G 



THE PHASE RULE AND HETEROGENEOUS 



EQUILIBRIUM 



[Gibbs, I, pp. 96-100] 



GEORGE W. MOREY 



I. Introduction 



Treatises on the Phase Rule usually deal with heterogeneous 

 equilibrium from a purely geometrical point of view, making use 

 of the familiar equation, F = n-\-2 — r, in which F is the 

 number of degrees of freedom, n the number of components, 

 and r the number of phases, as a qualitative guide, and depend- 

 ing on the Theorem of Le Chatelier for determining the effect 

 of change of conditions on the equilibrium. It is unfortunate 

 that the subject has been developed in this manner, instead of 

 by the direct application of the equations which were developed 

 by Gibbs. The Phase Rule itself is but an incidental qualita- 

 tive deduction from these equations, and the justification of the 

 geometrical methods is their derivation as projections of the 

 lines and surfaces "of dissipated energy," painstakingly ex- 

 emplified* by Gibbs. While in the first portion of the "Equilib- 

 rium of Heterogeneous Substances" the actions of gravity, 

 electrical influences, and surface forces are excluded from con- 

 sideration, these restrictions are later removed, thus rendering 

 unnecessary the various "extended" Phase Rules which have 

 been proposed to remedy this supposed defect. 



II. Equation [97] and the Phase Rule 



1 . Equation [97] . The Phase Rule may be derived from Gibbs' 

 fundamental conditions for equilibrium [15-21], but Gibbs' 

 own treatment is intimately connected with his equation [97] 



* Equilibrivun of Heterogeneous Substances, Gibbs, I, 118 et seq. 



233 



