Universality of maximum-work efficiency of a cyclic heat engine based on a finite system of ultracold atoms

Abstract We study the performance of a cyclic heat engine which uses a small system with a finite number of ultracold atoms as its working substance and works between two heat reservoirs at constant temperatures T h and T c (<T h ). Starting from the expression of heat capacity which includes fin...

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Autores principales:	Zhuolin Ye, Yingying Hu, Jizhou He, Jianhui Wang
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/942ab639066b4056bb70eea1884eefb0
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spelling	oai:doaj.org-article:942ab639066b4056bb70eea1884eefb02021-12-02T12:32:01ZUniversality of maximum-work efficiency of a cyclic heat engine based on a finite system of ultracold atoms10.1038/s41598-017-06615-z2045-2322https://doaj.org/article/942ab639066b4056bb70eea1884eefb02017-07-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-06615-zhttps://doaj.org/toc/2045-2322Abstract We study the performance of a cyclic heat engine which uses a small system with a finite number of ultracold atoms as its working substance and works between two heat reservoirs at constant temperatures T h and T c (<T h ). Starting from the expression of heat capacity which includes finite-size effects, the work output is optimized with respect to the temperature of the working substance at a special instant along the cycle. The maximum-work efficiency η mw at small relative temperature difference can be expanded in terms of the Carnot value $${{\boldsymbol{\eta }}}_{{\boldsymbol{C}}}={\bf{1}}-{{\boldsymbol{T}}}_{{\boldsymbol{c}}}/{{\boldsymbol{T}}}_{{\boldsymbol{h}}}$$ η C = 1 − T c / T h , $${{\boldsymbol{\eta }}}^{{\boldsymbol{m}}{\bf{w}}}={{\boldsymbol{\eta }}}_{{\boldsymbol{C}}}/{\bf{2}}+{{\boldsymbol{\eta }}}_{{\boldsymbol{C}}}^{{\bf{2}}}({\bf{1}}/{\bf{8}}+{{\boldsymbol{a}}}_{{\bf{0}}})+{\boldsymbol{\ldots }}$$ η m w = η C / 2 + η C 2 ( 1 / 8 + a 0 ) + … , where a 0 is a function depending on the particle number N and becomes vanishing in the symmetric case. Moreover, we prove using the relationship between the temperatures of the working substance and heat reservoirs that the maximum-work efficiency, when accurate to the first order of η C , reads $${{\boldsymbol{\eta }}}^{{\boldsymbol{m}}{\bf{w}}}={{\boldsymbol{\eta }}}_{{\boldsymbol{CA}}}+{\bf{O}}$$ η m w = η CA + O (ΔT 2). Within the framework of linear irreversible thermodynamics, the maximum-power efficiency is obtained as $${{\boldsymbol{\eta }}}^{{\boldsymbol{mp}}}={{\boldsymbol{\eta }}}_{{\boldsymbol{CA}}}+{\bf{O}}$$ η mp = η CA + O (ΔT 2) through appropriate identification of thermodynamic fluxes and forces, thereby showing that this kind of cyclic heat engines satisfy the tight-coupling condition.Zhuolin YeYingying HuJizhou HeJianhui WangNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-12 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Zhuolin Ye Yingying Hu Jizhou He Jianhui Wang Universality of maximum-work efficiency of a cyclic heat engine based on a finite system of ultracold atoms
description	Abstract We study the performance of a cyclic heat engine which uses a small system with a finite number of ultracold atoms as its working substance and works between two heat reservoirs at constant temperatures T h and T c (<T h ). Starting from the expression of heat capacity which includes finite-size effects, the work output is optimized with respect to the temperature of the working substance at a special instant along the cycle. The maximum-work efficiency η mw at small relative temperature difference can be expanded in terms of the Carnot value $${{\boldsymbol{\eta }}}_{{\boldsymbol{C}}}={\bf{1}}-{{\boldsymbol{T}}}_{{\boldsymbol{c}}}/{{\boldsymbol{T}}}_{{\boldsymbol{h}}}$$ η C = 1 − T c / T h , $${{\boldsymbol{\eta }}}^{{\boldsymbol{m}}{\bf{w}}}={{\boldsymbol{\eta }}}_{{\boldsymbol{C}}}/{\bf{2}}+{{\boldsymbol{\eta }}}_{{\boldsymbol{C}}}^{{\bf{2}}}({\bf{1}}/{\bf{8}}+{{\boldsymbol{a}}}_{{\bf{0}}})+{\boldsymbol{\ldots }}$$ η m w = η C / 2 + η C 2 ( 1 / 8 + a 0 ) + … , where a 0 is a function depending on the particle number N and becomes vanishing in the symmetric case. Moreover, we prove using the relationship between the temperatures of the working substance and heat reservoirs that the maximum-work efficiency, when accurate to the first order of η C , reads $${{\boldsymbol{\eta }}}^{{\boldsymbol{m}}{\bf{w}}}={{\boldsymbol{\eta }}}_{{\boldsymbol{CA}}}+{\bf{O}}$$ η m w = η CA + O (ΔT 2). Within the framework of linear irreversible thermodynamics, the maximum-power efficiency is obtained as $${{\boldsymbol{\eta }}}^{{\boldsymbol{mp}}}={{\boldsymbol{\eta }}}_{{\boldsymbol{CA}}}+{\bf{O}}$$ η mp = η CA + O (ΔT 2) through appropriate identification of thermodynamic fluxes and forces, thereby showing that this kind of cyclic heat engines satisfy the tight-coupling condition.
format	article
author	Zhuolin Ye Yingying Hu Jizhou He Jianhui Wang
author_facet	Zhuolin Ye Yingying Hu Jizhou He Jianhui Wang
author_sort	Zhuolin Ye
title	Universality of maximum-work efficiency of a cyclic heat engine based on a finite system of ultracold atoms
title_short	Universality of maximum-work efficiency of a cyclic heat engine based on a finite system of ultracold atoms
title_full	Universality of maximum-work efficiency of a cyclic heat engine based on a finite system of ultracold atoms
title_fullStr	Universality of maximum-work efficiency of a cyclic heat engine based on a finite system of ultracold atoms
title_full_unstemmed	Universality of maximum-work efficiency of a cyclic heat engine based on a finite system of ultracold atoms
title_sort	universality of maximum-work efficiency of a cyclic heat engine based on a finite system of ultracold atoms
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/942ab639066b4056bb70eea1884eefb0
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_version_	1718394229391097856

Universality of maximum-work efficiency of a cyclic heat engine based on a finite system of ultracold atoms

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