Vaporization of Liquids. 295 



(= 1*979J), and M the molecular weight of the liquid, we have 



T _ RT vdv 



Li ~JM(v-bf 



or integrating from the interior of the liquid to that of the 

 vapour, 



T RT/ 1 »'-& b b \ fQ . 



hi = mV°z^b + ^rb-^rbj> ' ■ (9) 



in which v and v' are the specific volumes of the liquid and 

 saturated vapour respectively. 



By the method of its derivation, eq. (9) is general, and 

 gives the relation between the specific volumes and the 

 differences of potential JL^, due to any system of bodily 

 forces acting on a vapour the size of whose molecules is not 

 negligible compared with their free paths. 



The assumptions employed above as to the effect produced 

 by the volume of the molecules are the same as those which 

 lead to van der Waals's characteristic equation for fluids : 



(p+£)(r- 



.. RT 



Equation (9) may therefore also be derived from this, and the 

 ordinary hydrostatical equations of equilibrium in a somewhat 

 simpler way, although this gives no account of the molecular 

 actions which constitute the process. 



As the assumptions involved in the term — 2 are not 

 necessary, let p-, v 



P(v-b) = ~ (10) 



be the relation between the pressure and volume of the fluid 

 in the region of varying density, —p being the actual pressure 

 (molecular included with external), b may be not necessarily 

 independent of the temperature, but if it be not variable with 

 v, we can differentiate (10) at constant temperature and 

 obtain 



*<-».+ ¥-S=° (") 



The ordinary equation of hydrostatical equilibrium in the 

 surface-film is 



dp = pdY, (12) 



where dY is the element of potential of the bodily forces on 

 the liquid, and p the density. Substituting for dp from (II), 



