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Journal of Physics Conference Series

Quantum Lenoir Engine with a Multiple-eigenstates Particle in 1D Potential Box

Yohanes Dwi Saputra

Published Jan 1, 2021• 7 citations
Publisher

Abstract

Abstract QLE which has the working substance of a quantum system, a single particle confined in a one-dimensional potential box, has been constructed theoretically in this paper. The quantum system replaces the role of the classical system which has a working substance in the form of gas confined in a piston cylinder. The piston that moves back and forth is substituted by a 1D potential box wall that can move freely to change the width of the potential box. In this way, the three classical thermodynamic processes in the CLE (Classical Lenoir Engine), namely isochoric, isotherm, and isobar, can be analogous to the quantum system. Finally, we find that the thermal efficiency formulation of QLE has the similarity of shape to the CLE efficiency equation. However, a higher ratio of specific heat for QLE makes the efficiency value greater than CLE at each same compression ratio.

DOI
10.1088/1742-6596/1726/1/012016

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AIP conference proceedings•Jan 1, 2020•4 citations
Abstract QLE which has the working substance of a quantum system, a single particle confined in a one-dimensional potential box, has been constructed theoretically in this paper. The quantum system replaces the role of the classical system which has a working substance in the form of gas confined in a piston cylinder. The piston that moves back and forth is substituted by a 1D potential box wall that can move freely to change the width of the potential box. In this way, the three classical thermodynamic processes in the CLE (Classical Lenoir Engine), namely isochoric, isotherm, and isobar, can be analogous to the quantum system. Finally, we find that the thermal efficiency formulation of QLE has the similarity of shape to the CLE efficiency equation. However, a higher ratio of specific heat for QLE makes the efficiency value greater than CLE at each same compression ratio.
Lenoir engine based on the quantum system has been studied theoretically to increase the thermal efficiency of the ideal gas. The quantum system used is a single particle (as a working fluid instead of gas in a piston tube) in a one-dimensional infinite potential well with a wall that is free to move. The analogy of the appropriate variables between classical and quantum systems makes the three processes for the classical Lenoir engine applicable to the quantum system. The thermal efficiency of the quantum Lenoir engine is found to have the same formulation as the classical one. The higher heat capacity ratio in the quantum system increases the thermal efficiency of the quantum Lenoir engine by 56.29% over the classical version at the same compression ratio of 4.41.
A dual engine with one particle in a three-dimensional symmetry potential well, as a quantum working fluid, has been modeled. This research is based on the possibility to enhance the efficiency of a classical dual engine based on the 1st law of thermodynamics. The quantum system used is a modified analogy from the classical thermodynamic system, which is the ideal gas in the piston cylinder. By assuming the ideal gas pressure as a potential wall mechanical force, the ideal gas volume as the width of the potential well, and the ideal gas temperature as the total energy expectation value for a single particle, a dual quantum engine can be built theoretically. The five processes that work on each classical dual cycle can be analogous to the quantum system. The result is the similarity thermal efficiency equation of a quantum dual engine and the classical one. Besides, the heat capacity ratio of the quantum dual engine is greater than the classical engine which causes the efficiency of the quantum version to outperform the classical version when it is in the same mechanical ratio conditions.
A quantum ericson-engine that consists of a single particle with multiple states, has been explored. It is a quantum analogy to the classical ericson-engine consisting of a combination of two isothermal processes and two isobaric processes. By analogizing a particle in a one-dimensional infinite potential well as a gas in a piston-cylinder, quantum thermodynamic processes in a quantum ericson-engine can be explained from the analogies of classical processes such as isothermal, and isobaric. The results of the research show that the thermal efficiency of the quantum ericson-engine has similarities with the classical ericson-engine.
A quantum dual-engine is a machine that applies a dual cycle in a quantum system. This machine is a quantum analogy to the classical dual-engine consisting of a combination of classical Otto engine and classical Diesel engine. By analogizing a particle in a one-dimensional infinite potential well as a gas in a piston-cylinder, quantum thermodynamic processes in a dual cycle can be explained from the analogies of classical processes such as adiabatic, isochoric, and isobar. This research examines the value of thermal efficiency and other aspects of the quantum dual-engine with the study of literature. The results of the research show that the thermal efficiency of the quantum dual-engine has similarities with the classical dual-engine. Under the same mechanical ratios condition, the thermal efficiency of a quantum dual-engine has a higher value than the thermal efficiency of its classical engines.
We evaluate quantum Otto, Diesel and Brayton cycles employing multiple-state 1D box system instead of ideal gas filled cylinder. The work and heat are extracted using the change in the expectation of Hamiltonian of the system which leads to the first law of thermodynamics to quantum system. The first law makes available to redefine the force which is in fact not well defined in a quantum mechanical system and then it is applied to define the quantum version of thermodynamic processes, i.e. isobaric, isovolume and adiabatic. As the results, the efficiency of quantum Otto engine depends only on the compression ratio and will be higher than the efficiency of quantum Diesel which can decrease by the widening of expansion under isobaric process. The efficiency of quantum Brayton engine may reach maximum on certain combination between the wide of box under isobaric expansion and compression, under certain conditions. The amount of levels participated in the quantum heat engine system will potentially reduce the performance of the quantum heat cycles consisting isobaric process, but it can be resisted using isobaric process controller.
A single particle-based quantum dual engine in a two-dimensional symmetrical potential well has been studied to determine its thermal efficiency formulation. This quantum efficiency of the engine will be compared to the classical version, the gas in the piston tube, which is considered still needs to be improved its efficiency according to the second law of thermodynamics. By analogizing the variables that exist in the classical system to the quantum system, heat energy and work for the five thermodynamic processes in a quantum dual cycle can be extracted. The main result is obtained that the thermal efficiency of a dual quantum engine has similar formulations with the classical counterpart. The higher heat capacity ratio of the quantum system has the effect of higher efficiency of the quantum dual engine than the efficiency of the classical version at the same compression ratio, cut-off ratio, and pressure ratio.