375 



same. The introduction in X (eq. 11) of tiie term depending on the 

 cohesion (f ^ and even = 1) will not produce any fundamental 

 change in the relation. 



8. We shall now consider equation (5) as the equation of state 

 of a substance with molecular transformation. According to this 

 equation the isothermals representing the comprevSsibility obtain a 

 shape which does not essentially differ from that of a substance 

 without molecular transformation (« = const). This is best recognized 

 in the simplest case where k=zl and s =^0, that is for equation 

 (4') connected with (12'), when the equation of state would be: 



el \ V — oj V 



1 / el \ 1 



the function — loo { 1 -\ , which takes the place of in 



ev ^ \ v — bj V — b 



the original equation of state of vam der Waals has in the main 



a similar course to the latter function, with which it coincides to a 



first approximation (large volume or small value of e^, i. e. weak 



association) : as v decreases from oo to b, the function increases 



1 

 steadily from to oo , more slowly, however, than -. It follows 



V— 



that the isothermals of the associating substance intersect the normal 

 set (ttv =: 0), towards lower pressures (consequently towards lower 

 temperatures), as v becomes smaller. 



Again the change of b with v does not bring about an essential 

 difference in this result. As regards a dependence of a on «, this 

 again cannot modify the shape of the isothermals fundamentally ; 

 but it can have an important influence on the whole set of isothermals 

 in the sense, that the possibility of neighbouring isothermals intersecting 

 each other is not excluded, whicli might give rise to special 

 phenomena. But it is not our intention to inquire into this further 

 on this occasion. 



9. Before going on let us for a moment longer consider equation 

 (13), in which a and b are constants. The critical point, as determined 



by the conditions ( — 1 = and I ^ 1 =: 0, corresponds to a tempe- 

 rature which is given by 



2a (l_M-f |/l — M + M^)(l + l/l — M-f w») 



Tj. z=. — , . . (14) 



bR (2- M-hl/1— M^M*)» 



where 



