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Journal of Applied Physics

Optimization criteria for an irreversible quantum Brayton engine with an ideal Bose gas

Feng Wu, Lingen Chen, Fengrui Sun, Chih Wu, Fangzhong Guo

Published Mar 1, 2006• 29 citations
Publisher

Abstract

The purpose of this paper is to study the optimal performance for an irreversible quantum Brayton engine consisting of two constant-frequency branches connected by two irreversible adiabatic branches. The solution of the generalized quantum master equation of a thermal system is obtained in the Heisenberg picture. The optimization region (or criteria) for an irreversible quantum Brayton engine is obtained. The relationship between the dimensionless power output P* versus efficiency η for the irreversible quantum Brayton engine with heat leakage and other irreversible losses are derived.

DOI
10.1063/1.2176083

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The purpose of this paper is to study the optimal performance for an irreversible quantum Brayton engine consisting of two constant-frequency branches connected by two irreversible adiabatic branches. The solution of the generalized quantum master equation of a thermal system is obtained in the Heisenberg picture. The optimization region (or criteria) for an irreversible quantum Brayton engine is obtained. The relationship between the dimensionless power output P* versus efficiency η for the irreversible quantum Brayton engine with heat leakage and other irreversible losses are derived.
The purpose of this paper is to establish a model of an irreversible quantum Brayton engine using many noninteracting spin systems as the working substance and consisting of two irreversible adiabatic and two isomagnetic field processes. The time evolution of the total magnetic moment M is determined by solving the generalized quantum master equation of an open system in the Heisenberg picture. The time of two irreversible adiabatic processes is considered based on finite-rate evolution. The relationship between the power output P and the efficiency eta for the irreversible quantum Brayton engine with spin systems is derived. The optimally operating region (or criteria) for the engine is determined. The influences of these important parameters on the performances (P and eta) of the engine are discussed. The results obtained herein will be useful for the further understanding and the selection of the optimal operating conditions for an irreversible quantum Brayton engine with spin systems.
It is considered that the cycle of a quantum heat engine using many non-interacting spin-1/2 systems as the working substance is composed of two adiabatic and two isomagnetic field processes and is referred to as a spin quantum Brayton engine cycle. Based on the quantum master equation and semi-group approach, expressions for the efficiency and power output of the cycle are derived. By using numerical solutions, the power output of the heat engine subject to finite cycle duration is optimized. The maximum power output and the corresponding parameters are calculated numerically. The optimal region of the efficiency and the optimal ranges of temperatures of the working substance and times spent on the two isomagnetic field processes are determined, so that the general optimum performance characteristics of the cycle are revealed. Moreover, the optimal performance of the cycle in the high-temperature limit is also analysed in detail. The results obtained here are further generalized, so that they may be directly used to describe the performance of a quantum Brayton heat engine using spin-J systems as the working substance.
An irreversible model of a quantum refrigeration cycle working with many noninteracting harmonic oscillators is established. The refrigeration cycle consists of two adiabatic and two constant-frequency processes. The general performance characteristics of the cycle are investigated, based on the quantum master equation and the semigroup approach. The expressions for several important performance parameters such as the coefficient of performance, cooling rate, power input, and rate of entropy production are derived. By using numerical solutions, the cooling rate of the refrigeration cycle subject to finite cycle duration is optimized. The maximum cooling rate and the corresponding parameters are calculated numerically. The optimal region of the coefficient of performance and the optimal ranges of temperatures of the working substance and times spent on the two constant-frequency processes are determined. Moreover, the optimal performance of the cycle in the high-temperature limit is compared with that of a classical Brayton refrigerator working with an ideal gas. The results obtained here show that in the high-temperature limit a harmonic quantum Brayton cycle may be equivalent to a classical Brayton cycle.
The cycle model of a regenerative quantum heat engine working with many noninteracting harmonic oscillators is established. The cycle consists of two isothermal and two constant-frequency processes. The performance of the cycle is investigated, based on the quantum master equation and semigroup approach. The inherent regenerative losses in the two constant-frequency processes are calculated. The expressions of several important performance parameters such as the efficiency, power output, and rate of the entropy production are derived for several interesting cases. Especially, the optimal performance of the cycle in high-temperature limit is discussed in detail. The maximum power output and the corresponding parameters are calculated. The optimal region of the efficiency and the optimal ranges of the temperatures of the working substance in the two isothermal processes are determined.
A model of a quantum heat engine with heat resistance, internal irreversibility and heat leakage and many non-interacting spin-1/2 systems is established in this paper. The quantum heat engine cycle is composed of two isothermal processes and two irreversible adiabatic processes and is referred to as a spin quantum Carnot heat engine. Based on the quantum master equation and the semi-group approach, equations of some important performance parameters, such as power output, efficiency, entropy generation rate and ecological function (a criterion representing the optimal compromise between exergy output rate and exergy loss rate), for the irreversible spin quantum Carnot heat engine are derived. The optimal ecological performance of the heat engine in the classical limit is analyzed with numerical examples. The effects of internal irreversibility and heat leakage on ecological performance are discussed in detail.
Bose-Einstein condensation is a quintessential characteristic of Bose systems. We investigate the finite-time performance of an endoreversible quantum Brayton heat engine operating with an ideal Bose gas with a finite number of particles confined in a d-dimensional harmonic trap. The working medium of these engines may work in the condensation, noncondensation, and near-critical point regimes, respectively. We demonstrate that the existence of the phase transition during the cycle leads to enhanced engine performance by increasing power output and efficiencies corresponding to maximum power and maximum efficient power. We also show that the quantum engine working across the Bose-Einstein condensation in N-particle Bose gas outperforms an ensemble of independent single-particle heat engines. The difference in the machine performance can be explained in terms of the behavior of specific heat at constant pressure near the critical point regime.