HETEROGENEOUS EQUILIBRIUM 253 



in which Av^^ and At?^^ have been substituted for 



^,' _ ," _ (^' _ :,-) ^, j and ^v' - -n" - ix' - x") ^^,], 



respectively. This appHes to any two-phase equiUbrium ; if we 



have in addition a third phase, denoted by triple accents, we 



have another equation of the same form. Elimination of dy 



, dt 

 between the two equations and solving for t7/ gives 



^ _ 1 a/x2 Av^'' {x' - X") - Ai;^^ {x'" - X") 



dx" ~ ~ I - X" dx" At;32 ^^12 _ ^yl2 ^^32 ^ ^ 



This is a general equation which applies to any three-phase 

 equilibrium in a two-component system. 



r \ dV'l 



The terms of the form v' - v" - {x' - x") -^, requu-e 



some discussion. In equation (6) [129] the volume and en- 

 tropy terms represent difference in specific volume and 

 specific entropy, and, taken as a whole, represent the volume 

 and entropy changes taking place along the three-phase curve. 

 Equation (12) refers to two phases in a two-component system, 

 and hence to a divariant equilibrium. The coefficients of dp 

 and di in this case refer to the volume and entropy changes 

 which take place when one gram of the first phase separates 

 from a large quantity of the second, a type of change called 

 "differential," "partial," or "fictive." 



11^.. Correlation of the i-x and p-t Curves. Consider the 

 application of equation (14) to the t-x curve of KNO3 in the 

 binary system, H2O-KNO3, and let the phases with single, 

 double, and triple accents be vapor, liquid (saturated solution), 

 and solid, respectively. The equation then becomes 



dt 1 dfi2 Av'^ (x" - x^) - AV^ jx' - x^) 



dx'' ^ ~ 1 - x" dx" Av'^ At;"' - Aw"^ Arj'^ 



1 9/i2 



The terms :j 77 and —y, are necessarily positive. In the 



denominator, Av^^ is usually negative, Ar;"' always positive, 

 hence the first term is usually negative. In the second term, 



