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 \(\frac{3}{2} k T\), the effused ones have a mean kinetic energy \(2 k T, T\) being the quasistatic equilibrium temperature of the gas.

(b) Assuming that the effusion is so slow that the gas inside is always in a state of quasistatic equilibrium, determine the manner in which the density, the temperature, and the pressure of the gas vary with time.