(a) Considering the loss of translational energy suffered by the molecules of a gas on reflection from a receding wall, derive, for a quasi-static adiabatic expansion of an ideal nonrelativistic gas, the well-known relation
PVγ=const.,
where γ=(3a+2)/3a, a being the ratio of the total energy to the translational energy of the gas.
(b) Show that, in the case of an ideal extreme relativistic gas, γ=(3a+1)/3a.