Re: macroscopic vs microscopic degrees of freedom

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Sun, 31 Oct 1999, John Denker wrote:

> ... In many cases of interest, a qualitative separation of timescales
> suffices.  Quantifying the timescale is unnecessary.
>
> 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.)

But I have room for and understand the utility of other viewpoints.  I
understand that you might simply be saying that the frictionally induced
internal energy is rapidly thermalized in situ creating a "hot" region
along the bottom of the block with a reasonably well defined temerature
that is different from the temperature in the rest of the block.  It is
quite possible to specify reasonable temperatures for different parts of a
large enough system because thermalization itself takes place on time
scales that depend on the size of the region you are talking about.

> In a finite pond, if the water is macroscopically stationary before
> paddling and also macroscopically stationary afterward, after the eddies
> have died out, then I can paddle for hours with no effect other than
> heating the water.  On my specified timescale, paddling has done no
> mechanical work at all on the water.  No work.  Just heat.

I understand your viewpoint.  I don't particularly like it because it
seems to me to confuse "macroscopic forms of internal energy" with "work"
and "microscopic forms of internal energy" with "heat."  Furthermore, I
believe that "most physicists" would agree with me.  However, I take no
comfort from that fact if true and I suffer no embarrassment if it turns
out that I am wrong.  I don't care how many people do it your way or my
way.  We can both do physics as long as we don't make mistakes.

> The distinction between work and heat rests on the notion of entropy.

And I would say that it depends on the notion of "thermalized" versus
"nonthermalized" internal energy.

> ... in a typical canoeing situation, you don't have a ghost of a chance
> of harvesting the eddy-energy before it is thermalized.
>
> Even on moderately-short timescales (before the eddies have fully
> thermalized) I would be pretty uncomfortable calling the eddies "work".

Here we agree, though perhaps for different reasons.  The conventional
definition of work is a mechanical *transfer* of energy.  I would call the
eddies mechanical or nonthermalized forms of internal energy.

> ...  I am also uncomfortable calling them "heat" on this timescale.

And again we agree, again perhaps for different reasons.  The conventional
definition of heat is a thermal *transfer* of energy.

> Perhaps we need a third term.  I might go for the term "dissipated
> energy" which includes out-and-out heat plus eddies that are destined to
> turn into heat.

And I like "internal energy," but to each his or her own.

> James Prescott Joule operated his paddle-wheel and called the long-term
> result heat.  Lots of other people do the same.

Perhaps.  I don't really care.

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm