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# Re: [Phys-l] T dS versus dQ

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?

Bob at PC

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of Carl Mungan
Sent: Tuesday, January 12, 2010 1:38 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] T dS versus dQ

So that's the question: Is there any scenario in
which it is not OK to replace dQ by either dE or
T dS? If so, what is the scenario, and why is
dQ irreplaceable? Operationally, how do I measure
dQ in this scenario, and/or how do I calculate it?

I have an ideal gas in a thermally insulated cylinder and piston. I
suddenly compress the piston. To be specific, suppose the piston's
speed profile starts from zero, rapidly (practically stepwise) rises
up to the speed of sound, then drops rapidly back to zero once the
gas is compressed by dV (which is negative). In practice I might
accomplish this by having a huge weight sitting on the piston which
is at the top end of the cylinder and held in place by a pin. I pull
out the pin and let the piston fall a distance dx until it slams into
a stop.

I think we have T dS > 0 (because the process is certainly
irreversible), dQ = 0, dE > 0 (because work -P dV was done on the
gas) and so it doesn't look like dQ can be equal to either T dS or
dE. I "computed" dQ by noting that the cylinder (including the
piston) is thermally insulated (and I'm further helped that the
process is so fast there isn't time for heat transfer even if it
weren't insulated, noting that no thermal insulation is perfect in
the real world).

Okay, fire away. -Carl
--
Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363
mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/
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