THERMODYNAMICAL SYSTEM OF GIBBS 79 



infinitely little from the state in question", the criteria are evi- 

 dently necessary for equilibrium. For if there is any possible 

 change for which (Srj)^ ^ does not hold, since no passive 

 forces or resistances to change are operative, this change will 

 take place. Also, in this case, the inequality in the equations 

 cannot apply, since for every change of the system there is a 

 similar one of opposite sign, so that if for a certain change of 

 state (577) e < we should have (St/), > for a similar change of 

 opposite sign. In this case, we may therefore omit the sign of 

 inequality and write as the condition of equihbrium 



(577), = 0, i.e. (de), = 0. (13) [10] 



"But to prove that the condition previously enunciated is in 

 every case necessary, it must be shown that whenever an 

 isolated system remains without change, if there is any infini- 

 tesimal variation in its state, not involving a finite change of 

 position of any (even an infinitesimal part) of its matter, which 

 would diminish its energy . . . without altering its entropy, . . . this 

 variation involves changes in the system which are prevented by 

 its passive forces or analogous resistance to change. Now, as 

 the described variation in the state of the system diminishes 

 its energy without altering its entropy, it must be regarded as 

 theoretically possible to produce that variation by some process, 

 perhaps a very indirect one, so as to gain a certain amount 

 of work (above all expended on the system)." We have 

 seen that according to the second law of thermodynamics, a 

 change which can be made to yield work may take place spon- 

 taneously, and will do so unless prevented by passive forces. 

 "Hence we may conclude that the active forces or tendencies of 

 the system favor the variation in question, and that equilib- 

 rium cannot subsist unless the variation is prevented by passive 

 forces." 



III. Definition and Properties of Fundamental Equations* 



7. The Quantities ^, f, x- At this point, Gibbs proceeds to 

 apply the criterion of equilibrium to deduce the laws which 

 determine equilibrium in heterogeneous systems. For this 



Gibbs, I, 85-92. 



