THERMODYNAMIC AL SYSTEM OF GIBBS 163 



or 



r d(mjv) l 

 L dfJ'n J 



= 00. (239) [184] 



'• liU • ■ • ftn — l 



But, by (56), 



m„/v = {dp/dnn)t. w M„_i> 



so that (239) becomes 



d'^p 

 dn„^ 



Similarly, we may obtain 



= 00 



(240) [185] 



d^p d'^p d^p , , , 



"Any one of these equations [185], [186], may be regarded, in 

 general, as the equation of the limit of stability. We may be 

 certain that at every phase at that limit one at least of these 

 equations will hold true." 



XI. Critical Phases* 



35. Number of Degrees of Freedom of a Critical Phase. A 

 critical phase is defined as one at which the distinction between 

 two coexistent phases vanishes. For example, at the critical 

 point of water, the liquid phase and the vapor phase become 

 identical. Again, in Figure 8, the curves CA and CB represent 

 the compositions of the two coexistent liquid phases in the 

 system phenol-water at different temperatures at a constant 

 pressure. As the temperature rises, the curves representing the 

 compositions of the two coexistent phases approach each other, 

 and at the point C the two phases become identical. Similar 

 phenomena are met with in ternary mixtures. Let Si and S^ 

 be two liquids which are incompletely miscible at a certain 

 temperature and pressure, but which both form homogeneous 

 solutions in all proportions with a third Hquid Sz. If we add 



* Gibbs, I, 129-131. 



