50 



in which i'"^:--^, Fk=[~^-z~), f = -, (1, = ^, d^z^~. Here jj 

 p dT \p dijk Pk ^1 i\ 



denotes the pressure of coexistence, v^ and v^ the specific vohiines 

 of the coexisting Hquid and vapour phases. 



If onlj b=f{v), (f> would be =i 1 at all temperatures, and not 

 only at the critical temperature. But as it has been found that (p 

 increases from 1 to about 1.4, when the temperature falls from Tk 

 to about V, Tk (cf. also v. d. W. loc. cit., and v. L. B., p. 1100— 1101) 

 — it follows that necessarily either a must contain a function 

 of V, besides l-.v^, or a (or also b) must still be a (non-linear) func- 

 tion of 7\ 



Van der Waals thought he could allow for this by putting 



in which x represents the relative number of quasi-associated mole- 

 cules. Since besides on 7', ,x will depend on v in a high degree, 

 a function of v has been applied here to a. The dependence of the 

 tem])erature may be neglected, as in case of (quasi) association under 

 the influence of the molecular forces the generation of heat may be 

 put =0 (cf. also V. D. W. loc. cit., and v. L. I, p. 291 ; A, p. 771) 

 But apart from the insufficient justification of the above relation in 

 my opinion, especially as far as the coefficient 7» (hi general =1 — k) 

 is concerned — it will be shown in what follows that every function 

 0=r.f{v) for «/t,2 will lead to contradictions, when it would have to 

 account for the great decrease of the quantity (p in the immediate 

 neighbourhood of the critical temperature, while at the same time 

 ƒ =7, r = 2,l and 5 = 3,8 remain. The said decrease is so con- 

 siderable at Tk, that ( -— ) may be put = — 7 (?« = T : Tf, cf. 



ydmjk 



V. L. B, p. 1101 et seq.) 



We therefore put e.g. a=:akO, in which 6 = f{v Wk). The quan- 

 tity a may therefore be for some reason or other (e.g. quasi association, 

 see above) a function of v — and hence in case of coexistence of 

 two phases also indirectly of 2\ 



The direct dependence on T, which we shall discuss later, is left 

 entirely out of account for the present. 



From 



RT akd 

 ^ = 7 r (l«) 



V — b V 



follows in a quite analogous way as was derived above in § 1 : 



