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Some features of hydro- and thermodynamics, as applied to atmospheres and tostellar structures, are puzzling: 1. The suggestion, first made by Laplace,that our atmosphere has an adiabatic temperature distribution, is confirmed forthe lower layers, but the reason why it should be so is understood onlyqualitatively. 2. Arguments in which a concept of energy plays a role, in thecontext of hydro-thermodynamical systems and gravitation, are often flawed, andsome familiar results concerning the stability of model stellar structures,first advanced at the end of the 19th century and repeated in the most moderntextbooks, are less than completely convincing. 3. The standard treatment ofrelativistic thermodynamics does not allow for a systematic treatment ofmixtures, such as the mixture of a perfect gas with radiation. 4. The conceptof mass in applications of general relativity to stellar structure isunsatisfactory. It is proposed that a formulation of thermodynamics as anaction principle may be a suitable approach to adopt for a new investigation ofthese matters.  We formulate thermodynamics of ideal gases in terms of an action principleand study the interaction between an ideal gas and the photon gas, or heat. Theaction principle provides a hamiltonian functional, not available intraditional approaches where familiar expressions for the energy have nooperative meaning. The usual polytropic atmosphere in an external gravitationalfield is examined, in order to determine to what extent it is shaped byradiation.  A new formulation of the concept of radiative equilibrium is proposed.

Thermodynamics with an Action Principle, heat and gravitation (2nd version)