Wow! OK. I was thinking about this and was going to say that, you know, 99.999..% (add as many nines as you want) more than I do... some guy on usenet. Anyway that was great!! How to put numbers on your cooling mechanism, my problem is that at the start the gas all leaves by flow, like pouring water out of a bucket... all the molecules(m's) leave, fast and slow. Then later on pumping is all about the fast ones leaving. With some transition region in between. You most likely know where, those regions are. (I can guess, or look at wiki.) So do some guesstimate, from this point on all the m's only leave by hitting a wall and bouncing out.. with "no" energy before they hit the wall. then count m's and ratio to the area, do the heat capacity... around room temp all the m's are pretty much equal.
That's crude but will give some number. George H.