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Re: Thermo explanation of gas filling its space



The entropy is a function of the number of available states, not just
energy levels.
The answer to your question is perhaps most easily seen for the classical
case, where the entropy is a function of the available phase space (which
quantum mechanics will quantize into countable states).
The phase space is (delta V)*(delta P), the product of available
coordinate space and available momentum space.
Expansion into a larger coordinate space will alone involve an entropy
increase.

Bob

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor

----- Original Message -----
From: "Dave Hamilton" <djhamil@TELEPORT.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Sunday, December 10, 2000 11:45 AM
Subject: Thermo explanation of gas filling its space


In my annual grapple with entropy (every year I teach AP physics, I
battle
this demon), I asked a question of a chemist who had explained that,
when
gases fill a larger volume, they have a larger number of available
energy
levels and therefore greater entropy. That prompted me to ask the
following:

I understand about the close-spacing of the translational/rotational
energy
levels and can see why the gaseous state allows many more energy
levels than
the liquid state. However, I fail to understand how the spreading of
the
gas molecules into a greater volume results in a greater number of
possible
energy levels.

Here is the reply:

It's a straightforward extension of the quantum mech analysis of the
energy
levels available to a particle in a box. A particle in a larger box
has
similar wave functions but they are closer together, thus,
energetically, they
are more accessible for molecules -- without any greater total energy
than
when they were in a smaller box.

This I know to be true qualitatively -- from reading and talking with
quant
mech guys.

But you, as a physicist, could help me (and yourself) by checking QM
texts or
physics QM people and telling me about some details of this "energy
levels of
particles in a small vs.a large box" case: First, I know and it is
common
knowledge that translational energy levels are so close together that
they
cannot be individually determined spectroscopically (the way other
energy
levels are quantitatively established -- rotational in the IR spectra,
and
vibrational there also (in the shorter IR), whereas excitational are
in the
visible and UV). But can those translational energy levels be
experimentally
detected "as a group", let's say, or some other packet? i.e., is there
experimental data to prove this "closer levels in large than small
box" QM
idea, or is it totally from calculations/theory?

Can anyone help out here?