Vaporization of Liquids. 297 



This expression, however, does not seem to give very accurate 

 results ; it is of a different form from (9), although of course 

 were van der Waals's equation strictly true it would be equi- 

 valent to it. 



Equation (9) for the heat of vaporization contains what is 

 to a certain extent an arbitrary constant b. b is not, however, 

 in reality completely arbitrary, as it can be calculated approxi- 

 mately from the critical volume, although the approximation 

 is very rough, or it could, if necessary, be estimated with 

 sufficient exactness by substituting in van der Waals's equation 

 the specific volumes of the liquid at two different pressures. 

 As, however, there seems some theoretical reason to believe 

 that b is slightly variable with the temperature*, it seems 

 better, instead of calculating the heats of vaporization of dif- 

 ferent liquids with approximate values of b, to test the formula 

 by calculating b for different temperatures of the same liquid 

 from the other quantities of the equation, either to see if it 

 keeps constant or to determine its variation. The values 

 obtained in this way may be tested by applying them in the 

 equation 



(*+£)(«-&) = 



RT 

 M 



to see if they give satisfactorily constant values of a (this 

 equation being used here for the liquid state only, where it 

 holds very approximately, although the constant may change 

 considerably through such a large range as that from the liquid 

 to the vapour). 



The only two cases in which the heats of vaporization have 

 been measured with any accuracy at different temperatures 

 are water and benzene. Below are the values of b and a cal- 

 culated for these substances by means of (9), the headings of 

 the columns denoting the quantities expressed by those letters 

 in the earlier part of the paper. (Volumes are given in c.cs., 



the latent heat in gr. calories, and a is in units such that -^ 

 is a pressure in dynes per sq. cm.) 



as going on after the molecules have reached the upper layer). The 



work \pdv done in this way, however, goes to increase the kinetic 



energies of other molecules of the system, and is immediately made up to 

 the expanding molecules by radiation, so that the system as a whole does 

 not lose this heat. If part of this work to the extent p(v'—v) is done 

 on the atmosphere, as when evaporation is actively going on, it must of 

 course be supplied to the liquid as extra heat. 



* Sutherland, Phil. Mag vol. xxxvi. (1893) p. 507. 



