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Re: [Phys-l] T dS versus dQ



This long thread remains quite interesting......

Carl Mungan wrote in part

... these two limits leave a big working range - any quick
motion of the piston by a human arm is bound to be just fine. Carl

On 02/11/2010 05:30 PM, John Mallinckrodt wrote in part:

Notice that a) not until the piston speed is nearly half the rms
speed of the gas molecules does this formula give final temperatures
that are even as large as those predicted for an infinitely slow,
isentropic compression and that b) for piston speeds much greater
than the rms speed, the formula gives enormous final temperatures
that would never begin to be realized due to rapid conduction of heat
to the walls. I conclude that the formula has very limited
applicability and, thus, as Carl does, that the Adiabatic Gas Law
apparatus suffers no noticeable ill-effects due to the non-
quasistatic nature of the compression.

That's all fine _in the scenarios to which it applies_.

However, we should not treat the result as a Universal
Truth, especially given that we know of other scenarios
where the result does not hold.

I'm thinking in particular of the _acoustic_ scenario.

If you push/pull on the gas with a sound transducer, you
can heat it up just fine, with no need for implausibly
high velocities or other heroic measures. The heating
_per cycle_ will be small, but if you do it 10,000 times
per second for a long time, it adds up to something quite
significant.

I think the acoustic scenario has a good bit of pedagogical
value.
-- The average dV is zero.
-- Therefore the average P times the average dV is zero:
〈P〉 • 〈dV〉 = zero [1]
-- You can even arrange that the average P is zero, by
using a differential piston, so that:
〈P〉 • 〈dV〉 = zero squared [2]

-- However, equations [1] and [2], while amusing, have
very little practical importance, because what matters is
not the product of averages but rather the average of the
product:
〈P • dV〉 = strongly nonzero [3]