48 WILSON ART. c 



and hence yij;2i^3 = ah/p and 



^3 d log p 



d log t 



- 1. 



The value Vs is that at which the rising (unstable) part of the iso- 

 thermal cuts the horizontal line and is not attainable by experi- 

 ment. But on substituting this in the equation we have 



by -f- 



/ d log p _ \2 dlogp _ 2 

 Vdlogi / dlogt 



which is sometimes useful in working with coexistent phases 

 when we are willing to put conjfidence in the equation of van der 

 Waals. 

 The general equation of state 



p = F'{v) + tf'iv), 



of which van der Waals' is a special case, maybe discussed. For 

 this (dp/dt)v is again a function /'(t;) of v and at constant vol- 

 ume is constant, so that the isometric lines in the p^diagram are 

 straight. We have 



,/, = -F(v) - tf(v) + $(^), 



€ = -F(v) -f$(0 - t^'{t). 



If we use for $ (t) the expression ct — ct logt, thene = —F{v) + d. 

 At any rate both e and 77 consist of a function of the volume 

 plus a function of the temperature. It is to these equations 

 that we naturally look for some improvement upon van der 

 Waals'. 



Lecture XXX. Let us make the hypothesis that there is an 

 equation of state which is independent of the substance, pro- 

 vided only we measure p, v, t in the appropriate units. What 

 results could be obtained? There is one state of the substance 

 which is physically defined, namely, the critical state. It is 

 therefore P = p/pc, V = v/vc, T = t/tc which are the variables 



