34 WILSON 



ART. C 



The thermodynamic surface e(r}, v) represents the various 

 states of a substance. There is a plane tangent to the surface 

 at three points representing the three phase possibihties, sohd, 

 Hquid, vapor. If the energy, entropy and volume of unit 

 masses of the substance in contact with each other in solid, 

 liquid and vapor state are es, vs, Vs] cl, vl, Vl', tv, -qv, Vy, respec- 

 tively, then the energy, entropy and volume of a unit mass of 

 which ms is solid, rtiL is liquid, mv is vapor are 



e = mses + rriLf-L + rrivtv, 



V — msrjs + mLr]L + nivVv, 



V = msVs + MlVl + mvVv, 



with 7ns + niL + mv = 1. There are developable surfaces "cor- 

 responding to the equihbrium between liquid and vapor, be- 

 tween solid and liquid, and between sohd and vapor. There are 

 curved surfaces to represent the pure phases vapor or liquid or 

 sohd. The thermodynamic surface is constituted of all these 

 parts. In addition to this there may be parts of the surface 

 which may be actually realized to some extent corresponding to 

 supersaturation when the liquid fails to crystallize and super- 

 heating when the liquid fails to vaporize. Such parts of the 

 surface must lie inside the surface as viewed from the positive 

 end of the entropy axis because they must represent states in 

 which the entropy is less than it is in states into which the 

 substance may spontaneously go. 



Let A and B be any two points of the thermodynamic surface 

 which represents the entirely stable states. The segment AB 

 must lie within (or on) the surface as viewed from the positive 

 entropy axis. For consider any point P on AB and instead of 

 the unit of substance for which the surface is given consider a 

 mixture of AP/AB units of the substance in the state represented 

 by A with PB/AB units of substance in the states represented 

 by B. The energy and volume and entropy of the mixture are 



_ AP PB 



