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... It would seem
that, without giving students the impression that entropy is conserved,
one could compute how much entropy was generated by the fast compression
by calculating how much entropy would have to be reversably transferred
(from an infinite collection of infinite heat reservoirs) into the gas
after it had been compressed reversably to the same final volume, in
order to bring the gas up to the final temperature resulting from the
rapid compression.
... I prefer, however, to think about the work done in terms of
force (and displacement of the piston) rather than pressure (and
volume change of the gas), because the pressure in the gas is ill-
defined. Indeed, the pressure that you want to use in this
calculation can only be determined finding the force applied to the
gas by the piston and then dividing by the piston area.