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Re: Thermo explanation of gas filling its space



At 08:45 AM 12/10/00 -0800, Dave Hamilton wrote:
when gases fill a larger volume, they have a larger number of available
energy levels and therefore greater entropy.

That statement reflects an important truth, which we will discuss in a
moment, but first we should fend off some quibbles.

Quibble #1: It is sloppy to speak of counting "energy levels". We should
count _states_. If there are two states with the same energy, they both count.

Quibble #2: We have an OTBE problem. We need to know what Other Things
are Being held Equal during the expansion.
-- It is certainly possible to take 1 liter of gas and expand it to 2
liters in such a way that there is no significant increase of entropy. In
this case there is a one-to-one correspondence between old states and new
states, and a one-to-one correspondence in the occupation thereof.
-- There also exist several different ways of letting 1 liter expand
into 2 liters in such a way that the entropy increases. The question seems
to tacitly assume isothermal expansion, but this is certainly not the
general case or the only case of interest.


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

> A particle in a larger box has similar wave functions

Yes.

> but they are closer together, ...

Closer in energy, that is. That's correct. That's the key idea.

> ... thus, energetically, they are more accessible for molecules

That's true if we assume isothermal expansion or something like that.

If in contrast we assume isentropic expansion, the gas cools during
expansion and the higher-numbered states are not more accessible.

> translational energy levels are so close together that they
> cannot be individually determined spectroscopically

I suppose that's true, for typical-sized boxes and typical spectrometers.

> is there
> experimental data to prove this "closer levels in large than small box" QM
> idea, or is it totally from calculations/theory?

That's an odd question, because there is essentially nothing in physics
that is "totally from calculations/theory". Essentially everything is
connected to experimental data by some chain of calculations. Sometimes
the chain is longer or shorter. I will assume that the question is asking
for an experiment that supports this result with a relatively short chain.

The first thing that comes to mind is the work on "quantum dots". You can
fabricate metal dots that serve as small boxes to confine electrons. The
particle-in-a-box states for these electrons are sufficiently widely spaced
to be directly accessible by spectroscopic techniques.
http://www.phy.duke.edu/~rps/coll99/tinkham.html
http://chemphys.colorado.edu/www/research/research.html#nanotech

One might also cite Davisson and Germer.
http://www.nobel.se/physics/laureates/1937/davisson-bio.html

Innumerable other experiments could also be cited, with some degree of
connection to this result. Once you accept QM, i.e. a wave-mechanical
description of matter, then all sorts of connections can be seen. For
instance, imagine isentropic expansion of 1 liter of photons. The correct
result follows from the Doppler shift from the moving piston. Therefore
every cop's radar gun is an experiment supporting this result.