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

• From: John Denker <jsd@av8n.com>
• Date: Sat, 20 Jan 2018 16:07:51 -0700

On 01/20/2018 03:28 PM, Robert Cohen asked:

I am curious as to whether anyone can confirm the explanation given
in the Jan 2018 "Figuring Physics" solution provided in the Physics
Teacher:

http://aapt.scitation.org/doi/10.1119/1.5021443

Basically, the question is whether cooling would occur if molecules
of every speed in a liquid had an equal chance of escape from the
surface. The answer given in the column is no, with a rationale that
the cooling occurs because the faster ones are the ones that are
leaving and the slower ones are left behind.

The reason I ask is because I used to use somewhat similar logic but
stopped,

You're smart to be skeptical of this approach.

I stopped for two reasons. First, the "slow molecules left behind"
implies that the remaining liquid becomes cooler than the vapor that
is produced. Second, I feel it obscures the fact that the process of
leaving (which is a sort of bond breaking) requires an extraction of
energy from the surroundings, regardless of whether the molecules
involved were initially going faster or slower.

I reckon it's even worse than that.

1) First of all, there /aren't/ any such liquids, so
set. You can imagine the imaginary liquid to have any
properties you like.

2) Even if, very hypothetically, a liquid had a uniform
velocity distribution at time t=0, a picosecond later it
wouldn't. Very little evaporation would occur during
that interval.

3) The introductory course, insofar as it touches on
thermodynamics at all, focuses on /equilibrium/ thermo.
A hypothetical liquid with a uniform velocity distribution
would be so far from equilibrium that temperature would
be undefined and undefinable.

4) The usual high-school approach to thermo starts with
an ideal gas, consisting of a bunch of noninteracting
particles. Each particle has a well-defined speed, hence
a well-defined kinetic energy, and no other energy of any
kind.

Unfortunately, that picture doesn't work for solids or
liquids or even non-ideal gases. So the idea of framing
the issue in terms of "the" speed alone is dead on arrival.

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

I could go on, but you get the picture.
Don't waste your time on this.