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then E is not a function of state during the time that
the piston is provoking sound waves, shocks, et cetera
in the fluid. The analysis crashes and burns at this
point. We cannot proceed in this direction
Certainly (Duuuh!)!
The equations of state apply only to
definable.EQUILIBRIUM STATES,
where the state variables are definable.
If
you want to apply equilibrium thermodynamics
to the PROCESS, then choose a
reversible process which connects the initial and final states with an
infinite series of equilibrium states.
This is much ado about nothing.