THERMODYNAMICS OF RADIATION. 337 



increased volume and the work done on the boundary, and the new 

 energy density will correspond to a lower temperature </0. The 

 pressure will fall say to P - d~P. We shall assume that the radiation is 

 so altered in quality that at every stage of the adiabatic expansion it 

 remains full radiation for the temperature to which it is reduced. We 

 shall seek to justify this assumption below. 



3. When the adiabatic expansion is completed, and the temperature 

 is 0-dO replace the reflecting surface by one fully radiating and sur- 

 rounded by a conductor maintained at dO. Now compress the sphere 

 at - dO to such an amount that 



4. On replacing the fully radiating surface by a totally reflecting 

 one, an adiabatic compression will restore the system to the original 

 volume and temperature. 



This cycle may be represented by Fig. 191, and evidently the net 

 work done is dP'iirr-dr. 



Every part of the process is reversible, and indeed we have a Carnot 

 cycle. Hence 



(j 

 substitute for dQ = 



and for dP = ^- 



a 



<7E 



and we have ^- -=- 



" Jii 



Integrating log 0* = log E + constant 



then E = a# 4 



v 4R 



and since -Hi = -=- 



4" 



Comparing this with the value of the radiation, page 250, 



R = r0* 



Ua 



we see that = cr. 



4 



Full Radiation remains full Radiation in any Adiabatic 



Change. Let us now examine this assumption, on which the rever- 

 sibility of the cycle depends. Imagine an enclosure containing full 

 radiation at 6, and let it expand adiabatically till the energy density 

 corresponds to that in full radiation at 6 dd. But let us suppose that 

 the energy, though of the same density, is not of the same quality as 

 the full radiation for 6 dO. Suppose, for example, that the red is in 

 excess and the blue in defect. Put into the enclosure substances at 

 dB, absorbing and radiating respectively red and blue rays. The 



Y 



