From Steam Engines to Chemical Reactions: Gibbs’ Contribution to the Extension of the Second Law

The present work analyzes the foundations of Gibbs’ thermodynamic equilibrium theory, with the general aim of understanding how the Second Law—as formulated by Clausius in 1865—has been embodied into Gibbs’ formal system and extended to processes involving chemical reactions. We show that Gibbs’ principle of maximal entropy (and minimal energy) is the implicit expression of Clausius’ Second Law. In addition, by making explicit some implicit passages of Gibbs logical path, we provide an original formal justification of Gibbs’ principle. Finally we provide an analysis of how Gibbs’ principle—conceived for homogeneous isolated systems with fixed chemical composition—has come to be applied to systems entailing chemical transformations.