THERMODYNAMICAL SYSTEM OF GIBBS 143 



The conditions of equilibrium between the original parts of 

 the system have already been established. They are: 



t = T,p = P, (189) 



Ml ^ Ml, li2^M2, ... Hn^ Mn, (190) 



i.e., the temperature and pressure have uniform values T and P 

 throughout the system, and the potential of the component Si 

 has the value Mi in all parts of the system of which *Si is an 

 actual component and may have a value greater than Mi in 

 those parts of which it is a possible, but not an actual com- 

 ponent. In using (187) we suppose that the total entropy and 

 the total volume are constant, and since also in the case under 

 consideration no component can be formed out of others the 

 total amount of each component is also constant. The equa- 

 tions of condition are thus 



(191) [39] 



(192) [40] 



(193) 

 25m„ + ZDnin = 0. 



Inserting the values of t, p, fxi, etc., and of Zdrj, Z8v, XSmi, etc., 

 as given by these equations, in (187), we obtain 



SDe - TSDt; + P^Dv - M{LDmi ... - Mn^Dnin ^ 0, (194) 



or 



De - T-Dri + PDv - MiDmi ... - Mn-Drrin ^ 0, (195) 



for each of the new parts. This is the condition which must 

 be satisfied in addition to the conditions relating to the equilib- 

 rium of the initially existing parts of the system. Gibbs shows 

 that when there are r relations of the type (188) between the 

 components the same condition holds, but there are then r 

 relations of the type 



aiMi + a^Mi . . . + a„M„ = (196) [43] 



between the potentials. 



