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

[John Denker <jsd@av8n.com>]

On 01/22/2018 09:26 AM, Paul Nord wrote:

> It seems that the physics concept Hewitt is trying to show is simply that
> 'liquids cool by evaporation because the faster molecules leave the
> surface.'  That concept seems fundamentally sound.

That's a common misconception, but it is fundamentally
wrong.  The fact that it violates the first law of
thermodynamics (i.e. conservation of energy) should
make you suspicious, as Robert Cohen pointed out.

I am reminded of the guy who calculated

	 16     1
	---- = ---
	 64     4

and explained it by "canceling the sixes".  Even if
the numerical result is correct, the explanation is
not reliable nor portable nor in any way useful.

Hewitt's hypothetical gas does not exist, but if it
did, it would start out at absolute zero temperature,
since it occupies zero volume in phase space.  So for
this reason alone, it cannot cool when it evaporates.

  Actually zero volume violates the Heisenberg
  uncertainty principle, so that's yet another
  fundamentally unsound aspect of the setup.

A zero-temperature gas would almost certainly warm up
immediately, if you so much as looked at it, for reasons
unrelated to Hewitt's velocity-selector argument.

Hewitt seems to be using low-level reasoning by analogy,
treating the liquid as a very peculiar high-density gas
rather than as a real liquid ... and the argument is
still wrong even then!

Let me spell it out:  Suppose we have a high-density
ideal gas sitting in a container.  The top of the
container is open, but the gas is mostly confined,
with the help of a strong gravitational field.  The
earth's atmosphere is sorta like this, except that
in our example the gas is very near equilibrium and
therefore isothermal.

        |       .
        |       .
        |   B   .  --escape-->
        |       .
        |       |
        |       |
        |   A   |     Z
        |       |
        |       |
        |_______|_______________________


If you find a high-energy molecule in region A, it
might be able to climb up the gravitational potential
and get to region B, from whence it can escape via
the porous wall and accumulate in region Z.

The key idea is that if the B-walls are only very
slightly porous, the gas in region B is at the
same temperature as in region A!  Think about this.
Perhaps the most fundamental result in thermodynamics
is that if two subsystems can exchange energy, then
equilibrium is isothermal.  If you don't agree with
this, there is no point in discussing anything else.
This details of why this must be so are discussed in
any decent treatment of the subject.  Moore&Schroeder
have a lovely diagram.  Feynman also has a nice discussion.
  http://physics.weber.edu/schroeder/statmech.pdf
  https://www.av8n.com/physics/thermo/temperature-ds-de.html

This is *not* expansion against a piston.  It is
essentially free expansion of an ideal gas.  The
expansion must be isothermal.  The fact that the
molecules we identified as "fast" in region A
are the ones that are escaping does not change
the conclusion, because by the time they get to
region B they aren't fast any more.

If you are familiar with Joule-Thompson expansion,
we can arrive at the same result using fewer words,
because the whole apparatus, including the porous
walls, can be considered a J-T expansion ... and
the J-T inversion temperature of an ideal gas is
zero.  No cooling occurs.

  By way of contrast, if the ideal gas expanded by
  doing work against a piston, then it would cool.

Without the piston, the expansion has to be isothermal;
otherwise it would not conserve energy.

We conclude that selective departure of the "fast"
molecules is neither necessary nor sufficient to
explain cooling by evaporation.

Hewitt's alleged explanation doesn't work for a high-density
ideal gas, and it doesn't work for sublimation from a
solid, so let's not pretend it works for ordinary liquids.

> We might like to add a few caveats about surface tension, energy
> distribution, and equilibrium.  But isn't it basically true that if such a
> strange liquid existed, it wouldn't cool by evaporation?

The zero-temperature liquid would not cool, but please
let's not explain it by "canceling the sixes".

Hewitt's oeuvre is a rich source of misconceptions that
you might not find elsewhere,
  https://www.av8n.com/physics/hewitt.htm
and the uniform-velocity gas appears to be original.

However, the underlying velocity-selector misconception
is not original with him.  A friend of mine, back before
he won his Nobel Prize, once used this argument in an
informal setting.  Somebody (not me) called him on it,
and to his credit he didn't argue the point.  It took
him about a femtosecond to figure out the correct physics,
and to restate the point he wanted to make in correct
terms.