This comment addresses the paper by Sarasua and Abal (2016 Eur. J. Phys. 37 055103). Driven by an incorrect interpretation of the Clausius relation, those authors demonstrated the equivalence of the Kelvin–Planck statement of the second law and the principle of entropy increase. In addition to the necessary clarification of the Clausius relation, we propose an improved version of the demonstration made in the aforementioned paper, since the one carried out therein is restrictive. Our aim is to clarify issues that, being didactically and pedagogically relevant, are also subtle.