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

[Robert Cohen <Robert.Cohen@po-box.esu.edu>]

Let me see if I can take a stab at this.

I'll start with the simple situation of a gas in a one-dimensional container (so the particles only travel along that one dimension),
made up of particles of identical speeds under no attraction and totally elastic collisions.   That way the speeds remain identical.

I then add a small attraction so that if I remove the "top" of the container, the fluid doesn't necessarily spit out the top.  This can
then be considered a liquid.  The speeds won't always be identical at any given time but on average they are.

At any given time, only the particle at the top is exposed to the vacuum above and thus only that particle can "leave" the liquid
state and fly away as a free particle.  That particular particle need not be the "fastest" of them all, does it?  Does it even need
to be going faster than the "average" of them in order to leave?

I'd argue it doesn't.  It just needs to be going fast enough to overcome the attraction.  And, while undergoing the escape process,
it slows down AND the particle it was attracted to slows down.  This leads to a cooling of both, independent of whether it was
initially going faster than those it "left behind" or not.

In other words, the real physics is on the cooling that results from the "breaking" of the bonds (so to speak).  Focusing on the
speed of those left behind (what JD calls "cancelling the sixes") allows students to ignore the real physics.

________________________________________
From: Phys-l [phys-l-bounces@mail.phys-l.org] on behalf of John Denker via Phys-l [phys-l@mail.phys-l.org]
Sent: Monday, January 22, 2018 7:16 PM
To: Phys-L@Phys-L.org
Cc: John Denker
Subject: Re: [Phys-L] Figuring Physics solution Jan 2018

On 01/22/2018 03:03 PM, Jeffrey Schnick wrote:

> Why are you writing about a uniform-velocity gas?

Velocity is a typo.  I should have said speed.  My bad.

As for the rest, I was trying to be as charitable as
possible to Hewitt.  In computer science there is a
class of problems called NP-complete that are (probably!)
rather hard.  Hewitt's question belongs to a class I
call ESP-complete, because the only way to begin to
answer it is to read the mind of the person who asked
it.

> Hewitt didn't say anything about a uniform-velocity gas or liquid in
> the question under discussion.

Not in the "question" strictly speaking ... but his
proffered /answer/ makes it clear that he imagined
the escape probability to depend on speed, perhaps
normally, perhaps always.

It wouldn't be fair to students to expect them to start
from Hewitt's answer and work backwards, but it's more
than fair to Hewitt.

Even /with/ the answer I find it impossible to make
sense of the question, even under the most charitable
assumptions.

In particular, he seems to think his liquid can evaporate
with no latent heat, so calling it a liquid instead of a
dense gas seems to be a distinction without a difference.

==

I did not previously publicly discuss the interpretation
that says the hypothetical liquid has a wide range of
speeds, but all speeds evaporate equally.  So here goes.
This doesn't make any sense either.  You could go in
there with a siphon and remove a parcel of liquid, with
the original liquid speed-distribution, and this would
leave the temperature unchanged ... but we call that
siphoning, not evaporation.  At some point you have to
convert that parcel from liquid to vapor, which involves
the latent heat somehow.  So either something cools, or
you provide heat from outside, or ... I give up.  It
was meant to be a simple question, and nobody has yet
suggested anything resembling a simple-yet-correct
interpretation.

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

If anybody can come up with a set of assumptions that
allow the question to be mapped onto real physics,
without contradictions or gross complexity, please
speak up.
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