Thermodynamics of Radiation. 875- 



emission under equilibrium conditions at the slowly expand- 

 ing wall of the enclosure, it is easy to see why the latent heat 

 of a particular frequency per unit volume should be different 

 from the density of the energy-stream of the same frequency 

 together with the external work. The higher frequencies 

 are being continually degraded into lower during the motion, 

 so that the actual net amount of a high frequency emitted 

 may be greatly in excess of the quantity Ap per unit volume 

 which would be required if there were no degradation of 

 frequency. On the other hand, for a low frequency, the 

 amount required to maintain the energy-stream at its equi- 

 librium value is greatly reduced by the return of energy 

 degraded from the higher frequencies. The two effects 

 balance in the case of full radiation at the mean point where 

 T(dp/dT) v =4p. 



The nature of the effect considered may also be illus- 

 trated by a consideration of the relation between the partial 

 differential coefficients. If (dp/dT) x represents the rate of 

 change of p with T in adiabatic expansion when \T or v/T is 

 constant, we have the general relations, representing Wien's 

 displacement law (1), 



T(dp/dT) x =3p=v(dp/dv) x =T(dp/dT) v +v(dp/dv) T . . (2) 



Similar relations hold for q and u, which are simply propor- 

 tional to p. The latent heat T(dp/dT) v is not equal to 4p, 

 but to Zp — v(dp/dv)'£' The coefficient (dp/dv^is obviously 

 positive on the low frequency side of the curve representing 

 p plotted against v at constant temperature, where the latent 

 heat is less than 3p. It vanishes at the maximum of the 

 pressure curve, where T(dp/dT) v =3p, but it may attain large 

 negative values for high frequencies. 



The Entropy, and Intrinsic Energy. — If the latent heat is- 

 represented by T(dp/dT) v per unit range and volume, the 

 entropy should be simply (dp/dT) v . The internal latent heat 

 per unit volume, T(dp/dT) v —p, or the intrinsic energy denoted 

 by E/u in the previous paper, is the energy carried by the- 

 stream of a particular frequency, and given up on conden- 

 sation in addition to the work p. It follows from Wien's- 

 displacement law (1) that the ratio, E/pr, of the intrinsic 

 energy to the pressure, must be some function of (v/T) T 

 depending on the distribution. It was assumed in the pre- 

 vious paper that E/p?; for full radiation was of the form 

 hv/T (where b is a constant required by the arbitrary nature 

 of the units) on the ground that the intrinsic energy of a 

 given quantity varies as the frequency. This assumption 

 fixes the distribution in full radiation, and leads to the 



