  Molecular clouds are supported by thermal pressure, magnetic pressure, and
turbulent pressure. Each of these can be modeled with a polytropic equation of
state, so that overall the total pressure is the sum of the individual
components. We model the turbulent pressure as being due to a superposition of
Alfven waves. The theory of polytropes is generalized to allow for the flow of
entropy in response to a perturbation, as expected for the entropy associated
with wave pressure. The equation of state of molecular clouds is "soft", so
that the properties of the clouds are generally governed by the conditions at
the surface. In general, the polytropes are not isentropic, and this permits
large density and pressure drops to occur between the center and the edge of
the polytropes, as is observed.
