70 BUTLER ART. D 



criterion of equilibrium, which may be stated in several different 

 ways. The statement of Clausius, that the entropy of an 

 isolated system tends to a maximum, implies that equilibrium 

 is reached when the entropy has the maximum value which is 

 consistent with its energy, and when there is no possible change, 

 the energy remaining constant, which can cause a further 

 increase of entropy. 



Also, the entropy of a system remains constant if the latter 

 does not undergo any irreversible changes and if it does not 

 receive any heat from its surroundings. Any change of its 

 energy under these conditions must be the result of work done 

 on or by the system against external forces. We have seen 

 that if a system is not in equilibrium, it may undergo changes 

 from which work can be obtained and which therefore result in a 

 decrease of energy. A system is therefore in equilibrium, if 

 there is no possible change, which does not involve a change of 

 entropy, whereby its energy can be decreased. 



In making use of these criteria of equilibrium we need only 

 consider infinitesimal changes, for every finite change must 

 begin by being an infinitesimal one and if no infinitesimal change 

 is possible it is evident that no finite change can occur. If 

 (Srj),, (5e), represent the change of entropy and energy in any 

 infinitesimal change of the system in which the energy and 

 entropy respectively remain constant, the two criteria of equilib- 

 rium stated above may be expressed by the statement that 



{b-n), ^ Oand (5e), ^ 0, 



for all possible changes. 



Gibbs first discusses in detail the equivalence and validity of 

 these criteria, and the conditions to be observed in using them. 

 An analysis of his discussion is given in the following chapter, 

 but the reader who does not wish, at this stage, to consider 

 these elaborate arguments need only read Section 4 on the 

 Interpretation of the Conditions and may then proceed to the 

 discussion of their application which begins with Chapter III. 



11. The Criteria of Equilibrium and Stability 



2. The Criteria. Gibbs begins his discussion of the equifib- 

 rium of heterogeneous substances by stating in the following 



