The
simplest things one can do microscopically are things like detailed balance estimates, and so far I haven't made Joe happy even with what I've attempted there, although I think he realizes that my
answer is irrelevantly imprecise (or he should realize it once he follows the reasoning in the
algebra above that lays out how air can be isothermal and still have the MB velocity distribution from the bottom out to where the assumptions of thermodynamics break down anyway, because to many, many digits when meters is the mean free path of the gas and meters.