336 



HEAT. 



that it can be surrounded at will by a perfectly conducting substance 

 maintained at any desired temperature. Let us further suppose, and 

 this is the essential feature of the method of working, that the sphere 

 can be compressed against or extended by the pressure of the radiation 



E 



P = without doing any work on or receiving any energy from the 



o 



matter or ether or whatever we suppose to be the medium in which the 

 radiant energy is localised. Let us suppose, in fact, that the surface 

 of the sphere is a sort of semi-permeable membrane, permeable to the 



P 



BJP 



\ 



volume 



FIG. 191. 



radiation medium, but impermeable, when we so choose, to the radiation 

 and its energy. 



Now let us take the radiation-filled space through the following 

 cycle : 



1. Start at temperature with the inside surface fully radiating, 



E 



and allow the surface to be pushed out by the pressure P = ^ from 



o 



radius r to radius dr, increasing the volume by 4irr 2 dr. The surface is 

 surrounded meanwhile by a conductor maintained at 0, so that not only 

 is work P x fan&dr done, but radiant energy E x \-nr\lr is supplied to fill 

 the extra volume. Hence the total supply of energy at Q is 





4:7rr z dr x 



2. Now make the inside surface of the sphere non-conducting and 

 totally reflecting, and allow the radiation within to push out the 

 surface a little further, no energy being received from outside. This is 

 an adiabatic expansion. The energy density decreases, both through the 



