524 RICE 



ART. L 



liquid, it is limited by the fact that implicitly it regards the 

 liquid as divisible into elements infinitesimally small com- 

 pared to the range of molecular attraction, and this is not the 

 case in actual fluids. However, molecules although not 

 mathematically infinitesimal in size are so small that great 

 numbers of them exist even in any "physically small" volume 

 of a gas. By "physically small" we mean small in so far as our 

 capacity to deal with it experimentally is concerned. Under 

 such conditions we can apply certain well-known statistical 

 results which will prove of service to us later when we shall 

 endeavor to supplement the thermodynamical arguments of 

 Gibbs' treatment by considerations based on molecular 

 structure. 



The previous discussion introduced us to an expression which 

 represents the potential energy of one molecule with respect to 

 its surrounding neighbors. It is given in (1), and ostensibly it is 

 proportional to n, the numerical concentration of the molecules. 

 We have already noted the hypothesis of infinite subdivision 

 of the fluid on which this is based. But even if we waive that 

 difficulty we must draw attention to the fact that the factor 

 multiplying n is a function of the lower limit of the integral, 

 viz., I. Now this limit is by no means so definite as the upper 

 limit. Undoubtedly, if the concentration is not too great, we 

 may take it to be a fixed quantity so that the expression in (1) 

 may be regarded as varying directly with n;and as we have 

 seen it then supplies the theoretical basis for van der Waals' 

 cohesion term. But as the concentration increases, or as the 

 temperature rises so that molecular impacts are on the average 

 more violent and penetration of molecule into molecule more 

 pronounced, the quantity I itself will become a function of 

 concentration and temperature. Thus the linearity in n of the 

 function expressing this mutual potential energy disappears at 

 sufficiently high concentrations. We shall still require this 

 conception of the potential energy of one molecule with respect 

 to the others or, to put the definition in another form, the change 

 of energy produced by introducing one more molecule into the 

 system, and we shall consider it as some function of concentra- 

 tion and temperature. Of course, one part of this change will 



