89 



df (Po{l-,c) <Po.v 



/(V'^') + (>^ Ih'^^i (l-'^') — f^2'l^.'^' — ^'i: (l-'O ~^j-j, ^1,(1 -•«) '~ — 



ÖQ all air 



(Pq{\.-x) (Po.v 



-'"'-Th' ""■''liF"="- 



In this /{Q'V) is the free energ}^ of a homogeneous phase with 

 the .1' and q existing in h, and hence 



— MRT log {v — b,^) — - 4- 3IRT |(1 — .r) log {l—.v) + .v log a]. 



V 



The energy for M^ grams of the tirst component amounts to 



f 1 = <^i— «11 Q (1 — ■^') — «12 Q^v — 5 c„ — ^- k C,2 ^ 



and for 31, grams of the second component : 



^, = C, — a,, (> (1 - w) — a,, () .t- — è c,, ~ I c„ -^— . 



« 

 We get therefore for our equations (1) for the first component : 



" ()(l-a') div dli^ 



, JT 





^nlm.iVu, ''-] a,,Q'(l-w')—a,„o'a;''—^,c,, ic,„ . (I,) 



' ' 'n^o'{\-w') ''^^ ^ ''^ ' '' dh' ' ' dh' ^ '^ 



and for the other component: 



jJTj d^Q{l-w) d^QX 



k ^^>2^\' -I «12 (> (l-'^O — «22 (> '^ — 5 <^12 -.r2 ^ ^22 ~, ,V = 



« (>^ dh dli 



= i "^.A^^V; -f V - «12(?'(l-^-')-«22<y- - h C,, -^,T-^ ~ k «22-^ (I2) 



" () .?; all- dli 



In this rr represents the j?M;'/iVJ pressure so tiiat in the liomogeiieoiis 

 phase ,rr is the partial pressure for the first component, and .^„t the 

 partial pressure for the second component. ,.t -(- .^.t 1=/). In ihe 

 direction of the capillary layer these partial i)ressures are represented 



by 1.T2 and ,rr,, so that ,rr^ ^ ^T^=p^. 



The expres?-ion — ^ — ^~ or "^—, tlierefore, represents the work done 



(>(1 — X) 1 X 



on a quantity M^ of grams of the first component when it leaves the 

 phase. The phase being composed of J/j (1 — x) -\;-M^x grams in a volume 



V 



V, M, grams of the first component will occupy a volume . 



1 — X 



