598 



The state of equilibriiiin : 



As ill Siippl. Leiden N». 246 ^ 5: — ff{i\) may represent tlie 

 potential energy with respect to the mutual forces for a pair of 

 molecules with the mutual distance r,, where for Vj > r (f{)\)=0. 

 For a set of three molecules the total potential energy is: 



_ <p (r„ r„ r,) =: - \rf{r,) f ^(r.) f c;(0|, ... (10) 



where we assume, that the attraction between two 'molecules is not 

 changed by the presence of a third molecule. 



The condition for the energy is then: 

 Hz= S^n^,n,.\-h^^nii](f{i\)-^:S ^ iii,yi-i<P{r^,r,,r,) — const {l\) 



d>' dw di) (Ir (/" t/'i'/raf/r, 



For the state of equilibrium we then find after some reductions 

 e.g. for the distribution of the molecu^les into single molecules, into 

 molecules belonging lo pairs, into molecules belonging to sets of 

 three, with the required degree of approximation: 



na=n\[ r^--j-hP^2P-'^E-S)\ 



n 11 



V V 



n' \ n 



V \ V 



ni^-\P { ~{l>P-'iP'-R)\, ' (12) 



n 

 Uc = - 'S, 



V 



where passing tVom summations to integrals: 











(13) 



'''i''i'''»'i24:Jt^i\i\i\ di\dr^dr^. 



Deducing further the entropy, then the free energy i|' and from 

 this the pressure, we finally find for the second virial coeflicient: 



B~V,n{h-P) (H) 



analogous with Siippl. Leiden N". 246 equation (40), and for the 

 third : 



C — \n'' {^h'-?>bP+2,P'-\-'6R-2S) .... (15) 



§ 8. Developmenl for rigid spheres inithout attraction. As first 



