LEWIS. — FREE ENERGY AND EQUILIBRIUM. ^23 



This equation of equilibrium, which is at the same time a simple for- 

 mula for the heat of vaporization, has been deduced for all cases in which 

 there is no change in the molecular weight or in the specific heat at con- 

 stant volume during vaporization. Let us, in the following table, com- 

 pare for a few substances the experimentally determined values of L with 

 those calculated from equation (36). 



R is in such units that L will be in gram-calories, and equals 1.98. 

 The values of h^ are obtained from the coefficient of thermal expansion of 

 the liquid by equation (33). For the value of Vg, the molecular volume 

 of the vapor, in the cases in which they have not been experimentally 

 determined, I have used the volume which a gram-molecule of a perfect 

 gas would have under the same conditions. The error thus introduced 

 will be negligible, for a large error in v^ or in fi — \ will affect only 



The results are very interesting, the calculated values being in each 

 case about two thirds of the observed. The explanation of the lack 

 of agreement must lie in the failure of the substances to comply with 

 the conditions named above. We have no reason to suspect, in the 

 case of all these substances, the polymerization of the molecules in the 

 liquid state. We are therefore again led to the belief that the specific 

 heat at constant volume is, in general, different in the liquid and gaseous 

 states. Moreover, I think that it is possible to show this in another, 

 entirely independent way. The specific heat at constant pressure of a 

 substance is the sum of two quantities, one representing the internal 

 change in energy and the other the external, that is, 



'dW\ ^fdv 



c„ = 



dT jp ' \dTyp 



P[tiA^ (37) 



* Kopp: .Tahresber. der Cliem., 1860. 

 t Pisati, Paterno : Jaliresber., 1874. 

 \ Young, Thomas : Phil. Mag., XXXIV. 508. 

 § Brix : Pogg. Ann., LV. 841. 

 II Wirtz: Wied. Ann., XL. 438. 

 IF For 32.9^ Andrews: Pogg. Ann., LXXV. 501. 

 ** Scliiff: Lieb. Ann., CCXXXIV. 338. 



