Abstract
Heat engines used to output useful work have important practical significance, which, in general, operate between heat baths of infinite size and constant temperature. In this paper, we study the efficiency of a heat engine operating between two finite-size heat sources with initial temperature difference. The total output work of such heat engine is limited due to the finite heat capacity of the sources. We firstly investigate the effects of different heat capacity characteristics of the sources on the heat engine’s efficiency at maximum work (EMW) in the quasi-static limit. Moreover, it is found that the efficiency of the engine operating in finite-time with maximum power of each cycle is achieved follows a simple universality as , where is the Carnot efficiency determined by the initial temperature of the sources. Remarkably, when the heat capacity of the heat source is negative, such as the black holes, we show that the heat engine efficiency during the operation can surpass the Carnot efficiency determined by the initial temperature of the heat sources. It is further argued that the heat engine between two black holes with vanishing initial temperature difference can be driven by the energy fluctuation. The corresponding EMW is proved to be .
Highlights
As one of the most useful devices in modern society, the heat engine converts the heat extracted from the heat sources into useful work, which is one of the core fields in thermodynamic research [1,2,3,4,5,6,7,8,9].Early heat engine research was limited to reversible cycles in the quasi-static limit, with which, as stated by the Carnot’s theorem [1], the achievable maximum efficiency of heat engines is the so-called Carnot efficiency ηC = 1 − TL /TH, where TH (TL ) is the temperature of the hot bath
In finite-time thermodynamics, for a heat engine working between two constant temperature heat sources, the universality of the efficiency at maximum power ηMP is generally written as a function of ηC, as ηMP =
We studied the efficiency of a heat engine working between two finite-size heat sources in both quasi-static and finite-time cases
Summary
As one of the most useful devices in modern society, the heat engine converts the heat extracted from the heat sources into useful work, which is one of the core fields in thermodynamic research [1,2,3,4,5,6,7,8,9]. We discuss the effects of finite-size heat sources with different heat capacity characteristics on heat engine’s efficiency, in both quasi-static and finite-time circumstances. The bounds in the latter two cases for ηMW and η FT in this table are limited to the heat source having a positive and constant heat capacity. The paper is organized as follows: In Section 2, we first generally discuss the influence of the heat capacity of the finite-size heat sources on the efficiency of the heat engine at maximum work (EMW).
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