360 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



If the temperature of three coexistent phases of three components 

 is maintained constant, the pressure is in general a maximum or 

 minimum when the composition of one of the phases is such as can be 

 produced by combining the other two. If the pressure is maintained 

 constant, the temperature is in general a maximum or minimum when 

 the same condition in regard to the composition of the phases is 

 fulfilled. 



Stability of fluids. A criterion of the stability of a homogeneous 

 fluid, or of a system of coexistent fluid phases, is afforded by the 

 expression 



-t'q+p'v-[j. l 'm 1 -fjL 2 'm 2 ...-iuL n 'm n , (14) 



in which the values of the accented letters are to be determined by 

 the phase or system of phases of which the stability is in question, 

 and the values of the unaccented letters by any other phase of the 

 same components, the possible formation of which is in question. We 

 may call the former constants, and the latter variables. Now if the 

 value of the expression, thus determined, is always positive for any 

 possible values of the variables, the phase or system of phases will 

 be stable with respect to the formation of any new phases of its 

 components. But if the expression is capable of a negative value, 

 the phase or system is at least practically unstable. By this is meant 

 that, although, strictly speaking, an infinitely small disturbance or 

 change may not be sufficient to destroy the equilibrium, yet a very 

 small change in the initial state will be sufficient to do so. The 

 presence of a small portion of matter in a phase for which the above 

 expression has a negative value will in general be sufficient to produce 

 this result. In the case of a system of phases, it is of course supposed 

 that their contiguity is such that the formation of the new phase does 

 not involve any transportation of matter through finite distances. 



The preceding criterion affords a convenient point of departure in 

 the discussion of the stability of homogeneous fluids. Of the other 

 forms in which the criterion may be expressed, the following is 

 perhaps the most useful : 



// the pressure of a fluid is greater than that of any other phase 

 of its independent variable components which has the same temper- 

 ature and potentials, the fluid is stable with respect to the formation 

 of any other phase of these components ; but if its pressure is not 

 as great as that of some such phase, it will be practically unstable. 



Stability of fluids with respect to continuous changes of phase. 

 In considering the changes which may take place in any mass, 

 we have often to distinguish between infinitesimal changes in existing 

 phases, and the formation of entirely new phases. A phase of a fluid 

 may be stable with respect to the former kind of change, and unstable 

 with respect to the latter. In this case, it may be capable of continued 



