A first--order irreversible thermodynamic approach to a simple energy converter

Abstract

Several authors have shown that dissipative thermal cycle models based on Finite-Time Thermodynamics exhibit loop-shaped curves of power output versus efficiency, such as it occurs with actual dissipative thermal engines. Within the context of First-Order Irreversible Thermodynamics (FOIT), in this work we show that for an energy converter consisting of two coupled fluxes it is also possible to find loop-shaped curves of both power output and the so-called ecological function against efficiency. In a previous work Stucki [J.W. Stucki, Eur. J. Biochem. vol. 109, 269 (1980)] used a FOIT-approach to describe the modes of thermodynamic performance of oxidative phosphorylation involved in ATP-synthesis within mithochondrias. In that work the author did not use the mentioned loop-shaped curves and he proposed that oxidative phosphorylation operates in a steady state simultaneously at minimum entropy production and maximum efficiency, by means of a conductance matching condition between extreme states of zero and infinite conductances respectively. In the present work we show that all Stucki's results about the oxidative phosphorylation energetics can be obtained without the so-called conductance matching condition. On the other hand, we also show that the minimum entropy production state implies both null power output and efficiency and therefore this state is not fulfilled by the oxidative phosphorylation performance. Our results suggest that actual efficiency values of oxidative phosphorylation performance are better described by a mode of operation consisting in the simultaneous maximization of the so-called ecological function and the efficiency.