Page:Scientific Papers of Josiah Willard Gibbs.djvu/442



New Haven, January 8, 1887. Professor ,

Dear Sir,—Please accept my thanks for the proof copy of your "Report on Electrolysis in its Physical and Chemical Bearings," which I received a few days ago with the invitation, as I understand it, to comment thereon.

I do not know that I have anything to say on the subjects more specifically discussed in this report, but I hope I shall not do violence to the spirit of your kind invitation or too much presume on your patience if I shall say a few words on that part of the general subject which you discussed with great clearness in your last report on pages 745 ff. (Aberdeen). To be more readily understood, I shall use your notation and terminology, and consider the most simple case possible.

Suppose that two radicles unite in a galvanic cell during the passage of a unit of electricity, and suppose that the same quantities of the radicles would give $$\theta \epsilon$$ units of heat in uniting directly, that is, without production of current; will the union of the radicles in the galvanic cell give $$J \theta \epsilon$$ units of electrical work? Certainly not, unless the radicles can produce the heat at an infinitely high temperature, which is not, so far as we know, the usual case. Suppose the highest temperature at which the heat can be produced is $$t''$$, so that at this temperature the union of the radicles with evolution of heat is a reversible process; and let $$t'$$ be the temperature of the cell, both temperatures being measured on the absolute scale. Now $$\theta \epsilon$$ units of heat at the temperature $$t$$ are equivalent to $$\theta \epsilon \frac{t'}{t}$$ units of heat at the temperature $$t'$$, together with $$J\theta \epsilon \frac{t - t'}{t}$$ units of mechanical or electrical work. (I use the term "equivalent" strictly to denote