Heat energy, analogies, lecture demos

[William Beaty <billb@ESKIMO.COM>]

On Wed, 8 Sep 1999, Daniel L. MacIsaac wrote:

> Yay Bill: defy the thermal inquisition and be a martyr representing all we
> heat-loving dissidents on PHYS-L :^).  After this post I'll step back
> and toast some marshmallows over you  :^).  I'm behind you all the way.


The Voices tell me, "Joan, turn your leg over a bit, it's not quite done
on that side."    :)


> I also like to use the term heat (rather than say the the movement of the
> thermal energy gradient) to describe how energy can propogate along a
> conductor.  There is research on experts and chidren's understandings of
> thermal phenomena that led to the development of curricula addressing
> student difficulties with thermodynamic phenomena.  This curriculum (by
> Marcia Linn at UC Berkeley -- online at their CLP and KIE websites) uses
> the same approach preferred by mechanical engineers -- "HEAT"!
>
> Linn, M. C. & Songer, N. B. (1991).  Teaching thermodynamics to middle school
> students: What are appropriate cognitive demands?  Journal of Research in
> Science Teaching, 28(10), 885-918.

Excellent!

Here's one interesting aspect: suppose we have two pendulums.  Suppose we
set one of them to swinging.  Suppose both of them are mounted on a table,
and because the table moves very slightly, the swinging pendlum over time
swings a bit less and less, while the non-swinging pendulum swings more
and more.

This is an analogy for "Heat conduction".  The stored energy in the
swinging pendulum is analogous to the "Heat energy" trapped in a single
atom.  The moving table is analogous to both the infrared "photon"
component of heat transfer, and also the acoustic/mechanical "phonon"
component. (Perhaps we should mount magnets on the pendulum bobs, that way
the magnets could perform the "photon" transfer, while the wiggling table
would illustrate how "phonons" communicate heat between atoms.

If one swinging pendulum tried to move a thousand other non-swinging
pendula on the same table, or better still, if a thousand swinging
pendulua tried to move a thousand non-swinging pendula, then we would have
a much better analogy for the transfer of atomic-oscillatory "heat
energy."  Heat is "energy" in the same way that the trapped waves within
an RLC resonant circuit is "energy."  It is "energy" in the same way that
the raised orbital of the electron in an optically-pumped atom is
"energy."

Here's an analogy that people can actually demonstrate during a lecture.
Set up an air track with a number of carts.  Connect the carts together
with weak springs (use springs which are pre-stretched, so that they can
both compress and expand as needed.)  Turn on the air track, then slowly
move the end cart back and forth.  All the other carts respond.  This
demonstrates a normal sound wave, and a standing wave will be created as
the wave reflects from the impedance-mismatch of the end cart.

Now, damp out the wave and start again, but this time wiggle the end cart
as fast as you possibly can.  No "sound wave" will propagate.  Instead,
the adjacent cart will slowly start wiggling.  After awhile, the next one
will wiggle too.  The spread of "wiggling" occurs very slowly.  It vaguely
resembles sound waves, yet its propagation velocity is immensely slower.
It propagates by "diffusion" rather than by large, coherent waves.

It occurs because at high frequencies the wavelength is short, and if the
wavelength is short enough, each cart represents a resonator, and each
spring represents a mismatched impedance which prevents the energy within
the resonantor from spreading instantly to the neighboring carts.  If we
plot the propagation velocity of sound waves in the carts versus
frequency, the velocity is as you'd expect at the low frequencies.
However, at high frequencies the velocity starts dropping.  When the
wavelength of the sound approaches the spacing of the carts, the
propagation velocity goes to zero.  This illustrates that heat is sound!!!
"Heat" is "hypersound".

Well, its really not that simple, because when we're dealing with trapped
vibrations in atoms, the atoms can start ejecting photons rather than
simply causing their neighbors to vibrate.  As with the pendulums, we'd
have to mount some vertically-pointing magnets on the air-track carts in
order to supply an electromagnetic coupling between them.  When one cart
pushes/pulls on another via its spring, that is "phonon heat transfer".
When the magnets do the pushing/pulling, that's "photon heat transfer."



> So you're not alone in liking "heat", though you may be the advocate
> with the longest patience and fastest typing skills on PHYS-L these days.

Just spend years as a programmer, where you're paid to type!  (An office
worker job might be even better as training.)  The more I type, the faster
I get, and I fear that soon I'll hit a singularity, will counter all
possible arguments in zero duration, and my keyboard will entirely vanish
from normal spacetime.



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