Abstract

Thermal equilibrium in a gravitational field is examined using the standard tools of thermodynamics but including the relativistic effects associated with the mass energy relation. It is found that an appropriately defined temperature is not constant at equilibrium but decreases with increasing gravitational potential. The gravitational red shift is a simple manifestation of this. In terms of this temperature the local thermodynamic properties are independent of the gravitational potential. It is also found possible to define another temperature which is uniform at equilibrium. However, use of this temperature requires that the thermodynamic properties (for example, melting points) be explicit functions of the gravitational potential.

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