LEWIS. — A NEW SYSTEM OF THERMODYNAMIC CHEMISTRY. 275 



(3) Lower F once more to E, under the constant pressure II — dn. 



(4) Raise the temperature to T. 



The total work done by the pistons D and C is zero, since they are 

 under constant pressure and finally return to their original positions. 

 The whole work done by the system is, therefore, the work done by the 

 piston F. This is obviously the sum of the following four terms : 



A 1 = lit'', 



i. = - lido', 



A z = - (n - dH)(v< - dv'), 



^4 = 0. 



The sum of these terms, neglecting the differential of the second order, 

 is v'dH. This is the total work done by the system during the cycle, 

 and therefore from the second law of thermodynamics, 



v'dU = QdT, 



where Q is the heat absorbed in process (1). Q is the sum of three 

 terms. The first is the increase in internal energy when one mol of Xi 

 passes from A to B, which we may call Z7j XII) . The second is the 

 osmotic work, ITr', which is equal to RT. The third is the work done 

 by the pressure P acting on piston D, which is equal to — Pc where v 

 is the partial molecular volume of X x as before. 

 Hence, 



,^n r XII1 + RT-Pv 

 dT T 



RT 



Now v' = — — , 



, ,, , rf Inn if +BT-Pv 



and therefore ~dT~ = RT 2 — 



Combining this equation with equations III and IV, as we did in 

 deriving equation VIII, we have 



/gin A 



V ^T )p, n ~ 



ffjxip + ffjiv) — Pv 

 RT 2 



The sum of Z7 (XII) and U aV) is the increase in internal energy when 

 one mol of Xi passes from an infinite quantity of the mixture into a 



