LEWIS. FREE ENERGY AND EQUILIBRIUM. 21 



later in discussing certain relations between the liquid and gaseous state. 

 The way in which a and b change with varying conditions of a liquid is 

 illustrated by the following values, calculated for fluor-benzol, from the 

 data given by Young.* For the values at high pressures p is not negli- 

 gible compared with ~ x , equation (33) will not give exact results, 



and recourse must be had to the original equation of van der Waals. 

 v represents molecular volume in litres, p is expressed in atmospheres, 

 and b and a in units corresponding. 



By extrapolation from these val- 

 ues we find for v .270 the 

 critical volume 270 



From the critical data a and b are 



determined to be 270 



It is evident that the values of a and b obtained from the data for the 

 thermal expansion of a liquid are entirely consistent with those deter- 

 mined from the critical data. The change of l> with the volume is well 

 shown by the figures, and is typical. Regarding the variation in a, how- 

 ever, it is not possible to say whether it is due to change in volume or 

 change in temperature, or both. 



It must be emphasized that in all the preceding work on gases and 

 liquids we are dealing with substances composed of a single molecular 

 species. Gases and liquids in which dissociation or association occur are 

 not within the scope of this section. 



(B.) Heterogeneous Systems. 



1. Gases and Liquids. — The simplest case of heterogeneous equilib- 

 rium in a system composed of a single molecular species is that between 

 a simple liquid and its vapor. We may apply to this case the general 

 equation of equilibrium (11 a). If we consider the specific heat at con- 



* Phil. Mag., XXXIII. 153. 



