and Electronic Potential Energy. 251 



the following simple principle, that a molecule attracts its 

 six nearest neighbours with a force 4<?V/R 4 , and that its 

 effects on all other molecules may be neglected. 



1. The so-called internal molecular pressure, the Kp 2 of 

 Laplace and the a/v 2 of van der Waals. 



The attraction of a molecule for one neighbour having the 

 average value 4#V/R 4 , the attraction per unit area of matter 

 lying on one side of a plane exerted on that lying on the 

 other is 4e 2 s 2 /R 6 . If m is the mass of a molecule and p( = l/v) 

 is the density of the substance, W = m/p, so we may write 



Kp 2 = a/v 2 = 4*V/R 6 = ±e 2 s 2 p 2 lm 2 = ±e 2 s 2 /m 2 v 2 . . (1) 



2. The internal virial ^ . J 22 rf(r). 



"With f(r) to denote the attraction between two molecules 

 at distance r apart, this evaluation becomes easy. Let us 

 make it for unit mass of the substance consisting of n mole- 

 cules in volume v. For a molecule and each of its six 

 immediate neighbours rf(r) becomes 4g 2 s 2 /R 3 . The first 2 

 extends only to the six nearest neighbours, so 



Zrf(r) = 2±e 2 s 2 /W. 



Then 22 rf (r) = 24?ie V/R 3 , 



and J . J 22 rf (r) = 6ne 2 s 2 IR B = 6»^V/m= 6n 2 pe 2 s 2 



= 6pe 2 s 2 /m 2 = ?>Kp/2. . . (2) 



3. Molecular potential energy. 

 The potential energy of a molecule and one nearest neigh- 

 bour for an attraction 4eV/R 4 is 4eV/3R 3 . For the six 

 nearest neighbours it is Se 2 s*/R?, and for the n molecules in 

 volume v it is n/2 times this, the factor ^ being introduced 

 to avoid counting the mutual energy of two molecules twice 

 in the summation. So for the potential energy of unit mass 

 we have 



±ne 2 s 2 /U z = 4:n 2 e 2 s 2 p=4:pe 2 s 2 /m 2 = Kp. . . (3) 



4. Surface energy. 

 First let us take the imaginary case of a substance whose 

 surface is common with that of a vacuous space. A molecule 

 on the surface has now only five nearest neighbours, if we 

 carry our cubical scheme right up to the surface. The at- 

 traction of one nearest neighbour would be unbalanced by an 

 equal opposite force. So a process of adjustment takes place 

 in the surface layer of molecules. Part of the adjustment 



S2 



