SURFACES OF DISCONTINUITY 525 



be the average kinetic energy of one molecule ; with that we are 

 not^ seriously concerned; it is the average potential energy of a 

 molecule with regard to all the others with which we wish to 

 deal, and we shall represent it as a function of the concentra- 

 tion, say 6(n). As stated, if n is sufficiently small d{n) is simply 

 a multiple of n and is, according to our conventions, negative, 

 approaching the value zero as n approaches zero. But at 

 sufficiently large concentrations d{n) will reach a minimum 

 (negative) value and as the effect of intermolecular repulsive 

 force begins to make itself more marked in the great incompres- 

 sibility of the fluid, 6{n) will increase in value with further 

 increase in the value of n and must be considered as theoreti- 

 cally capable of reaching any (positive) value, however large, 

 unless density is to grow without limit. 



9. Distribution of Molecules in Two Contiguous Phases 



Now suppose that we have two phases of the fluid in a 

 system, represented by suffixes 1 and 2. The gain in energy 

 of a molecule when it passes from the second phase to the first is 

 d{ni) — d{n2). (We are assuming that the average kinetic 

 energy of a molecule is the same in each phase.) It is a well- 

 known result familiar to those acquainted with the elements of 

 statistical mechanics that the concentrations in the two phases 

 are related by the equation 



where k is the "gas constant per molecule," i.e., the quotient of 

 the gas constant for any quantity of gas divided by the number 

 of molecules in this quantity.* 



♦ For a gram-molecule, ft = 8.4 X 10^; A^ = 6.03 X lO^^; so A; = R/N = 

 1.36 X 10"^^ Exp (x) is the exponentialfunctionofx, viz., the limit of the 

 infinite convergent series 



X x^ x' 



^'^ri'^21'^3!'*' ■••■' 



exp(a;) = e', 

 where e is the Napierian base of logarithms. 



