152 BUTLER 



ART. D 



Therefore the phase for which (201) has the least value will be 

 found among those having the temperature T and potentials Mi, 

 Mi, etc., and in determining the stability of the given fluid we 

 need only consider phases in which the temperature and 

 potentials have these values. In this case the given fluid wfll be 

 stable unless the expression (206) is capable of having a negative 

 value. 



The conditions of stability are thus stated by Gibbs in the 

 following very simple form: 



"// the pressure of the fluid is greater than that of any other 

 phase of the same components which has the same temperature and 

 the same values of the potentials for its actual components, the 

 fluid is stable without coexistent phases; if its pressure is not as 

 great as some other such phase, it will he unstable; if its pressure 

 is as great as that of any other such phase, hut not greater than 

 that of every other, the fluid will certainly not be unstable, and in all 

 probability it will be stable {when enclosed in a rigid envelop which is 

 impermeable to heat and to all kinds of matter), hut it will he one 

 of a set of coexistent phases of which the others are the phases which 

 have the same pressure." 



For example, consider a solution of carbon dioxide in water. 

 If the pressure of a vapor phase at the same temperature, and in 

 which carbon dioxide and water have the same potentials as in 

 the solution, is greater than the pressure of the solution, the latter 

 is unstable; but if the pressure of a vapor phase which satisfied 

 these conditions is less than that of the solution, the latter is 

 stable (with respect to the formation of a vapor phase). A 

 vapor phase containing carbon dioxide and water at the same 

 potentials as in the solution, and having the same temperature 

 and pressure could obviously coexist with the solution, but a 

 quantity of such a solution in a confined space is stable. 



X. Stability in Respect to Continuous Changes of Phase* 



S9. General Remarks. In order to test whether a homogene- 

 ous fluid is stable with respect to the formation of phases which 

 differ from it infinitely little (which are termed by Gibbs, 



* Gibbs, I, 105-115. 



