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I have to strongly disagree with David here. The derivation of absolute
temperature (as a measure of the average translational kinetic energy per
molecule due to random motion) IS, IMO, very accessible to AP level students
and IS a very good example of how a concept such as temperature that seems
far afield from their basic kinematic and dynamic studies can be shown to
arise from just such studies.
To be sure, the Algebra text derivations do
not consider any of David's subtleties and usually starts with an assumption
of the Universal Gas Law as part of the derivation.
But that being said,
looking at the wall collisions as a source of the pressure, the change in
momentum in such collisions, the time of flight between ends of the box,
etc., etc. is a very important exercise for this level of student to work
through. It really shows how to work out new physics from old, basic
principles.