1199 



The temperature function ƒ (6) can evidently generalij be represented 

 by the equation 



/<*' = ' + è ('> 



We now get instead of [a), in relation with (2) and (3) : 



bn a RT ba — a B 



pv = RT-^RT^ — RT-\ ? ^ET^r- • • (8) 



V 



in which b^, and a are given by (5) and (1) as functions of the 

 temperature. B represents the so-called "second" virial coefficient, 

 when — as we have supposed — i? is = oo (very great). Otherwise 

 B is still a function of v (through the volume distribution factor t), 

 and instead oi' B : v can be written {B : v) -{- (C -. v') -|- etc., in which 

 B, C, etc. are still only functions of the temperature. 



When we neglect the possible influence of v on the quantity a — 

 hence when we do not take the volume too small — only the 

 influence of the factor t, at the collision remains. When we write 

 for this (see also ^ 9) : 



b V 



''^-T 7' • • (9) 



Oq V — 



then b^ in (8) becomes bg X^t^, and we may write: 



/ b \ a V a 



pv = RT(\+ - - ^ i^r - -, 



\ V — by V V' — o V 



i.e. 



a RT 



P + -, = 7 (10) 



V v—b 



through which Van der Waals' well-known separation of the two 

 constants a and b has been brought about. We repeat once more that 

 this was, therefore, only possible by this, that only ior b^ a volume 

 distribution factor with v : v — h appears, and not for a, after which 

 the factor RT in the virial of collision can be united with the 

 principal term RT. 



We should, however, never forget that the quantity b thus intro- 

 duced for V — b is an entirely fictitious b, and is in no direct relation 

 with the real quantity b^ = {b(,)^ X f{f>)- For b follows namely 

 from (9): 



b - hq X --r (9«) 



1 -f T,— 



V 



SO that b can only be expressed in b^ , when t^ is known in 

 another, independent way as function of v, which has not yet 



