118 B. Galitzine on Radiant Energy. 



Let the heat required be Q{. Then, as in the first case, 

 Q,i = e 1 h 1 + ~PJi 1 . 



ei and Pj denote respectively the energy contained in unit 

 volume, and the light or heat pressure, at temperature T t . 



Now let A be replaced by a perfectly reflecting wall, and 

 let the piston B be moved farther away to a distance h 2 . In 

 this process an amount of work t will be done, but as the 

 operation is an adiabatic one the temperature must gradually 

 decrease from Tj to T 2 . 



\dh (9) 



- 



The principle of conservation of energy gives us 





e^-eji^ Vdh; (10) 



or, for an infinitely small displacement, 



-d{eh) = Fdh (10a) 



This having been done, we can again replace the reflecting 

 wall A by a perfectly black surface, and either (1) gradually 

 reduce this surface to zero temperature, and then, without 

 doing any work, push the piston B back to A; or (2) keep 

 the black surface at constant temperature T 2 and then bring 

 back the piston B to A against the constant pressure P 2 (this 

 latter being Boltzmann's operation). The last process neces- 

 sary to complete the cycle is the heating of A to temperature 

 T x ; this requires no energy, as its mass is infinitely small. 

 In both cases the cycle of operations is reversible. Applying 

 formula (4), the second law of thermodynamics gives us the 

 following set of equations: — 



«i+Pi 



^= A \f l i S rfT = t h=,h ^i P T (U) 



Ti 



From these we obtain 



%+p 8 , *i+p, , _ n 



m n 2 Ffi 'h — U, 



±2 J-l 



or 



'e + Y 



i + Ju 

 or, having regard to (10a), 



dieli) + Fdh + hd? - ^ (e + P) dT = ; 



