346 KEYES ART. J 



as the expression for the entropy of a mass m of the pure gas. 

 Using this entropy equation and (IV) and substituting in [87] 

 there is obtained 



V 



yp = md + mE — met log t — mat log — — mUt, (5) [260] 



which is identical except for slight rearrangements with [260]. 

 Differentiation with respect to t at constant volume and 

 applying a change of sign gives 



/9A V 



I — I = mc log f + ma log — + mH = n, 



\at/v,m ^ 



(6) [262] 



which is the entropy of the pure gas. The pressure is given 

 likewise by changing the sign and differentiating with respect 

 to volume at constant temperature, i.e., 



\dV/t,m 



"^ = p. (7) 12631 



V 



The energy and heat capacity are formed by operating on 

 ^f-i = xpT, where r represents reciprocal temperature, as 

 follows : 



c = r-f^) = md + mE, (8) 



\ OT /v.m 



\ OT^ /v.m 



t2 



Finally the chemical potential may be found by differentia- 

 tion with respect to m, keeping v and t constant, 



( 



aA , , ^ 



— • ) = u = d — dlogt — atiog- 

 dm/v. t m 



-}- at - Ht-\- E. (10) [264] 



Thus every quantity of thermodynamic interest may be 

 obtained from the Helmholtz free energy function (\J/ = e — trj) 



