Using kinetic theory, derive the relationship: if a gas has n moles and the total translational KE is (3/2)nRT, then for a diatomic gas with rotational energy also included, the total internal energy U at temperature T (f=5) is:

Not all gas molecules move at the same speed - the Maxwell-Boltzmann distribution shows the spread, with the most probable speed v_p slightly less than the average v_avg, which is slightly less than the root-mean-square speed v_rms used in the pressure formula.