Re: KE & temperature

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

Regarding Chuck Britton's question:

> How does the concept of 'Zero Point' energy apply to this mean KE : T ratio?

The short answer is that it *doesn't* apply.

The proportionality between mean translational KE and T is predicated on:
A) *a classical system*, and B) a power law KE as a function of momentum.
When one considers 'Zero Point' energy one is looking in the extreme
quantum regime where A) is strongly violated. Quantum mechanice violates
the Equipartiion theorem.  At sufficiently low temperature the typical
particle energies become so low that quantum mechanics (and/or quantum
statistics) is necessary to properly describe the microscopic states. At
such temperatures the proportionality breaks down.  This is *another*
reason why it is dangerous to mentally think of mean KE as always being
measured by the absolute temperature.  It just so happens that the regime
of applicability of this proportionality is quite good for many useful
applications involving particles made of atoms and molecules.  BTW, for
electrons in metals *room temperature* is strongly in the low temperature
degenerate quantum regime since the relevant Fermi temperature for those
electrons is many thousands of kelvins.  Thus the mean translational
energy per electron is not proportional to the absolute temperature in
such solids.  The KE/T proportionality is strictly a *classical* effect.

> Specifically, Low Temperature quantum system such as the He isotopes
> have substantial motion that can not be removed by lowering the
> temperature.

True, and for such systems the value of T is not directly proportional
to the mean translational KE per particle.  The temperature dependence
is more complicated in these instances.

David Bowman
David_Bowman@georgetowncollege.edu