606 Albert P. Mathews 



latent heat of vaporization close to the critical temperature. 

 The only assumption made here is that Mills' or Dieterici's 

 formula for the internal latent heat is more correct close to 

 the critical temperature than the internal latent heat computed 

 by Biot's formula. 



5. Finally "a" is computed from the number of valences 

 and the molecular weight by the formula: a = C(M X Val) 2/3 . 



1. Computation of "a" from the Surface Tension 



The surface film is determined by the difference of cohesive 

 attraction in the vapor and liquid. The surface energy must, 

 hence, be a function of the difference in cohesive energy in the 

 liquid and vapor, or of the expression a(i/V/ i/VJ. This 

 cohesive energy has been lost in passing the liquid through 

 the surface layer which separates the two states and should 

 be calculable from the surface tension. 



Suppose we have a sphere of a gram mol of a liquid in con- 

 tact at all points with its saturated vapor. Its density is 

 uniform except in the surface film where it decreases by a 

 series of steps from liquid to vapor density. The surface 

 film may be conceived as a series of concentric shells, each a 

 molecular diameter thick, and each outer one less dense than 

 the inner until the state of uniform vapor density is reached. 

 Furthermore, on passing from one of these molecular shells 

 lying within to the one next beyond it, always the same amount 

 of cohesive energy will be lost, if the density diminishes uni- 

 formly from shell to shell. 



The surface tension T, is the tension along a line i cm. in 

 length in the surface film and one molecular layer deep. It 

 represents the force necessary to stretch the surface, that is 

 to rupture one of these shells, and thus drag one, or more, 

 molecules from the inner core of uniform density into the first 

 concentric shell; and of course the force necessary to drag 

 molecules from the first shell to the second, and from the second 

 to the third and so on, since the same force is necessary to 

 drag molecules from each inner shell to the next outer. This 

 tension, T, is numerically equal, also, to the surface tension 



