Re: Thermal Energy

[Bernard Cleyet <anngeorg@PACBELL.NET>]

"... is it (rot. KE) the only example of the property (energetic) of a
body invariant, but not = 1/2 * kT / dof?"

I meant a single body.

bc

P.s. Much of this discussion is "theory",  as  eventually all the described will "thermalize."  So one must just say the relaxation time is very long compared to the commonly thought "thermal" relaxation.  I do acknowledge and thank JM for pointing out his meaning of rot. KE being "internal energy."
 
 
 

John Mallinckrodt wrote:

On Tue, 5 Mar 2002, Bernard Cleyet wrote:

> OK!   Is it (rot. KE) the only example of the property (energetic) of a
> body invariant, but not = 1/2 * kT / dof?

Translated into English, I think I understand the question to be,
"Is rotational KE the only example of an invariant system energy
that is not determined by 1/2 kT per degree of freedom?"

Not at all.  JUST for example, consider a system consisting of 100
macroscopic bodies constrained to slide along a linear bar with
each body connected to its neigbors by identical springs as
indicated below.
     _      _      _      _           _      _
  --|_|vvvv|_|vvvv|_|vvvv|_|vv ... vv|_|vvvv|_|--

This object can rotate; it can vibrate linearly in 99 modes that
involve the springs; it can vibrate torsionally in another 99
modes that involve the springs; it can vibrate in something like
10^23 modes (give or take many orders of magnitude) that do NOT
involve the springs at all (i.e., each individual macroscopic body
has its own individual vibration modes.)

The rotational modes and the 198 spring-involving vibrational
modes can easily be populated with energy in excess of 1/2 kT.
In fact, some number of the NON spring-involving vibrational modes
can probably also be populated with energy in excess of 1/2 kT.
(For instance, let the 100 macroscopic bodies be "bells.")  All of
these qualify very well as internal energy in the sense that the
total energy in all of these modes is invariant with respect to
the choice of reference frame.

Rotational KE is somewhat unique in the following sense: Barring
external interactions the angular momentum of the system will be
conserved and it will not be possible to thermalize the rotational
energy.  In this regard, it is more like translational KE which is
subject to the dictates of linear momentum conservation.  On the
other hand, no external interactions are required to thermalize
the vibrational modes.

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