﻿Laic of Molecular Attraction. 105 



we know three points on an isotherm of the equation 



W=/(V), 



where W is the internal work of expansion and V is the 

 volume, we can completely determine n by the application of 

 equation (1). 



Consider unit mass of a normal liquid at volume V and 

 temperature T. Imagine it io expand isothermally under a 

 negligibly small external pressure until the volume has 

 increased by an amount AV equal to the increase in volume 

 when the liquid is heated over a range of one degree. The 

 work done must be given by 



w=c P -c t , 



where C p and C v are the specific heats of the liquid at con- 

 stant pressure which is relatively small and at constant volume 

 respectively. We then obtain the equation 



Now the values for C p — C v for liquids are not generally 

 known, but can be calculated from compressibility data by 

 aid of the thermodynamic formula 



ci — n — - \dt ) 



\d F ) 



or 



T 



C -C = \. , 

 p v J v/3 



\dt 



where T is the temperature, J the mechanical heat equivalent, 

 v the specific volume, and /3 ihe compressibility coefficient of 

 the liquid at the temperature T. 



Table I. below contains the values of C p — C v for some 

 liquids calculated in this manner. Errors in these values 

 are due principally to inaccuracies in the experimental 



data for j3 and — . In some cases, the values of j3 have 



been obtained by extrapolation of results at pressures higher 

 than one atmosphere. It is of course, strictly speaking, 

 necessary to consider only values of /3 which refer to a 

 pressure of one atmosphere ; but data are also included in 

 the table when the pressures at which /3 was determined are 

 comparatively small. 



