296 Mr. S. K. Milner on the Heats of 



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

 vapour, we obtain 



y/ Y - RT r Vdv 



V - Mj, (v-t>)*> 



which, with JL; written for V— V, is the same equation as 

 (9) for the internal heat of vaporization. 



Another expression for the latent heat might similarly be 

 obtained from the other term of the characteristic equation 

 by writing the pressure in the liquid as 



p=p'-\ — -, p f being the vapour-pressure. 



In the film of varying density, p would also contain terms 



depending on — ; but on integration between places where 



the densities are constant these would vanish from the final 

 result, and the internal latent heat would become * 



}££■*(*>- J. *g -j> .'. <-, 



* It seems to have been usual to assume that the total latent heat of a 

 Tapour is given by j v pdv. Thus Nernst (' Theoretical Chemistry,' 

 p. 209), writing the pressure in the liquid 



makes the internal heat of vaporization 



a result only half as great as (13). Consideration of the process, how- 

 ever, seems to show that the internal heat is the same thiog as the 

 difference of potential V — V, and that therefore its value is given by 



rv'ap or J v flp For the molecules in moving from the liquid to the 



vapour and doing work against the molecular forces change their kinetic 

 energies by an amount V— V, or \ vdp per gram into potential energy. 

 This amount of heat is therefore taken from the system, and remains in 

 the vapour as potential energy. At the same time, as they move up 

 through the region of varying density, they expand and lose kinetic 



energy = ^pdv (although it is not necessary for a molecule to have the 



extra energy indicated by this to be able to pass from one layer to the 

 next considered in the deduction of (9)— the expansion may be considered 



