Kinetic Theory of Gases. 799 



so that in this case, with our previous notation, 



P v=mT + 1 { mibe^- M } + o (J) , (22) 



which confirms equations (19) and (20). This result is in 

 itgreement with Keesom\s *, obtained by yet another inde- 

 pendent method — the calculation of the entropy. 



§ (11). Particular molecular models. — The molecular models 

 which are of interest are those in which the attraction (1) 

 varies as the inverse 5th power of the distance, <j*(r) = ur~ s , 

 and (2) is constant over a certain range and zero outside 

 that range, <j>{r) = A, {cr<r<d); 0(r)=O, (r>d). The 

 latter may be regarded as the natural successor of the model 

 originally proposed by Young in his theory of capillary 

 forces. In the first model it is essential for convergence to 

 take 6'>4; the physical meaning of this restriction has 

 already been commented on in § 5. 



(i.) The inverse s th -poiver law. — If we take ${r) = ar~ s we 

 have 



n c)=S> (,,> ^') 



>•.-••■ (23) 



For the second virial coefficient B we combine (19) and 

 (20), expand e 2jU(r \ and integrate term by term. We obtain 

 after reduction 



b=™ (1-3 1 (MM^_ I (m 



where 5 = §77\NV 3 , its classical meaning. 



(ii.) Young's model. — In this case we have 



n(r) = 0, (r>d), - 



= A(d-r), (d>r>a), I. . . ( 2 5) 



= A(d-a) 3 (a>r). 



The integral for x (0) can be evaluated in finite terms by 

 integration by parts. We obtain after reduction, 



X[ j 2j I \Z a + 2jA + (2jAf + (2jA)*) e 

 * Loc. cit. p. 264. 



