An analytical treatment of the quasistatic part of the second law of thermodynamics using Kelvin's principle

Abstract

Using the conventional Kelvin statement of the second law of thermodynamics, an analytical treatment of the quasistatic part of this law is developed. Essentially, it is a mathematical version of a well known paper by Zemansky in which he proposes an alternative approach to that of Caratheodory, discarding both Caratheodory's principle and Caratheodory's theorem on differential forms. Zemansky's basic idea is retained, but his pedagogical argument concerning the existence of an integrating factor for the heat differential form is replaced by more precise reasoning of a local nature. The mathematical tool used is differential geometry as employed in modern presentations of thermodynamics.