Consider the effusion of molecules of a Maxwellian gas through an opening of area a in the walls of a vessel of volume V.
(a) Show that, while the molecules inside the vessel have a mean kinetic energy 23kT, the effused ones have a mean kinetic energy 2kT, T being the quasi-static equilibrium temperature of the gas.
(b) Assuming that the effusion is so slow that the gas inside is always in a state of quasi-static equilibrium, determine the manner in which the density, the temperature and the pressure of the gas vary with time.