How Does an Ideal Gas Sphere Expand in a Vacuum?

[afallingbomb]

I thought of what seems to be a very classical problem but I can't find a solution for it.

At t=0 you have a sphere of radius, R, made up of an ideal gas at a temperature, T, and pressure, P. The sphere is sitting in an infinite vacuum. At t>0 you allow the sphere to expand freely outward. Are there analytical solutions to the velocity (of the surface or perhaps along any point on the radius), density, and other state variables (P, T, etc) as they evolve through time? Thank you!

 

[PhaseShifter]

Essentially you have an area of low pressure (vacuum, or "gas with zero pressure") containing a smaller region of higher pressure (the sphere). Wouldn't this propagate at the same speed sound propagates within the gas, like other pressure disturbances?

I suppose you would get a better picture of what would really happen by using statistical mechanics, but then you have to decide what the surface of the sphere is, since there is no upper limit on the speed of gas molecules. (They do become exponentially more uncommon at higher speeds, though.)