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Journal of Physics D Applied Physics

The optimal performance of a quantum refrigeration cycle working with harmonic oscillators

Bihong Lin, Jincan Chen, Ben Hua

Published Jan 29, 2003• 17 citations
Publisher

Abstract

The cycle model of a quantum refrigeration cycle working with many non-interacting harmonic oscillators and consisting of two isothermal and two constant-frequency processes is established. Based on the quantum master equation and semi-group approach, the general performance of the cycle is investigated. Expressions for some important performance parameters, such as the coefficient of performance, cooling rate, power input, and rate of the entropy production, are derived. Several interesting cases are discussed and, especially, the optimal performance of the cycle at high temperatures is discussed in detail. Some important characteristic curves of the cycle, such as the cooling rate versus coefficient of performance curves, the power input versus coefficient of performance curves, the cooling rate versus power input curves, and so on, are presented. The maximum cooling rate and the corresponding coefficient of performance are calculated. Other optimal performances are also analysed. The results obtained here are compared with those of an Ericsson or Stirling refrigeration cycle using an ideal gas as the working substance. Finally, the optimal performance of a harmonic quantum Carnot refrigeration cycle at high temperatures is derived easily.

DOI
10.1088/0022-3727/36/4/313

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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 pump working with many non-interacting harmonic oscillators is established. The cycle consists of two isothermal and two constant-frequency processes. The general performance characteristics of the cycle are investigated, based on the quantum master equation and semi-group approach. Expressions for some important performance parameters, such as the heating load, coefficient of performance, power input, and rate of the entropy production, are derived. Some interesting cases are discussed. Especially, the optimal performance of the cycle in the high-temperature limit is discussed in detail. Some important characteristic curves of the cycle, such as the heating load versus the coefficient of performance, the power input versus the coefficient of performance, the entropy production rate versus the coefficient of performance, and so on, are presented. The maximum heating load and the corresponding coefficient of performance are calculated. Moreover, the optimal power input, cycle time and temperatures of the working substance in the isothermal processes are analyzed. The optimal region of the coefficient of performance and the optimal ranges of the temperatures of the working substance in the two isothermal processes are determined. In addition, it is proved that the results obtained here can be directly used to derive the optimal performance of a harmonic quantum Carnot heat pump.
Based on the quantum master equation and semi-group approach,the general performance characteristics of the cycle working with many noninteracting harmonic oscillators are investigated,which consists of two isothermal and two adiabatic processes.Expressions for some important performance parameters,such as the coefficient of performance,cooling rate,power input,and rate of the entropy production are derived.Especially,the optimal performance of the cycle in high-temperature limit is discussed in detail.The results(obtained) here can provide some new theoretical bases for the optimal design of refrigeration cycle of unconventional working substance in the low-temperature.
A new model of a quantum refrigeration cycle composed of two adiabatic and two isomagnetic field processes is established. The working substance in the cycle consists of many non-interacting spin-1/2 systems. The performance of the cycle is investigated, based on the quantum master equation and semi-group approach. The general expressions of several important performance parameters, such as the coefficient of performance, cooling rate and power input, are given. It is found that the coefficient of performance of this cycle is in the closest analogy to that of the classical Carnot cycle. Furthermore, at high temperatures the optimal relations of the cooling rate and the maximum cooling rate are analysed in detail. Some performance characteristic curves of the cycle are plotted, such as the cooling rate versus the maximum ratio between high and low ``temperatures'' of the working substances, the maximum cooling rate versus the ratio between high and low ``magnetic fields'' and the ``temperature'' ratio between high and low reservoirs. The obtained results are further generalized and discussed, so that they may be directly applied to describing the performance of the quantum refrigerator using spin- J systems as the working substance. Finally, the optimum characteristics of the quantum Carnot and Ericsson refrigeration cycles are derived by analogy.
The general performance characteristics of an irreversible quantum refrigeration cycle using many non-interacting spin-1/2 systems as the working substance and consisting of two adiabatic and two isomagnetic field processes are investigated, based on the quantum master equation and semi-group approach. Expressions for several important performance parameters such as the coefficient of performance, cooling rate and power input are derived. By using numerical solutions, the cooling rate of the refrigeration cycle subject to the 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 the temperatures of the working substance and the times spent on the two isomagnetic field processes are determined. 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 the quantum refrigeration cycle using spin- J systems as the working substance.