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AIP conference proceedings

Quantum-Carnot engine for particle confined to 2D symmetric potential well

Idrus Husin Belfaqih, Trengginas Eka Putra Sutantyo, Teguh Budi Prayitno, Anto Sulaksono

Published Jan 1, 2015• 11 citations
Publisher

Abstract

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.

DOI
10.1063/1.4930654

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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.
Carnot cycle consists of isothermal and adiabatic processes which are reversible. Using analogy in quantum mechanics, these processes can be well explained by replacing variables in classical process with a quantum system. Quantum system which is shown in this paper is a particle that moves under the influence of a cubic potential which is restricted only to the state of the two energy levels. At the end, the efficiency of the system is shown as a function of the width ratio between the initial conditions and the farthest wall while expanding. Furthermore, the system efficiency will be considered 1D and 2D cases. The providing efficiencies are different due to the influence of the degeneration of energy and the degrees of freedom of the system.
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.
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.
A Brayton engine is one of the heat engines that convert heat energy into mechanical work. This engine is often implemented on turbojet engines of airplanes and gas turbines. However, the efficiency of a classically Brayton engine still needs to be improved according to the second law of thermodynamics. This research presents a Brayton engine on 2D symmetric potential well. The used method is modeling analogy of the first law of thermodynamics and then it is implemented into a quantum system with the single-particle as a working substance. The primary result obtained is the efficiency formulation of a quantum Brayton engine for 2D symmetric potential well which is similar to the 1D quantum Brayton engine and the classical Brayton engine. Quantum Brayton engine in 2D has a higher efficiency compared to the 1D and the classical one.
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.
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.