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

• From: John Denker <jsd@av8n.com>
• Date: Sun, 17 Jan 2010 01:54:19 -0700

On 01/16/2010 08:27 PM, LaMontagne, Bob wrote:
Yes it does the work mgh, but it produces significant KE of the
piston.

No, the KE of the piston is not significant. It is not
even relevant.

in a sample of gas. There is an interesting discussion to
why anybody would be interested in what happens inside the
body of the piston. We are not interested in the momentum
that flows into the piston and stays there; rather we are
interested in the momentum that flows via the piston into
the gas.

What happens to the gas is determined by the F(t) and
x(t) profile of the face of the piston, the face facing
the gas. I can easily achieve the same force and position
profile with a heavy piston or a light piston. In these
two cases, the KE of the piston is different but the
effect on the gas is the same. IMHO this proves that
the KE of the piston has got nothing to do with the
phenomena we are interested in. This proof seems both
transparent and rigorous, and should satisfy experts and
non-experts alike.

Other lines of reasoning come to the same result, as
previously discussed.

Here's yet another argument that yields the same result:
In Carl's original statement of the scenario, he mentioned
a supersonic piston. Well, consider the simple case of a
_constant velocity_ supersonic piston in a long tube, or
an aircraft in steady supersonic flight. The mass and KE
of the piston and/or aircraft is a constant of the motion,
and is obviously irrelevant. The shock it produces is
highly dissipative, so this is a useful model system. The
physics of shocks is well (albeit not widely) understood.
http://www.grc.nasa.gov/WWW/K-12/airplane/oblique.html

take it as a little teaching challenge.

The ball is in your court. The challenge is to explain
why the KE of the piston is anything more than a red