( 

 364 KEYES ART. J 



and 1712" /mi" = r", 



(—, - -^^ dp = (^,- ^)dt +(h- T, ) dp,', (74) 

 \W2 W2 / \m2 m2 / \r r / 



(—> - ^) dp = (— , - ^) dt + (r' - r") dM2'. (75) 

 \mi mi / ^ \mi mi / 



When r' is equal to r" the ratios of the components in both vapor 

 and Hquid phases are identical, and the system resembles a pure 

 substance in its thermodynamic behavior (mixture of constant 

 boiling point). To show this, add equations (74) and (75), 

 put (m/ + m2') = M' = 1, {mi" + m2") = M" = 1, and since 



(76) 



(77) 



The v' in this formula is the volume of one gram of the vapor 

 mixture in equilibrium with the liquid mixture of constant 

 boiling point t, and v" the volume of a gram of the latter liquid 

 at t. The heat required to evaporate one gram of the special 

 composition is, therefore, 



X = i f (.' - v"). (78) 



The heat of evaporation generally, and other quantities per- 

 taining to a binary mixture may be obtained from the equations 

 (73) when dm' and dn2 are known. A convenient trans- 

 formation of form is the following, whereby the potentials are 

 expressed in terms of the quantities a', a", dr', and dr". To 

 carry out the transformation use is made of the following rela- 

 tionships obtained from [92] by cross differentiation, tempera- 

 ture and pressure being kept constant. 



