LEWIS. — FREE ENERGY AND EQUILIBRIUM. 5 



diverse systems. Moreover, we are led to the above expression for free 

 energy change by the kinetic theory, the extended application of which 

 to much more complicated cases than that of a perfect gas has already 

 produced important results. 



The term n R T\n — may be written in the form 



— nRT\x\i\ + nRT\nv.^. 



Then we may consider that the quantity — nRT \ni\ represents an 

 essential part of the free energy of n gram-molecules of a simple sub- 

 stance in a given state, and similarly, nRT\\\ v.^ , a similar part of tlie 

 free energy in another state, and we may write for the free energy of 

 one gram-molecule of a simple substance the entirely arbitrary equation, 



where Xi represents that part of the free energy not contained in the term 

 — R Tin t'l ; differentiating this equation, 



^^^-Rlnv.+y,, (3) 



dxi 

 where y^ = — . 



Now substituting in equation (2 a), 



(^^ = - RTlnv,+y,T+ IX, f M. (4) 



Differentiating this at constant volume, 



Comparing this with equation (3), 



d^ ^l^,dM_ di/i _ 1 dm, 1 dM 



dr'^ dT'^dT~ ' dT~ TdT~l'dT' 



Since 5sli in this case represents the internal energy of one gram- 



molecule, at constant volume will be equal to the molecular heat 



capacity, at constant volume, which may be designated by c^^ . There- 

 fore, 



