Quasi-static processes, reversibility and the limits of thermodynamics

Abstract This work presents, by means of the classical formalism of thermodynamics courses, a study of the relation between the quasi-static nature of a thermodynamic process and its reversibility. In addition, from the results obtained by assuming the reversibility of a thermodynamic process composed by a fundamentally irreversible sub-process, we explore the limits of application of the Laws of Thermodynamics and the nuances contained in its general formulations. We consider that this paper has two well defined purposes: didactic and fundamental. The didactic point of view is evident when we use the calculus techniques for the extraction of the thermodynamic quantities in the infinitesimal processes and by putting the reader in contact with the techniques of proof by contradiction (if a hypothesis leads to a contradiction, then it can not be assumed). Both techniques can be seen as essential in the approach of a huge number of problems in physics. From the fundamental point of view, we have been able to evidence the intimate relationship between the First and Second Laws of Thermodynamics when we deal with the determination of the conditions of reversibility and existence of thermodynamic processes.