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Re: [Phys-L] Hydrostatics question



On 07/22/2013 02:48 AM, Peter Schoch wrote:
Now, while I know that works _ideally_, won't the air temperature
rise in the tube? Since we are compressing it, that means doing work
on it, and there is a heat transfer and thermal energy change?

Yes, no, and maybe. The devil is in the details. There is some
interesting real-world physics involved here.

1) Yes, the air gets hotter when you compress it.

2) However, it turns out that on typical human time-scales, and
on typical laboratory length-scales, the air might return to
the ambient equilibrium temperature so quickly that you don't
notice the temperature effect. Maybe.

3) On the third hand, even if you don't notice the temperature
effects in the barometer experiment, there are lots of other
situations where you can get badly fooled by neglecting such
effects.

3a) In particular, Isaac Newton famously calculated the
speed of sound and got the wrong answer, because he assumed
that sound would compress the air isothermally. In fact, at
ordinary acoustic frequencies and wavelengths, sound is very
nearly adiabatic, not isothermal.

Note that as always, the word "adiabatic" is ambiguous; I
need to specify that in this context I intend *both* meanings,
i.e. negligible entropy production *and* negligible flow of
entropy from one air parcel to another.

3b) If you quickly fill a high-pressure tire such as a bicycle
tire, if you fill it to the "right" pressure, you may well
come back in a few minutes and find that a goodly amount of
the pressure has gone away. The air didn't leak out, but the
energy and entropy did.(*)

==============================

.... heat transfer and thermal energy ....

I've been trying to train myself never to use terms like "heat"
and "thermal energy". These are dangerously unscientific terms.
They are all the more dangerous because they /almost/ make sense.
There are four or five different mutually-inconsistent definitions.
In any particular context, an expert could maybe figure out what
meaning was intended, but maybe not, and students and other non-
experts are going to crash and burn.

Fortunately, this problem is rather easy to fix. For example,
in the sentence marked (*) above, one might be tempted to say
"the heat leaked out" ... but it is much more scientific to
say the energy and entropy leaked out. This is slightly more
verbose, but only slightly, and IMHO well worth it.