CHAPTER XX. 

 THERMODYNAMICS OF RADIATION. 



General Principle The Pressure of Radiation The Normal Stream of Radia- 

 tion, the Total Stream, and the Energy Density The Pressure on a fully 

 Radiating Surface The Relation between E and in full Radiation, the Fourth 

 Power Law Full Radiation remains full Radiation in any Adiabatic Change 

 Relation between Volume and Temperature in an Adiabatic Change Entropy 

 Application of Doppler's Principle Change of Energy in a given Wave Length 

 Change of Energy of each Wave Length in an Adiabatic Expansion of full 

 Radiation Maximum Value of Energy for given Range of Wave Length Form 

 of the Function expressing the Distribution of Energy in the Spectrum. 



General Principle. The thermodynamic theory of radiation starts 

 with the idea that a space containing radiation resembles the working 

 substance in a heat-engine, in that it exerts pressure on its boundary, 

 that it can be compressed or extended, that it can receive more energy 

 as radiation from the boundary and can part with energy to the boundary 

 by absorption, and finally that it can be taken round a cycle. This most 

 fruitful idea is due to Bartoli, who in 1875 * showed that it was possible 

 by means of radiation to transfer heat from a colder to a hotter body in 

 a manner which will be understood from what follows in this chapter. 

 Though the details of his calculation require amendment, he showed that 

 the possibility of such transfer implies that radiation shall press against 

 any surface upon which it falls, f 



In 1884 Boltzmann| took up Bartoli's method. He used Maxwell's 

 electromagnetic theory of radiation, according to which a pencil of 

 light or radiation, incident normally on a surface, exerts a pressure 

 on that surface equal to the energy per c.c., or equal to the energy 

 density in the pencil. This pressure has now been shown to exist 

 by Lebedew, and by Nichols and Hull.|| Taking an enclosure full of 

 radiant energy from a fully radiating surface, round a Oarnot cycle, Boltz- 

 mann showed that the density of the energy in a uniform temperature en- 

 closure containing full radiation is proportional to the fourth power of 

 the temperature, that is, he deduced Stefan's law. The subsequent 

 development of the theory is largely due to Wien.U 



* Bartoli's most important paper was not fully published at first. It is given in 

 full in Exner's Repertorium der Physik, xxi., 1885, p. 198. 



f Another proof of such pressure is given by Larmor, Radiation, Encyc. Brit., 

 10th ed., xxxii. It depends on the energy in a train of waves of given amplitude 

 being inversely as the square of the wave length. 



J Wied. Ann., xxi., 1884, p. 364. 



Maxwell's Electricity and Magnetism, 1873, vol. ii., contains the first account of 

 this pressure. 



|| Lebedew, Congres Int. dc Phys., ii. p. 133 ; Nichols and Hull, Am. Acad. Arts 

 and Sciences, xxxviii., 1903, p. 559 ; Pressure of Light, S.P.C.K. 



IT Congres Int. de Phys., ii. p. 23. 



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