THERMODYNAMIC AL SYSTEM OF GIBBS 



155 



represent a phase having energy e, entropy 77 and volume v 

 (Fig. 6), The points representing adjacent phases form a 

 surface. Let E be a point on this surface, representing a phase 

 having the energy e + Ae, entropy rj -{- Arj and volume v + Ay. 



Fig. 6 



If the tangent plane to the surface through the point D, cuts the 

 vertical line through E at E', the ordinate of the point E' is 



de de 



e + — At? + — Av. 

 ay] 



dv 



Since 



dr] 



t, 



dv 



P, 



the vertical distance EE' is thus equal to Ae — /A77 + pAv. 

 Thus, (210) is positive when the e, 77, v surface for adjacent 

 phases lies above the tangent plane, taken at the point repre- 

 senting the phase in question. Any phase for which this 

 holds true is stable with respect to continuous changes. 



