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

[John Denker <jsd@av8n.com>]

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
Hewitt's question is asking about properties of the null
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.