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Re: [Phys-L] Figuring Physics solution Jan 2018

Here is some real physics that is interesting in its
own right ... and also bears indirectly on this month's
Figuring Physics flap.

There are two stable isotopes of helium, ordinary
4He and the somewhat rare 3He. Both remain liquids
down to absolute zero at ordinary pressures.

3He is a fermion, and at low temperatures this is
a big deal. You get a Fermi liquid, with a Fermi
temperature of about 5 K. At temperatures below
100 mK you get a highly /degenerate/ Fermi liquid.

This is reasonably analogous to the electrons
in a metal, which have a Fermi temperature of
thousands of degrees, so they are quite
degenerate at room temperature. It's also
analogous to nucleons in nuclei, and to neutron
stars. These systems have been studied in
tremendous detail.

3He is a real system that I reckon is as close
as you can come to the "uniform speed" liquid
that Hewitt spoke of. The kinetic energy of
every particle is on the order of 5 K; more
specifically there is a thin spherical shell
in energy-space with radius 5 K and thickness
on the order of kT.

Now this degenerate Fermi liquid does exist
and it does evaporate. It is particularly fond
of dissolving into liquid 4He, which is the same
physics as evaporation. This is the operating
principle of a 3He/4He dilution refrigerator, so
it has been exceedingly well studied.

The degenerate Fermi liquid has a very low entropy,
and after it evaporates the gas has a much higher
entropy, so this is about the most powerful refrigerator
you can imagine in this temperature range, relatively
speaking. However, the amount of cooling is still
T dS, and T is very small, so in absolute terms this
is not much cooling.

Hewitt's imaginary liquid can (at best) be considered
the limiting case of this real liquid, in the limit
as T goes to zero. In this limit you can still have
evaporation, but the cooling power goes to zero.
The liquid cannot be cooled by evaporation, obviously
because the cooling power is zero, and equally
obviously because it's already at absolute zero.

Take-home message:
-- the real physics sheds no light on the
velocity-selector argument;
-- conversely, the velocity-selector argument
sheds no light on the real physics.

If you want to understand the real physics, formulate
it in terms of E, T dS, and things like that.