J. TF[ Gihhs — Equilihrinni of Heterogeneous Substances. 509 



ill which de denotes the iucrement of tlie intrinsic energy of the cell, 

 de the quantity of electricity which passes through it, V and V" 

 the electrical potentials in masses of the same kind of metal con- 

 nected with the anode and cathode respectively, dQ the heat received 

 from external bodies, d Wq the work done by gravity, and d Tf^ the 

 work done by the pressures which act on the external surface of the 

 apparatus. 



The conditions under which we suppose the processes to take place 

 are such that the increase of the entropy of the apparatus is equal to 

 the entropy which it receives from external sources. The only exter- 

 nal source of entropy is the heat which is communicated to the cell 

 by the surrounding bodies. If we write drf for the increment of 

 entropy in the cell, and t for the temperature, we have 



d}j = -^. (692) 



Eliminating dQ, we obtain 



de={V'- V")de + tdif-^dW,,-\-dWj>, (693) 



or 



It is worth while to notice that if we give up the condition of the 

 reversibility of the processes, so that the cell is no longer supposed 

 to be a perfect electro-chemical aiDparatus, the relation (691) will still 

 subsist. But, if we still suppose, for simplicity, that all parts of the 

 cell have the same temperature, which is necessarily the case with a 

 perfect electi'o-chemical apparatus, we shall have, instead of (692), 



, ^ dO 



f?V^y^, (695) 



and instead of (693), (694) 



( Y" _ V') de -S^ds + t di] + d TFe + d TFp. (696) 



The values of the several terms of the second member of (694), for 

 a given cell, will vary with the external influences to which the cell 

 is subjected. If the'cell is enclosed (with the j^roducts of electrolysis) 

 in a rigid envelop, the last term will vanish. The term relating to 

 gravity is generally to be neglected. If no heat is supplied or with- 

 drawn, the term containing di] will vanish. But in the calculation of 

 the electromotive force, which is the most important application of 

 the equation, it is generally more convenient to supjiose that the tem- 

 perature remains constant. 



