358 KEYES ART. J 



mi ^ Pi 

 V a\t 



m-i p2 



— = "~ ' etc. 



(49) [275] 



and 



r? = ^ (miHi + mi(ci + ai) log t + miai log — j- 



Where v is the volume of the mixture the entropy becomes 



ry = /, (miHi + wiCi log t + miai log — j- (50) [278] 



The latter equation requires that the entropy of a gas in a 

 mixture of volume v and temperature t be the same as though 

 it existed alone at the volume v, the temperature remaining 

 unchanged. The result may be exhibited in another form. 



The total volume v is given by the expression - 2aimi where y is 



the total pressure of the mixture. Substituting in (50) [278] 

 there is obtained 



rj = 2 ( ^1^1 + ^1 ^1 ^og t + m,a, log — ^^ y (51) [278] 

 \ HaimJ 



but V is a quantity which is called the partial pressure for 



ZaiTWi 



the gas with subscript (1), i.e., pi, and 2pi = p, which is equa- 

 tion [273]. It follows then that if a gas exists in the pure 

 state at pressure p and temperature t its entropy in the gas 

 mixture of pressure p will differ from that in the pure state by 



— miai log z , which is the same thing as — ri/C log Xi, 



Zttimi 



where Xi = —, the mol fraction, and C"^ = Miai (see equation 



[298], Gibbs, I, 168), where Mi is the molecular weight. 



18. Implications of Gihhs' Generalized Dalion's Laio Apart 

 from Ideal Gas Behavior. The discussion, Gibbs I, 156-157, 



