HETEROGENEOUS EQUILIBRIUM 237 



system, such as water, in which the liquid coexists with its own 

 vapor at a series of pressures and temperatures. There are two 

 equations of the form of (1) [97], one for the vapor and one for 

 the hquid. If we denote vapor and Hquid by the indices v and I, 

 and use, as we shall hereafter, the capital letters V and H 

 (capital eta) lor total volume and total entropy, respectively, 

 these equations are 



'V'dp = R^dt + m^'dn, 



and 



V^dp = Wdt + m^dfx. 



It will be remembered, from the derivation of these equations, 

 that the quantities V and H refer to the total volume and total 

 entropy of the mass considered ; in this case, where there is only 

 one component, to the total volume and entropy of the m grams 

 contained in each phase. If we divide each equation through 

 by the mass w, they take the form 



v^dp = -q^dt + dfi, 

 v^dp = 17'rfi + dny 



in which the lower-case letters are used to denote specific 

 volume and specific entropy, as opposed to the total volume and 

 total entropy, denoted by the capital letters. We can eliminate 

 dn between these equations by subtraction, giving us 



(y" - v^)dp = (tj" - y]^)dt 



or 



dp rf — 7j' 

 dt V — v^' 



Since dR = dQ/t, which on integration at constant tempera- 

 ture yields AH = — , this reduces to the usual Clausius-Clapey- 



V 



ron equation 



dp _ AQ 



dt ~ t{v^ - vO • 



