Re: macroscopic vs microscopic degrees of freedom

[brian whatcott <inet@INTELLISYS.NET>]

At 07:16 10/31/99 -0800, John Mallinckrodt wrote:

> > In particular, consider the case of the ordinary block sliding on the
> > ordinary table, which is where I came into this thread.  The thermalization
> > timescale is fantastically short compared to the natural, conventional
> > timescale in the problem (i.e. the duration of the sliding motion).
>
> I believe I might say just the opposite.  The sliding ceases quite
> quickly. The internal energy of the block increases by some definite
> amount during that same period.  Then, over a substantially longer time
> period that depends on the size of the block and its thermal conductivity,
> that nonthermalized internal energy becomes thermalized internal energy in
> keeping with the second law.  (Of course, during that same time scale the
> block is likely to gain or lose internal energy through thermal exchanges
> with its surroundings.)..

> John Mallinckrodt

It's interesting to look at the historical basis of the description
 of the time rate of temperature change through solid materials.

This was due to the person who sometimes lectured Napoleon as a
mature student on mathematical analysis at the new Ecole Polytechnique,
 who had served as a Benedictine novice Monk for two years, who
carried on the role of State Governor (Prefect Departmentale), and
while in that position, won an academic prize offered by a blue-ribbon
 panel of mathematicians: Laplace, Lagrange, & Legendre no less.
(Hard to visualize such a coup these days...)

 I refer of course to Baron Fourier, son of a poor tailor; developer
of the two dimensional boundary equation.

His propensity for working with the prevailing power structure, what
one might call a Vichysoise tendency was his undoing on Napoleon's
 return from Elba. He was however restored with the help of another
former pupil to the directorship of the Bureau of Statistics, where
he remained in an overheated overclothed environment for the rest
of his life.

It is no fun when you needs must begin by developing a temperature
scale:
0 = melting ice:   1 = boiling water at a given pressure as an
alternative to referring to an octogesimal degree [degree Reaumer]

He discussed this -
du/dt = k [d^2u/dx^2 + d^2u/dy^2]
for u = temp t at point x,y of a plane, and k is a characteristic
 constant of the material called diffusivity.

For one dimensional 'heat flow' he developed the series in sin and
 cosin we call the Fourier series.
[...also previously used by Euler and others]

His descriptions feature heat flows which don't necessarily suit the
modern ear. He talks of heat as measured by temperature, as far
 as I can see. What an engineer might call sensible heat.

He seems to share none of John M's scuples about the thermalization
of internal energy - like an engineer he seems to talk more in terms
of heating, indicated by a temperature rise.


References:
Theorie Analytique de la Chaleur (Theory of Heat) 1822
J Fourier
Enc Brit 15th Ed 7-577 "Fourier, Jean-Baptiste-Joseph, Baron"

Respectfully



brian whatcott <inet@intellisys.net>
Altus OK