_, - PBl .- OF THE AMKKICAN ACADEMY. 



The work done daring this cycle at D, C\, and ('.., ia zero, Bine 

 the anal position ia the same as the initial, and the presi 

 is constant throughout the cycle. Therefore the total work done by 

 the system daring the cycle is that done by the pistons \\ and 

 which i illows : 



In operation (1), 



Aj = llj'i + ILl'o. 

 In operation (2), 



A, = - ivr, - n,./ r,. 



In operations (3) and (4), except for a differential of the second 

 order, 



A z + A* = - (iix + dih){ \\ - dV x ) - (n, + </ii,m r, - d i 



By the second law of thermodynamics the sum of these terms, the total 

 work of a reversible isothermal process, r ust be zero. Hence, 

 neglecting differentials of the second order, 



JV/ITi + JV/IJo = 0. 



Since we are dealing with ideal solution-, 



.. .V,A7' . r .V/,7' 



r 1 = - 5r and r^-^--, 



hence iVVlnirx + A', 7 In II, = 0. 



Now the activity £i of Xi in A is always the same as in B b and & in A 

 is the same as in B, ; hence, applying equation III (j> and T being 



constant-,) we have, 



AV/hu, + X,71n4-, =0, XV 



which may also be written 



Ay i ain& + iyyin& \ =0 XVA 



\ dN X Jl\T 



or /Wln^4..Vjln£A m 



V oN % Jr.T 



