  Some features of hydro- and thermodynamics, as applied to atmospheres and to
stellar structures, are puzzling: 1. The suggestion, first made by Laplace,
that our atmosphere has an adiabatic temperature distribution, is confirmed for
the lower layers, but the reason why it should be so is understood only
qualitatively. 2. Arguments in which a concept of energy plays a role, in the
context of hydro-thermodynamical systems and gravitation, are often flawed, and
some familiar results concerning the stability of model stellar structures,
first advanced at the end of the 19th century and repeated in the most modern
textbooks, are less than completely convincing. 3. The standard treatment of
relativistic thermodynamics does not allow for a systematic treatment of
mixtures, such as the mixture of a perfect gas with radiation. 4. The concept
of mass in applications of general relativity to stellar structure is
unsatisfactory. It is proposed that a formulation of thermodynamics as an
action principle may be a suitable approach to adopt for a new investigation of
these matters.
  We formulate thermodynamics of ideal gases in terms of an action principle
and study the interaction between an ideal gas and the photon gas, or heat. The
action principle provides a hamiltonian functional, not available in
traditional approaches where familiar expressions for the energy have no
operative meaning. The usual polytropic atmosphere in an external gravitational
field is examined, in order to determine to what extent it is shaped by
radiation.
  A new formulation of the concept of radiative equilibrium is proposed.
