Properties of a Mixture of Liquids. 399 



We may now write (2) as 



^A,p^,T)+/(A,-B, q ,p,T) + ( m + n)^ i f(A,B,q,p,T) = 4>'(A,p k ,T), 



$(B,p, T) +/(A, B, q, p, T) + (m + «) ^/(A, B, q,p,T) =</>'(B, p B ,T) ; 



or writing /(A, B, </, p, T) as / for short, and transforming 

 to q as the independent variable, 



4,(A, P ,T)+f+(q+l)1f^4>'(A,p A ,T), 



dq 



^(B,^T)+/- 2 ( ? + l)g=f(B, jPB ,T). 



Now the thermodynamic potential of a perfect gas may be 

 expressed in the form 



4>'(A, PA , T)=f (A,*,, T) + ^ log**, 



jt? being any other pressure, R the gas constant, and A the 

 molecular weight of the gas. Take for standard pressure the 

 saturation pressure of the pure vapour at the temperature 

 considered. Let this be 7Ta, 7Tb for the two substances. Then 



* (A, p, T) + /+ {q + 1) g = <p'( A, ,r A , T) + M log £i, 



*(B,p, T) +/-q(q+ 1)^ = *'(B, ttb, T) + 5£ i og |2. 



But the thermodynamic potential of a liquid varies exceed- 

 ingly little with pressure : so we will assume that 



0(A,p,T)=0(A, TA ,T); 



and the latter is equal to <f/(A, 7r A , T), for liquid and vapour 

 are in equilibrium at that temperature and pressure. Hence 



/- 2 ( 2+ .l)|/=flogg. 



(7) 



From (7) we obtain by addition and subtraction, 

 and 



/.xfbga + .i"!^^ . . (9) 



</ -f 1 A °7T A £ + 1 B & 7T B 



2 F 2 



