We calculate the efficiency of an endoreversible Carnot-type cycle in the maximum power regime by using a nonlinear heat transfer law (the so-called Dulong and Petit’s law of cooling). The results obtained from this model compare well (around 99% in some cases) with observed efficiencies for several power plants. The considered law of cooling includes conductive- convective and radiative contributions to the heat exchange between the working fluid and its surroundings. Our calculations improve considerably those obtained by means of a linear heat transfer law for the same power sources. We also analyze a nuclear power plant using an ecological optimization criterion for finite-time heat engines.
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.
In this work it is shown that a general property of endoreversible Curzon-Ahlborn-Novikov (CAN) cycles previously demonstrated can be extended for non-endoreversible CAN-cycles. This general property is based on the fact that at the so-called maximum ecological regime the efficiency is the average of the Carnot and the maximum-power efficiencies, and that in such a regime the power output is 75% of the maximum power of the CAN-cycle and the entropy produced is only 25% of that produced in the maximum power point. This property is independent of the heat transfer law.
This paper presents a general property of endoreversible thermal engines known as the Semisum property previously studied in a finite-time thermodynamics context for a Curzon–Ahlborn (CA) engine but now extended to a simplified version of the CA engine studied by Agrawal in 2009 (A simplified version of the Curzon–Ahlborn engine, European Journal of Physics30 (2009), 1173). By building the Ecological function, proposed by Angulo-Brown (An ecological optimization criterion for finite-time heat engines, Journal of Applied Physics69 (1991), 7465–7469) in 1991, and considering two heat transfer laws an analytical expression is obtained for efficiency and power output which depends only on the heat reservoirs’ temperature. When comparing the existing efficiency values of real power plants and the theoretical efficiencies obtained in this work, it is observed that the Semisum property is satisfied. Moreover, for the Newton and the Dulong–Petit heat transfer laws the existence of the g function is demonstrated and we confirm that in a Carnot-type thermal engine there is a general property independent of the heat transfer law used between the thermal reservoirs and the working substance.
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