90 Mr. W. Sutherland on the Law of Attraction 



AtJV 2 



molecules of A at distance r apart is — j-, and of two molecules 



Bm' 2 

 of B is — g— j we will assume that the mutual potential of a 



^AB m m' 



molecule of A and one of B at distance r is C ^h ? 



where C is a constant. 



Then for the mutual potential energy of all the molecules 

 of A before expansion we have an expression 



27rAamp A] log-, 

 ' i 

 where p A means the density of the gas A when its a mole- 

 cules are distributed through a volume Vi- Similarly for 

 the mutual potential of the molecules of B before expansion 

 we have 



L 



27rB brn'p^ log 



the value of r x being the same in each expression, because, 

 according to Avogadro's law, the molecules of different gases 

 under the same circumstances own equal volumes of space. 

 Leaving the quantity L of the same value in both expressions, 

 amounts to asserting that the molecular forces in the two 

 gases are quantities of the same order of magnitude. For 

 the mutual potential energy of a molecule of A and one of B 

 before expansion we have 



4ttC VAB m'p Ai log - ; 



and, therefore, for the mutual potential of the a molecules of 

 A and the b molecules of B we have 



4ttC */AB bm'p Ai log -. 



But by proceeding in the other order, that is by writing 

 down the mutual potential of the b particles of B and one of 

 A and then summing for the a particles, we would obtain 



AttC ^AB amp B log - . 



Thus for the total energy of the mixed gases before expan- 

 sion we have the expression (omitting common constants) 



Aa7np A +Bb m'p B +2C ^AB bmp A ; 



and after expansion, 



Aamp A ^ + Bbm'p B ^+2C v"AB bmp A j 



