Page:Scientific Papers of Josiah Willard Gibbs.djvu/444

physicists. It has, however, received the unqualified commendation of Professor Maxwell (although not with reference to this particular application—see his lecture on the "Equilibrium of Heterogeneous Substances," in the science conferences at South Kensington, 1876); and I do not see how we can do very well without the idea in certain kinds of investigations.

Hoping that the importance of the subject will excuse the length of this letter,

I remain,

Yours faithfully,

J. Willard Gibbs.

New Haven, November 21, 1887.

Professor Oliver J. Lodge,

Dear Sir,—As the letter which I wrote you some time since concerning the rendement of a perfect or reversible galvanic cell seems to have occasioned some discussion, I should like to express my views a little more fully.

It is easy to put the matter in the canonical form of a Carnot's cycle. Let a unit of electricity pass through the cell producing certain changes. We may suppose the cell brought back to its original condition by some reversible chemical process, involving a certain expenditure (positive or negative) of work and heat, but involving no electrical current nor any permanent changes in other bodies except the supply of this work and heat.

Now the first law of thermodynamics requires that the algebraic sum of all the work and, heat (measured in "equivalent" units) supplied by external bodies during the passage of the electricity through the cell, and the subsequent processes by which the cell is restored to its original condition, shall be zero.

And the second law requires that the algebraic sum of all the heat received from external bodies, divided, each portion thereof, by the absolute temperature at which it is received, shall be zero.

Let us write ${\text{W}}$ for the work and ${\text{Q}}$ for the heat supplied by external bodies during the passage of the electricity, and $[{\text{W}}],[{\text{Q}}]$ for the work and heat supplied in the subsequent processes.

Then⁠${\text{W}}+{\text{Q}}+[{\text{W}}]+[{\text{Q}}]=0,$

(1)

and⁠${\frac {\text{Q}}{t'}}+\int {\frac {d[{\text{Q}}]}{t}}=0,$

(2)

where $t$ under the integral sign denotes the temperature at which the element of heat $d[{\text{Q}}]$ is supplied, and tf the temperature of the cell, which we may suppose constant.