Abstract
Classical thermodynamics has been developed with the assumption that, either no gravitational fields are present in the thermodynamic systems, or that the fields act on the Newtonian mass of the systems only and not on any other kind of internal energy like heat. In order to find the exact thermodynamic relations for systems with gravitational fields, the wellknown Carnot cycles are used, taking into account the action of gravitation. The gravitation is described by general relativity. The Carnot efficiency is calculated in the case of stationary fields. Temperature for general relativistic systems can be defined with the help of Kelvin's principle analogously to classical thermodynamics, and the Carnot efficiency can then be expressed with temperatures instead of heat energies. In the case of strong gravitational fields, the Carnot efficiency can become equal to one even if the temperatures are both different from zero. Thermodynamic equilibrium can be expressed by using the Carnot efficiency, and it can be proved that for equilibrium the Tolman relation\(T\sqrt {g00} \) = constantholds quite generally for systems with stationary gravitational fields.
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For 1969–71 on leave of absence at the Center for Relativity Theory, University of Texas at Austin, Austin, Texas, as a Faculty Associate supported by the National Science Foundation (Grant No. GU-1598).
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Ebert, R., Göbel, R. Carnot cycles in general relativity. Gen Relat Gravit 4, 375–386 (1973). https://doi.org/10.1007/BF00771008
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DOI: https://doi.org/10.1007/BF00771008