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AIP conference proceedings

Quantum Brayton engine based on a single particle in the 2D symmetric potential well

Fikri Abdillah, Agus Rifani, Yohanes Dwi Saputra

Published Jan 1, 2020• 3 citations
Publisher

Abstract

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.

DOI
10.1063/5.0008338

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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.
Quantum Brayton engine efficiency with the massless boson particle as a working substance has been investigated. The research method used is analogy modeling of the first law of classical thermodynamics which is implemented into the quantum systems. The quantum system used is the single massless boson particle trapped inside the two-dimensional symmetrical potential well as a replacement for the classic system is an ideal gas in a piston tube. By replacing the working substance from the classical system into a quantum system, the four processes that form the classic Brayton cycle (two isobaric processes and two adiabatic processes) can be constructed on the quantum system. The final result indicates that the quantum Brayton engine with boson particle has a higher efficiency value compared to the classic version, but is lower than that engine when the massless boson is replaced with nonrelativistic particles. This occurs because of differences in Laplace's constant value in the three systems.
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.
A theoretical quantum Brayton engine research has been carried out using a potential box system to increase its thermal efficiency. The method applied in this research is a classical thermodynamics system model in the form of a piston tube containing a monatomic ideal gas analogous to a quantum model in the form of a potential box containing one particle. The efficiency formulation of the quantum Brayton engine obtained from this study is following the classical version. However, the efficiency value obtained on a quantum Brayton engine is higher when compared to its classic. It happens because the value of the Laplace constant owned by the Brayton quantum version is 3, while the classic version is 5/3.
A quantum Brayton engine using a massless Boson trapped in a one-dimensional potential well as a working substance has been constructed to be studied. We used a modified analogical model by the first law of thermodynamics for a quantum system implementation. The system was built with Klein Gordon equation, relativistic quantum mechanics Hamiltonian, without the mass term of the Hamiltonian and it was trapped in a one-dimensional potential well. Then, it underwent the quantum ideal Brayton cycle process. The quantum Brayton process consisted of adiabatic compression, isobaric expansion, adiabatic expansion, and isobaric compression processes. This relativistic quantum mechanics Brayton engine has found that the efficiency formulation was similar to the classical one. This study obtained the conformity results between the quantum relativistic and classical Brayton engines. By this cycle process, we also invented that the ratio of heat capacity under constant pressure and volume of the system was 2. It could indicate that the efficiency of quantum relativistic Brayton engine is higher than 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.
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.