Page:Scientific Papers of Josiah Willard Gibbs.djvu/380

the phenomena exhibited in the direct combination of the substances, is corroborated by the experiments of M. Favre, who has observed an absorption of heat in the cell in which this acid was electrolyzed.^[1] The electromotive work expended must therefore 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 difference 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 relations of energy and entropy.

In some cases there is a striking correspondence between the electromotive force of a cell and the rate of diminution of its energy per unit of electricity transmitted, the temperature remaining constant. A Daniell'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 differences to the determinations of M. Favre,^[2] estimating energy in calories, we have for each equivalent (32.6 kilogrammes) of zinc dissolved

$(V''-V')\Delta e={\text{24327}}^{\text{cal}},$$\Delta \epsilon =-{\text{25394}}^{\text{cal}},$$\Delta Q=-{\text{1067}}^{\text{cal}}.$

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.^[3] The value of $\Delta Q$, 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 value of $-\Delta Q$, and increase that of $(V''-V')\Delta e$, which was obtained by subtracting $-\Delta Q$ from $-\Delta \epsilon$.

It appears that under certain conditions neither heat nor cold is produced in a Grove's cell. For M. Favre has found that with different degrees of concentration of the nitric acid sometimes heat

1. See Mémoires des Savants Étrangers, sér. 2, t. xxv, no. 1, p. 142; or Comptes Rendus, t. lxxiii, p. 973. The figures obtained by M. Favre will be given hereafter, in connection with others of the same nature.
2. See Mém. Savants Étrang., loc. cit., p. 90; or Comptes Rendus, t. lxix, p. 35, where the numbers are slightly different.
3. A comparison of the experiments of different physicists has in some cases given a much closer correspondence. See Wiedemann's Galvanismus, etc., 2^te Auflage, Bd. ii, §§ 1117, 1118.