EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 339 



to be a perfect electro-chemical apparatus, 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 electro-chemical apparatus, we shall have, instead 

 of (692), 



dn^> (695) 



and instead of (693), (694) 



(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 products 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 supplied or withdrawn, the term containing drj will vanish.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 suppose that the temperature remains constant. 



The quantities expressed by the terms containing dQ and dr\ in 

 (691), (693), (694), and (696) are frequently neglected in the con- 

 sideration of cells of which the temperature is supposed to remain 

 constant. In other words, it is frequently assumed that neither 

 heat nor cold is produced by the passage of an electrical current 

 through a perfect electro-chemical combination (except that heat 

 which may be indefinitely diminished by increasing the time in 

 which a given quantity of electricity passes), and that only heat 

 can be produced in any cell, unless it be by processes of a secondary 

 nature, which are not immediately or necessarily connected with 

 the process of electrolysis. 



It does not appear that this assumption is justified by any sufficient 

 reason. In fact, it is easy to find a case in which the electromotive 



force is determined entirely by the term t-^- in (694), all the other 



terms in the second member of the equation vanishing. This is true 

 of a Grove's gas battery charged with hydrogen and nitrogen. In 

 this case, the hydrogen passes over to the nitrogen, a process which 

 does not alter the energy of the cell, when maintained at a constant 

 temperature. The work done by external pressures is evidently 

 nothing, and that done by gravity is (or may be) nothing. Yet an 

 electrical current is produced. The work done (or which may be 

 done) by the current outside of the cell is the equivalent of the work 

 (or of a part of the work) which might be gained by allowing the 

 gases to mix in other ways. This is equal, as has been shown by 



