Physics. — ''The equation of state of an associfttim/ substance". 

 By Prof. J. E. Verschaffelt. Supplement N". ^2a to the Commu- 

 nications from the Physical Laboratory of Leiden. (Commu- 

 nicated by Prof. H. Kamerijngh Onnes). 



(Uommunicated in the meeting of June 30, 1917). 



1. A few years ago it was pointed out l)y Kohnstamm and 

 Ornstein ^) that van der Waals' equation of state is not consistent 

 with Nernst's thermodynamical theorem. Taking this theorem in 

 the form which Planck ") has given it, viz. the entropy of a system 

 in a condensed state at the absolute zero under its own vapour- 

 pressure, i. e, under zero pressure, is zero, ') which means that the 

 entropy -difference between this condition and any other (excepting 

 the ideal gas-condition) is finite, the contradiction consists in the 

 equation of state of van der Waals giving for v = b (the limiting 

 volume) a value of the entropy which is lower than that for any 

 other volume by an infinite amount ^). 



This objection only applies, however, to the equation iy its original 

 form, i.e. with a, b, and R constant; for it is evident, that it must 

 be possible by making these quantities change in a suitable manner 

 to bring about not only a qualitative, but even a complete quanti- 

 tative agreement between the equation of state and observation, and 

 thus also with Nernst's theorem, if the latter is really in accordance 

 with the experimental system of isotheruials. In particular it will 

 be clear that agreement with Nernst's theorem ^) can be obtained 



1) These Proceedings. XIII (2), p. 700. Gomp. W. Nernst These Proceedings 

 XIV (1) p 201. 



3) Thermodynamik. 4e Aufl., 1913, p. 266. 



') According to Nernst and Planck the entropy at the absolute zero should even 

 be zero under any other pressnre, i.e. should be independent of llie pressure. Gomp. 

 however Max B. Weinstein Ann. d. Phys., (4), 52 (HM 7), p. 21S; (4), 53 1917, p. 47. 

 Vid. also Paul S. Epstein Ann. d. Phys., (4), 53 (1917), p. 76.) 



*) Indeed, according to v. d. Waals Sv — Sb =1 - — I dv =\R log (?;- 6)1 



J \0J Jv *• 



b 



The two further important inferences to be drawn from the theorem : I — | =0 



and Cp = for the condensed state at T=0, which seem to be confirmed by 

 observations at low temperature, are not satisfied by this equation of stale either. 

 °) That is : S,- — S(, can be made finite. 



