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arXiv:2010.01581

The efficiency of simple Quantum Engine Stirling and Ericsson cycle

Enock Oluwole Oladimeji, Emmanuel Chukwuebuka Umeh, Abamba Oghenetega

Published Oct 4, 2020• 2 citations
arXivHTMLPDF

Abstract

The quantum engine cycle serves as an analogous representation of the macroscopic nature of heat engines and the quantum regime of thermal devices composed of a single element. In this work, we follow the formalism of a quantum engine proposed by Bender et al. [1] where they observed quantum Carnot cycle with a single particle of mass m confined to an infinite one-dimensional potential well of width L as a working medium. Using this model, a quantum-mechanical analogue of the Stirling cycle [SC] and Ericsson cycle [EC] have been constructed through changes of both, the width of the well and its quantum state. The efficiency of quantum engines is derived, which is found to be analogous to classical thermodynamic engines. Keywords: Quantum thermodynamics, Quantum mechanics, Ericsson cycle, Stirling cycle, Quantum heat engines, Nano-engines.

DOI
10.48550/arxiv.2010.01581

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The quantum engine cycle serves as an analogous representation of the macroscopic nature of heat engines and the quantum regime of thermal devices composed of a single element. In this work, we follow the formalism of a quantum engine proposed by Bender et al. [1] where they observed quantum Carnot cycle with a single particle of mass m confined to an infinite one-dimensional potential well of width L as a working medium. Using this model, a quantum-mechanical analogue of the Stirling cycle [SC] and Ericsson cycle [EC] have been constructed through changes of both, the width of the well and its quantum state. The efficiency of quantum engines is derived, which is found to be analogous to classical thermodynamic engines. Keywords: Quantum thermodynamics, Quantum mechanics, Ericsson cycle, Stirling cycle, Quantum heat engines, Nano-engines.
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A cyclic thermodynamic heat engine runs most efficiently if it is reversible. Carnot constructed such a reversible heat engine by combining adiabatic and isothermal processes for a system containing an ideal gas. Here, we present an example of a cyclic engine based on a single quantum mechanical particle confined to a potential well. The efficiency of this engine is shown to equal the Carnot efficiency because quantum dynamics is reversible. The quantum heat engine has a cycle consisting of adiabatic and isothermal quantum processes that are close analogues of the corresponding classical processes.
The quantum engine cycle serves as an analogous representation of classical heat engines for microscopic systems and the quantum regime of thermal devices is composed of a single element. In this work, the Quantum-Mechanical properties of a non-linear quantum oscillator described by the Woods-Saxon [WS] model are examined. The Quantum-Mechanical analogue of the Carnot cycle was constructed using changes in both the width L of the well and the quantum state of the potential well. The efficiency of the quantum engine, consisting of adiabatic and isothermal processes based on the Woods-Saxon [WS] potential is derived. The result is shown to be analogous to that of the classical engine and found to agree, within an appropriate limit, with existing results obtained from other potential models. This implies that the [WS] potential can be used as an alternative model in quantum engines.
In a quantum Stirling heat engine, the heat exchanged with two thermal baths is partly utilized for performing work by redistributing the energy levels of the working substance. We analyze the thermodynamics of a quantum Stirling engine operating in finite time. We develop a model in which a time-dependent potential barrier changes the energy-level structure of the working substance. The process takes place under a constant interaction with the thermal bath. We further show that in the limit of slow operation of the cycle and low temperature, the efficiency of such an engine approaches Carnot efficiency. We also show that the maximum output power, for the strokes that affect the energy levels, is obtained at an intermediate operating speed, demonstrating the importance of a finite-time analysis.
A cyclic thermodynamic heat engine,which combines adiabatic and isothermal processes and consists of classical ideal gas as working substance,runs most efficiently if it is reversible.In this paper,A new cyclic model of quantum Carnot heat engine whose working substance consists of non-interacting extreme relativistic particles confined to an infinite potential well,is set up.It is shown that the engine whose cycle consists of adiabatic and isothermal quantum processes are close analogues of the corresponding classical processes and that the efficiency of this engine is equal to the Carnot efficiency because quantum dynamics is reversible.Consequently,the expectation value of the Hamiltonian in the expression of the efficiency is similar to the temperature in that of the classical one.