350 



KEYES 



ART. J 



where X, the heat of evaporation, is expressed in terms of a 

 constant Xo and a. One obtains on solving (25) 



Xo a 

 log p — — ~ + ~ log t + constant, 



at 



a 



(26) 



which is of the same form as Gibbs' equation [269]. The 

 procedure adopted in the footnote, however, brings to the fore 

 the precise nature of the assumptions upon which the resulting 

 vapor pressure formula rests. Moreover, it is more direct than 

 the above treatment, as may be easily shown. 



For the single accent phase (vapor) and the double accent 

 phase (condensed substance) we have* 



-v' dp -\- ri' dt + m' dtx' = 0,1 

 -v"dp + r,"dt + m"d^" = 0. 



(27) 



Gibbs proceeds to solve these equations and, from the equilib- 

 rium condition d/j,' = dn", to extract the pressure as a function 

 of t. But on solving the above pair of equations subject to the 

 same equilibrium condition there results 



v' m! 



v" m" 



dp = 



-(]' m' 



r," m" 



dt. 



(28) 



Expanding the determinants gives 



Wm" - v" m') ^ = {-n'm" - v"m'). 

 dt 



(29) 



If m' = 1 = m", and rj' — r\" is set equal to -, the entropy of 



transfer from the first to the second phase, we have the Clapey- 

 ron equation 



See equation [124], Gibbs, I, 97. 



