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Re: thermal energy



Dan wrote: (in two different posts);
. . .
One context where this comes up is the equipartition theorem.
I don't want to write simply U = fNkT/2 (where f is the number
of degrees of freedom per particle), because most systems
also contain other energy, such as energies in chemical bonds
and rest energies of all the particles. So instead I write
U_thermal = fNkT/2, with the understanding that under a limited
range of conditions, the change in U is the same as the change
in U_thermal. . . .

My question for you, Leigh: How do you write the equipartition
theorem as an equation that can be applied to an entire physical
system (as opposed to a single abstract "degree of freedom")?


Then Leigh wrote:

I haven't a clue. Since the equipartition theorem applies to a model
with quadratic degrees of freedom I guess I would say that the system
internal energy has equal magnitude contributions associated with
each quadratic degree of freedom, together with the caveat that one
must be far from the temperature where quantum phenomena are
important.
There's still lots of room for other terms. Remember, I'm teaching a
course in astrophysics right now. We deal with stars. There are lots
of non-quadratic energy terms in a plasma.


Two related comments. I think that limiting the equipartition theorem to
quadratic degrees of freedom is rather err, well "limiting".

I think one can extend the theorem to other sorts of degrees of freedom, of
course it no longer would be kT/2 per degree of freedom, but would have to
be changed to kT/2 for the quadratic guys and #### for the degrees of
freedom of type A and $$$$ for the one's of type B, etc etc.

And for Dan't comment, aren't some of those internal chemical energy degrees
of freedom quadratic in nature and included in the equipartition theorem.
E.g. any chemical bond that is reasonably modeled as a Hooke's Law spring
and therefore having vibrational kinetic and potential energy degrees of
freedom?

Joel Rauber