338 HEAT. 



red body will be heated and the blue will be cooled, and by establishing 

 a Carnot engine between them a little work can be obtained by equalis- 

 ing the temperatures and by gradually bringing back the radiation 

 towards the quality of full radiation. When we have arrived at this 

 quality the temperature will be a little below - dO. Now remove the 

 red and blue bodies and compress adiabatically till the original volume 

 is reached. Since we started on this compression at a temperature 

 below 6 dO, when we arrive at the original volume we shall have a 

 temperature below 0. Again, we shall have, by supposition, a quality 

 differing from full radiation, and we can again insert different absorbing 

 bodies, get out a little more work and lower the temperature still further 

 in reducing to full radiation. Hence we have in the end the original 

 volume, but colder, and we have obtained work in the process. That is, 

 we have obtained work in a process the net result of which is merely 

 the cooling of a body which may be, if we like, the coldest body in the 

 system. This we must consider as contrary to experience, and so we 

 reject the supposition on which it is based, that full radiation after an 

 adiabatic change ceases to be full radiation. 



Relation between Volume and Temperature in an Adiabatic 



Change Of Volume. Let a volume V contain full radiation at tem- 

 perature 6 and with energy density E. Then the total energy is 



W = VE 



Now let V change adiabatically to V + rfV. If P is the radiation 

 pressure the work done is 



But this is equal to the diminution in internal energy, or 



8 



or 



Integrating EVi = constant 

 But E = a0 4 



Then 0*V* - constant 



or 0V* = constant 



If the space maintains the same shape V* is proportional to the linear 

 dimension r. Then 



dr = constant. 



Entropy. If < is the entropy per volume 1, then in an adiabatic 

 change <f>V is constant. 



But EV* is constant also and so is ESV. Hence 

 < is proportional to E* or to 6 s 



Application of Doppler's Principle in an Adiabatic Expansion. 



If a train of waves is reflected at a surface which is itself moving, then by 



