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International Journal of Applied Mathematics Sciences and Technology for National Defense

Infinite spherical well as model of quantum carnot engine

Khazali Fahmi, Aditya Tri Oktaviana, Endah Kinarya Palupi

Published Jan 27, 2023• 1 citation
Publisher

Abstract

The potential well is a simple example that generally used to present an understanding of quantum mechanics. In this article, we used infinite spherical well model to evaluate the thermodynamic processes in a quantum Carnot engine. The energy of the particles depended on the value of n and l lead to complex calculations. For simplicity we used the φ100 and φ200 quantum states to determine work and efficiency of a quantum Carnot machine. The results obtained show that efficiency depends on the value of which is the ratio of RC and RB.

DOI
10.58524/app.sci.def.v1i1.175

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The potential well is a simple example that generally used to present an understanding of quantum mechanics. In this article, we used infinite spherical well model to evaluate the thermodynamic processes in a quantum Carnot engine. The energy of the particles depended on the value of n and l lead to complex calculations. For simplicity we used the φ100 and φ200 quantum states to determine work and efficiency of a quantum Carnot machine. The results obtained show that efficiency depends on the value of which is the ratio of RC and RB.
A quantum-mechanical analog of the Carnot engine reversibly working at vanishing temperature, shortly termed the quantum-mechanical Carnot engine, is discussed. A general formula for the efficiency of such an engine with an arbitrary confining potential is presented. Its expression is purely given in terms of the structure of the energy spectrum. Dependency of the efficiency on the form of a potential as an analog of the working material in thermodynamics implies nonuniversality of the engine. This may be due to the absence of the second-law-like principle in pure-state quantum mechanics.
Carnot model of heat engine is the most efficient cycle consisting of isothermal and adiabatic processes which are reversible. Although ideal gas usually used as a working fluid in the Carnot engine, Bender used quantum particle confined in 1D potential well as a working fluid. In this paper, by following Bender we generalize the situation to 2D symmetric potential well. The efficiency is express as the ratio of the initial length of the system to the final length of the compressed system. The result then is shown that for the same ratio, 2D potential well is more efficient than 1D potential well.
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.
In this article, we study the quantum Carnot engine using a one-dimensional infinite well potential model in which two particles are non-interacting, indistinguishable and have the same mass. We find that the efficiency of this model is the same as that of the one-dimensional infinite potential well model in which there is one particle. Moreover, efficiency can be measured only when L_C/L_A≥2, where L_A and L_C are the potential well widths during isothermal and adiabatic expansion, respectively.
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.