234 MOREY ART. G 



vdj) = Tjdt + niid/jii + nhdm . . . + nindun, (1) [97] 



in which v and ?; refer to the volume and entropy of m.i + ma 

 ... -^ Mn units of the phase considered, p and t to the pressure 

 and temperature, and /x to "the potential for the substance 

 in the homogeneous mass considered." The chemical potential, 

 /x, is defined by the equations 



Ml 



^/^\ Jdr\ ^/ix\ =(^\ (2) [104] 

 \dmi/„,v.m \dmi/t.v.m \dmi/„,p,m \dmi/t.p,m' 



in which e, \p, x, and f refer, respectively, to the energy and the 

 three Gibbs' thermodynamic functions defined by the equations 



The first of these, rp, is the quantity defined by Heknholtz* as 

 the free energy, and commonly designated by that name in 

 Continental writings; the second, x, the quantity variously 

 known as heat content, enkaumy and enthalpy ;t the third, ^, 

 the quantity called free energy by Lewis. J The definition of fx 

 is evidently symmetrical with respect to e, ^, x and f , and it 

 should not be considered as specially related to any one of 

 these quantities. 



2. Derivation of the Phase Rule. Equation (1) [97] expresses 

 a necessary relationship at equilibrium between the intensive 

 properties of any phase, and this relationship itself is a con- 

 sequence of the fundamental condition for equilibrium, namely, 

 that in an isolated system the entropy shall be a maximum for 



* Helmholtz, Sitzb. preuss. Akad. Wiss. 1, 22 (1882). 



t The term enthalpy, proposed by H. Kamerlingh Onnes (Leiden 

 Comm. No. 109 (1909), p. 3) is, in the author's opinion, the best for the 

 designation of this important quantity. 



X The thermodynamic quantities of Gibbs refer to a total mass of 

 (mi + m2 + ... TO„) units of the phase or system in question, while some 

 of the names subsequently applied to the Gibbs functions refer by defini- 

 tion to a gram molecular weight. That, for example, is the diflference 

 between Gibbs' f and Lewis' free energy. 



