting. The plates are drawn tightly 
together by the rivetters with their hammers— but the 



vi] Expansion of Solids 77 

contraction of the rivet as it cools will always exert an 
additional force. 

The forces exerted by expansion and contraction of 
an iron bar may be shewn very strikingly by means of 
the apparatus sketched in plan in Fig. 29. JS is an iron 
bar having a screw thread and a large nut S at one end 
and a hole through which a cast iron pin P is inserted 
at the other end. The screw can be adjusted so that 
the bar is held rigidly between the end fixtures on the 
metal base. If the bar is heated the pin P will be broken 
or the bar B will buckle. The force of contraction can 
also be shewn by placing the pin and the nut on the 
other sides of the end fixtures and tightening up whilst 
the bar is hot. On cooling the pin will be broken. 




Fig, 29 

Small automatic switches for switching an electric 
lamp on and off at frequent intervals are amongst other 
applications of the expansion of metals. 

If two equal lengths of different metals be rivetted 
together closely then when this compound bar is heated 
it will bend so that the metal which expands the greater 
amount will be on the outside of the curve. On cooHng 
it will bend in the opposite direction. Fire alarms 
which operate an electric bell are often made on this 
principle, and the balance wheel of a watch is compen- 
sated in the same way. 



78 Ea^pcmmcm of Sollth [ch. 

Some disadvantages of expansion and contraction. 
Nobody suffers more from the drawbacks of expansion 
than the engineer. Fortunately the effects can always 
be compensated — but such compensation has to be 
nicely adjusted and necessarily adds to the cost. Every- 
one knows why railway lines are laid in sections, why 
no two rails butt on to one another, why the rails are 
"fixed" in chairs with wooden wedges, and why they 
are "fixed" together with fish plates. And a" httle 
calculation will shew why the lengths of the rail sections 
in use are not greater than they are. It would be bad 
for rolling stock, rails and passengers if we had to 
leave large gaps between sections : and even as it is 
there is a distinct difference between summer and winter 
travelling. 

Tramway rails are buried— and thus we have not 
the same trouble because the rail temperature will 
never differ appreciably from the earth temperature. 
But of course it is too costly a method for long distance 
railways. 

Every branch of structural engineering has to take 
this expansion and contraction into consideration. 
The Forth Bridge is built in such a way that a total 
change of length of 18 inches must be allowed for 
between winter and summer. Clearly, it must not 
be taken up all at one place. 

Furnace bars must fit loosely : pipe joints of exposed 
gas or water mains must be telescopic : patterns for 
castings must be Qf such a size that they take account 
of the contraction of the metal, and sometimes must be 
designed specially to prevent fractures which may be 
produced by one part of the casting coohng quicker than 
another part and setting up undesirable stresses. 



VI] 



Expansion of Solids 



79 



I 



The standard yard measure is only correct kt one 
temperature, 60° F. 

A clock regulated by a pendulum will gain or lose 
as its pendulum contracts or expands. There are many 
devices for compensating pendulums all 
of which depend upon the fact that 
different substances expand differently. 
The gridiron pendulum affords us a 
useful example since this principle is 
also applied to other compensations. 
Fig. 30 illustrates this. Two different 
metals are used, iron and zinc. The 
iron rods can expand downwards and 
the zinc rods can expand upwards. 
The lengths of / and Z are chosen so 
that the total expansion of the iron 
is the same as that of the zinc. In 
this way the position of the centre of 
gravity of the pendulum bob will re- 
main constant. 

Surface or superficial expansion. 
If we take a square of a metal of side 
1 foot and heat it, it will expand in all 
directions. If we heat it 1° and if its 
coefficient of expansion is K then each 
side will he, {\ + K) feet. Therefore its 
area wiU become (1 + KY square feet, Fig. 30 

that is 1 + 2K + K^ square feet. That is to say the 
coefficient of superficial expansion is {2K + K'^). Now 
since K is always a very small quantity it follows that 
K^ will be much smaller and indeed is so small that 
it can be neglected in comparison with 2K. It is 
therefore usual to say that the coefficient of superficial 



}{0 E.vpansicni of Sol'uh [CH. vi 

expansion is twice that of linear expai}f<ion and of course 
is expressed in square meoMire. 

Cubical or voluminal expansion. In the same way 
if we take a cube of 1 foot side and heat it 1° of tempera- 
ture each side will become I + K feet and its volume 
will become {I + Kf cubic feet or I + 3K + 3K^ + K^ 
cubic feet. The coefficient of cubical expansion is thus 
{3K + 3Z2 + K^) but again we may neglect {3K^ + K^) 
in comparison with 3K, and it is usual to say that the 
coefficient of cubical expansion is three times that of 
linear expansion expressed in cubic measure. 

EXAMPLES 

1. What is the expansion of an iron rail 37 feet long at 00° F. 
when it is heated to 140° F. ? The coefficient of expansion of the 
rail = 0-000012 per degree Centigrade. 

2. The distance from London to Newcastle is 27 1 miles. What 
is the total expansion of the rails between the lowest winter tempera- 
ture (say 10° F.) and the highest summer temperature (say 120° F.) ? 

3. What must be the length of a rod of zinc which will expand 
the same amount as 39-2 inches of iron? See table on p. 76 for 
coefficients of expansion. 

4. A plate of copper is 10" x 8" at 15° C. What will be its 
area at 250° C. ? 

5. A sphere of brass has a diameter of 2-2"' at 32° F. What will 
be its volume and what its diameter at 212° F. ? 

6. The height of a barometer at 15° C. is found to be tO cms. 
when measured with a brass scale which is correct at 0° C. What 
is the true height of the barometer ? 

7. A certain rod is 36 inches long ai 0° C. and 30-04 inches at 
50° C. What is the coefficient of expansion of the rod ? 



CHAPTER VII 

EXPANSION OF LIQUIDS 

Obviously we are only concerned with change of 
volume in the case of liquids, since they have no 
rigidity. Further they must be in some kind of a 
containing vessel and since in all probability this will 
expand we shall have to be careful to distinguish 
between the real and the apparent expansion of the 
liquid. The experiment illustrated by Fig. 20 indicates 
this. If we know the increase in the volume of the 
containing vessel and the apparent increase in the 
volume of the liquid the real expansion of the liquid 
will be the sum of the two. 

The coefficient of real expansion will therefore be 
greater than the coefficient of apparent expansion by 
an amount equal to the coefficient of expansion of the 
material of the containing vessel. 

Most liquids— molten metals excepted — do not ex- 
pand uniformly. Fig. 31 is a graph illustrating the 
relationship between the volume and the temperature 
of a given mass of water. It is seen that the change 
in volume per degree of temperature is an increasing 
quantity after a temperature of 4° C. has been passed. 
It is therefore clear that we cannot give a number which 
represents the coefficient of expansion of water. We 
can give it for a definite range of temperature, but that 

P.Y. 6 



82 



ExpansiitH <>/ Liquids 



[CH. 



is all. Thus between the temperatures of 4° C. and 
14° C. the mean coefficient of expansion (real) of water 
is 0-00007. but between the temperatures of 50° C. and 
60° C. it is 0-00049. 



1-0020 
1-0010 

1-000 








/ 




^^ 


^ 


/ 










( 


fC 4° { 


>" 1 


0° 1 


5° 20° 



Temperature 
Fig. 81. Volume and Temperature of Water 

Methods of determination of coefficient of expansion. 

The apparent coefficient, in glass, may be obtained 
readily by means of a glass bulb (of known volume) 
having a stem graduated in terms of the bulb's volume. 
This is filled to a certain point up the stem. It can 
then be immersed in a bath the temperature of which 
can be adjusted to any desired value, and the apparent 
volume at each temperature can be read off. 

The real or absolute expansion is usually determined 
by comparing the density of the liquid at one known 
temperature with its density at 0° C. or at any other 
known temperature. As density is the mass of a unit 
volume it follows that as the volume of a given mass 



I 



VIl] 



Expansion of Liquids 



83 



increases, its density decreases. Fig. 32 illustrates a 
form of apparatus by means of which this measurement 
may be made. The hquid to be tested is placed in the 
large U-tube, each limb of which is surrounded by a 



/ 



Steam inlet 



Steam 
outlet 



-^ 



-^~ 



& Water 
I outlet 



Cold water 



Fig. 32 



jacket through which we can run cold water or steam 
or water at any desired temperature. The U-tube is 
open to the atmosphere and if both limbs are at the 
same temperature the liquid will be at the same level 
in each. If we pass ice cold water through one jacket 

6—2 



84 E.rjMUision of LiqultLs [oh. 

and steam through the other then the density of Hcjuid 
in the hot hmb will be less than that in the cold limb 
and therefore we shall get a difference in level since 
a longer column of hot liquid will be needed to balance 
a given column of cold liquid. We then measure the 
heights of the columns H and h and note the tempera- 
ture of the two jackets. 

The heights H and h are inversely proportional to 
the densities which we may call Dq and D^ . 

The densities are inversely proportional to the 
volumes. 

Therefore the heights are directly proportional to 
the volumes. 

That is to say H : h = volume at the higher tem- 
perature : volume at the lower temperature. 

Therefore the coefficient of expansion between the 
temperatures chosen 

, H-h 

A (difference in temperature) ' 

There have been several elaborations of this prin- 
ciple of measurement notably by Regnault and Callendar : 
but the fundamental principle is the same and the 
elaborations aim at producing greater accuracy. 

Peculiar behaviour of water. If we look at Fig. 31 
again we notice that as the temperature of water is 
increased from 0° C. the volume of the water decreases 
and becomes a minimum at 4° C. after which it increases 
again. Water is unique in this respect and the tempera- 
ture at which th6 water has its least volume is known 
as the temperature of maximum density, namely 4° C. 
or 39-2° F. The unit of mass on the metric system is 
one gramme, which is the mass of a cubic centimetre of 
water at 4° C. 



% 



vii] Expansion of Liquids 85 

The immediate effect of this pecuUar behaviour of 
water is the preservation of animal and vegetable life 
in lakes and ponds in winter time. The water below 
the ice will never fall below this temperature of 4° C, 
or 39-2° F. because at any other temperature higher or 
lower it will be Ughter bulk for bulk and will therefore 
remain on top. As a pond cools down (it should be 
noted that this cooling will only take place at the 
surface) the water at the top will contract and sink 
until the whole pond is at 4° C. On further cooling 
the surface water will become lighter and will remain on 
the top and so will ultimately freeze. But the water 
below the ice will be at 4° C. Water and ice are bad 
conductors of heat and thus the pond will never become 
frozen to any great depth. It is well known that an 
ice coating on a pond should be flooded each night if it 
is desired to get thick ice on the pond. 

The table given below shews how the density and 
the volume of water changes between the temperatures 
of 0° C. and 8° C. 



Temperature 


Density 


Relative volume 


0°C. 


0-99987 


100013 


2°C. 


0-99997 


1-00003 


4°C. 


1-00000 


1-00000 


6°C. 


0-99997 


1-00003 


8°C. 


0-99989 


1-00012 



CHAPTER VIII 

EXPANSION OF GASES 

As we saw in Chapter III the volume of a gas depends 
upon the pressure to which it is subjected. It therefore 
follows that in considering how volume changes with 
temperature we shall have to be careful to keep the 
pressure of the gas constant, 

Charles found that gases expand uniformly and that 
as far as he could ascertain all gases have the same 
coefficient of expansion, namely 0-00366. As a matter 
of fact later experimenters have found that this is not 
strictly true, but it is sufficiently near the truth for our 
purpose. 

Gases expand much more than do soHds or Uquids 
under equal conditions and we have therefore to be 
more careful and particular about our definition of the 
coefficient of expansion. We must remember that the 
coefficient of expansion of volume of a gas is the increase 
in volume of a unit volume at 0° C. when heated from 0° 
to 1° C. 

We had better look at the importance of this. Let 
us suppose for exa6iple that that coefiicient of expansion 
was ^th. Now a volume of 1 at 0° C. would become 
M at 1° C, and 1-2 at 2° C. and so on. But if we take 
the volume of 1-1 at 1° C. and to find its volume at 
2° C. we were to take jj^ ol 1-1, viz. 0-11, and add this 



CH. viii] Expmisimi of Gases 87 

on to the original volume we should get a volume of 
1-21 at 2° C. 

This does not agree with the result we get by working 
from 0° C. So that if we are given that a certain gas 
has a volume of 1-1 at 1° C. and we are asked to find 
its volume at 2° C. we must first find what its volume 
would be at 0° C. and calculate from that point. 

In cases where the coefficient is small we need not 
bother to find the volume at 0° C. since the error caused 
would be quite negligible for practical purposes. We 
have adopted this view already in our examples on the 
expansion of solids, but in the case of a gas it will be 
necessary to work from the temperature of 0° C 

Charles' Law. Charles' law states that if a given 
mass of a gas be kept at a constant pressure and heated, the 
increase in the volume will be directly proportional to the 
increase in the temperature. 

If we represent the volume of a given mass of gas 
at constant pressure by Vq at 0° C. and by Fj at some 
temperature t° C. then according to our definition the 
coefficient of expansion K will be given by 

Fo(«-0) FoX^ ' 
i.e. the change in volume per unit volume at 0° per 
degree C. 

/. F,-Fo=FoxZx«, 

.-. F, = (Fo X Z X + Fo, 
or Vt == Fo (1 + Kt). 

Therefore we can easily find the volume at 0° C. and 
from that we can find the volume at any other desired 
temperature. 

Example. A given mass of a certain gas is 12 c.c. 



iW Expansion of Gaaes [ch. 

at a temperature of 15° C. ; what will it be at 60° C, 
the coefficient of expansion being 0-00366 ? 
Firstly we find the volume at 0° C. 
^15= ^o(l + -00366 X 15), 
12 = Fo(l + 15 X -00366), 

Then we find the volume at 60° C. from 
^60= ^o(l + -00366 X 60), 
.-. F6o= 11-375 X 1-2196 
= 13-875 c.c. 



Experimental verification. Charles' law may be 
verified and the coefficient of expansion of a gas 
determined by the dilatometer method similar to that 
described in the previous chapter. 

A bulb of known volume having a graduated stem 
can be arranged as shewn in Fig. 33. The bulb and 




Fig. 33 

part of the stem can contain air or any other gas and 
this is shut off from the outside air by means of a small 
pellet of mercury P which also serves as an index. If 
the volume of the bulb is fairly large compared with 
the stem the errors due to the exposed part of the stem 
will be very small, but the range of temperature which 
can be covered will not be very great. This should be 



viii] Expansion, of Gases 89 

determined by a preliminary experiment. Then the 
bath is heated up to the highest permissible temperature 
and readings are taken, as the bath cools, of tempera- 
tures and volumes. These can be plotted graphically 
and coefficients can be calculated from the various 
readings. The volume at 0° C. can be determined by 
experiment or can be obtained from the graph. 

Any bulb and stem may be readily calibrated by 
filling with mercury, and then weighing the mercury 
required. Similarly the volume per inch of tube can 
be determined by measuring the length of any pellet 
of mercury in the tube and then weighing it. From 
the density of the mercury and its mass the volume 
is calculated since density is the mass of a unit volume. 

There are again many more refined and elaborate 
devices for the verification of Charles' law, but if the 
principle of this is understood, the refinements can be 
appreciated quite readily by the intelligent student. 

Variation of Pressure with Temperature. We all 
know that if we confine a gas to a given space and heat 
it the pressure of that gas increases. Such pressure 
plays the all-important part in internal combustion 
engines and in the use of explosives. We have all 
witnessed the disasters to our air balloons in bygone 
days when they got too near to the fire. 

Regnault shewed that if the volume of a given mass 
of a gas was kept constant and its temperature increased 
the increase in the pressure was directly proportional 
to the increase in temperature. 

He found moreover that the coefficient of increase 
of pressure — namely the increase in the pressure of a 
unit pressure at 0° C. when heated 1° C. — was the same 
as the coefficient of increase in volume, -00366 or ^j.^. 



90 



Exj/ansiou of (jiittfs 



L<;ii. 




Fig. 34 



A simple form of apparatus for the verification of 
this law is shewn in Fig. 34. A hulb which contains 
the gas O is immersed in a bath B the temperature of 
which can be varied at will 
and determined by the ther- 
mometer T. The bulb is con- 
nected by a fine bore tube to 
one of the limbs of a U -tube — 
similar to the apparatus used 
for the verification of Boyle's 
law (page 43). By raising or 
lowering the right-hand limb 
R the mercury in the left-hand 
limb can be kept at the same 
position for various tempera- 
tures of the bath. The actual 
pressure of the gas at each 
temperature will be the atmospheric pressure in inches 
or centimetres of mercury plus or minus the difference 
in the levels of the mercury in L and R in inches 
or in centimetres — the volume of the gas being kept 
constant at each temperature by the adjustment 
of JR. 

Absolute zero of temperature. If, instead of using 
a mercury thermometer for the measurement of tem- 
perature, we use a gas thermometer — either on the 
constant volume or on the constant pressure principle — 
we should find a theoretical minimum temperature 
below which we^ could not use it. That is to say if we 
assume for a moment that the law of Charles and the 
corresponding pressure-temperature law hold good for 
all temperatures we should find that at a temperature 
of — 273° C. gases would have no volume and would 



viii] Expansion of Gases 91 

exert no pressure. This temperature is called the 
absolute zero of the perfect gas thermometer. 

Now it is not considered possible to annihilate 
matter at all, so that we must feel that there is a way 
out of this mystery. It lies in the fact that gases 
change into liquids before they reach that temperature 
and after that they no longer follow Charles' law. 

According to the Kinetic Theory of Gases (page 8) 
the pressure of a gas is caused by the agitation or bom- 
bardment of its molecules. Therefore if the gas exerted 
no pressure its molecules must be stationary. It is 
further suggested that as a body contains more and 
more heat the movement of its molecules is increased 
and vice versa. Therefore if we can reduce a gas to 
such a temperature that it exerts no pressure there 
will be no molecular movement and no heat. That 
temperature would therefore be the lowest possible or 
the absolute zero of temperature. 

The temperature of — 273° C. has never been 
reached in practice although in recent times the 
temperature of — 269° C. has been obtained. 

Fig. 35 shews a volume -temperature graph, volumes 
being plotted vertically and temperatures horizontally. 
If we get readings of the volume of any mass of a gas 
between 0° C. and 100° C. and then produce the graph 
backwards (assuming Charles' law to hold good) until 
the volume is zero we find that the temperature for this 
condition is - 273° C. 

It will be quite clear to our readers that if this point, 
— 273° C, were made the origin of the graph, that is to 
say if it were both a zero of temperature and volume, we 
could say that the volume was directly proportional to 
the temperature calculated from this zero. 



92 



ExpanMOit of Gaiio 



[CH. 



From tills we have adopted another temperature 
scale — called the Absolute scale — having the tempera- 
ture of — 273° C. as its zero and being equal to the 
Centigrade scale reading + 273. Thus 0° C. = 273° A., 

57° C. = 57 + 273 = 330° A., 

and - 38° C. = - 38 + 273 = 235° A., 

and so on. Charles' law may now be stated thus: 




©"A 73'A 



-IOO°C 

I 

I 
I 
I73''A 



IOO°C 200°C 

Temperature \ 

I I I 

273°A 373°A 473°A 



Fig. 35 

that the volume of a given mass of a gas kept at a constant 
pressure varies directly with the absolute temperature. 

Thus if PJi be the volume at Tj° Absolute, and Fg 
be the volume at ^2° Absolute, then 

Fi ^ Tj _ tj° C. + 273 
Fa" T2"^2°C. + 273' 
In the same way it can be seen that if the volume 



viii] Expansion of Gases 93 

is kept constant the pressure will vary directly as the 
absolute temperature : 

P, ^ TIA. 

P2 ^2°A.- 
Finally if we consider possible variations of each of 
the three quantities pressure, volume and absolute tem- 
perature, we shall find that 

when Pj, Fj and T^ are the pressure, volume and 

absolute temperature in one case, and Pg, V2 and T^ 

those in the second case. 

Examples. (1) Let us take the example on page 88. 

A given mass of a gas is 12 c.c. at 15° C. ; what will 

it be at 60° C. ? 

Vi Ti . 12 _ 15+2 73 _ 288 
Fa ~ ^2 ' • • F2 " 60 + 273 ~ 333 ' 

••• ^2= ^-^jgl^- 13-875 c.c. 

We see that it is much easier to solve the problem 
this way. 

(2) A mass of air has a volume of 24 c.c. at a 
temperature of 27° C. and a pressure of 30" of mercury. 
What will'be its volume at 77° C. and a pressure of 
20" mercury? 

•^2^2 ^ 2 

24 X 30 300 



• • F2 X 20 350 ' 
„ 24x30x350 ,„ 
•• ^^ = -20-^3-00 ^1^^- 

Absolute-Fahrenheit scale of temperature. Before 



94 Expamion of Gases [CH. viii 

concluding this chapter it may be well to point out that 
the absolute zero of temperature on the Fahrenheit 
scale would be — 459- 2°. By adding 459-2 to any 
Fahrenheit reading we shall get an Absolute-Fahrenheit 
scale. This scale could be used for the above calcula- 
tions. 

For example : If a certain gas has a volume of 
12c.c. at 59° F., what will be its volume at 140° F.? 
Fi _ Ti°A. 
F2 T2°A.' 
and using the Absolute-Fahrenheit scale T^ is 

459-2 + 59 = 518-2° 
and Tg is 459-2 + 140 = 599-2°, 

12 518-2 
• • F2 ~ 599-2 ' 
. „ 12 X 599-2 ,^„^^ 

EXAIklPLES 

1. A certain mass of air has a volume of 50 cubic inches at 
16° C, what will be its volume at 0° C. and at IW V.. the pressure 
being constant ? 

2. A certain mass of air has a volume of 3 cubic feet when the 
temperature is 27° C. and the pre-ssure is 15 lbs. per square inch: 
what will be its volume when the temperature is 227° C. and the 
pressure is 150 lbs. per square inch ? 

3. A certain mass of a gas at a temperature of 59-8° F. has a 
volume of 36 cubic feet, the pressure being 20 lbs. per square inch. 
If the temperature be increased to 212° F. what must be the pressure 
in order to keep the volume the same ? 

4. The volume of a certain mass of gas is 8 cubic feet at 15 lbs, 
pressure and temperature 20° C. If the pressure be doubled find the 
temperature to which it must be heated so that its volume becomes 
6 cubic feet. 



CHAPTER IX 

MEASUREMENT OF HEAT 

One of the effects which heat may produce when 
given to matter is an increase in temperature. This 
effect is not inevitable, but generally speaking a body 
becomes hotter when it receives heat. An exception 
may be quoted at once. If we put a vessel of water 
over a furnace we shall find that the water will get 
hotter and hotter (as shewn by a thermometer placed 
in it) until it starts to boil. But we shall find that it 
does not get any hotter after that. We may increase 
the temperature of the furnace as much as we please 
but the thermometer will not rise beyond the boiling 
point. Of course the water will boil away more quickly, 
and the heat is being used to produce this change of the 
state of the liquid. 

However, whenever heat is given to a substance 
which is neither at its boiling point nor melting point 
an increase in temperature will follow. It is readily 
conceivable that if two equal quantities of a substance 
are given equal quantities of heat they will be equally 
affected so far as temperature increase is concerned. 
It is also conceivable that if a certain quantity of heat 
be given to a substance and it produces a certain in- 
crease in its temperature, twice the quantity of heat 
will produce twice the increase in temperature. For 



96 Measurement of Heat [ch. 

all practical purposes this is true (just as a pint of 
liquid will rise to twice as great a level in a cylindrical 
vessel as half a pint) but actually it is not strictly the 
case. We shall, however, assume that it is, since the 
very small error involved is of little or no account in 
engineering practice. 

Unit of Heat. A unit quantity of heat energy is 
defined as that quantity necessary to raise the tempera- 
ture of a unit mass of water through one degree of 
temperature. 

Thus on the British system of measurement a unit 
of heat is the heat necessary to raise the temperature 
of 1 lb. of water through 1° F. This is called a British 
Thermal Unit and is commonly used by mechanical 
engineers. 

The quantity of heat necessary to raise the tem- 
perature of 1 gramme of water through 1° C. is the 
unit of heat on the metric system of measurement. 
This is called a Calorie. 

These units are not equal of course : and since there 
are 453-6 grammes to the pound and ^ of a degree 
Centigrade to the degree Fahrenheit it follows that 
there are 252 calories to the British thermal unit. 

It will be noted that water is chosen ^s the standard 
substance. We shall see presently that different sub- 
stances require different quantities of heat per lb. to 
produce one degree rise in temperature. 

Every unit mass of water will require a unit of heat 
for every degree its temperature is raised : and con- 
versely, on cooling, every unit mass will give out a unit 
of heat per degree fall in temperature. Thus the heat 
necessary to raise the temperature of 3 lbs. of water 
from 60° F. to 212° F. will be 3 x (212 - 60), viz. 



ix] Measu7'ement of Heat 97 

3 X 152 or 456 b.th.u. The heat given out by 4-5 lbs. 
of water cooHng from 60° F. to 32° F. will be 
4-5 X (60 — 32), viz. 126 b.th.u. That is to say the 
heat required or yielded by any mass of water M when 
it undergoes a change of temperature from t-^ to t^ 
will be 

M X (^2° - ^1°) units. 

The units will be calories if M is in grammes and 
t^ and ^2 s-re Centigrade ; and they will be British 
thermal units if M is in lbs. and ^^ and t^ are Fahrenheit. 

Specific Heat. If we take equal masses of iron and 
copper and heat them to the same temperature and 
then plunge them into two equal vessels of water at 
the same temperature, we shall find that the vessel 
into which we plunged the iron will become a little 
hotter than the other one. This suggests that the iron 
must have given out more heat than the copper. The 
heat given out must have been received by the water : 
and its temperature would rise. In the same way if we 
take equal masses of other different substances at equal 
temperatures and plunge them into separate equal 
vessels of water we shall find that these different sub- 
stances give out different quantities of heat. 

The quantity of heat necessary to raise the temperature 
of a unit mass of a substance through 1° is called the 
specific heat of that substance. 

The specific heat of copper, for example, is 0-094. 
That is to say 0-094 British thermal unit of heat will 
raise the temperature of lib. of copper through 1° ^, 
It also means that 0-094 calorie of heat will raise the 
temperature of 1 gramme of copper through 1° C 



9H 



Meamtrement of Meat 



CH. 



The following table gives the specific heats of some 
substances : 



«ilvfr (»or)r) 

Copper ()()!»4 

Iron 0112 

Mercury ... . . ... ... OO'.i'.i 

Glass ()•!!) 

Turpentine ... ... ... ... 0-43 

AluminiuTu ... ... ... ... 0-21 

Lead 0031 

Water • 1 

Ice 0-502 

Hydrogen (constant pressure) ... 3-402 

Air (constant pressure) 0-2427 

Air (constant volume) 0-171.5 



The fact that water has such a high specific heat 
compared with most other things is not generally 
appreciated by the man in the street. He is always 
inclined to think that a kettle absorbs as much if not 
more heat than the water it contains, and may even 
advocate the use of thinner kettles. Let us consider 
how much heat will be absorbed by a kettle made of 
copper, weighing 2 lbs., and containing 3 lbs. of water 
when heated from 70° F. to 212° F. 

Firstly, the kettle : 

1 lb. of copper heated through 1° F. will require 
0-094 unit of heat, 

therefore 2 lbs. of copper heated through 1° F. will 
require 2 x 0-094 units of heat, 

therefore 21bs. of copper heated through (212 — 70)°F. 
will require 142 x 2 x 0-094 units of heat. 

That is to say the kettle will absorb 26-7 units. 



ixj Measurement of Heat 99 

Secondly, the water : 

1 lb. of water heated through 1° F. will require 
1 unit of heat, 

therefore 3 lbs, of water heated through 1° F. will 
require 3 units of heat, 

therefore 3 lbs. of water heated through (212 — 70)°F. 
will require 3 x 142 units of heat. 

That is to say the water will absorb 426 units. 

Thus we see that the total heat absorbed by the kettle 
and the water is 452-7 units of which only 26-7 units 
are taken by the kettle. 

Water Equivalent. We could have taken it in a 
simpler way than this. Since 1 lb. of copper only 
absorbs 0-094 unit of heat for each degree rise in tem- 
perature, we can say that 1 lb. of copper is only 
equivalent to 0-094 lb. of water, since 0-094 lb. of water 
would absorb 0-094 unit for each degree increase. 
Therefore we could say that the kettle — viz. 2 lbs, of 
copper — was equivalent to 2 x -094, viz. 0-188 lb. of 
water, so far as the absorption of heat is concerned. 
We could then take it that the kettle and the water 
were together equivalent to 3-188 lbs, of water, and if 
3-188 lbs, of water are heated from 70° F, to 212° F. 
the heat required will be 3-188 x (212 - 70), viz. 
452-7 units, which agrees with the previous answer. 

Thus we can say that the mass of any substance 
multiplied by its specific heat is the water equivalent of 
that substance. This is of some assistance to us in our 
experiments connected with the measurement of heat. 

Measurement of Specific Heat. The substance 
whose specific heat is to be determined must be weighed, 
and it is heated in some way or other to some known 
or measurable temperature. It is then dropped into 

7—2 



100 Measurement of Heat [ch. 

a vessel containing a known quantity of water at 
a known temperature. The "mixture" is thoroughly 
stirred and its temperature is taken. From these particu- 
lars the specific heat of the substance may be calculated. 

It will be seen at once that there are certain practical 
difficulties connected with this experiment. Pre- 
cautions must be taken to avoid loss of heat as the 
substance is being dropped into the water ; and again, 
precautions niust be taken to prevent loss of heat from 
the water to the surrounding air. 

The vessel containing this water is usually called a 
calorimeter and generally consists of a cyhndrical copper 
vessel which is suspended inside a similar but larger 
vessel by means of three silk threads. The surfaces 
are kept well polished and the calorimeter losses are 
thus reduced to a minimum. In addition to this it is 
usual in important measurements to arrange that the 
first temperature of the water in the calorimeter shall 
be as much below the temperature of the surrounding 
air as the second temperature is above. In this way 
we get a slight gain balancing off a slight loss. 

The arrangement for heating the substance generally 
takes the form of a steam jacket J, J as shewn in Fig. 36. 
The substance S is suspended inside and a thermometer 
T is fixed near it. The heater is fixed on an insulating 
base with a sliding shutter which has the effect of 
opening or shutting the heater. The calorimeter is 
placed directly beneath the centre of the heater. When 
the jacket is heated and its temperature has been 
noted, the shutter is opened and the substance is lowered 
into the calorimeter as speedily as possible. The calori- 
meter and its contents are then removed, stirred, and 
the temperature read. 



IX] 



Measurement of Heat 



101 



Let us suppose that the following results were 
obtained. 

Mass of calorimeter empty 45 grammes. 

Material of calorimeter, copper of specific heat 0-094. 

(N.B. Only the inside vessel should be weighed as 
the outer vessel does not absorb any heat.) 

Mass of water in calorimeter 132 grammes. 

Original temperature 15° C. 




Shutter 



Calorimeter 



Fig. 36 

Mass of substance in calorimeter 116 grammes. 
Original temperature of substance in heater 92° C. 
Final temperature of "mixture" 22° C. 
The water equivalent of the calorimeter 

= 45 X 0-094 = 4-2 grammes. 



102 Meamirement of Heat [CH. 

Therefore the total equivalent mass of water 

= 132 + 4-2 - 136-2 grammes. 
Therefore the heat received 

= 136-2 X (22'- 15) = 953-4 units. 
Now this heat must have been given out by 116 
grammes of substance cooling from 92° to 22°, that is, 
through 70°. 

Therefore the heat which would be given out "by 
1 gramme cooling through 1° 

= ,?«--, = <>••''■ 

116 X 7 

Therefore the specific heat of the substance = 0-117. 

In all heat measurements our results are determined 
from the following fact : 

Heat received by calorimeter and water = heat given 
by substance inserted. 

There is no need for us to express any of this as 
mathematical formulae. The fundamental ideas are 
quite simple, and the examples can be and should be 
worked out from first principles. 

Calorific value of fuels. It is often very important 
that engineers should know how much heat is given by 
burning a known quantity of different kinds of fuel. 
As we have said before we buy fuel for the heat energy 
which we can get out of it, and the cheapest fuel is 
that w^hich will give the greatest amount of heat for 
every shilling which we pay for it. 

The number of heat units per unit of mass of fuel is 
called the calorific value of that fuel. 

One of the methods of determining this value is by 
the use of the Darling calorimeter, the main ideas of 
which are illustrated by Fig. 37, 



IX] 



Measurement of Heat 



103 



A known mass of the fuel is placed in a small 
crucible C which is placed inside a bell jar B. This 
jar is fastened down to a special base plate. The 
products of combustion can only leave the jar through 
the outlet at the bottom of the base-plate, and this 
outlet R is like a watering-can rose with very fine holes. 
A supply of oxygen — which, of course, is necessary for 
the combustion of the fuel — is admitted at the top of 



Oxygen 
inlet 




Fia;. 37 



the bell jar and its rate can be regulated by means of 
a regulator. 

The bell jar and its attachments thus form a small 
furnace and this is immersed in an outer vessel containing 
a known quantity of water at a known temperature. 



104 Meatturemi'ut of Iddt [oh. 

The fuel is then ignited (this being done by means of 
a small piece of platinum wire heated by an electric 
curi^nt) and the flow of oxygen is regulated so that 
the "flue gases" formed by the burning fuel bubble 
slowly up through the water. Thus they give out their 
heat to the water. 

When the fuel has completely burned itself out the 
water is allowed to flow inside the jar so that we can 
be quite sure that all the heat generated has been 
absorbed by the water. The temperature is then taken 
and the calorific value is calculated as shewn below. 

Mass of water = Mw lbs. 

Water equivalent of calorimeter: Bell-jar, etc. 
= Mc lbs. 

(This water equivalent is usually given by the makers 
of the calorimeter, but of course it can be calculated or 
determined by experiment. In this case a record would 
be kept for future use.) 

Total equivalent mass of water = Mw + Mc = M lbs. 

Original temperature of water = t° F. 

Final temperature of water after fuel has been 
burned = t° F. 

Therefore heat received by water = M x (ig — ^i) b.th.u. 

Mass of fuel burned = P lbs. 

Therefore if M {t^ — tj) b.th.u. were given by the 

combustion of P lbs. — ^A, — - British thermal units 

would be given by 1 lb. in burning. 

And this is the calorific value of the fuel. 

The results could all be taken with metric units, if 
desired, and the calorific value in calories per gramme 
could be determined. 



IX j Measurement of Heat 105 

The following table shews the calorific values of 
some fuels in British thermal units per lb. of fuel. 



Methylated alcohol 


11,320 


Steam coal 


15,600 


Benzol 


17,750 


Bituminous coal 


14,600 


Petrol 


20,000 


Coal gas (London) 


500 B.TH.U. 


Paraffin oil 


19,000 




per cubic foot 



Two values for the Specific Heat of a Gas. The 

reader has already noted that two values are quoted 
on page 98 for the specific heat of air. It has been 
found that if the volume is kept constant the gas ab- 
sorbs less heat per degree of temperature than it does if 
it is allowed to expand at constant pressure. This is an 
interesting and important matter to engineers. The 
explanation is to be found in the fact that if the gas 
expands it has to do work in pushing back the surround- 
ing atmosphere, just as if it were pushing back a piston 
in an engine cylinder. This work is done at the expense 
of some of the heat which is being given to it and there- 
fore we have to give it more heat to raise its temperature 
through each degree than would be necessary if it was 
not expanding. The additional heat represents the 
work which the gas is doing in -expanding. 

The methods for the determination of these specific 
heats are of a very refined order, and the details cannot 
be dealt with in this little volume. 



106 M(<if<i(i< iiif III ill' Ilfttf [<n. IX 



EXAMPLES 

1. Find the heat necessary to raise the temperature of 3-5 lbs. 
of water from 59° F. to 212° F. If the same amount of heat be given 
to 17-5 lbs. of iron at 59° F. to what temperature would it be raised ? 
The specific heat of iron = 0-1 12/ 

2. 4-8 lbs. of copper at 177° F. are plunged in 3 lbs. of water at 
60° F. and the resulting temperature of the mixture is 75-6° F. 
What is the specific heat of the copper? 

3. A copper calorimeter (sp. heat -094) weighs 0*2 lb. and 
contains 0-75 lb. of water at 50° F. What is the water equivalent 
of the calorimeter and the total equivalent weight of water of 
calorimeter and contents? It is found that when 2-5 lbs. of iron 
at some unknown temperature are placed in the calorimeter the 
temperature rises to 60° F. How much heat did the iron give out 
and what must its original temperature have been? Sp. heat dl 
iron -3 01 12. 

4. If all the heat given by 0-02 lb. of coal of calorific value 
15,600 B.TH.u. per lb. were given to a glass vessel containing 3 lbs. 
of water at 60° F. (the glass vessel weighing 2-7 lbs. and having a 
specific heat of 0-19) to what temperature would it be raised? 

5. A mass of 200 grammes of copper of specific heat 0-1 is 
heated to 100° C. and placed in 100 grammes of alcohol at 8° C. 
contained in a copper calorimeter of 25 grammes mass : the tem- 
perature rises to 28° C. What is the specific heat of the alcohol ? 

6. 3-5 lbs. of water at 200° F. are mixed with 5 lbs. of water 
at 60° F. the cold water being poured into the hot which is con- 
tained in a copper calorimeter of 1 lb. weight and specific heat 0-1. 
Find the temperature of the mixture (a) neglecting the calorimeter, 
(6) taking the calorimeter into account. 



CHAPTER X 



FUSION AND SOLIDIFICATION 

The third important effect of heat upon matter is 
that known as a change of physical condition such, for 
example, as the change of a substance from the sohd to 
the Hquid form. If such a change is effected without 
producing any change in the chemical constitution of the 
substance it is called a physical cJiange of state. When 
heat is given to ice it changes to water (which is 
chemically the same thing) and if more heat be given 
it will ultimately change again to steam, which again 
has the same chemical composition. 

When heat is applied to coal chemical changes take 
place, and the same applies to many other substances. 
But if no chemical change is produced then the physical 
change is produced : and we shall only consider such 
change in this volume. 

Melting Point of a Solid. The temperature at which 
a solid melts — that is to say changes into the liquid 
form — is called the melting point of that solid. Different 
substances have different melting points as the following 
table shews. 

Iron (wrought) 1600° C. 



Ice 


0°C. 


Aluminium 


600 


Antimony 
Bismuth ... 


440 
26.5 


Brass 


1015 


Carbon . . . 


3500 


Copper . . . 
Gold 


1050 
1250 


Iridium . . . 


1950 



Iron (cast) .. 


1100 


Lead 


325 


Mercury 


. - 39-5 


Platinum . . 


. 1700 


Silver 


. 1000 


Steel 


. 1350 


Tin 


. 231 


Tungsten . . 


. 3200 


Zinc 


. 420 



!()}{ Fusion it 11(1 Solidification [CH. 

The melting point is usually a well-defined tempera- 
ture though there are some substances like glasg, for 
example, which become plastic and slowly change to 
the fluid state. It is difficult to determine the exact 
melting point of such a substance. 

The solidifying point or freezing point of a liquid is 
that temperature at which it changes from liquid to 
soUd. This temperature is the same as the melting 
point. That is to say, ice melts at 0° C. and water 
freezes at 0° C. 

Heat required to melt a solid. In order to melt a 
soHd it is not enough to heat it to its melting point. 
Additional heat must be given when this temperature 
is reached and it will be found that such heat does not 
produce any increase in temperature until the whole of 
the soUd is melted. If some ice be placed in a vessel and 
the vessel be heated over a furnace it will be found that 

(a) the temperature of ice will increase if it were 
below 0° C. at the start : 

(6) when it reaches 0° C. it will remain stationary 
until every particle of ice is melted : 

(c) when the ice is all melted then the temperature 
of the water will rise. 

During this experiment the ice and water must be 
kept thoroughly stirred. 

The same thing exactly applies to the melting of 
any other substance though equal masses of different 
substances do not all require the same quantity of heat 
energy to melt them after the melting point has been 
reached. In this respect ice requires more heat than 
is required by any of the metals given in the above 
list. The reader must think this over carefully and 
see that he understands exactly what is meant. 



x] Fusion and Solidification 109 

Latent Heat of Fusion. The quantity of heat 
necessary to change a unit mass of a solid at its melting 
POINT to liquid at the same temperature is called the 
latent heat of fusion of that substance. 

For example the latent heat of fusion of ice (on the 
British system of measurements) is 144. That is to 
say 144 b.th.u. of heat are required to change 
1 lb. of ice at 32° F. into 1 lb. of water at 32° F. 
Conversely when 1 lb. of water at 32° F. freezes to ice 
at the same temperature it must give up 144 b.th.u. 
of heat. 

On the metric system the quantity of heat necessary 
to melt 1 gramme of ice at 0" C. and change it to water 
at 0° C. is 80 calories. 

The latent heat of fusion of a few substances is 
shewn below. 

Latent heat in British thermal units per lb. of 
substance. 



Ice ... 


144 


Bismuth 


23 


Zinc ... 


i51 


Sulphur 


17 


Silver 


38 


Lead . . . 


9-6 


Tin ... 


25-6 


Mercury 


5 



- An interesting experiment, which illustrates how 
melting points may be determined and demonstrates 
at the same time the fact that heat is absorbed or 
yielded by a substance in changing its physical state, 
may be performed by placing some paraffin wax, or better 
still some naphthalene, in a boiling tube and heating 
this tube in a water bath. The bath should be 
heated until all the wax has melted. A thermometer 
should then be placed in the hquid formed and the 
bath allowed to cool. Readings of the thermometer 



110 



Fiution and Solidiji cation 



[CH. 



should then be taken at regular intervals of time — say 
every half-minute. It will be noted that the thermo- 
meter falls steadily to a certain "temperature after which 
it remains stationary (or in some cases it may even 
rise again slightly) for several minutes. During this 
stationary period it will be noted that the wax is 
solidifying, and when it has all become solid the tem- 
perature will start to fall again. 

Fig. 38 gives two graphs (one for wax and the other 
for naphthalene) shewing how the temperature falls with 

90 



80 



70 



V 


\ 






















\ 


\ 


■ 




















\ 





y 






















\ 


\ 






















\ 


\^ 


\ 










<^ 












\ 


N 


v/ 








:^ 


k 












\ 








\ 












^\ 


^-7v 












\ 












^ 


^t( 












^ 




X' 


\^\ 






^ 


















^ 


^ 







2 4 6 8 



10 
Mini 


12 

ites 


14 


16 


18 


20 22 24 


Vm. 


38 











the time. The melting point is that temperature at which 
the cooUng temporarily ceases. The explanation lies in 
the fact that on solidifying the substance gives out heat, 
and this heat suffices to prevent the temperature from 
falling. In the case of substances with a more defined 
melting point than wax the heat given out on soUdifi- 
cation will cause the temperature to increase. This is 
shewn on the naphthalene graph. It should be pointed 



x] Fusion and Solidification 111 

out that the melting point of the naphthalene is given 
by the horizontal part of the graph. 

We may also compare, roughly, the latent heat of 
each substance by noting the length of time during 
which the temperature remains practically constant. 
The longer the time the greater must be the quantity 
of heat given out. Of course, the reader will see that 
such comparison could only be made if equal masses of 
substances were used and allowed to cool under equal 
conditions. This in turn would mean that only sub- 
stances with approximately equal melting points could 
be compared in this way. From our curves we can see 
that the naphthalene has a greater latent heat than the 
wax. 

Change of volume with change of state. It is found 
that some substances, like water, increase in volume in 
passing from the hquid to the solid state. That is to 
say a given mass of the substance will have a greater 
volume in the solid state than in the liquid state at the 
same temperature. We say that such substances expand 
on solidification. Other substances contract on solidifi- 
cation. 

This is important to engineers for many reasons. 
Firstly, whenever a casting is made we have a liquid 
changing to solid. If that substance contracts on 
solidification the chances are that we shall not be able 
to get a good casting- — that is to say a well defined 
casting — because the metal will shrink away from the 
sand mould. If we can use a metal which expands 
slightly on solidification, or one which does not change 
in volum.e, we shall get sharp castings which will not 
need so much machining. Metals like copper and iron 
contract on solidification. Antimony and bismuth 



112 Ftmon ami Solidificafion [CH. 

expand on solidification. Some alloys like type-metal 
(an alloy of lead, tin and antimony) expand on solidifi- 
cation. In fact that is the sole reason why this par- 
ticular alloy is used for making type. Some readers 
may have seen castings which were ready for immediate 
assembling on being taken out of the sand. They are 
sharply defined, have smooth surfaces, and do not 
require any machining. 

Secondly, if there is going to be any appreciable 
change of volume then account will have to be taken 
of this in the size of the pattern. The volume of the 
pattern will be the volume of the molten metal. 

Again, especially in the case of larger castings, the 
metal nearer to the sand will solidify first, so that when 
the inner portions sofidify stresses are produced due to 
internal contractions or expansions, and these may 
cause the casting to break. 

It is well known that water expands on sofidification. 
Water pipes are burst in winter time by that expansion. 
It is that same expansion which breaks up the soil for 
the farmer. 

Determination of the Latent Heat of Fusion of ice. 
A calorimeter, of known water equivalent, containing 
a known mass of water at a known temperature is 
taken, and into this are dropped small pieces of dry 
ice (each piece must be carefully dried with flannel). 
This process is continued until the temperature of 
water has been reduced several degrees and when all 
the pieces of ice which have been introduced are seen 
to be melted the temperature is taken. The calorimeter 
and its contents are weighed again so that the mass -of 
ice which has been melted may be determined. From 
this the latent heat may be calculated. 



x] Fusion and Solidification 113 

The heat given out = (total equivalent mass of 
water) x (fall in its temperature). 

The heat received = (mass of ice x latent heat of 
fusion) + (mass of . ice x rise in temperature from 
melting point to final temperature). 

It will be seen that unless the temperature of the 
water is reduced to the melting point then the ice will 
receive heat firstly to melt it and secondly to heat the 
melted ice up to the final temperature of the water in 
the calorimeter. 

Since the heat received = heat given out, 

the latent heat is easily determined. 

In performing the experiment it is well to start with 
the temperature of the water a few degrees above and 
to stop adding ice when it is the same number of degrees 
below the temperature of the room. The pieces of ice 
should be small and clean, and they should not be 
touched by the naked fingers. 

Solution: Freezing mixtures. Whenever a solid 
dissolves in a liquid without producing any kind of 
chemical change the temperature of the liquid is 
reduced. A chemical change always generates heat : 
and thus when a solid is dissolved in a liquid and pro- 
duces a chemical combination the liquid will be heated 
if the chemical change is greater than the physical 
change and vice versa. 

A mixture of salt and pounded ice or snow falls to 
a temperature as low as — 22° C. or — 7-6° F., according 
to the proportions of ice and salt. 

Effect of Pressure on the Melting Point. The 
temperature at which a solid melts is only slightly 
affected by pressure. Ordinary changes in atmospheric 
pressure do not produce any measurable effect upon 

V. Y, 8 



114 i'nsiiui iind So/if/t/ica/ ioti |('H, X 

the melting point, but it greater pressures be applied it 
is found that 

(a) substances which expand on solidification have 
their melting points lowered by an increase in pressure, 
and 

(6) substances which contract on solidification have 
their melting points raised by an increase in pressure. 

That is to say ice can be melted by the application 
of great pressure, but of course the water so formed will 
be below the temperature of the freezing point and will 
freeze again at once when the pressure is released. 

The making of a snowball ; the freezing together of 
two coUiding icebergs ; the progress of glaciers, are all 
explained by this. 

EXAMPLES 

1. How much heat would be necessary to heat up 3 lbs. of ice 
from a temperature of 10° F. to its melting point, to melt it, and to 
heat the water to the boiling point ? The specific heat of ice is 0-5 
and its latent heat is 144 on the BritLsh system. 

2. Compare the quantities of heat necessary to melt 4 lbs. of 
each of the following substances assuming thai they are all at' 32° F. 
to start with : ice, silver and lead. See pages 107 and 109 for melting 
points and latent heats, and page 98 for specific heats. 

3. A cavity is made in a large block of ice and into it is put 
an iron sphere at a temperature of 1000° F. The iron weighs 
0-64 lb. and its specific heat is 0-112. How much water will be 
formed in the cavity? 

4. How many heat units on the c.g.s. system would be given 
out by half a litre of water in cooling down from 15° C. and freezing 
at 0° C. ? If this heat were given to 1 lb. of lead at 15° C. to what 
temperature would it be raised ? (Melting point, 325° C. : specific 
heat, 031 : latent heat, 9-6.) 



CHAPTER XI 

VAPORISATION 

Just as a solid may be changed to the Hquid form 
by the apphcation of heat so can a hquid be changed 
to the gaseous form. This change of physical state is 
called vaporisation, the reverse change (from gas to 
liquid) being called condensation. 

Vaporisation can take place either by the process 
known as evaporation or by the process of boiling or 
ebullition. These processes differ from one another. 
Evaporation takes place at all temperatures but it 
only takes place from the surface of a liquid. If equal 
quantities of water are placed in different vessels — one 
an open shallow dish, the other a tall narrow flower 
vase, for example — and left over night in the same 
room after having been weighed, it will be found next 
morning that the shallow vessel has lost more weight 
than the other one. We all know how a cork in a 
bottle will prevent evaporation : how an imperfect cork 
is a useless thing in a scent or other spirit bottle. 

Ebullition or boiling will only take place at one 
definite temperature for a given liquid at a given pressure, 
and it takes place throughout the whole mass of the 
Uquid. 

Boiling Point. We will deal with ebullition first. 
A hquid is said to be boifing when bubbles of vapour 

8—2 



IIU VnjHfn'siifioii [CH. 

fomied at the bottom of the vessel rise up throughout 
the mass of the hquid and "burst" into tlie space 
above. Such bul)bles must not be confused with the 
more minute air bubbles which may rise up as soon as 
heat is supplied. 

As soon as the liquid commences to boil its tempera- 
ture tvill cease to rise. The temperature of the hquid 
when this happens will be the boiUng point of that 
liquid : the temperature of the vapour in the space 
above will be the boihng point of that liquid which 
is formed by the condensation of the vapour. For 
example, if we boil some salt water we shall find that 
the temperature of the hquid is higher than that of the 
vapour above it. As we know, the vapour is steam 
and it will condense to water. Therefore the tempera- 
ture of the vapour is the boiling point of water: but 
the temperature of the hquid is the boiling point of 
that particular sample of salt water. 

As a general rule if the hquid is of the same chemical 
composition as the vapour above it we take the tem- 
perature of the vapour, because the boiling point of a 
hquid is shghtly affected by mechanical impurities and 
by the material of the containing vessel. 

Effect of Pressure on the Boiling Point. If we test 
the boiling point of a hquid on different days we shall 
find that it varies and that it is sHghtly higher when 
the barometer is higher. This suggests that the 
boiling point is affected by pressure. Complete in- 
vestigation leads to the discovery that a given hquid 
may be made to boil at any temperature within wide 
limits and that an increase in pressure raises the boiling 
point of all liquids whilst a decrease in pressure lowers 
the boihng point. 



I 



XI] 



Vaporisation 



117 



The reader naturally enquires what is the boiling 
point of a Uquid? The answer is that we must define 
the boiling point of a given liquid as the temperature 
at which it boils at some definite pressure, and that the 
boiling points of all liquids should be taken at that 
pressure. The pressure chosen for this purpose is the 
normal atmospheric pressure- — that is to say the pres- 
sure of the atmosphere when the barometric height is 
30 inches of mercury. This pressure is sometimes 
called a pressure of 1 atmosphere and is equivalent 
to 14-7 lbs. per square inch. Thus the boiling point 
of water is 100° C. or 212° F. when it is boiled in a 
vessel open to the atmosphere and the barometer 
stands at 30 inches. 

If the water be boiled in a vessel which can be closed 
- — like the boiler shewn in 
Fig. 39— it will be found 
that, as the steam pressure 
inside increases, the boiling 
point will rise as shewn by 
the thermometer. The pres- 
sure can be determined by 
means of a pressure gauge, 
either of a direct reading 
pattern or of the pattern 
shewn in the figure. This 
is a U-tube having fairly 
long limbs. Mercury is put 
into this and when it has the 
same level in each limb then 
the pressure of the steam 
must be equal to that of the atmosphere. As the steam 
pressure increases the mercury will be forced down the 




Fig. 39 



118 



VaporisaUon 



[CH. 



left and up the right limb and the steam pressure will 
then be greater than the atmospheric pressure by an 
amount represented by the difference in level of the 
mercury in each hmb. That is to say, if the difference is 
6 inches and the atmospheric pressure is 30 inches then 
the steam pressure must be equivalent to that produced 
by a 36 inch column of mercury. Thus the relationship 
between the pressure of the steam and its temperature 
can be determined within the ranges possible with the 
apparatus. 

Fig. 40 is an illustration of a converse experiment. 
It shews how water may boil 
at a lower temperature than 
100° C. by reducing the pressure 
upon it. Some water is put 
into a round-bottomed flask 
and boiled. When it is boiling 
and steam is issuing freely we 
know that all the air has been 
driven out of the flask. The 
flame is removed and a cork 
with a thermometer is fitted. 
Then some cold water is 
squeezed out of a sponge on 
to the flask and it is noticed 
that the water inside at once ^'J^- *^ 

begins to boil again. The colder the water in the 
sponge the more vigorous will be the boihng of the water 
inside the flask, but of course the thermometer will 
indicate a rapidly falling temperature. 

Obviously the cold water will cause some of the 
steam inside to condense : this condensation will reduce 
the pressure : this reduction will lower the boiling point 




Hi= 



^^ 1 



XI] 



Vaporisation 



119 



and the water will boil. There is always the risk of 
the flask breaking in this experiment, and it should be 
made of good quality glass, and of the shape shewn. 

Temperature of steam at different pressures. The 
graph shewn as Fig. 41 indicates the temperature of 



400 
350 
300 
250 
200 










,-^ 












^ 










/ 












/ 


/ 












/ 














/ 














100 

































5 


K 


)0 1 


50 2( 


)0 2> 


30 3C 






Pressure in lbs. per sq. inch 
Fig. 41 

steam at various pressures. At atmospheric pressure, 
14-7 lbs. per square inch, the temperature of the steam 
is 212° F. At a pressure of 150 lbs. per square inch it 
is 358° F. : at 200 lbs. per square inch it is 381° F. and 



1 20 Vaporisation [oh. 

at 300 lbs. pressure it is 417° F. The average working 
steam pressures lie between 150 and 200 lbs. per square 
inch. Since the relationship between pressure and 
temperature can be obtained from the above graph, 
and since the relationship between the height of a place 
above sea level and the atmospheric pressure at that 
place compared with sea level pressure can also be 
obtained from a similar graph, it is quite obvious that 
height above sea level may be measured by finding the 
boiling point of water at various heights. 

Evaporation. As we have said before this process 
goes on at all temperatures but only from the surface 
of a liquid. Our common experiences have taught us 
that some liquids evaporate much more quickly than 
others. We all know that petrol, scent, alcohol and 
benzoline will evaporate very quickly indeed, and 
we know the necessity for well-fitted stoppers for the 
vessels containing such liquids. We also know from our 
own experiences how water will evaporate or dry up 
more quickly on some days than on others. We know 
too that it is not entirely a question of temperature. 
We can think of hot close days in summer when water 
will not dry up at all. On such days the atmosphere is 
said to be saturated with water vapour : it cannot hold 
any more, and consequently no more evaporation of 
water can take place. That will not affect the evapora- 
tion of other liquids : but if the atmosphere could 
become saturated with petrol vapour (we hope that it 
never will) then even petrol would cease to evaporate. 
That indeed is the secret of the cork in a bottle. The 
space in a bottle jibove the liquid soon becomes satu- 
rated ; and then the liquid cannot evaporate any more : 
but if there were no cork to the bottle then the vapour 



XI J Vaporisation 121 

would go out into the atmosphere in a vain attempt 
to saturate that. 

Heat necessary for Evaporation. Although this 
process goes on quietly and at all temperatures yet heat 
is necessary for its accomplishment. If a little alcohol, 
or petrol, or, better still, ether be poured on to the hand 
a sensation of cold will be experienced. Yet if the tem- 
perature of the liquid be taken it will be found to be 
the same as that of the room in which it is. The 
sensation of cold is brought about by the fact that the 
liquid absorbs heat more or less rapidly from the hand 
in proportion to its rate of evaporation. Thus the 
ether will feel colder than the alcohol, which in turn 
will feel colder than water — though in fact all three will 
have practically the same temperature*. 

The rate at which they evaporate depends upon 
their boiling point and upon the condition of the space 
above them. A liquid with a low boiling point will 
evaporate much more quickly than one with a high 
boiling point — other things being equal. Nevertheless 
the liquid will require heat and the greater its rate of 
evaporation the more heat it will need. Some readers 
may have been unfortunate enough to have had their 
gums frozen prior to a tooth extraction. The "freezing " 
is produced by the rapid evaporation of ether absorbing 
much heat from the gum. 

The cooling effect produced by "fanning" the face 
is due to the fact that the fan is continually replacing 

* When a liquid evaporates the portion of liquid remaining 
will generally have its temperature diminished. How much it is 
diminished will ' depend upon the quantity of liquid, the rate of 
evaporation and the rate at which it receives heat from external 
sources. 



122 Vaj)orisafi(Hi [vH. 

the air near to the face with comparatively fresh and 
unsaturated air so that evaporation of the moisture on 
the face can proceed more rapidly. This evaporation 
can only take place by absorbing heat from the face : 
hence the coohng sensation. The same thing applies 
to the common method of finding which way the wind 
blows : that is by holding a moistened finger in various 
directions. That direction in which it feels coldest is 
the direqtion from which the wind is proceeding. 

Vapour Pressure. Every kind of vapour exerts 
some pressure. The pressure which it exerts depends 
upon the amount of vapour present and upon the 
temperature. If the temperature is constant then as 
more and more liquid evaporates the pressure of the 
vapour will increase until the space is saturated with 
that vapour. Thus it follows that at a given tempera- 
ture a particular vapour will exert a maximum pressure 
when the space is saturated. 

But though a space may be saturated with one 
vapour it can hold other vapours. And the total 
pressure in any enclosed space will be the sum of all 
the pressures produced by the several vapours. (This 
is known as Dalton's law but it is only approximately 
true in most cases.) 

If a space be saturated %ith vapour and the tem- 
perature be increased it will be found that the pressure 
increases — though not proportionately. It will also be 
found that when the vapour pressure is equal to that 
produced by 3.0 inches of mercury the temperature will 
be the boiling point of that substance. 

And from this it has been shewn that a liquid will 
boil whenever the pressure acting upon it is equal to 
its saturated vapour pressure. Therefore we can boil 



xi] Vaporisation 123 

a liquid at any temperature provided that we can 
adjust the pressure upon it to equal that of its saturated 
vapour pressure at that temperature. The boiling 
point of a liquid may therefore be defined as that 
temperature at which its vapour pressure is equal to 
that of 30 inches of mercury. 

Boyle's Law and Vapour Pressure. If a saturated 
vapour occupies a definite volume and we reduce the 
volume, then if Boyle's law were to hold good the 
pressure of the vapour would be increased thereby. 
Actually however nothing of the kind occurs. The 
saturated vapour pressure cannot be increased except 
by an increase of temperature. We find on reducing 
the volume that some of the vapour condenses : but 
the pressure remains the same. Boyle's law does not 
hold good ! 

An experiment was performed by Dalton to illus- 
trate this. He made an ordinary mercury barometer 
using a longer tube than usual and a longer cistern 
(Fig. 4:2, A). Then he introduced a drop of ether into 
the tube by means of a bent pipette. This rose to the 
top and immediately evaporated, the pressure of the 
vapour causing the mercury to fall a little (B). Then he 
introduced a little more ether and a further fall of the 
mercury resulted. . So he continued until he noticed 
that the ether ceased to evaporate, shewn by the 
appearance of a layer of ether Uquid on the top of the 
mercury (C). He then found that the introduction of 
more ether did not increase the pressure — the liiercury 
remained at the same height — but simply added to the 
quantity of ether liquid floating on top of the mercury. 
Then he lowered the barometer down into the cistern 
{D and E) thereby diminishing the volume of the space 



Vnporixdt'um 



[CH. 



above the mercurv, but he found that the pressure was 
not alt<>red — shewn by tlie mercury remaining at the 
same level. At the same time he noticed that the 
quantity of liquid ether above the mercury increased. 
Then he gradually withdrew the tube out of the cistern 
so increasing the volume of the space above the mercury. 




Fig. 42 

But again he found that the pressure remained constant 
and that the quantity of liquid ether diminished. When 
he was able, to get the tube high enough so that all the 
liquid ether had disappeared {F) then he found a slight 
drop in pressure shewn by the mercury rising [O). 

He thus found that so long as a space is saturated 
with vapour that vapour will not obey Boyle's law : 



XI J Vajjorisation 125 

that no change in pressure could be produced by altering 
the volume of the space so long as the space was saturated. 
He also found by further experiment that Boyle's law 
does not hold good even when a space is not saturated ; 
but that the further the space is from saturation the 
closer does it follow the law. 

Temperature and Vapour Pressure. An increase in 
temperature will cause an increase in pressure in either 
a saturated or an unsaturated space. 

If a space be unsaturated a decrease in temperature 
will also cause a decrease in pressure, but if the tempera- 
ture be lowered sufficiently (depending upon the vapour 
under experiment) the space will become saturated and 
some of the vapour will condense : but the pressure 
will decrease so long as the temperature is decreased. 

Charles' law does not hold good : but it is approxi- 
mately true in the case of non-saturated spaces ; and 
the further the space is from saturation the closer does 
that space obey the law. 

Latent Heat of Vaporisation. Heat is necessary to 
vaporise a liquid whether the process of vaporisation is 
that of evaporation or of ebullition. The number of 
units of heat required to change a unit mass of a liquid 
into the gaseous state without a change in temperature is 
called the latent heat of vaporisation of that liquid. 

It has been found that this is not a constant quantity 
for a given substance : it depends upon the temperature 
at which vaporisation takes place. However, it is usual 
to speak of the latent heat of vaporisation of a substance 
as the quayitity of heat necessary to clmnge a unit mass of 
the liquid at its normal boiling point to vapour at the same 
temperature. 

We are chiefly concerned with water and steam. 



126 Voporisaffo)f [ch. 

The latent heat of vaporisation oi uatei' — more com- 
monly called the latent heat of steam — is 066 British 
thermal units per pound, or 537 calories per gramme. 

This means that in order to change 1 lb. of water 
at 212° F. into 1 lb. of steam at 212° F. we have to 
supply 966 British thermal units of heat. Conversely 
when 1 lb. of steam at 212° F. condenses to water at 
the same temperature it gives out 966 British thermal 
units. 

Sensible Heat and Total Heat. If we have 1 lb. of 
water at 60° F. and we wish to convert it to steam at 
atmospheric pressure we shall have to give it heat 

(1) to raise its temperature from 60° F. to 212° F. and 

(2) to convert it from water at 212° F. to steam at 
212° F. 

For this we shall require (1) (212 — 60) x 1 units, 
and (2) 966 x 1 units, that is to say 1118 units in all. 

The heat which produces a change in temperature 
is often called the sensible heat. In the case just 
quoted the sensible heat amounts to 152 units. The 
sum of the sensible heat and the latent heat is called 
the total heat. 

Determination of the Latent Heat of Steam. In this 
measurement it is necessary to pass a known mass of 
dry steam into a calorimeter of known water equivalent 
containing a known mass of water at a known tempera- 
ture. This steam will heact the water and from the 
increase in temperature we can easily find how much 
heat the water and the calorimeter have received. Now 
all this must have been given out by the steam and it 
gave it (a) in condensing, (6) in cooling down from water 
at the boiling point to water at the final temperature of 
the calorimeter. As we can easily calculate this latter 



xi] Vajmrisatio^i 127 

amount, we have only to subtract it from the total 
heat received by the calorimeter and the remainder 
must represent the heat given out by the steam in 
condensing without change in temperature. We can 
then calculate how much a unit mass of steam would 
have given out and the latent heat of steam is deter- 
mined. 

The usual method is as follows : 

Weigh the inner vessel of the calorimeter. 

Partially fill with water and weigh again. 

From this get the weight of the water. 
^ Add to this the water equivalent of the calorimeter. 

Take the temperature of the water. 

Then allow dry steam to pass into the water. 

When the temperature of the water has risen some 
20 degrees shut off the steam, stir well, and take the 
final temperature of the water in the calorimeter. 

Weigh again so that you may get the mass of the 
steam condensed. 

Calculate the value of the latent heat of steam. 

The chief points of importance in the performance 
of this experiment are (a) to be sure that the steam 
which is passed into the calorimeter is quite dry and 
does not carry any water particles with it ; and (6) to 
prevent loss of heat due to radiation from the calori- 
meter. The steam may be made dry by using some kind 
of a steam dryer such as that shewn in Fig. 43. The 
loss of heat can be reduced to a minimum by arranging 
that the temperature of the water in the calorimeter 
shall be as much below the temperature of the room 
at the beginning of the experiment as it is above it 
at the end. Thus the loss and gain of heat will approxi- 
mately balance. 



\'2i\ 



Viijutnsntitnt 



[CH. 



There is nothing difficult about the calculations. 
The only point which is likely to be overlooked is that 
the heat given out by each unit mass of steam in con- 
densing down to the final temperature is the total heat, 
and that this is the sum of the sensible heat and the 
latent heat. 



Steam 
entry 



Exhaust ^ 
for condensed 
water 




Steam exit 
to Calorimeter 



Fig. 43 



Variation of Latent Heat of Steam with Temperature. 
Regnault fovmd that the latent heat of steam was not 
a constant quantity. He found that as the tempera- 
ture at which the steam is produced increases (due to 
increased pressure upon the water) the latent heat 
decreases and vice versa. 

It has been shewn that the variation is approxi- 
mately as follows: for each degree F. above the 
boiling point (212°) the latent heat of steam is dimin- 
ished by 0-695 b.th.u. per lb. of steam, and for each 
degree F. below the boiling point the latent heat is 
increased by 0-695 b.th.u.. per lb. of steam. 



xi] Vaporisation 129 

Thus at a temperature of 300° F. the latent heat of 
steam will be 966 less 0-695 unit for each degree above 
212°. That is to say the latent heat will be 

966 - (88 X 0-695) - 966 - 61-16 = 904-84- 

Similarly at a temperature of 180° F. (that is under 
reduced pressure) the latent heat of steam would be 
966 + {(212 - 180) X 0-695} = 988-24. 

On the metric system of units the variation is 
0-695 calorie per gramme for each degree Centigrade 
above or below the boiling point (100° C). 

Pressure and Temperature of Saturated Steam. 

Although we know that an increase in pressure 
causes an increase in temperature of the steam above 
boiling water yet no definite law connecting these 
quantities has been expressed. Certain empirical 
formulae have been deduced to enable one to calculate 
the pressure at some known temperature or vice versa, 
and these formulae are often used for the purpose. 
It is more usual, however, for engineers to use tables 
which have been drawn up from the formulae. These 
tables shew at a glance the value of the pressuie 
for any temperature. The graph shewn in Fig. 41 is 
plotted from such a table. 

Pressure and Volume of Saturated Steam. Again 
there is no simple law connecting the pressure and the 
volume of saturated steam. This will be discussed 
again in the chapter on Thermo -dynamics. 

Hygrometry. Hygrometry is the measurement of 
the amoimt of water vapour present in the air. The 
actual amount of water vapour present in a given mass 
of air is called the absolute humidity of that air. This is 
determined by passing a known volume of the air 
through some previously weighed tubes containing 

p.y. 9 



130 Vaporisation [CH. 

some substance (like calcium chloride) which will 
readily absorb all the water vapour. The tubes are 
again weighed and the increase represents the amount 
of water vapour which was present in that particular 
sample of air. 

The absolute humidity of the air varies from day to 
day. But so far as our sensations are concerned we 
may easily be led into errors in this respect. In the 
early morning or after sunset we might assume that 
there is more vapour in the air than at noon, whereas 
the converse might be true. Or in other words it does 
not follow that, because the air is saturated on one 
occasion and not on another, the actual amount of 
vapour present is greater. 

When the air feels "dry" more vapour is necessary 
to saturate it. When it feels "moist" it is saturated 
or nearly saturated. Further when the temperature is 
high more vapour will' be necessary to produce satura- 
tion than when it is low. Thus it is quite possible that 
the absolute humidity on an apparently "dry" day in 
summer is greater than on an apparently "moist" day 
in winter. 

The ratio of the quantity of water vapour actually 
present in a given volume of air to the quantity which 
would be necessary to produce saturation at the same 
temperature is called the relative humidity. 

Thus when the relative humidity is 1 the air is 
saturated and the smaller the relative humidity the 
further is the air from saturation. 

The Dew-point. The temperature at which the 
amount of vapour actually present would produce 
saturation if a volume of the air were cooled at constant 
pressure is called the dew-point. This temperature will 



xi] Vaporisation 131 

always be lower than the air temperature unless the 
air be saturated or supersaturated, in which case rain 
will be falHng. Dew may be regarded as "local" rain: 
the word local being used to indicate the immediate 
neighbourhood of blades of grass, etc., which become 
very cold at night due to excessive radiation of heat 
(see p. 148). 

Instruments used to determine the dew-point are 
called Hygrometers. There are several different forms 
and the principle consists in cooling d(5wn some surtace 
to which a thermometer is thermally connected until 
a film of dew appears. The temperature is read, and 
the cooling process discontinued. When the film dis- 
appears again the temperature is read again and the 
mean of these readings is the dew-point. 

So far as the dew-point of the atmosphere is con- 
cerned these readings must be taken out of doors, other- 
wise the dew-point found is simply that of the air in the 
room in which the experiment was performed and this 
would afford no index of the atmospheric conditions. 

The wet and dry bulb hygrometer is very commonly 
used though its users do not bother as a rule to find 
the dew-point. The instrument consists of two similar 
thermometers placed side by side. One of these has 
some musHn round its bulb and some cotton wick 
attached to this muslin dips into a vessel of water. 
The water runs up the wick and so keeps the muslin 
moist. This moisture evaporates, absorbing heat from 
the thermometer which therefore records a lower 
temperature than the dry bulb thermometer. Clearly 
the lower the dew-point the more rapid will be the 
evaporation of the water on the muslin and the lower 
will be the wet bulb thermometer reading. This 

9—2 



132 Vupoi'imtwa [CH. XI 

reading is not the dew-point: but tables have been 
drawn up by means of which the dew-point may be 
obtained from the readings of the two thermometers. 

This instrument is generally quoted in the daily 
meteorological reports and the readings of the dry and 
wet bulb thermometers are given. The man in the 
street understands that if the difference of the readings 
is great the air is dry and there is no immediate prospect 
of rain ; whilst if the wet thermometer is nearly as 
high as the dry thermometer he had better be provided 
with an umbrella. For once in a way the man in the 
street is on the right path. 

EXAMPLES 

1. 10 lbs. of steam at 212° F. are condensed into a large vat of 
ice at 32° F. How much ice will be melted, assuming that the 
temperature of the vat remains at 32° F. all the time ? 

2. Steam is condensed by allowing it to pass through a large 
length of coiled tube in a vessel containing 120 lbs. of water. The 
original temperature of the water was 59° F. and after 15 minutes 
it was found to be 130° F. : how much steam was condensed? 

3. How much heat would be necessary to convert 12-5 lbs. of 
ice at 32° F. to steam at 212° F.? Give the answer in British 
thermal units and in calories. 

4. If a boiler receives 120b.th. units of heat per minute through 
every square yard of its surface, the total surface being 6 sq. yards, 
and if its temperature be 280° ¥. while it is fed with feed water at 
1 10° F., what weight of steam would you be able to dj*aw off regu- 
larly per hour? (The latent heat of vaporisation at 280° may be 
calculated as shewn at top of page 129.) 

5. Steam is admitted into a water cooled condenser through 
which 20 gallons flow per minute. The water on entering the con- 
denser is at 60° F. and on leaving has a temperature of 100° F. 
How much steam is being condensed per minute ? 



CHAPTER XII 

TRANSMISSION OF HEAT 

There are three modes by which heat may be trans- 
mitted from one point to another. The first is by 
conduction and it is in this way that heat is transmitted 
through soUds. If one end of a metal bar be heated 
the other end will soon become hot provided that the 
bar is not very long. The heat seems to pass from 
molecule to molecule from the warmer end to the 
colder end and will continue to pass so long as there 
is any difference of temperature between the ends. 

The process is comparatively slow : it is not to be 
compared with the speed of light or sound or electricity, 
or of heat transmitted by another process called 
radiation. 

Different substances conduct differently. In general 
terms we all know that silver is the best conductor of 
heat — -as it is of electricity — though it is quite possible 
that most of us do not know quite what we mean when 
we say it. One reader may be thinking that the heat 
travels more rapidly along silver than along anything 
else : another may be thinking that it is not so much 
a question of speed as of quantity — that is to say that 
more units of heat can pass at the same speed : another 
may think that both speed and quantity must be taken 
into account. 



134 Transmission of Heat [ch. 

If two equal rods of copper and bismuth be coated' 
with wax and one end of each be put in a Bunsen flame 
it will be found that the wax melts more quickly along 
the bismuth at the start but ultimately more wax is 
melted on the copper than on the bismuth bar. 

The point of this experiment is that the specific 
heat of the bismuth being less than that of the copper 
a smaller quantity of heat is required to raise its 
temperature. Thus its wax starts to melt before that 
on the copper. But since more of the copper's wax is 
melted ultimately it follows that at corresponding 
points along each bar the temperature of the copper 
was higher than that of the bismuth and that more 
heat units per second were passing along the copper 
bar than along the bismuth bar. 

Thermal Conductivity. In order to compare con- 
ductivities of different substances it will be necessary 
to measure the quantity of heat which is transmitted 
through equal distances, equal cross sectional areas, in 
equal times and with equal differences of temperature 
at the extremities of the equal distances. 

The thermal conductivity of a substance is the 
quantity of heat which passes in unit time through 
a unit length having a unit cross sectional area when 
the temperature at each end differs by one degree. 

It is fairly evident that the quantity of heat whicli 
will pass through any length will be directly proportional 
to the difference in temperature at the ends, directly 
proportional to the area of cross section, directly pro- 
portional to the time and inversely proportional to 
the length. 

If the thermj^l conductivity of the substance be 
known then the quantity of heat passing in any known 



XIl] 



Transmission of Heat 



135 



time, along any known length of known cross sectional 
area with a known difference of temperature between 
the ends may be calculated. 

Conductivity of Wire Gauze. If a spiral of copper 
or silver wire be placed over the wick of a lighted candle, 
as in Fig. 44 (a), the flame will be extinguished at once 
due to the fact that the copper conducts away the heat 
so rapidly that the temperature is lowered below the 
temperature of ignition. If however the spiral be 
heated first and then placed over the lighted candle 
wick the flame will not be extinguished. 




Fig. 44 



In the same way if a piece of fine wire gauze be 
placed over a Bunsen burner, as in Fig. 44 (6), and if the 
gas be lighted below the gauze it will be found that it 
does not burn above the gauze. If the gauze be raised 
and lowered it will be found that the flame rises and 
falls with it. Of course gas is coming through the 
gauze and this can be lighted in the ordinary way. 
If the gas is extinguished and then turned on again 
the gas can be lighted above the gauze and it will not 
burn below. A yet more striking experiment is to 
soak a piece of cotton-wool in alcohol and place it on 
a piece of wire gauze. The gauze is then brought down 
over a lighted flame and the alcohol will burn — but it 



I'AG Tran»iniAmon of Heat [ch. 

will only burn below tJie gauze, and if tlie piece of cotton 
wool be picked up from the gauze "the flame" will not 
come with it. 

The explanations for all these simple experiments 
lie in the fact that the gauze is a good conductor of heat : 
that it conducts heat away rapidly in all directions over 
its surface and having a large surface exposed to the air 
keeps comparatively cool. Thus the temperature on 
the other side of the gauze from that on which the flame 
is playing is lower than the temperature of ignition of 
gas or alcohol as the case may be. 

Miner's Safety Lamp. It is generally known that 
in most coal mines there is so much inflammable gas 
evolved from the coal that the presence of a naked 
flame would cause a disastrous explosion. The pro- 
perty of wire gauze as shewn above was used by Sir 
Humphry Davy in the design of a safety lamp for 
use in such mines. The main idea of the lamp is that 
the flame (a small oil flame) can only receive its supply 
of air through some fine wire gauze, and further it is 
surrounded by gauze. 

Now although the inflammable gases may go in with 
the air supply and burn inside the lamp yet the flame 
cannot strike back through the gauze. 

The lamp serves too as a danger signal. If there is 
much gas burning inside the lamp the miner knows that 
the proportion of inflammable gases is too great at that 
place and he should immediately report the fact so that 
better ventilation be secured. 

Further, if the air is foiil the lamp will burn less 
brightly and it may even go out altogether. 

In most mines every lamp is lighted and tested, by 
being lowered into a well of coal gas, before it is given to 



XIl] 



Transmission of Heat 



137 



the miner. It is also locked so that he cannot uncover 
the flame. 

Conduction in Liquids. With the exception of the 
molten metals, liquids are comparatively bad con- 
ductors of heat. Liquids are always heated from 
below : we never think of putting the furnace at the 
topmost part of a boiler. An experiment may be per- 
formed in a manner shewn in Fig. 45, where we have, 
a tall vessel of water with 
a number of thermometers 
projecting from it at various 
depths. When some cold water 
is put into this vessel all the 
thermometers will read alike. 
If a pan containing some 
burning coals or some other 
source of heat be applied to 
the top of the water it will be 
found that the various thermo- 
meters are only very slightly 
affected even after a consider- 
able lapse of time. On the 
other hand we know that if the source of heat be applied 
to the bottom of the vessel the whole of the water will 
become hotter in a comparatively short time. 

We know also that if the same experiment were per- 
formed with a solid block of metal there would be no 
appreciable difference between top heating and bottom 
heating. 

Convection. When the water is heated at the 
bottom the lower portion receiving heat expands and 
therefore becomes lighter bulk for bulk than the water 
above it. Consequently it rises, colder water descending 




Fig. 45 



138 



Trmntmiasinn of Heat 



[CH. 



to take its place. This, in turn, is heated, expands, 
becomes lighter and rises. In this way we get the 
water circulating in the v-essel; warm and light water 
continually rising whilst the cooler and heavier water 
sinks to take its place. As the warm water rises it 
gives out some of its heat to the surrounding colder 
water. Thus we see that the particles of water move 
•and all the upward moving particles are carrying and 
distributing heat. This process of transmission of heat 
is called convection and the currents of water set up are 
termed convection currents. 

This can be shewn very ejffectively by means of a 
simple experiment illustrated in Fig. 46. A vessel of 




^ 




- -y 



W" 



^^^rJMmr^-^ 



Fig. 46 



water (this may be a flat lantern cell so that it can be 
placed in a lantern and projected upon a screen) has 
two thick wires leading down to a small coil of thin 
wire at the bottom. Two or three crystals of potassium 
permanganate are dropped down to this spiral and they 
will dissolve colouring the water at the bottom. 
A current of electricity is then passed through the 
spiral which becomes warm. This warms the coloured 



XIl] 



Transmission of Heat 



139 



water which then rises and we can see the convection 
currents by watching the paths of the coloured 
streams, which follow the courses shewn by the 
dotted lines in the diagram. The process will continue 
until all the water is uniformly hot and uniformly 
coloured. 

This principle is the basis of heating by hot water 
circulation. The circulation takes place quite naturally 
and Fig. 47 illustrates a simple 
system of such heating. The 
boiler- — or more properly, heater 
— is placed at the lowest part 
of the building and the hot 
water rises whilst the colder 
water descends to take its place. 
The method is sometimes called 
central heating — that is to say 
one fire will provide the heat for 
all the rooms and corridors. The 
system is often used in large 
buildings, theatres, churches, 
educational institutions and the 
like, but is not often met with 
in private houses in this country. 
In America it is the general rule. 

Its general efficiency, economy and cleanliness 
deserve that it should meet with wider favour than it 
does : though it seems highly probable that electric 
heating will prove to be too strong a rival as soon as 
electrical energy is more universally adopted. 

Convection Currents in Gases. Gases are also bad 
conductors of heat, and heat may be transmitted 
through gases by convection. When heat is appHed 




Fig. 47 



140 Tninsiitlssiitii <>/ lleitt [CH. 

to a gas the portion in the ininiediat^^ neighbourhood 
of the source of heat expands, becomes hghter and 
tends to rise. Since this expansion is greater than in 
the case of Htjuids the convection current will be set 
up much more quickly and it will move with a greater 
velocity. The existence of these convection currents 
is readily shewn in many ways. 

In an ordinary dwelling room where there is a fire 
the heated lighter air ascends the chimney. This is 
useful in that it carries the smoke and soot : but it has 
the serious drawback of carrying up a tremendous 
proportion of the total heat energy of the fire. 
This is one of the causes of the overall inefficiency 
of steam engines : so much of the total energy of the 
furnaces is carried up the flues by the air convection 
currents. 

From another point of view these flue convection 
currents are useful for they assist in the promotion of 
proper ventilation. If air is ascending the chimney 
fresh air must be drawn into the room at the same rate. 
This may come through special ventilator ducts, or 
through open doors and windows, or — as is too often 
the case — through the cracks and joints of imperfectly 
fitting doors and windows. This fresh air is not only 
necessary and beneficial to any occupants of the room 
but it is also necessary for the proper burning of the 
fire. 

A simple illustration of this is shewn in Fig. 48. The 
apparatus consists of a small box which is provided with 
two tubes or chimneys as shewn and a glass front. 
A candle placed under one of the chimneys represents 
a fire. When the candle is lighted convection currents 
will circulate in the directions shewn by the arrows. 



XIl] 



Transmission of Heat 



141 



This can be seen quite clearly by holding a piece of 

smouldering brown paper over 

each tube in turn: in one 

case the smoke will be drawn 

down : in the other it will be 

blown up. If the left-hand 

chimney be corked up the 

flame will burn less brightly 

and will be extinguished as 

soon as it has exhausted the 

oxygen supply in the box. 

Fig. 49 illustrates a method 
of room or hall ventilation 
which depends upon convection currents — as indeed 
all systems of "natural ventilation" (as opposed 




Fig. 48 



Inlet 




Flap 
outlet 



Fig. 49 

to forced ventilation by power fans) do. An air inlet 
is provided near to the floor and in front of this a 
radiator is fixed. The radiator may be hot water, 



142 TrauKnu'stiion of Heat [CH. 

steam or electric. The air about this radiator expands 
and rises and fresh air is drawn in through the inlet. 
Outlets are provided round the tops of the walls : the 
outlet shewn being a hinged flap which acting like a valve 
will only allow air to pass out. An advantage of this 
system is that the fresh air is warmed on entering the 
room. The circulation of the convection currents will 
be demonstrated further by the blackening of the wall 
above and behind the radiator at an earlier date than 
that of the other walls. 

Radiation. Conduction and convection of heat are 
processes which require material mediums for the heat 
transference. We know however that heat can be 
transmitted from one point to another without the aid 
of matter : the heat energy which we receive from that 
great source of energy the sun is transmitted through 
milhons of miles of space. This process of transmission 
is called radiation, and it takes place with the velocity 
of light, namely 186,000 miles per second. But the 
process is not confined to vacuous spaces for radiation 
can take place through matter and it can do so without 
necessarily raising the temperature of that matter. 

To account for these facts the generally adopted 
theory is briefly as follows, A hot body is said to be 
in a state of vibration. These vibrations are trans- 
mitted as such by means of a hypothetical medium 
termed the aether of space. This medium is assumed 
to be weightless : to pervade all space and the interior 
of all matter: and to be highly elastic since it can 
transmit the vibrations with an enormous velocity. 
The theory fits in with all observed facts and it serves 
for the transmission of light as well as of heat. 

According to this the fact that heat energy can be 



XIl] 



Transmission of Heat 



143 



transmitted through air, or rock salt, without producing 
any appreciable increase in temperature, is explained 
by the assumption that the heat does not travel as heat 
but as vibrations which will be transmitted hke waves 
through the aether. When these waves fall upon any 
matter they may be reflected ; they may pass through 
as waves; they may be absorbed; or some or all of 
these possibiUties may take place. 

If the matter becomes hotter then we say that some 
of the waves are being absorbed and they give up their 
energy in the form of heat. If the matter does not 
become hotter then the waves are either being reflected 
or transmitted. 

Reflection and Absorption of Heat. A simple 
experiment is illustrated by Fig. 50. Two metal plates 








Fig. 50 

A and B of the same size and material are placed at 
equal distances from a source of heat such as a red hot 
iron ball. The plate A is polished whilst B is covered 
with a coating of lamp-black or some dull black paint. 
From the back of each plate a small tongue of metal 



144 TnutsniissioH of Heat \vn. 

projects and on each of tliesc tongues a small piece of 
yellow phosphorus is placed. In a very short time the 
phosphorus behind the black disc will ignite — but the 
phosphorus behind the polished disc will not ignite at 
all. 

This is only one experiment of many which can be 
performed to shew that light polished surfaces are good 
reflectors of heat (as they are of light) whilst dark and 
rough surfaces are bad reflectors but good absorbers. 
A fireman's polished brass helmet reflects the heat: 
a guardsman's helmet does the same thing. Light 
coloured clothing is cooler to wear in summer time than 
is dark clothing, since the latter is a bad reflector and 
a good absorber of heat. 

Transmission and Absorption of Heat. Heat may 
be reflected from mirrors in exactly the same way as 
light. If an arc lamp be placed at the focus of a concave 
mirror the reflected beam — like a searchUght beam — 
wiU consist of both light and heat waves. If this beam 
falls upon another concave mirror it will be converged 
to the focus. The temperature of the air through which 
this beam passes will not be appreciably altered : nor 
will it be affected at the focus. But a piece of phos- 
phorus placed there will ignite immediately. It is only 
when the heat waves fall upon some substances (most 
substances be it said) that they give up their energy as 
heat. Fig. 51 illustrates this. 

If such a beam as that mentioned above be allowed 
to pass through a strong solution of alum it will be 
found that most of the heat waves have been stopped 
and the phosphorus placed at the focus of the second 
mirror will take longer to ignite if indeed it ignites at all. 
The solution of alum will get hot. If a solution of 



xii] Transmission of Heat 145 

iodine in carbon bisulphide be substituted for the alum 
it will be found to stop practically all the light but will 
allow the heat to pass through as will be shewn by the 
ignition of the phosphorus. 

Rock salt will transmit the heat waves readily. 
Glass behaves rather remarkably : it will transmit the 
heat waves if they proceed from a source at a high 
temperature but it stops them if they come from a low 
temperature source. It is this property which makes 
glass so valuable for greenhouse purposes. The heat 
waves from the sun pass through readily enough and 
give up their energy to the plants inside ; but after 
sunset when the plants are giving out heat instead of 
receiving it the glass will not transmit the heat waves 
and thus acts as a kind of heat trap. 



Focus 



Fig. 51 

Radiation from different surfaces. Different sur- 
faces having the same temperature radiate heat at 
different rates. One simple experiment to illustrate 
this may be performed with two equal cocoa tins from 
which the paper covering has been stripped. One of 
the tins should be painted a dull black (a mixture of 
lamp-black and turpentine will serve for this purpose) 
and through the lid of each a hole should be made large 
enough to take a thermometer. The tins are then 

p. y. 10 





14() 



TraiutmisHion of Heat 



[CH. 



filled with boiling water and it will be found that the 
blackened vessel cools much quicker than the bright 
vessel. Readings of the two temperatures can be 
taken at equal intervals of time and "curves of cooling " 
can be plotted. 

The usual methods of comparing the radiating 
properties of different surfaces are by means of a 
thermopile and galvanometer. The two constitute 
a sort of electrical thermometer which is much more 
sensitive than any expansion thermometer. The prin- 
ciple of this thermopile wiU be taken in the electricity 
course, but it may be stated here that when the tem- 
perature of the exposed thermopile face increases a 
current of electricity is set up which causes the needle 
of the galvanometer to be deflected. The greater the 
temperature the greater will be the current and the 
consequent deflection of the needle. 

Fig. 52 shews a thermopile being used with a " LesUe 





To Galyanometer 



Fig. 52 

cube " which is simply a metal cube in which >i|jater may 
be boiled. The faces of the cube may be treated in 



xii] Transmission of Heat 147 

different ways : or they may be made of different 
metals or covered with different materials. In this 
way a simple method is provided for heating a number 
of different surfaces to the same temperature. The 
thermopile is placed the same distance away from each 
face in turn and the permanent deflection of the 
galvanometer needle gives a measure of the rate at 
which the thermopile receives heat from each face. 
If it receives more heat per second in one case than in 
another then clearly its temperature will rise to a 
higher degree. 

It will be found in general that pohshed surfaces do 
not radiate heat so well as dull surfaces and that light 
coloured surfaces are worse radiators than dark surfaces. 

A polished metal teapot does not require a "tea- 
cosy" : a dirty one does, for two reasons. 

The "vacuum" flasks so largely used in these days 
depend upon this for their property of retaining the 
temperature of any liquids placed in them. They con- 
sist of a double walled glass vessel and the space 
between the two walls has the air driven out of it 
whilst a small quantity of quicksilver is vaporised 
inside. The inter- wall space is then sealed and the 
quicksilver condenses on the inside of the walls — 
forming a complete mirror coating. Thus the flask 
does not absorb the heat readily and what it does 
absorb it does not radiate readily. The absence of 
air from the space between the two walls of the flask 
prevents convection currents, but it is the non-radiating 
property of the silvered surface which is the main 
cause of the insulating property of the flask. 

Flame radiation. The amount of radiation from 
a flame depends very much upon its nature. The 

10—2 



148 Transmission of Heat [CH. xii 

luminosity of a candle flame depends upon the presence 
of solid particles of carbon within it, and the same 
appUes to the old-fashioned batswing gas flame. If 
the gas of a burner be mixed with air before ignition 
— as in the case of a Bunsen burner or a gas stove or 
the burner of an incandescent gas — the soUd particles 
of carbon do not exist in it for any appreciable time 
and very little light or heat is radiated. At the same 
time this flame is hotter than the batswing flame and 
can raise the temperature of substances to a greater 
degree. A gas mantle placed over such a flame becomes 
hotter and gives out more light and radiant heat than 
it would if it were placed over the batswing flame. 

Formation of Dew. After sunset the earth radiates 
some of the heat it has received during the day, and 
a fall of temperature results. If the night be cloudy 
then the clouds reflect and radiate heat back again 
so that the fall in temperature is not very great. If 
the night be clear the heat is radiated into space and 
the temperature falls much more. 

The earth thus becomes cooled and often to a tem- 
perature below the dew-point (see p. 130). Dew is 
generally deposited upon blades of grass whilst it is not 
noticeable upon bare earth or stones because the blades 
of grass are excellent radiators and become very cold 
and are also bad conductors so that they do not 
receive any heat from the earth by conduction. 

Straw is an excellent radiator and a bad conductor 
and because of this it is possible to freeze water during 
the night in hot regions of India and other places by 
putting some water in a shallow vessel and standing it 
upon a heap of straw. 



CHAPTER XIII 

THERMODYNAMICS 

In Chapters IV and V we pointed out that heat 
might be considered as a form of energy, and we shewed 
some of the methods by means of which other forms 
of energy could be changed into the form which we 
call heat. The most primitive method of generating 
sufficient heat to kindle a fire consists in causing friction 
to be developed rapidly between two dry pieces of wood 
— preferably and most easily by bending one piece into 
the form of a rough brace and using one end as a "bit" 
in the vain endeavour to bore a hole in the other piece. 
The operator will not be successful in boring but he 
will soon find that the "bit" will ignite. The energy 
which is converted into heat energy is the mechanical 
energy of the operator. 

Experiments have been performed by means of 
which the relationship between the amount of mechani- 
cal work expended and the quantity of heat produced 
has been ascertained. 

Mechanical Equivalent of Heat. The amount of 
mechanical work which must be done so that when it 
is all converted into heat it will produce one unit of 
heat is called the mechanical equivalent of heat. Many 



1 50 Thei'mo-Df/namics [CH. 

different kinds of experiments have been performed 
by various experimenters and the results obtained are 
all in close agreement. 

On the British system of units it has been found 
that in order to produce one British thermal unit of heat 
by the expenditure of mechanical energy, 778 foot-lbs. 
of work must be done. 

On the metric system 4-2 joules (or 4-2 x 10' ergs) 
must be done in order to generate 1 calorie. 

Method of Determination. Count Rumford and 
Dr Joule were the experimentalists whose names are 
most generally associated with the determination of 
the mechanical equivalent of heat. Rumford's experi- 
ments were performed by boring cannon with sharp 
and blunt borers. In the latter case more work had 
to be done in the boring operation and proportionately 
more heat was developed. Dr Joule's apparatus con- 
sisted of a paddle arrangement which he rotated in 
a special calorimeter containing a known mass of water 
at a known temperature. The paddle wheel was made 
to rotate at a uniform rate by means of an arrangement 
of falling weights. In order to prevent the water from 
turning round with the paddle, some fixed arms pro- 
jected inwards from the wall of the calorimeter. The 
weights were allowed to fall through a known distance : 
they were then quickly wound up again without turning 
the paddle wheel and allowed to fall again: and this 
was repeated until an easily measurable rise of tempera- 
ture was produced iii the water. The total work done 
by the falling weights was then calculated, and the 
amount of heat generated was determined by the 
product of the total equivalent weight of the water and 
calorimeter and paddles and the increase in temperature. 



XIII 



Thermo- Dynmnics 



151 



From this the work done per unit of heat generated was 
readily ascertained. 

A favourite laboratory method of malting this 
determination is that in which the apparatus shewn 
in Fig. 53 is used. 




Fig. 53 



The "calorimeter" consists of two brass cones Cj 
and O2 which can revolve on one another about a vertical 
axis. If Oj is fixed C^ can be turned round by means 



152 Thermo- hiiiin III irs [ch. 

of a weiglit W on a piece of string which is fixed to a 
large wooden pulley P at the top of the apparatus. On 
the other hand if Cj be rotated in the opposite direction 
to that in which the weight would rotate C^ it can be 
seen that at a certain speed of rotation the tendency of 
the weight to fall could be exactly balanced. If the 
speed of Cj were increased then W would rise : if it were 
decreased W would fall. Thus if we rotate Cj at such 
a speed that W remains stationary it follows that the 
work which we do per revolution must be exactly the 
same as if the weight had fallen through such a distance 
that it turned C^ through one revolution. And it there- 
fore follows that the work done per revolution when we 
keep W stationary is given by the product of W and 
the circumference of the pulley P. 

This is the method by means of which the work 
which is done in overcoming the friction of the cones 
is determined. The outer cone Cj is held by two pins 
projecting from an insulating base B. This in turn is 
fixed to a vertical spindle 8 which can be rotated by 
means of a belt DB which passes round a small driving 
pulley DP. In order to make it easy to count the total 
number of revolutions there is a worm thread T on the 
spindle and this engages with a toothed wheel R having, 
say, 100 teeth, every ten of which are marked. A fixed 
pointer on the supporting arm of the toothed wheel 
serves as recorder. The inner cone Cg is fixed to the 
top pulley by means of two projecting pins. 

The cones (both of them) are weighed and their 
w^ater equivalent is determined. The inner cone is 
then partially filled with mercury and the whole weighed 
again in order to get the weight of mercury. The water 
equivalent of the mercury is then calculated and the 



xiii] Thermo- Dynamics 153 

sum of the two water equivalents gives the total water 
equivalent of the cones and the mercury. 

Mercury is used because it has a small specific heat 
and is a good conductor. Thus we can get a greater 
rise in temperature than we should get if we used water : 
and in this way we reduce the possible errors of tempera- 
ture reading. 

The temperature of the mercury is taken, and then 
the spindle is rotated at such a speed that W remains 
steady. This requires a little experience and some 
prehminary trials are necessary. 

When the temperature has risen through a reason- 
able and readable range the rotation is stopped and 
the final temperature and the total number of revolu- 
tions are determined. 

The mechanical equivalent is determined as follows : 

Heat : Mass of the cones = M^ lbs. Specific heat 
of cones = 8^. 

Water equivalent of cones = M^ x 8^ lbs. 

Mass of mercury = Jf„j lbs. Specific heat of 
mercury = 8^- 

Therefore water equivalent of mercury = M^ x 8^ 
lbs. 

Therefore total water equivalent of cones and mer- 
cury = M^8c + M^8^ = Jf lbs. 

Original temperature of mercury = 1°!^. 

Final temperature of mercury = ^2° ^• 

Therefore units generated = M {t^ — t-^) b.th.u. 
= H units. 

Work : Weight on the pulley string = W lbs. 

Circumference of pulley = G feet = ttD feet, where 
D = diameter in feet. 

Number of revolutions = N. 



\i>4 r/iniHO-JJi/namics [en. 

Therefore total work done = WON foot-lbs. =- J 
foot -lbs. 

Relationship : Since H units of heat are produced 
by J foot-lbs, of work therefore 1 unit of heat will be 

produced by rj foot-lbs. 

Therefore the mechanical equivalent of heat = ^ 

11 

foot-lbs, per b.th.it. 

Fundamental principle of the Heat Engine. Just as 
mechanical work may be converted into heat so by 
proper arrangements heat may be converted into 
mechanical work. Any device by means of which 
this may be done is called a heat engine, and it would 
be well if we consider at this stage how such an engine 
does work at the expense of heat energy. 

The thoughtful student might argue that in the case 
of a steam engine although heat energy is necessary to 
produce the steam which forces the piston along the 
cylinder yet the steam comes out of the exhaust as 
steam and has not given out any heat except that 
necessary to warm up the piston and cylinder in the 
first instance. Such argument however would be 
wrong, for it can easily be shewn that heat is given out 
by the steam as it expands in the cylinder, anxi the 
energy of the steam engine is represented by the energy 
given out during this expansion. 

Let us imagine that we have a tall cylinder and that 
it is fitted with a piston which when loaded with a 
number of weights sinks do^vn into the cylinder and 
so compresses the air in it. If we then remove the 
weights one by one the air will expand and will 
do work in raising up the piston and the remaining 



xiii] Thermo- Dynamics 155 

weights. Now if the weights be removed in sufficiently 
quick succession it will be found that the air is cooled 
by its expansion. We therefore conclude that some of 
the heat energy of the air has been converted into the 
mechanical work necessary to lift the weights, and 
therefore the temperature of the air must be reduced. 

On the other hand if the air be compressed it will be 
found that its temperature rises and we conclude that 
the mechanical work done in compression is converted 
into heat. Probably all our readers know how hot the 
end of a bicycle pump gets after a few rapid strokes of 
the piston. 

But — to return to our tall cylinder with its weighted 
piston — after we have compressed the air and so heated 
it, if we allow it to cool down again to the temperature 
of the surrounding air and then allow the piston to rise 
once more we shall again find that the air is cooled. 
The point here aimed at is that though we may produce 
heat by compression yet if we allow it to disappear we 
shall nevertheless take heat away again on expansion. 
Work must be done on the air in compressing it : that 
work is changed to heat and the temperature of the air 
rises. Work must be done by the air in expanding and 
it is done at the expense of some of the heat energy of 
the air which is thereby cooled. 

The reader may remember that in our chapter on 
specific heat we stated that the specific heat of a gas is 
greater if the volume of the gas be allowed to change 
as it is heated than it is if the volume of the gas be 
kept constant during heating. The reason for this is 
now obvious. If when heating a gas it expands it 
must be doing work. The gas need not be actually 
pushing a piston along a cylinder, but as it expands 



150 Tlicnno-Djimtmim [CH. 

it must be pushing air away from it and therefore must 
be doing mechanical work. The energy for this must 
come from somewhere : it comes from the heat energy 
of the air and so the air would be cooled. Therefore 
to keep the air up to its temperature more heat would 
have to be given to it than would have been necessary 
had the air not been expanding. 

The reader will be able to see that the difference 
between the amount of heat necessary to raise the 
temperature of a given mass of gas through a certain 
range without any change in volume, and that necessary 
to produce the same temperature change when the gas 
is expanding, will represent the amount of energy which 
is changed from heat energy to mechanical energy. 

In the case of the steam engine if we measure the 
quantity of heat energy in each lb. of steam as it enters 
the cylinder and again as it leaves, the difference will 
represent the amount of energy which each lb. of steam 
gives out to the engine as mechanical energy. If we 
know the number of lbs. of steam per minute which are 
passing through (an easily determined quantity), then 
we have at once the means of calculating the mechanical 
energy given per minute by the steam, and from that 
the horse-power. This, of course, does not give the 
horse -power which the engine will yield : that wiU 
depend upon the efficiency of the engine. 

Effect of compression and expansion on saturated 
steam. We saw on page 124 that when a space was 
saturated a change of volume did not affect the pressure 
if the temperature remained constant. We are now in 
a position to see that unless the change in volume is 
effected very slowly indeed the temperature will be 
increased on compression and this increase might be 



xiii] Thermo- Dynamics 157 

sufficient to convert the space into a non-saturated one 
(or a superheated one). Indeed in the case of steam 
this is the case, for if saturated steam be suddenly- 
compressed in a space from which no heat can escape 
the consequent rise in temperature is such that the 
space becomes superheated — that is to say instead of 
the compression producing condensation of the steam 
in the cyUnder as we should expect it to do from 
Dalton's experiments on saturated spaces (page 124), 
enough heat is developed to raise the temperature 
sufficiently to render the space hot enough to be able 
to hold even more water vapour. 

On the other hand if saturated steam be allowed to 
expand, doing the full amount of work of which it is 
capable during the expansion, it loses so much heat 
that, notwithstanding the increased volume, condensa- 
tion takes place. 

When this happens in the cyhnder of an engine the 
condensed water accumulates. This is called priming. 
In all steam engines working expansively means are 
taken to prevent this condensation — such, for example, 
as surrounding the cylinder with a steam jacket. 

If superheated or non-saturated steam be used 
then, of course, this condensation wiU not occur if the 
steam is sufficiently far from saturation. 

Isothermal and Adiabatic expansion. If the volume 
of a given mass of gas be changed without any change 
of temperature it is said to be changed isothermally. 
From what we have seen above it follows that such 
isothermal change of volume can only be produced 
provided that heat is taken from or given to the gas. 
As it is compressed then heat must be taken from the 
gas in order that its temperature shall not rise. As it 



158 Thermo- DjfnamicM [CH. 

is expanded heat must be given to it to prevent the 
temperature from falling. Boyle's law, for example, 
is only true for an isothermal change : it states that 
the temperature must be kept constant. The curve 
which we plotted to shew tlie relationship between 
pressure and volume of a gas at constant temperature 
is called an isothermal curve connecting pressure and 
volume. 

If, on the other hand, the gas be contained in some 
vessel which will not permit it to receive or lose heat, 
then as it is compressed its temperature will rise and 
as it expands its temperature will fall but the quantity 
of heat will remain constant. Such a change is said 
to be adiabatic or isentropic. Boyle's law is not true 
for adiabatic expansion or compression. On compres- 
sion the temperature will be raised and therefore the 
gas will occupy a greater volume at a given pressure. 
On expansion the gas wiU be cooled and the volume will 
be less than it would be at a given pressure. Fig. 54 
shews the difference : the curve IBL is an isothermal 
or Boyle's law curve shewing the relationship between 
pressure and volume : the curve ABC is the adiabatic 
curve for the same mass of gas. The point B is the 
starting point and if the gas be compressed adia- 
batically its volume wiU not fall as much as it would 
if compressed isothermally, and vice versa. Thus the 
adiabatic curve is steeper than the isothermal curve. 

For the same reasons it follows that if we compress 
a gas adiabatically the mean pressure necessary to 
produce a given change in volume will be greater than 
that necessary to produce the same change in volume 
if the gas be compressed isothermally. Therefore it 
follows that more work must be done to compress 



XIIl] 



Thermo- Dfpiamics 



159 



a gas adiabatically than isothermally and more work 
will be given out by a gas expanding adiabatically 
than isothermally. 

The Indicator diagram. If we can plot a curve which 
shews the pressure on a piston at each position of its 
motion along a cylinder we can then get the mean 
pressure from the curve. If we know this mean pressure 
in lbs. per square inch and the area of cross section of 
the piston and the length of its stroke in the cylinder 




Volume 
Fig. 54 

we can calculate the total work done upon it per stroke. 
If, further, we know the number of strokes which it 
makes per minute we can determine the rate of working 
or the horse -power yielded by the steam. 

Such a curve shewing the relationship between 
pressure and position of piston is called an indicator 
diagram. 

If the pressure on the piston were constant through 
the full length of the stroke and then dropped suddenly 
to zero at the end, the diagram would be like that 



160 



Thermo- Dynamics 



[CH. 



shewn in Fig. 55. The height OA represents the steam 
pressure on the piston and the position of the piston 
in the cyUnder is represented by such distances as 
OM, OC. 

The point C represents the end of the stroke. As 
the piston returns again to we are assuming that 
the pressure upon it is zero and when it reaches O 
the pressure suddenly becomes OA again. 




i I I i I I I I 

I ! I I I I I I 

I ■ I I I I I I 

! > I I I ' I ■ 

I nI I 1 B 



o 



M 



Position of Piston along Cylinder 
Fig. 55 

If such conditions were possible and such an in- 
dicator diagram were obtained the horse-power of the 
engine concerned could be readily determined. 

Let A represent the area of the piston in square 
inches. 

Let P represent the average pressure* upon the 

* By this is meant the net average pressure or the average 
difference of pressure on each side of the piston. 



XIIl] 



Thermo-Dynamics 



161 



piston — both journeys along the cyhnder being con- 
sidered. In this case the pressure is constant and is 
represented by OA on our diagram. The return 
journey pressure is zero in this case. 

Then P y, A = total force in lbs. on the piston. 

Let L = length of stroke in feet. 

Then PAL = force x distance = work in foot-lbs. 
for each journey of piston to and fro. 

If iV^ = no. of to and fro movements per minute. 

Then PLAN = foot-lbs. per minute. 

Fig. 56 represents more nearly the actual relation- 
ship between the pressure and the position of the piston. 




Atmospheric 
line of pressure 



Position of Piston along cylinder 
Fig. 56 

The portion of the diagram AB indicates that for the 
first part of the stroke the pressure is constant (practi- 
cally, in fact, the boiler pressure). At the point B the 
steam port'is shut and the steam expands as the piston 

P.Y. 11 



162 Thermo- Dynamics [ch. xiii 

continues its motion, but the pressure falls as shewn by 
the curve BC. At the point C the exhaust port is 
opened and the pressure falls rapidly to atmospheric 
pressure shewn at D which is the extremity of the stroke. 
The piston then returns and when back again at the 
point E the exhaust port is closed so that the small 
amount of steam left in the cylinder shall act as a 
cushion to assist the return of the piston. This steam 
becomes compressed as the piston approaches and 
the pressure rises as shewn by the curve EF. When 
the piston reaches O the steam port is opened again 
and the pressure rises at once to the point A. 

In order to find the indicated horse-power with the 
aid of this diagram it is clear that we shall need to find 
the average pressure on the cyhnder during the complete 
to and fro motion of the piston. The net average 
pressure will be the difference between the average 
outward pressure and the average return pressure. On 
the outward journey when the piston is at L the pressure 
is LN, on the return journey the pressure is LM at the 
same position. Therefore the net or useful pressure is 
represented by the difference, namely MN. It will be 
seen that the net average pressure per complete cycle 
will be given by the average of such lengths as FA, QR, 
MN. Thus if a sufficient number of such ordinates be 
drawn at equal distances apart and their mean length 
determined — in terms of the pressure scale — we shall 
get the net average pressure at once. 

If the engine w^re to exhaust into a condenser in 
which the pressure was less than the atmospheric 
pressure then the return part of the diagram DE would 
fall below the position shewn : in which case it is clear 
that the net mean pressure would be greater. 



INDEX 



Absolute scale of temperature 90 
Absolute zero 92 
Absorption of heat 143-4 
Adiabatic expansion 157 
Advantages of expansion 76 
Airships 46 

Alcohol thermometer 68, 70 
Apparent expansion of liquid 81 
Archimedes, Principle of 24 
Atmospheric pressure 37, 40 

Balloons 46 

Barometer 41; standard 42 

Boiler test 31 

Boiling point 64, 115 

Boyle's Law and vapour pressure 

123 
Boyle's Law for gases 42 
British Thermal Unit 96 
Buoyancy 22 

Calorie 96 

Calorific value of fuels 102 

Calorimeter 100; Darling's 103 

Capillarity 32 

Celsius 65 

Centigrade scale 65 

Charles' Law 87 

Classification of matter 8 

Clinical thermometer 71 

Coeificient of expansion of gas 86 ; 

of liquid 82; of solid 73 
Compensation for expansion 79 
Compression of saturated steam 156 



Condensation 1 15 
Conduction of heat 133 
Conductivity, thermal 134 
Conservation of energy 54 
Convection 137, 139 
Conversion of temperature scales 

68 
Cubical expansion 80 

Dalton's Law 122 
Darling's calorimeter 103 
Densities, table of 11 
Density 9 ; relative 25 
Dew, formation of 148 
Dew point 130 
Diagram indicator 159 
Diffusion 34 
Displacement 25 
Dyne 50 

Elasticity 12 

Energy 52; conservation of 54; 

kinetic 52; potential 52 
Erg 50 

Evaporation 115, 120 
Expansion 72-94; of saturated 

steam 156 

Fahrenheit scale 65 

Feed- water pump 31 

Fixed points of temperature 63 

Flame radiation 147 

Floating bodies 23, 46 

Foot-pound 48 



164 



Imlesc 



Foot-poundal 49 

Force 2, 48; units of 49 

Freezing point 63 

Freezing points of liquids 108 

Fusion 107 

Gases, ex{)ansian of 8fi 
Gases, properties of 37-46 
Gravitation, force of 2 
Gridiron pendulum 79 

Heat and temperature 60 
Heat engine, principle of 154 
Heat, latent 126; sensible 126; 

specific 97; total 126; unit 

of 96 
Heat, mechanical equivalent of 

149 
Hooke's law 13 
Horse-power 56 
Horse-power of steam engine 

160 
Hot water circulation 139 
Humidity 129 
Hydrometers 28 
Hygrometers 131 

Indicator diagram 159 
Inertia 5 

Isentropic expansion 158 
Isothermal expansion 157 

Joule 50, 150 

Joule's experiment 150 

Kilowatt 56 
Kinetic energy 56 
Kinetic theory 7, 91 

Latent heat of fusion 109; of 

vaporisation 125 
Leslie cube 146 
Limits of elasticity 12 
Liquid, expansion of 81 



Liquid pressure 16, 24; pro- 
perties 15 

Mass 4; units of 51 
Matter, classification of 8; inde- 
structibility of • 2 ; structure of 
7 ; properties of 1 
Maximum and minimum thermo- 
meters 70 
Maximum density of water 84 
Mechanical equivalent of heat 149 
Melting point 107 ; effect of 

pressure on 113 
Modulus of elasticity 7 
Motion 3; energy of 62 

Potential energy 62 

Power 54 

Pressure and boiling point 63, 
116; and melting point 113; 
in liquids 16, 24; of gases 38 

Principle of Archimedes 24; con- 
servation of energy 54 

Pumps 29 

Pyrometer 69 

Radiation of heat 142 
Reaumur temperature scale 66 
Reflexion of heat 143 
Relative density 26 
Rigidity 9 

Safety lamp 136 

Saturated steam 119, 129 

Saturation 120 

Scales of temperature 66 

Sensible heat 126 

Solidification 106 

Solidification, change of volume 

on 111 
Solids, properties of 11 
Solution 113 

Specific gravity 25; bottle 28 
Specific heat 97 ; of gases 105 



Index 



165 



States of matter 1 

Steam, temperature and pressure 

of 64, 116; latent heat 125; 

total heat 126 
Strain 12 
Stress 13 

Structure of matter 7 
Superficial expansion 79 
Superheated space 157 
Surface tension 33 

Tables — calorific values 105; co- 
efficients of expansion 76 ; den- 
sities 1 1 ; latent heats 109 ; 
melting points 106; specific 
heats 98; volume and temper- 
ature of water 85 

Temperature 59; absolute zero 
of 91; absolute scale of 92; 
fixed points 63; scales 65 

Temperature and pressure of 
steam 64, 116 

Tension, surface 33 

Thermometers 61; self -registering 
70 



Thermopile 146 
Torsion 13 

Total heat of steam 126 
Transmissi9n of heat 133 

Unit of force 48; of heat 96; 
of power 55; of work 49 

Vacuum flask 147 
Vapori sation 115 
Vapour pressure 122; and tem- 
perature 125 
Ventilation 140 
Viscosity 35 
Volumenometer It) 
Voluminal expansion 80 

Water equivalent 99 
Water, expansion of 82 
Watt 56 
Weight 2 
Weight of air 4 
Work 48; units of 49 

Young's modulus of elasticity 7 



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