Thermo explanation of gas filling its space

[Dave Hamilton <djhamil@TELEPORT.COM>]

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?