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!