304 The Heats of Vaporization of Liquids. 



van der Waals's equation, 



(*+ 5) <-»>-£ • • • • {14) 



v being the volume of the liquid, and a an absolute constant. 

 This is not quite the same thing as if b were eliminated 

 between (9) and (14), which would give 



a 

 T RT . P + ^ a (I 1\ 1 , , N 



as there is reason to believe that a varies a good deal from 

 the liquid to the vapour, although it remains fairly constant in 

 the liquid. However, at low temperatures, a/v /2 is negligible 

 with regard to p, and p with regard to a/v 2 , so that in this 

 case the total heat of vaporization would be sufficiently 

 expressed by 



T RT , a a 



L= JM l0g K + J^ 



(transferring ^p(v' — v) to the left-hand side of the equation). 



A calculation indeed shows that an equation of this form 

 expresses it with considerable accuracy at low temperatures. 

 Finallv, the equation for the heat of vaporization throws 



mi 



an interesting light on Trouton's well-known law that -^ 



is roughly constant for different liquids, L being the heat of 

 vaporization at the absolute temperature T of the boiling-point. 



From equation (9) it will be seen that -^- is a quantity 



depending on v, v r , and b. But v f , which is the only quantitj' 

 which would vary considerably from substance to substance, 

 only enters in the logarithm, and in the denominator of a small 

 term, and will consequently not greatly affect the result ; again 



-, and therefore r , is not greatly different for different 



v ' v— b 



liquids at corresponding temperatures, which may be consi- 

 dered the same as their boiling-points. -^ , therefore, at 



the boiling-point will not vary more than 20 or 30 per cent, 

 for most liquids, which is about the extent to which Trouton's 

 law applies. 



