THERMODYNAMIC AL SYSTEM OF GIBBS 



115 



when the temperature is a minimum. Figure 4 shows the 

 conditions under which aqueous solutions of ferric chloride are 

 in equilibrium with various solid compounds of the same 

 components. A maximum in the temperature-composition 

 curve occurs when the liquid phase has the same composition 

 as the solid compound with which it is in equilibrium.* 



(6) Systems of Three Components in Three Coexistent Phases. 

 In this case, we have three equations similar to (100): 



v' dp = 7]' dt + mi djxi + tn^' dm + mz dm, 

 v" dp = If]" dt + mi" dm + m2" dm + mz' dm, 

 v'"dp = r)"'dt + mi' "dm + m2"'dm + mz"'dm,, 



from which, by eliminating dm and dm, we obtain: 



(108) 



7] mi m2 

 v" mi" m/' 

 ■n'" mi'" m^" 



dt 



+ 



Ml m^ mz 

 m" irvi' mz" 

 mi'" W" mz'" 



dm- 



(109) [132] 



When the composition of one of the three phases is such as can 

 be produced by combining the other two, i.e., if we may take 

 quantities of the three phases such that 



m/ = mi" + mi", 



m^ = m" + mi" , 

 I 



mz = mz + m"'; 

 the last of these determinants is zero, so that when di = 0, 



and when dp = 0, 



dp 

 dm 



dt_ _ 

 dm 



* A more exhaustive discussion of systems of two components in two 

 phases is given on pages 175-177. Compare also Article H of this vol- 

 ume. 



