763 



RT 



8(r„-r„rr=— ....... (11) 



For the furtiier calculation of the repulsive virial we start from 



in which f{^) must be considered positive in case of attraction. 

 Performing' the summation, we get for pv. 



pv = RT-iNJ^dNQf{ij) , 



Qa 



in which dN — the number of molecules in a spherical shell of a 

 thickness iIq round the molecule that is thought spherical — is 

 represented by dJV = 4:^q* cIq X ii- X '^, in which n is the number 

 of molecules in the volume unit and t the factor of density, which 



b V 



is = 1 for infinitely large volume, but is represented b v t ^ 



bij V — 6 



for arbitrary volume. As our considerations for the present only 



refer to h^, we put therefore t = 1. We have divided by 2, because 



else on summation every pair of molecules would have been counted 



double. Further q^ is the molecule radius, corresponding with i\ in 



(11), whereas Qn corresponds with ?'„. Thus we get: 



to 



pv = RT - ■'/, :TN7ijQ*f {(.) d^ 



Qa 



As ^/tJiQo* X ^^ 4?7i = {bg)T=o, we also have 





Qa 



In this ƒ (o) — multiplied by 2, see above — is according to (10) 

 =: 2f (?'— /'o) = 28 (q — Q„). Further : 

 Qo 



Q' (Q - (>o) dQ = f ^ - ^J ^ = i {q.' - Qa') -iQo (Qo' - Qa*) 



Qa 



= -^Qo'{y-^^^' + ^'V')^ 



when Qa : po is put = x. Hence q^ is the normal lineary dimension 

 of the molecule before the impact, Qc representing the smallest 



1/2 (* Vr = '2X^liRT:N-^3RT:N. Bui the mean value of ]'-„ is =1/3 of that 

 of V"-, so that yl^(Vr)^n becomes =RT:N. 



