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

• From: curtis osterhoudt <flutzpah@yahoo.com>
• Date: Tue, 12 Jan 2010 11:00:21 -0800 (PST)

Note that my use of "non-adiabatic" in the previous email is quite useless, and probably even so useless as to be dangerous. I apologize.

/************************************
Down with categorical imperative!
flutzpah@yahoo.com
************************************/

________________________________
From: curtis osterhoudt <flutzpah@yahoo.com>
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Sent: Tue, January 12, 2010 11:51:07 AM
Subject: Re: [Phys-l] T dS versus dQ

Is P well-defined enough in such a non-adiabatic process to claim that the work done is P*dV?

/************************************
Down with categorical imperative!
flutzpah@yahoo.com
************************************/

________________________________
From: Carl Mungan <mungan@usna.edu>
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Sent: Tue, January 12, 2010 11:37:50 AM
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/
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l