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In this paper we study the thermodynamic performance of a Brownian heat engine, which is driven by temperature difference. Brownian particles move in a periodic single-barrier sawtooth potential under the action of an external load force, and contact an alternating hot and cold reservoir. The kinetic energy change of the Brownian particles and the heat leak between hot and cold reservoir are considered simultaneously. The dynamics of the Brownian particle is governed by the Smoluchowski equation. The expressions for heat flow, power output and efficiency are derived analytically. The influences of the height of barrier, the external load force and the heat reservoir boundary on efficiency and power output are discussed by numerical calculation. It is shown that the Brownian heat engine is irreversible when the irreversible heat flow caused by the kinetic energy change and the heat leak exist. The curve of the power output versus the efficiency is a loop-shaped one. When the barrier boundary coincides with the heat reservoir boundary, the heat engine has a maximum power output. The efficiency of the heat engine is enhanced, but the power output is reduced when the heat reservoir boundary is changed.
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Keywords:
- Brownian heat engine /
- heat leak /
- thermodynamic performance /
- irreversibility
[1] Hanggi P, Marchesoni F 2009 Rev. Mod. Phys. 81 387
[2] Astumian R D, Bier M 1994 Phys. Rev. Lett. 72 1766
[3] Parrondo J M R, Blanco J M, Cao F J 1998 Europhys. Lett. 43 248
[4] Ambaye H, Kehr K W 1999 Physica A 267 111
[5] Feynman R P, Leighton R B, Sands M 1963 The Feynman Lectures on Physics. (Vol. I) (Boston: Addison-Wesley) Reading 46.1
[6] Bttiker M 1987 Z. Phys. B 68 161
[7] van Kampen N G 1988 IBM J. Res. Dev. 32 107
[8] Landauer R 1988 J. Stat. Phys. 53 233
[9] van den Broeck C, Kawai R 2006 Phys. Rev. Lett. 96 210601
[10] Li N, Zhan F, Hanggi P, Li B 2009 Phys. Rev. E 80 011125
[11] Li N, Hanggi P, Li B 2008 Europhys. Lett. 84 40009
[12] Asfaw M, Bekele M 2004 Eur. Phys. J. B 38 457
[13] Asfaw M, Bekele M 2005 Phys. Rev. E 72 056109
[14] Asfaw M, Bekele M 2007 Physica A 384 346
[15] Derényi I, Astumian R D 1999 Phys. Rev. E 59 R6219
[16] Zhang Y P, He J Z, He X 2010 Commun. Theor. Phys. 54 857
[17] Zhang Y P, He J Z, Ouyang H 2010 Phys. Scr. 82 055005
[18] Zhang Y P, He J Z 2010 Chin. Phys. Lett. 27 090502
[19] Luo X G, Liu N, He J Z 2013 Phys. Rev. E 87 022139
[20] Hondou T, Sekimoto K 2000 Phys. Rev. E 62 6021
[21] Ai B Q, Xie H Z, Wen D H 2005 Eur. Phys. J. B 48 101
[22] Ai B Q, Wang L Q, Liu L G 2006 Phys. Lett. A 352 286
[23] Ai B Q, Wang X J, Liu G T 2003 Phys. Rev. E 68 061105
[24] Zhang Y, Lin B H, Chen J C 2006 Eur. Phys. J. B 53 481
[25] Lin B H, Chen J C 2009 J. Phys. A: Math. Theor. 42 075006
[26] Ding Z M, Chen L G, Sun F R 2010 Braz. J. Phys. 40 141
[27] Ding Z M, Chen L G, Sun F R 2010 Sci. China G: Phys. Mech. Astron. 40 16 (in Chiese) [丁泽民, 陈林根, 孙丰瑞 2010 中国科学 G辑: 物理学 力学 天文学 40 16]
[28] Asfaw M 2008 Eur. Phys. J. B 65 109
[29] Asfaw M 2014 Phys. Rev. E 89 012143
[30] Cheng H T, He J Z, Xiao Y L 2012 Acta Phys. Sin. 61 010502 (in Chinese) [程海涛, 何济洲, 肖宇玲 2012 物理学报 61 010502]
[31] Sancho J M, Miguel M S, Drr D 1982 J. Stat. Phys. 28 291
[32] Gao T F, Zhang Y, Chen J C 2009 Chin. Phys. B 18 3279
[33] Gordon J M, Huleihil M 1992 J. Appl. Phys. 72 829
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[1] Hanggi P, Marchesoni F 2009 Rev. Mod. Phys. 81 387
[2] Astumian R D, Bier M 1994 Phys. Rev. Lett. 72 1766
[3] Parrondo J M R, Blanco J M, Cao F J 1998 Europhys. Lett. 43 248
[4] Ambaye H, Kehr K W 1999 Physica A 267 111
[5] Feynman R P, Leighton R B, Sands M 1963 The Feynman Lectures on Physics. (Vol. I) (Boston: Addison-Wesley) Reading 46.1
[6] Bttiker M 1987 Z. Phys. B 68 161
[7] van Kampen N G 1988 IBM J. Res. Dev. 32 107
[8] Landauer R 1988 J. Stat. Phys. 53 233
[9] van den Broeck C, Kawai R 2006 Phys. Rev. Lett. 96 210601
[10] Li N, Zhan F, Hanggi P, Li B 2009 Phys. Rev. E 80 011125
[11] Li N, Hanggi P, Li B 2008 Europhys. Lett. 84 40009
[12] Asfaw M, Bekele M 2004 Eur. Phys. J. B 38 457
[13] Asfaw M, Bekele M 2005 Phys. Rev. E 72 056109
[14] Asfaw M, Bekele M 2007 Physica A 384 346
[15] Derényi I, Astumian R D 1999 Phys. Rev. E 59 R6219
[16] Zhang Y P, He J Z, He X 2010 Commun. Theor. Phys. 54 857
[17] Zhang Y P, He J Z, Ouyang H 2010 Phys. Scr. 82 055005
[18] Zhang Y P, He J Z 2010 Chin. Phys. Lett. 27 090502
[19] Luo X G, Liu N, He J Z 2013 Phys. Rev. E 87 022139
[20] Hondou T, Sekimoto K 2000 Phys. Rev. E 62 6021
[21] Ai B Q, Xie H Z, Wen D H 2005 Eur. Phys. J. B 48 101
[22] Ai B Q, Wang L Q, Liu L G 2006 Phys. Lett. A 352 286
[23] Ai B Q, Wang X J, Liu G T 2003 Phys. Rev. E 68 061105
[24] Zhang Y, Lin B H, Chen J C 2006 Eur. Phys. J. B 53 481
[25] Lin B H, Chen J C 2009 J. Phys. A: Math. Theor. 42 075006
[26] Ding Z M, Chen L G, Sun F R 2010 Braz. J. Phys. 40 141
[27] Ding Z M, Chen L G, Sun F R 2010 Sci. China G: Phys. Mech. Astron. 40 16 (in Chiese) [丁泽民, 陈林根, 孙丰瑞 2010 中国科学 G辑: 物理学 力学 天文学 40 16]
[28] Asfaw M 2008 Eur. Phys. J. B 65 109
[29] Asfaw M 2014 Phys. Rev. E 89 012143
[30] Cheng H T, He J Z, Xiao Y L 2012 Acta Phys. Sin. 61 010502 (in Chinese) [程海涛, 何济洲, 肖宇玲 2012 物理学报 61 010502]
[31] Sancho J M, Miguel M S, Drr D 1982 J. Stat. Phys. 28 291
[32] Gao T F, Zhang Y, Chen J C 2009 Chin. Phys. B 18 3279
[33] Gordon J M, Huleihil M 1992 J. Appl. Phys. 72 829
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