Re: Thermal Energy

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 12:18 -0500 03/06/2002, Michael Edmiston wrote:
> I am confused by Hugh Haskell's message and the followup by Bob Zanelli.
>
> Hugh uses the the words "random kinetic energy" and also the words "relative
> to the center of mass."  I am not clear whether he is saying these are the
> same.  (I believe they are not.)

By random kinetic energy, I meant to exclude any "organized motion"
such as rotational motion on a macroscopic scale (flywheel, e.g.) or
translation of the center of mass. Since rotation can occur even in
the c of m reference frame, it was my intention to exclude that
motion from the thermal energy of the system. But there is random
rotational motion, just like there is random translational motion,
and the random rotational motion should be included in the thermal
energy of the system. It seems to me that the reasonable criteria
are: any energy associated with the translation of the center of mass
and any net angular momentum (that is gross translation of the
system) should be excluded from the thermal energy. only that
translational motion which is truly random (that is, does not
contribute to any motion of the center of mass), and rotational
motion which is truly random (that is, does not contribute to the net
angular momentum of the system) should be considered when figuring
thermal energy.

> Bob picks up on this and says (and I paraphrase) if we only count the random
> motions as thermal, then the KE of rotation of the entire body is excluded
> from the thermal energy.
>
> I say... If we calculate the KE of each atom from each atom's velocity
> relative to the center of mass, and then we add all these energies, our
> result will not be the "random kinetic energy."  This result will be the
> random energy plus the energy of the "organized rotational motion" (as Hugh
> called it).

Agreed.

> This means, as I pointed out in my first post, we cannot use the definition
> that thermal energy is "the sum of the energies of the individual atoms
> relative to the center of mass" even though I am aware some people do this.

Also agreed. If I said this, I was in error. I intended to use the
phrase as you have stated it here.

> If we had a nice way to describe/calculate the "organized rotational motion"
> then we could say the thermal energy is... (KE relative to cm) minus (KE
> associated with organized rotation).  But it seems to me it is not clear how
> to pull off this separation for rotation (of random versus organized) like
> we do for translation.

If we add the angular momenta of each atom in the system and the
result is not zero, then the system is rotating about its center of
mass. The amount of the measured total kinetic energy of the system
associated with that angular momentum must be excluded from the
definition of thermal energy.

> For identifying external-translational-KE we identify an external inertial
> referance frame, and the ext-trans-KE is calculated by measuring velocities
> relative to that.  But the reference frame for organized rotational motion
> is the same as the reference frame for random motions... so what sort of
> operational definition do we use to separate these?

As I see it, we have to look at the total angular momentum of the
system as seen from the center of mass. If it is different from zero,
then the system is rotating and the energy associated with that
rotation is not thermal, i.e., that part of the rotational kinetic
energy is not random.

So how do we determine if our system is rotating? Good question. If
we sit at the center of mass and look out at the "fixed stars" and
note that they are moving across the sky relative to reference marks
within our system, then either we (the observer) are rotating, or our
system is rotating, relative to the "fixed stars." Of course, this
method breaks down for very slow rotations--ones comparable to the
any real rotation rate of the fixed stars. But I suspect that is a
pretty small class of rotations so we won't make too big a mistake by
ignoring them. If we want to determine if we are rotating, I guess
we'll have to assume we have some spatial extension so we can detect
some centrifugal forces within ourselves. Otherwise, I have no idea
how we would decide whether it was us or they system that was really
rotating.

It seems to me that we have taken a rather simple question and made
something really complicated out of it.

If I recall the original question, it was something like, "is the
internal energy of a golf ball different when it is sitting on the
ground than it would be when the ball is flying through the air?"

It seems to me that the answer is no, unless it got to be flying
through the air by being struck by a club or fired from a gun, or
something like that that could have agitated the atoms within the
ball and thus raised its temperature.

If the book's answer to the question was yes, then I would assume
that they wanted us to consider the translational and/or rotational
KE of the ball *as a system* as part of its internal energy, and that
seems to me to be contrary to all of our conventions on how we
account for energy. In other words, the book would be wrong.

I don't think we have to be too concerned about how we determine if
the ball is rotating or not. While measuring its spin may be a bit
difficult in practice, I have no difficulty visualizing it.

Hugh

--

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

(919) 467-7610

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