Latent Ihat of Vaporization of Liquids. 2G9 



Combining both equations one obtains 



dXJ=G v dT + (l-p)dv. 



Further, if (he change is a reversible one, the increment of 

 entropy may be expressed 



Since d\] and d<j> are complete differentials it follows that 



'dCv == ^i _^P (i) 



Sv BT BT' V ' 



and also 



1 BO _ ]_ 'di _ ]_ 

 T a*' T BT T 2 ' 



or BC B _~bl I / 9 x 



37-BT _ T (Z) 



Hence from (1) and (2) we obtain the usual expression 



The same expression may be obtained in the case of a 

 liquid by applying van der Waals' equation, and also by 

 introducing a modified form of Dupre's relation between the 

 internal pressure K of the liquid and the latent heat of 

 vaporization I per unit volume of the liquid. Thus, writing 

 van der Waals' equation in the form 



RT „ 

 P= — r-K, 



17 — 



one obtains on differentiating with respect to T, keeping the 

 volume constant, 



B^ _ ;>-* K _ dK 

 BT T BT ' 



or r r Bp_ TC _ T BK 



BT L W 



in which p is neglected compared with K. 



Now if we write (cf. il Note on the Internal Pressure of a 

 Liquid," Phil. Mag. July 1911) 



