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I'd like to suggest that much of the confusion here is the result
of a failure to appreciate that
kinetic friction is not a heating process.
I think this common confusion has to do with the fact that both
may be considered to involve distributed, microscopic works done
at the interface between two systems....
Note also that heating can be done reversibly while kinetic
friction is always irreversible. This is why, in order to
determine the temperature rise that accompanies kinetic friction,
we often construct an *alternate* path between initial and final
states that involves a heating process with an "equivalent" heat
transfer. ...
A. John Mallinckrodt