Heat theorem

In thermodynamics, the heat theorem, or “Nernst heat theorem”, is said to be embodied in the following two equations: [1]

and

where A is the maximum work available, from the German arbeit, meaning "work", U is the heat of reaction, representative of the change in the total energy of the system, S is entropy, and T is temperature. [2]

The heat theorem was formulated in 1906 by German physical chemist Walther Nernst. [2] In the years to follow, Nernst's heat theorem was molded into the third law of thermodynamics by German physicist Max Planck, which he used as a founding principle for his "quantum theory", along with his earlier usage of Boltzman's second law based idea of the equipartition of the energy of bodies into distinct units, i.e. energy elements, which formed the basis for the science of quantum mechanics, as the subject has come to be known. [3]

Third law
The heat theorem became the “third law”, of thermodynamics, in agreed upon namesake, sometime between 1907 and 1923. [3] Nernst’s heat theorem was being called a “new law of thermodynamics” (Otto Sackur, 1910), new “principle of thermodynamics” (Max Planck, 1910), and somewhere in his own lectures, Nernst had become his theorem the third law.

References
1. Washborn, Edward W. (1921). An Introduction to the Principles of Physical Chemistry from the Standpoint of Modern Atomistics and Thermodynamics (section: 14: The “Third Law of Thermodynamics” and the Nernst “Heat Theorem”, pgs. 110-). McGraw-Hill.
2. Gearhart, Clayton A. (2011). “Walther Nernst, Max Planck, Albert Einstein, and the Third Law of Thermodynamics”, 18-pgs. St. John’s University.
3. (a) Nernst, Walther. (1918). Die Theoretischen und Experimentellen Grundlagen des Neuen Warmesatzes (The theoretical and experimental foundations of the new heat theory). Publisher
(b) Planck, Max. (1917). Thermodynamik, 5th Ed. Publisher.
(c) Planck, Max. (1921). Die Entstehung und bisherige Entwicklung der Quantentheorie (The Origin and Historical Development of Quantum Theory). Publisher.
4. Lewis, Gilbert and Randall, Merle. (1923). Thermodynamics and the Free Energy of Chemical Substances (ch. 31: The Third Law of Thermodynamics, pgs. 435-54). McGraw-Hill.