Re: Ludwig Boltzmann, entropy

B Richardson <brich@xxxxxxxxxxxx> wrote:

>A snippet from Boltzmann at the website

>http://www.entropylaw.com/entropydisorder.html

><quote>
>As a consequence, a dynamically ordered state, one with molecules
>moving "at the same speed and in the same direction," Boltzmann
>(1974/1886, p. 20) asserted, is thus "the most improbable case
>conceivable...an infinitely improbable configuration of energy."
>Because this idea works for certain near equilibrium systems such
>as gases in boxes, and because science until recently was dominated
>by near equilibrium thinking, Boltzmann's attempted reduction of the
>second law to a law of disorder became widely accepted as the second
>law rather than simply an hypothesis about the second law, and one
>that we now know fails.
></quote>

>A flowing river. I know that the molecules aren't going in the
>exact same direction like photons in a laser beam, but the average
>direction vector is downstream and all the molecules are going
>there sometime soon. And wind blowing also. In both of those cases
>I would expect a subset of possible microstates (those with direction
>vectors going downstream or downwind) to be more probable that others
>and not tend toward a maximum. Are these examples where Boltzmann's
>hypothesis fails?

>Also, I believe that determining the number of possible microstates
>was not achievable in Boltzmann's lifetime, and he really had no
>idea how enormous the number would be for any temperatures
>greater than absolute zero.

>Anybody worked out the history of the "entropy = disorder" idea?

I hardly know where to begin.

The site you refer to above is the creation of Rob Swenson of
the Center for the Ecological Study of Perception and Action
University of Connecticut.

I did a quick read of the site. He's got a point of view
which isn't quite right, but not totally wrong either.

Here's the problem. Thermodynamics of the sort we normally
deal with is called "equilibrium" thermodynamics. What
Swenson is talking about is a perfectly valid field called
"non-equilibrium" thermodynamics. The first deals with
time-independent phenomenon, the second with time-dependent
phenomenon.

In non-equilibrium thermodynamics we deal with the production
of entropy per second, per hour, or whatever is a useful unit.
But in equilibrium thermodynamics there is no time. We consider
the transaction *after* it is finished. Hence we talk about
definite quantities of entropy.

The Boltzmann definition of entropy is quite OK for equilibrium
thermodynamics. But one must be careful as he used "ordered"
and "disordered" in a special sense -- essentially equivalent
to improbable and probable.

For instance, if all the molecules in the air in a room
were somehow placed in one corner and then let go, we'd
*never* expect them to ever all be in the same corner again.
(At least we'd certainly not hold our breath.)

In this sense Boltzmann noted that natural processes go
from situations that are less probable to ones that are
more probable. We do not observe the reverse in the
macroscopic world.

This is exactly equivalent to the observation that heat
goes from hot objects to cold objects spontaneously, but
NEVER goes in the reverse direction spontaneously.

(The equivalence isn't obvious, but is in fact true.)

Now your quite legal objection to Boltzmann's example
stems from a misunderstanding. In thermodynamics we
deal with systems at rest. That is, if the system is
moving, we move along with it. So in thermodynamics
we don't deal with flowing water, only with a body
of water that is stationary.

The reason for this is simple. Consider the energy.
Thermo deals with energy a lot. Actually it deals
with what is called the "internal energy" and not
simply the energy.

Why? Because any system has two types of energy. One
is the energy *inside* the system, the other is the
energy the system might have as a whole due to its
motion or what have you.

For instance my computer is stationary on my desk right
now. But in fact it is moving at a speed of roughly
a thousand miles an hour as the earth rotates. When
I talk about the energy in the computer I'm not interested
in the energy due to the earth's rotation.

I hope this has helped. If not, please ask more questions.

----- Paul J. Gans

.

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