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THE PRESSURE OF RADIATION AND CARNOT'S PRINCIPLE. [Nature, Vol. xcn. pp. 527, 528, 1914]
As is well known, the pressure of radiation, predicted by Maxwell, and since experimentally confirmed by Lebedew and by Nichols and Hull, plays an important part in the theory of radiation developed by Boltzmann and W. Wien. The existence of the pressure according to electromagnetic theory is easily demonstrated*, but it does not appear to be generally remembered that it could have been deduced with some confidence from therrnodynamical principles, even earlier than in the time of Maxwell. Such a deduction was, in fact, made by Bartoli in 1876, and constituted the foundation of Boltzmann's workf. Bartoli's method is quite sufficient for his purpose; but, mainly because it employs irreversible operations, it does not lend itself to further developments. It may therefore be of service to detail the elementary argument on the lines of Carnot, by which it appears that in the absence of a pressure of radiation it would be possible to raise heat from a lower to a higher temperature.
The imaginary apparatus is, as in Boltzmann's theory, a cylinder and piston formed of perfectly reflecting material, within which we may suppose the radiation to be confined. This radiation is always of the kind characterised as complete (or black), a requirement satisfied if we include also a very small black body with which the radiation is in equilibrium. If the operations are slow enough, the size of the black body may be reduced without limit, and then the whole energy at a given temperature is that of the radiation and proportional to the volume occupied. When we have occasion to introduce or abstract heat, the communication may be supposed
* See, for example, J. J. Thomson, Elements of Electricity and Magnetism (Cambridge, 1895, § 241); Rayleigh, Phil. Mag. Vol. XLV. p. 222 (1898); Scientific Papers, Vol. iv. p. 354.
t Wied. Ann. Vol. xxxii. pp. 31, 291 (1884). It is only through Boltzmann that I am acquainted with Bartoli's reasoning. from 0 to o, where a is the critical angle corresponding to 6 — |TT. In this S2, T'2 have the values given in (1). The second part of the range from 6' = a to &' — fyrr involves " total reflection," so that S2 and T2 must -be taken equal to unity. Thus altogether we have