Re: Thermal Energy

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 19:49 -0800 3/6/02, John Mallinckrodt wrote:
> Consider the following two systems:
>
> 1. Two identical particles attached at the ends of a spring and
> oscillating linearly.
>
> 2. To identical disks sharing the same axis, joined by a coil
> spring, and oscillating angularly.
>
> There is no contribution to motion of the CM and no contribution
> to the net angular momentum of the system in either case.  So do
> these oscillations represent thermal energy?

Neither of these examples represent random motion, so I would say,
no. But if they were part of a very large number of similar systems,
say a bunch of molecules in a gas, then this motion could be part of
the thermal energy, since some would be oscillating in one plane or
line, others in other planes, and at different amplitudes, etc. In
other words, their motion would be part of a random ensemble of
objects and hence their energy would be part of the total thermal
energy of the ensemble.

> If you try to exclude these two situations by adding simple
> vibrations to the list, I'll suggest you consider a bell which has
> a large number of relatively low frequency relatively simple
> vibration modes and an increasing density of increasingly complex
> vibration modes at progressively higher frequencies.  When first
> struck, the bell oscillates with a *lot* of energy in the low
> frequency modes and less and less energy in the higher and higher
> frequency modes.  Will you consider all of this to be thermal
> energy?  If not, where do you draw the line?

I don't think so. I realize that one can always create borderline
situations where it isn't clear which camp a system should be
considered, but I have always looked at the "thermal energy" thing as
that energy which does not contribute to the gross motion of the
system, in other words, translation of the center of mass or rotation
of the entire system about the center of mass. And further more, it
must be random energy of an ensemble of objects that make up the
system. Tempertaure of a system can be taken as a measure of this
random energy (and yes, I know temperature and energy are not the
same thing, but they are certainly related concepts)

When the random energy of a system is converted to translational
energy, the temperature drops, as when a CO-2 fire extinguisher is
fired. In that case, the random (mostly) kinetic energy of the gas in
the cylinder becomes at least in part the directed kinetic energy of
the stream of high velocity gas coming from the nozzle, at a much
lower temperature than the gas in the tank. But since there is still
a random component to the gas even in the stream from the nozzle, the
temperature is only reduced by some amount less than that associated
with the minimum possible energy state of the system (i.e., not to
absolute zero).
> I mention all of this only to show that "thermal energy" is a
> tricky if, I do believe, still useful concept.
If we try hard enough, we can make any concept "tricky." I rather
think that's what we have done with this thread. What started out as
a simple conceptual question, that might have been answered wrong by
the book in which it was asked, has become, what seems to me a major
exercise in obfuscation.

Sometimes, it doesn't pay to read more into a statement than was
originally intended. I'm reminded of those cartoons showing how a
simple request, like making a swing out of a truck tire hanging from
a rope tied to a tree branch, becomes an impossibly complex project
when visualized by various technical organizations. Or a request for
a package of Lifesavers candy turns into a requisition for every
conceivable type of high-tech rescue equipment as it moves through
the procurement chain.

I suspect the original poser of this question has, if he is still
paying any attention to the thread, learned far more about the
subject than he ever wanted to.

Hugh
--

Hugh Haskell
<mailto://haskell@ncssm.edu>
<mailto://hhaskell@mindspring.com>

(919) 467-7610

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