An Optimized Heat Engine Operating Between Finite- Sized Reservoirs

Abstract

Thermodynamics of a heat engine running between two reservoirs of finite size and with well defined temperatures that is not in equilibrium. Importantly practical, heat engines that produce useful work often operate between heat baths of limitless size and constant temperature. This study examines the effectiveness of a heat engine that operates between two limited-size heat sources with a temperature differential at startup. Due to the sources' finite heat capacity, the total amount of work that can be produced by such a heat engine is restricted. First, look into how various source parameters that affect heat capacity affect 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 η=𝜂஼/4+0(η2 C), where 𝜂஼is the Carnot efficiency determined by the initial temperature of the sources. Within the linear response regime, it is discovered that there exists a power-efficiency trade off depending on the ratio of heat capacities (γ) of the reservoirs for the engine; the uniform temperature of the two reservoirs at final time τ is bounded from below by the entropy production 𝜎௠௜௡∝ 1/τ. Further obtain a universal efficiency at maximum power of the engine for arbitrary γ. Our dings can be used to develop an optimization scenario for thermodynamic cycles with finite sized reservoirs in practice., the figure of merit, a quantity defined as a product of scaled power and scaled efficiency, is found to be greater than unity in range of 0 ≤ 𝜂஼ ≤ 1.025. The figure of merit of model IV, ψ generally decreases from its peak value of 1.095 with an increase in 𝜂஼ . Only in the medium 𝜂஼ 0.4 values, the optimum working condition is preferred to the maximum power working condition. Elsewhere, the maximum working condition is better than the optimum working condition for the model. In model IV, the figure of merits, ψ, slightly decreases from its value of about 1.095 to 1.01 as at 𝜂஼ increases from zero to 0.8.