510 J. W. Gibbs — Equilibrium of Heterogeneous Substances. 



The quantities expressed by the terms containing dQ tin({ dij m 

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

 eration of cells of which the temperature is supposed to remain con- 

 stant. 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 quan- 

 tity 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 i^-^ 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 cui'rent outside of the cell is the equivalent of the work 

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

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

 Lord Rayleigh,* to the work which may be gained by allowing each 

 gas separately to expand at constant temperature from its initial 

 volume to the volume occupied by the two gases together. The same 

 work is equal, as appears from equations (278), (279) on page 217, 

 (see also page 220,) to the increase of the entropy of the system 

 multiplied by the temperature. 



It is possible to vary the construction of the cell in such a way 

 that nitrogen or other neutral gas will not be necessary. Let the cell 

 consist of a U-shaped tube of sufficient height, and have pure hydro- 

 gen at each pole under very unequal [)ressures (as of one and two 

 atmospheres respectively) which are maintained constant by properly 

 weighted pistons, sliding in the arms of the tube. The difference of 

 the pressures in the gas-masses at the two electrodes must of course 

 be balanced by the difference in the height of the two columns of 

 acidulated water. It will hardly be doubted that such an apparatus 



* Philosophical Magazine, vol. xlix, p. 311. 



