A fallacious argument in the finite time thermodynamics concept of endoreversibility

Finite time thermodynamics is a well established field of applied thermodynamics. The key assumption of this approach is the validity of the concept of endoreversibility. In this article, a hypothesis is formulated, and subsequently formally proved, that this concept rests on a fallacious argument. The concept of endoreversibility is inherently inconsistent with the postulated set of assumptions because the internal reversibility of a thermal system appears to be contradictory to an existence of external finite area heat exchangers that communicate with the endoreversible internal part across the finite temperature gaps. The irreversibilities contributed by the system components are inherently interconnected. As a consequence, the maximum power efficiency between the given temperature levels T_L and T_H>T_L, as predicted by finite time thermodynamics assuming that the heat input into the system is free to vary, i.e., 1-(T_L/T_H)^1/2, is incorrect. In addition, the magnitude of this figure of merit may be even smaller compared to the efficiency of a real system.