Page:Scientific Papers of Josiah Willard Gibbs.djvu/443

Rh reciprocal convertibility, and not in the loose and often misleading sense in which we speak of heat and work as equivalent when there is only a one-sided convertibility.) Therefore the rendement of a perfect or reversible galvanic cell would be $$\text{J}\theta\epsilon \frac{t - t'}{t}$$ units of electrical work, with $$\theta \epsilon \frac{t'}{t''}$$ units of (reversible) heat, for each unit of electricity which passes.

You will observe that we have thus solved a very different problem from that which finds its answer in the Joule-Helmholtz-Thomson equation with term for reversible heat. That equation gives a relation between the and the reversible heat and certain other quantities, so that if we set up the cell and measure the reversible heat, we may determine the  without direct measurement, or vice versâ. But the considerations just adduced enable us to predict both the electromotive force and the reversible heat without setting up the cell at all. Only in the case that the reversible heat is zero does this distinction vanish, and not then unless we have some way of knowing á priori that this is the case.

From this point of view it will appear, I think, that the production of reversible heat is by no means anything accidental, or superposed, or separable, but that it belongs to the very essence of the operation.

The thermochemical data on which such a prediction of and reversible heat is based must be something more than the heat of union of the radicles. They must give information on the more delicate question of the temperature at which that heat can be obtained. In the terminology of Clausius they must relate to entropy as well as to energy—a field of inquiry which has been far too much neglected.

Essentially the same view of the subject I have given in a form more general and more analytical, and, I fear, less easily intelligible, in the closing pages of a somewhat lengthy paper on the "Equilibrium of Heterogeneous Substances" (Conn. Acad. Trans., vol. iii, 1878), of which I send you the Second Part, which contains the passage in question. My separate edition of the First Part has long been exhausted. The question whether the "reversible heat" is a negligible quantity is discussed somewhat at length on pages 510–519. On page 503 is shown the connection between the electromotive force of a cell and the difference in the value of (what I call) the potential for one of the ions at the electrodes. The definition of the potential for a material substance, in the sense in which I use the term, will be found on page 443 of the synopsis from the ''Am. Jour. Sci.'', vol. xvi, which I enclose. I cannot say that the term has been adopted by