FUNDAMENTAL EQUATIONS OF IDEAL GASES 357 

 but (/ii — El) /ait may be formed from [268] and expressed as 



Jmi - El) /ait 



Pi 



aieH^' 



(43) 



whence 



or 



iV = 2pi), 



amit 





(44) [277] 



The former may apply even when the gases are not ideal. 



17. Entropy of an Ideal Gas Mixture. Differentiating (42), 

 [273] and rearranging gives the following equations: 



dp = 2 



Ml -El 



aieh'^'e "'' (r ^iLJzZA 

 1 r" a^t ) 



dt 



+ s 



Ml — El 

 hi4Ci„ ait 



aie'T'e 



ait 



dm, 



(45) 



but by [98] 



dt + 



S[S] ^^" 



(46) 



dp = - dt ■{- / , — dfiu 



(47) 



whence using the value of 

 Ml — El 



ait 



= - hi + log 



('-9 



from [269] there results 



' = S [S {^' + <"■ + "^ '»« ' - "' "^ f}] ^''^ ■'''" 



