172 



Fig. 1 



deduce (lie two other cases. At 

 decrease of P the heterogeiieoiis 

 region arises, therefore, in the angu- 

 lar point C (fig. 1) and it expands, 

 while curve pq changes of course 

 its form and position, over the 

 f ti'iangle. Under a definite pressure 

 1 1 the terminatingpoint e of the liquid- 

 curve coincides with tlie termina- 

 tingpoint p of the saturationcurve, 

 under a definite other pressure e 

 coincides with q. 



When e coincides with q, we 

 may imagine in tig. 1 that the 

 liquidcurve is represented by qq^ 

 or by qq■^ ; in the latter case it 

 intersects the curve qp, in the first 



case it is situated outside this curve. When e coincides with p, we 

 may imagine that the liquidcurve is represented eitiier by /)/(fig. 1) 

 or by a curve, not drawn in the figure, whicli intersects pq. Now 

 we shall examine which of these cases may occur. 



To the equilibrium between a ternary liquid A\y, 1 — x — y. and 

 a binary vapour ij^A — y^ the conditions are true: 



ÖZ ^Z . dZ ÖZ, 



dZ ., ÖZ 



d.v '^ '"' dy dy dy. 



(1) 



Let us firstly consider the region L—G in the immediate vicinity 

 of the point C. As x,y, and y, are then infinitely small, we put: 

 Z= U-i- RTxhyx + RT y lay y and Z, = U, + ETy, logy. 

 The two conditions (1) pass then into: 



U- 



dU 

 0^ 



y 



du 



dy 



u, + y. 



0^1 



RT{x-\-y-y,) = 



+ RTlogy=:-^ + RT log y, 

 Ö!/ öy. 



(2) 



(3) 



Under a pressure Pr the region L-G in fig. 1 consists only of 

 the point C, and, therefore, .i- =: 0, y — and //i = ; then the 

 unary equilibrium: liquid 6'+ vapour C occurs. This is fixed by 

 Z=:Z^ or U =z Ui, wherein x=:0, y = and y, = 0. 



Let in fig. J the region Cdee^ make its appearance under a pres- 

 sure P(:-\-dP] the points e,, e, and c/ are then situated in the imme- 



