The first and second laws of thermodynamics are logically equivalent

Abstract

In the September 2022 issue of The Physics Teacher (TPT), Richard Kaufman and Harvey Leff showed the interdependence of the first and second laws of thermodynamics. Here, I go further and use the facts that the first law implies the second law, and that the second law implies the first law. This two-way implication establishes the logical equivalence of the first and second laws. Although the laws are logically equivalent (when one is true, then the other must be true), this does not mean that they are the same. The equivalence provides for a deeper and richer understanding of the laws of thermodynamics for students, teachers, and physicists. Surely, if we can know that the first and second laws are equivalent, then we should know.