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A thermodynamic impasse: A constant entropy irreversible process

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When the work produced by a reversible Carnot engine is subsequently degraded through a frictional mechanism into an equivalent amount of heat at the temperature of the cold reservoir, the universe of this reversible engine becomes identical to that of the commonly studied direct, irreversible transfer of heat from a hot to a cold body. The identity qualifier rests on the fact that in these two processes the changes experienced by the only two bodies affected -the heat reservoirs- are identical; situation that leads to the same entropy change for one process and the other. These coincidences notwithstanding, an essential difference separating these two processes is here identified: the fact that in the work-producing/workdegrading combination, the entropy change is determined not by the whole of the heat flowing from the hot to the cold body, as it happens in the direct transfer of heat, but by a fraction of it;with the remaining of the heat flowing irreversibly at constant entropy. The identification of this constant entropy irreversible process leads, in turn, to the unveiling of a contradiction between second law thermodynamicsÂ’ reversibility criterion, and itÂ’s supposedly empirical counterpart embodied by the principle: Heat cannot, of itself, pass from a colder to a hotter body.