J. W. Gibhs — Eqiiilibrmni of Heterogeneous Siibstmices. 515 



electromotive work expended must thei'efore have been less than the 

 increase of energy in the cell. 



In both cases of composition in definite proportions which we have 

 considered, the compound has more entropy than its elements, and 

 the diflerence is by no means inconsiderable. This appears to be the 

 rule rather than the exception with respect to compounds which have 

 less energy than their elements. Yet it would be rash to assert that 

 it is an invariable rule. And when one substance is substituted for 

 another in a compound, we may expect great diversity in the rela- 

 tions of energy and entropy. 



In some cases, there is a striking correspondence between the elec- 

 tromotive force of a cell and the rate of diminution of its energy per 

 unit of electricity transmitted, the temperature remaining constant. 

 A Daniel I's cell is a notable example of this correspondence. It may 

 perhaps be regarded as a very significant case, since of all cells in 

 common use, it has the most constant electromotive force, and most 

 nearly approaches the condition of reversibility. If we apply our 

 previous notation [compare (691)] with the substitution of finite for 

 infinitesimal dififerences to the determinations of M. Favre,* estimat- 

 ing energy in calories, we have for each equivalent (32,6 kilogrammes) 

 of zinc dissolved 



( F" - F') ^6=24327™'-, Jf = - 25394 '^^^'•, Zl <2 :rr - 1067 *="'•. 

 It will be observed that the electromotive work performed by the cell 

 is about four per cent, less than the diminution of energy in the cell.f 

 The A'alue of J Q^ which, when negative, represents the heat evolved 

 in the cell when the external resistance of the circuit is very great, 

 was determined by direct measurement, and does not appear to have 

 been corrected for the resistance of the cell. This correction would 

 diminish the vahie of — J Q, and increase that of ( V" — V) Ae^ which 

 was obtained by subtracting —AQ from —As. 



It appears that under certain conditions neither heat nor cold is 

 produced in a Grove's cell. For M. Favre has found that Avith dif- 

 ferent degrees of concentration of the nitric acid sometimes heat and 

 sometimes cold is produced. J When neither is produced, of course 



* See Mtm. Savants Strang., loc. cit., p. 90; or Comj^tes Rendus, vol. Ixix, p. 35, where 

 the numbers are slightly different. 



I A comparison of the experiments of different physicists has in some cases given 

 a much closer correspondence. See Wiedemann's Galvanismus, etc., 2'<' Auflage, Bd. 

 ii, §§ 1117, 1118. 



\ Mem Sarants Strang., loc. cit., p. 9H ; or Comptes Rendus, t. Ixix, p. 3*7, and t. 

 Ixxiii, p. 893. 



