The name of Willard Gibbs, who was the most distinguished American mathematical physicist of his day, is especially associated with the "Phase Rule," of which some account will be found in the article Energetics.
Wolcott Gibbs worked out the electrolytic separation of copper in 1865.
For cells in which the electromotive force varies with temperature, the full equation given by Gibbs and Helmholtz has also been confirmed experimentally.
The Phase Rule of Willard Gibbs, especially as developed by Bakhuis Roozeboom, is a most useful guide in such investigations.
The more general case is discussed in the article Energetics, and in the original memoirs of Willard Gibbs and others.
