44 WILSON ART. c 



The last two equations consist of sums of a function of v and a 

 function of t. The thermodynamic surface is 



r] = R log (y — 6) + c log (16) 



c 



or 



^=-- + ^(^73^0- (17) 



This surface is that which corresponds to following the sub- 

 stance through its partly stable and its unstable states which 

 correspond to the parts of the isothermals within the critical 

 locus; it is, therefore, not precisely the thermodynamic surface 

 discussed in Lecture XXI. 



We may obtain ^ = e — trj + pv a,s 



f = -- - Rt log {v - b) -\- ct - d log t + pv. (18) 



V 



This is not the desired form, which should involve p and t, but 

 the elimination of v would require the solution of a cubic equa- 

 tion. The condition for corresponding states is ^2 = Ti and this 

 reduces to (7) which was obtained above. 



Corresponding states. By introducing the values of a, 6, J? in 

 terms of pc, Vc, tc into the equation and using 



P = p/pc V = v/vc, T = t/tc, 



van der Waals' equation takes the form 



which is of the same form for all substances, but with pressure, 

 volume and temperature expressed as multiples of the (different) 

 critical values for the (different) substances. 



Lecture XXVII. The tangent plane to the thermodynamic 

 surface is 



e — eo = t{-n — Vo) — p(v — Vo). 



