Radial dependence of temperature for adiabatic expansion of ideal gas

Question

If the solar wind propagates out adiabatically with a constant speed and can be regarded as an ideal gas, how the solar wind temperature depend on radial distance from the sun $r$, i.e. $T$ as a function of $T(r)$?

Answer 1

I don't know if it could be of use for your problem, but the ideal gas with a homogeneous gravity field is well known classical problem of statistical physics. It induces a non-homogeneous concentration of particles.

For this result, you can visit problems 6.8 and 6.10 of Patrhia's statistical mechanics book.

I don't know how to add the "solar wind" to this solution. But in any case, the Hamiltonian would be the same, right? Wouldn't it just be a matter of adding a Gallilean transformation to the result?