EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 499 



gj = -p, where p is the pressure of the substance ; 



j- = 0, where is the temperature on the thermodynamic scale; 



= /i 1) where p., is the potential of the component (m,) with respect to the 



compound mass. 



Each of the component substances has therefore a potential with respect 

 to the whole mass. 



The idea of the potential of a substance is, I believe, due to Prof. Gibbs. 

 His definition is as follows : 



If to any homogeneous mass we suppose an infinitesimal quantity of any 

 substance to be added, the mass remaining homogeneous, and its entropy and 

 volume remaining unchanged, the increase of the energy of the mass, divided 

 by the mass of the substance added, is the potential of that substance in the 

 mass considered. 



The condition of the stable equilibrium of the mass is expressed by Prof. 

 Gibbs in either of the two following ways : 



I. For the equilibrium of any isolated system it is necessary and sufficient 

 that in all possible variations of the state of the system which do not alter its 

 energy, the variation of its entropy shall either vanish or be negative. 



II. For the equilibrium of any isolated system it is necessary and sufficient 

 that in all possible variations of the state of the system which do not alter its 

 entropy, the variation of the energy shall either vanish or be positive. 



The variations here spoken of must not involve the transportation of any 

 matter through any finite distance. 



It follows from this that the quantities 0, p, /v-/"^ must have the same 

 values in all parts of the mass. For if not, heat will flow from places of 

 higher to places of lower temperature, the mass as a whole will move from 

 places of higher to places of lower pressure, and each of the several component 

 substances will pass from places where its potential is higher to places where 

 it is lower, if it can do so continuously. 



Hence Prof. Gibbs shews that if @, P, M^..M n are the values of 0, p, ^...p,, 

 for a given phase of the compound, and if the quantity 



K= e - @r? + Pv - M 1 m 1 - &c. - M n m nt 



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