376 



KEYES 



ART. J 



meable membrane into the space between the pistons, constitut- 

 ing finally a mixture of the two gases originally in the pure state. 

 By moving the pistons together the separation can be effected. 

 With the gases in the pure state we have, 



rji = ruiCi log t + Wiai log — + miHi, 



Till 



772 = W2C2 log t + wi2a2 log — + m2i/2. 



W2 



(101) [278] 



But = Vi and = F2, while aimi + 02^2 = ( k 1 + 1^2) 7 



p p t 



pV 

 = —-, and after mixing each gas will occupy the total volume 



V 



F = Fi + F2, or 



F 



t;/ = viiCi log t + miai log — + rriiHi, 



V 



ri2 = W2C2 log t + m2a2 log — + niiHi. 



7VL2 



(102) 



The difference between the respective entropies after and 

 before mixing is given, therefore, by the following equations: 



Fi aimi 



,,-,, = -m,a, log - = -rma^ log ^^^^ ^ ^^^; 



F2 , ^2^2 



172 — •'72 = —nhai log — = — ?W2a2 log ; — ■' 



(103) 



since Fi/F = 



aiiui 



and F2/F = 



aiVii 



aitni + a2m2 



by the 



relations following (101) [278] above. 



Each difference is positive since the mol fractions are neces- 

 sarily each less than unity, and therefore an increase of entropy 

 has attended the mixing. If each gas is present in equal 

 amount the total increase becomes 



vV 

 {ami + a^rrii) log 2 = y log 2. (104) [297] 



