On the Uncertain Foundation of the Law that Entropy Increases I: The Egregious Error in Clausius Principle of the Equivalence of Transformations

The conceptual inconsistencies lying at the core of Clausius work leading to his principle of the equivalence of transformations, the name with which he originally designated the second main principle of the mechanical theory of heat, as well as those of the body of knowledge, namely current second law thermodynamics, which eventually replaced some of Clausius original notions are here located and their consequences discussed. At the light of our results the foundation of what is supposed to be the supreme law of nature appears to be not as firm as commonly believed. An experimental test is suggested for the notion on which the validity of the second law, as currently understood, is based, namely the zero total-entropy change for the reversible transformations of heat into work and vice versa. Many fail to grasp what they have seen, And cannot judge what they have learned, Although they tell themselves they know. Heraclitus [Fragments, Penguin Classics, 2001, p. 5]