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Since you specified a thermally insulated cylinder and piston, it
doesn't really seem to matter if you do the compression quickly or
slowly - the final temperature will be the same.
Since a reversible
adiabat will get you from the same initial state and to the same
final state, it appears dS = 0 as well as dq = 0. Is the supersonic
nature of the proposed compression an implication of a change in the
values of Cp and Cv so the slow reversible compression is not
equivalent?