Comment on the law of entropy increase in thermodynamics

Abstract

A common formulation of the law of increase of entropy, found in textbooks on thermodynamics, states that in a process taking place in a completely isolated system the entropy of the final equilibrium state cannot be smaller than that of the initial equilibrium state. This statement does not specify that thermal isolation is all that is needed for its validity, with no need for mechanical isolation. For the purpose of illustrating this situation, we exhibit examples of thermodynamic processes carried out with thermally isolated—although not mechanically isolated—systems, which we know to be allowed by the second law because the entropy of the system increases. We believe that the analysis presented in this paper may be useful in a first undergraduate course on thermodynamics.