What is the speed a gas expands into a vacuum? A gas in a Joule free expansion expands into an evacuated chamber. It does this with a certain speed. Since gas molecules move into the vacuum, that speed must be dependent on the molecules' mean speed. What is the speed a gas expands into a vacuum; is it the speed of sound?
 A: If we consider the vacuum chamber as an adiabatic system where no temperature change would occur in the gas, then depending on the gas temperature (which is not going to change in time) the kinetic energy of gas particles will define the speed at which the gas would expand. Distribution function can be expressed using Maxwell distribution function and momentum-kinetic energy relation can be correlated using below equation:

Where p is square of momentum vector, E is the kinetic energy and m is the mass of the gas particle.
Hope this helps.
A: Depends on the initial condition of the original volume of gas; the initial potential energy. Upon release into the vacuum the particles will reach a final (mean) speed. How the particles are allowed to expand also matters. Is it by a hypothetical sphere that suddenly vanishes, or are they allowed to expand through a nozzle? By the latter, the last particles would have slower final velocities than the initial as the space from which they leave becomes rarefied, the pressure decreased.
The transient, difficult to calculate. You need to know all the boundary conditions, the history. The steady state, much easier, if you can settle for mean velocity measure.
