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Re: Insulation/temp gradient



Brian wrote:
. . .
If you will forgive yet another electrical analogy, it is evidently
a comparable situation to a string of resistors in series.
. . .
Has our discussion about precision in language made analogies something
odious? Then we have lost something valuable. There is nothing to
apologize for. It would be a disservice to our students NOT to point
out such "analogies"; ie., cases where the same mathematical model is
commonly used to describe two or more different phenomena. The
mathematical models of thermal diffusion and electrical conduction in a
copper wire enjoy an exact isomorphism:

dQ/dt = k A (Delta T)/L and I = K A (Delta V)/L (K is the
electrical conductivity of copper.)

(This is surely not a purist's analogy - to compare dV and dT is not
quite respectable...) . . .
brian whatcott <inet@intellisys.net>
Altus OK

Why not respectable? It is the E field in the wire (whose average value
is Delta V/L) which "drives" the electrical current; it is a perfectly
good and highly useful analogy to compare this to the role of Delta T/L
in the conduction of heat (this noun is here a conscious violation of
something!). I would go even further and point out the electrical
resistance of the wire {L/(KA)} and its analogue in the heat conduction
equation.

Physics really has only a few basic mathematical models, and not many
more (maybe fewer) basic conceptual models. It is an important part of
our physics to realize that reality is something beyond all of these
models, and to notice that in our analyses one and the same mathematical
model may be paired with different conceptual models to describe
different phenomena. Part of our understanding is to notice, appreciate
and ponder (surely not disparage) the analogies that result.
--
Bob Sciamanda sciamanda@edinboro.edu
Dept of Physics sciamanda@worldnet.att.net
Edinboro Univ of PA http://www.edinboro.edu/~sciamanda/home.html
Edinboro, PA (814)838-7185