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Re: CONSERVATION OF ENERGY



Well done! In considering one aspect of the problem I overlooked some others.
I guess this is what makes Physics hard, but also interesting. It doesn't
yield well to be tied up in neat little packages. New considerations keep
croping up. An earlier post referred to physics as lies. Not quite the
right conotation but it does emphasize the danger in thinking that one has
given the "right" answer.

On Sat, 12 Jul 1997 23:10:43 EDT David Bowman said:
David Dockstader wrote:
<SNIP> .... However, as Al
Clark suggests, the experiment can be refined to the point where "almost
all" the energy goes into an increase of ave KE.

Not unless the plate and block are turned into ideal gases. The plate and
block are *solids*. As such the molecules are subject to nearly linear
restoring forces for displacements away from their equilibrium positions in
the lattice. This means that as long as the temperature is significantly
higher than the Debye temperature and significantly lower than the melting
point (such as at room temperature for steel), then the Dulong-Petit law
holds as a consequence of the equipartition theorem applied to the
intermolecular potential energies. Thus, just as much energy goes into the
potential energy between the particles as goes into the their kinetic
energies. Also since the plate and block happen to be metallic then a
non-trivial fraction of the energy goes into exciting more electron-hole
pairs near the Fermi energy in the conduction band as well. Since these
electron-hole pairs behave as quantum particles (because the temperature is
*much* colder than the Fermi temperature) one cannot separate their energies
into separate well-defined kinetic and potential energy contributions (since
the kinetic energy of a quantum particle does not commute with its potential
energy), although the expectations of these operators *is* well-defined in
thermal equilibrium. Still, it is best to just consider the composite
particle energies (kinetic + potential) as given by the detailed dispersion
relation for the conduction band near the Fermi energy defined by the lattice
electronic periodic pseudo-potential, as well as any other correlation energy
due to inter-electronic interactions.

David Bowman
dbowman@gtc.georgetown.ky.us