﻿246 On Molecular Thermodynamics. 



simply removed the fraction e of the whole phase, without 

 altering its composition, so that tt must have diminished by 

 en, that is 



whence (57) follows. 



When tt is either yjr, or Gibbs' "chemical potential," a 

 whole system of phases in equilibrium can be considered 



together, since then ^^ , etc., are the same in every phase. 



Without actually quoting Euler's theorem, Planck remarks, 

 in regard to yjr, that this relation means that yfr, as a function 

 of M : M 2 . . . ., is homogeneous and of the first degree, though 

 not, of course, in general linear, and the same remark applies 

 to our typical property tt. 



From (57) we can at once get a more practically useful 

 relation by differentiating both sides fully:-— 



that is, 



MS)* (58) 



Now equation (97) of Gibbs' classical paper reduces at 

 constant temperature and pressure to 



Xm^dfjbi = 



and is then simply (58) applied to Gibbs' " chemical 

 potential." 



(58) is therefore referred to in these papers as the 

 " Gibbs fundamental relation," but its general applicability 

 to any property of the type of it (for a single homogeneous 

 phase) is to be borne in mind. 



It is to be observed that while the constituents whose 

 masses are M 1 M 2 .... must be sufficient to produce the 

 phase under the conditions considered, they need not be all 

 necessary — they need not be the " general-thermodynamic " 

 components. And since also (obviously from the form of 

 (58)) MiM 2 . . . . need not be expressed in the same units we 

 see that equally valid is the form 



w (£) 



= 0, (59) 



the " molecular-thermodynamic " form, in which n x n 2 . 

 are the numbers present of the various molecular species. 



