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 versus efficiency. In a previous work Stucki [J. W. Stucki, Eur. J. Biochem. 109, 269 (1980)] used a FOIT approach to describe the modes of thermodynamic performance of oxidative phosphorylation involved in adenosine triphosphate (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 at both minimum entropy production and maximum efficiency simultaneously, 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 of the simultaneous maximization of both the so-called ecological function and the efficiency.

Connection between maximum-work and maximum-power thermal cycles

“…5 where the corresponding η MP curves (large dashed) are also showed along with the symmetric cases for both efficiencies. We have used well-known FTT numerical methods to plot the η MP curves [24][25][26]. Some interesting facts can be remarked from this figure: as mentioned before, for n = −2 (k = −1) both efficiencies η MW and η MP have the same limits when γ → 0 and γ → ∞.…”

“…As is well known,Q in/out , power output and MP-efficiency for CA-engines with heat transfer laws given by Eqs. (11) and (12), are numerically calculated in an easy and direct manner by maximizing the power output P given by the following equation [24][25][26],…”

Thermodynamic Optimization of an Electric Circuit as a Non-steady Energy Converter

“…This is a dimensionless paratemer which measures the quality of the coupling between spontaneous and non-spontaneous fluxes and comes directly from the thermodynamics' second law ( Figure 1) [10,13]. On the other hand, following the paper published by Stucki [14], it is suitable to take again the definition of the force ratio, given by [15] x = L 11 L 22…”

“…When we return to the time space by a reverse transformation, the inverted generalized equations satisfy the same reciprocal relationships as well as steady converters [16]. For this reason, this LCR circuit can be described using the same model presented in [10]. Now we have phenomenological coefficients space time dependent, which contain information about charging and saturation time of transient elements in the circuit.…”

“…In section 3 we will discuss the energetic behavior of this (2 × 2) converter, being that it can work in several operation well-known regimes (minimum dissipation, maximum power output, maximum efficiency, maximum ecological function, etc.) [10,12,17]. Additionally, we study the evolution of some characteristic functions when voltage sources are constant and when they depend periodically on time, in some of the above regimes.…”