Re: Thermal Energy - thermalization of rotational energy

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Thu, 7 Mar 2002, Michael Edmiston wrote:

> At this point we have John saying bulk rotational energy
> cannot be thermalized without an outside interaction.  We have
> Bob saying it happens all the time and he invokes entropy
> arguments.

I don't think Bob and I really disagree.  It is ultimately a
semantic issue.  Bulk rotational energy can change.  It can
increase (as in stellar formation) and it can decrease (as in the
transition to a red giant phase or in a supernova.  Furthermore,
when it decreases, some of it *may* end up being converted to what
I would call thermal energy.  Nevertheless, I would still say that
*the* bulk rotational energy of a system cannot be thermalized
without external interactions since, to me, thermalization would
require that it fluctuate around some value that could be
identified as 3/2 kT as with any other thermalized mode of energy
storage involving three degrees of freedom.

> John's reminder that we can connect bulk rotational energy to
> angular momentum about the center of mass is agood one:
> rotational KE = L^2/2I.
>
> I guess I was thinking that thermalization would include
> transfer of bulk rotation about the center of mass into
> rotation of individual components. But if angular momentum is
> conserved (because of no outside interactions) then the total
> L^2/2I doesn't change.

Be careful; the angular momentum can't change, but the rotational
inertia certainly can.

> John is saying this with an equation and Hugh is saying it
> with words.  So I think both are convincing me that
> condensation of rotating matter into a solar system is not a
> thermalization process.

I'd basically agree with that.  More specifically, I'd say that
the condensation of a solar system involves an enormous loss of
gravitational potential energy with lots of it converted to a
still mechanical form (i.e., rotational energy) and at least some
of it converted into thermal form.

> So, is that the key here?  Thermalization is not just the transfer of
> macroscopic motion into microscopic motion... but also requires the
> microscopic motion be random?  If so, I can live with that, but I am not
> sure I was alone in viewing simple transfer from macroscopic to microscopic
> as a thermalization process.

Again I think it is to some extent a matter of semantics.  But on
another issue, I do have a problem with what seems to me to be a
far too casual use of the word "random" in this thread.  Even if
one had a very large ensemble of objects with "randomly" arranged
energies, I would *definitely* not be willing to characterize the
energy as "thermal" unless they had been interacting for a "long
enough" time and had reached "thermal equilibrium." In other
words, thermal energy should require a *very* specific kind of
"randomness"--a Boltzmann distribution.  Another way of saying the
same thing is to say that the energy content in *all* modes should
fluctuate in a way that is compatible with being characterized by
a *single* temperature.

> Wouldn't another criterion for something being "thermalized"
> be whether the process could be reversed?  Once angular
> momentum has distributed itself from the bulk rotation of the
> cloud to rotations of individual planets, can it go back to
> the bulk again?  I guess it can do that when the star goes
> supernova.

Going supernova will radically reduce the bulk rotational energy
at the same time that it radically increases the gravitational
potential energy.  I guess I'm not sure what happens to the
"thermal energy" in the process.  You might suspect that it would
increase, but it certainly isn't necessary.

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm