(98) 



each others' neighbourhood — i. e. as far as their effect on the 

 pressure is concerned, in consequence of the "efficient" diminution 

 of the available volume. I do not know, if 1 have expressed myselt 

 clearly enough, but the attentive reader cannot fail to feel the analogy 

 of the two methods. 



The thermodynamic method, however, has this advantage that also 

 the influence of the mutual attraction of the molecules, of the variation 

 of energy in the formation of multiple molecule groups etc. can now 

 easily be taken into consideration. 



We will not enter here into the accurate solution of this important 

 problem, in which we are also confronted by pretty great difficulties, 

 but only give an approximating expression, which may be used in 

 the neighbourhood of the critical point. 



36. Let us imagine instead of n^ simple melecules n^ double, 72, 

 triple, n^ quadruple ones etc. all the molecules to be ?z-fold on an 

 average. Then according to (28) of § 30, when we rei)lace 



(1 -\ -{n-\)^)RT . 

 /v -f V.2 by m It : 





^v/H RT v-b 



(l-i?)(l + (n— l)/i)«-> (l+(n~l)^j«-i(i2T)''-i 



holds, so that we get {c' =. c : R"-'^) 



{v-bY~^ , 



z=: c 1 [V — o) e e 



1-^ 



If now in the neighbourhood of the critical point /? is put near 1, 

 i. e. if the multiple molecules are nearly all dissociated to simple 

 ones, and if we further assume ^0 = ^ (see § 34), we get by ap- 

 proximation : 



z=. c 1 {p — 0) e 



1-^ 



In this the association factor 71 (at the critical point) can be put 

 independent of v and T; in general this is, of course, not the case, 

 as on an average a smaller number (n) of molecules will be associated 

 to a compound molecule at high temperature and great volume than 

 at lower temperature and smaller volume. 



