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.)
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).
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.
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.
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?
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817
Hugh Haskell said...
My understanding of "thermal energy" has always been the
random kinetic energy of the atoms in an object (or collection of
objects, like a gas or a liquid), measured relative to the center of
mass of the system. That would exclude an organized rotational motion
of the system as well as translational kinetic energy of the center
of mass. In other words, "thermal energy," pretty much corresponds to
the kT energy associated with the system.
Bob Zannelli said...
I noticed my post on this was ignored but Hugh here hits the nail on the
head. Thermal energy is, as I pointed out in my earlier post, defined as the
potential and kinetic energy associated with the RANDOM motions of atoms in
an object. Therefore the KE associated with the ball in flight or the ball
rotating would be excluded from being considered thermal energy.