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In my annual grapple with entropy (every year I teach AP physics, Ibattle
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 availableenergy
levels and therefore greater entropy. That prompted me to ask theenergy
following:
I understand about the close-spacing of the translational/rotational
levels thanlevels and can see why the gaseous state allows many more energy
thethe liquid state. However, I fail to understand how the spreading of
possiblegas molecules into a greater volume results in a greater number of
energyenergy levels.
Here is the reply:
It's a straightforward extension of the quantum mech analysis of the
haslevels available to a particle in a box. A particle in a larger box
energetically, theysimilar wave functions but they are closer together, thus,
thanare more accessible for molecules -- without any greater total energy
quantwhen they were in a smaller box.
This I know to be true qualitatively -- from reading and talking with
texts ormech guys.
But you, as a physicist, could help me (and yourself) by checking QM
levels ofphysics QM people and telling me about some details of this "energy
commonparticles in a small vs.a large box" case: First, I know and it is
theyknowledge that translational energy levels are so close together that
energycannot be individually determined spectroscopically (the way other
andlevels are quantitatively established -- rotational in the IR spectra,
in thevibrational there also (in the shorter IR), whereas excitational are
experimentallyvisible and UV). But can those translational energy levels be
box" QMdetected "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
idea, or is it totally from calculations/theory?
Can anyone help out here?