中国物理B ›› 2009, Vol. 18 ›› Issue (3): 927-932.doi: 10.1088/1674-1056/18/3/015

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Reversible Carnot cycle outside a black hole

邓熙浩, 高思杰   

  1. Department of Physics, Beijing Normal University, Beijing 100875, China
  • 收稿日期:2008-06-21 修回日期:2008-07-11 出版日期:2009-03-20 发布日期:2009-03-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10605006), and the Scientific Research Starting Foundation for the Returned Overseas Chinese Scholars, Ministry of Education, China, and the Undergraduate Research Foundation

Reversible Carnot cycle outside a black hole

Deng Xi-Hao(邓熙浩) and Gao Si-Jie(高思杰)†   

  1. Department of Physics, Beijing Normal University, Beijing 100875, China
  • Received:2008-06-21 Revised:2008-07-11 Online:2009-03-20 Published:2009-03-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10605006), and the Scientific Research Starting Foundation for the Returned Overseas Chinese Scholars, Ministry of Education, China, and the Undergraduate Research Foundation

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摘要： A Carnot cycle outside a Schwarzschild black hole is investigated in detail. We propose a reversible Carnot cycle with a black hole being the cold reservoir. In our model, a Carnot engine operates between a hot reservoir with temperature T1 and a black hole with Hawking temperature TH. By naturally extending the ordinary Carnot cycle to the black hole system, we show that the thermal efficiency for a reversible process can reach the maximal efficiency 1-TH/T1. Consequently, black holes can be used to determine the thermodynamic temperature by means of the Carnot cycle. The role of the atmosphere around the black hole is discussed. We show that the thermal atmosphere provides a necessary mechanism to make the process reversible.

关键词: black hole, thermodynamics, Carnot cycle

Abstract: A Carnot cycle outside a Schwarzschild black hole is investigated in detail. We propose a reversible Carnot cycle with a black hole being the cold reservoir. In our model, a Carnot engine operates between a hot reservoir with temperature T1 and a black hole with Hawking temperature TH. By naturally extending the ordinary Carnot cycle to the black hole system, we show that the thermal efficiency for a reversible process can reach the maximal efficiency 1-TH/T1. Consequently, black holes can be used to determine the thermodynamic temperature by means of the Carnot cycle. The role of the atmosphere around the black hole is discussed. We show that the thermal atmosphere provides a necessary mechanism to make the process reversible.

Key words: black hole, thermodynamics, Carnot cycle

中图分类号:  (Quantum aspects of black holes, evaporation, thermodynamics)

  • 04.70.Dy
97.60.Lf (Black holes)