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Bob LaMontagne:
If you would take the time to read what I said - I assumed none of
the items you mention. I am simply assuming that insulated implies
no energy of any kind leaves the inside of the cylinder.
With all due respect, I read what you wrote very carefully and
responded respectfully. You didn't say "insulated," a somewhat
ambiguous term that might at least conceivably be construed as
"isolated." Rather, you (more properly) said "thermally insulated"
as did Carl. Thermal insulation rules out thermal energy transfers,
but not mechanical energy transfers, i.e. work. Indeed, Carl
explicitly indicated that a mechanical process would take place, one
that would necessarily do positive work on the system leaving it with
more energy than it had originally.
Adiabatic and ideal gas gives specific relationships between P, V,
and T that you can look up in any general physics text.
This is only true if by "adiabatic" you mean "isentropic." I think
it is pretty common, however, to understand "adiabatic" to mean that
the process involves no thermal energy transfer (i.e. "heat"). An
"isentropic" process is less ambiguously referred to as a "reversible
adiabatic" process. But Carl explicitly specified that his process
was irreversible.
My conclusion was simply that the final temperature after the
compression would be the same regardless of how fast it was done
and that in the end the sound and shock waves didn't matter.. How
do you get isothermal out of that?
It seemed to me to be a not completely unreasonable conclusion from
the fact that you explicitly (and incorrectly) stated that the final
temperature would be the same as the initial temperature. You also
said (incorrectly) that a reversible adiabat would take you from the
initial state to the final state. I took those two explicit
statements to suggest that you might think that a reversible
adiabatic process is the same as an isothermal process.
John Mallinckrodt
Cal Poly Pomona
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