Re: Entropy confusion, please help!

Uno Lapideus wrote:

Trying to explain entropy to kids, I find that I need some help with
understanding the concept...

You and me, both. Entropy can be thought of as either "energy not available for useful work", or "a measure of information/randomness", and probably a few other things.


The second law of thermodynamics is
usually stated as "Heat (energy) flows from higher temperature
objects to lower temperature objects, until thermal equilibrium is
reached" (please correct me if I'm wrong here...), sometimes as
"in a closed system, entropy (a measure of disorder) will always
increase" and sometimes as "natural processes cause things to move
from improbable and unstable orderly states (less entropy) to probable
and stable disorderly states (more entropy)."

So far, so good. Entropy is related to the flow of heat via the second law of thermodynamics. When you speak of "probable" and "disorderly" states, you are no longer talking about thermodynamics, but statistical mechanics, the foundation of thermodynamics. And statistical things (like the state of a system) are subject to fluctuations, and so it is possible that some fluctuations will decrease the entropy. The two pictures are not contradictory- in terms of statistical mechanics, there may be short times when heat flows from the cold object to the hot object. With a probability similar to that of a broken egg spontaneously re-assembling.

Now, for example, is not ice (water crystals) a "stable and
ordered" form, liquid water a a more random form, and steam the most
chaotic form, of H2O molecule "order"? I also remember reading
somewhere that "entropy is zero in an object that has no thermal
motion, such as a fictitious crystal at 0 K"...
This is where I find confusion: Since heat indeed flows from hotter to
colder objects , it seems to me that, at least in the water example,
entropy goes from higher to lower... And if "absolute zero" is
where we find the highest form of order (zero entropy), isn't
universal entropy running from maximum disorder (big bang, with its
very high temperature) towards minimum disorder (the absolute zero
"heat death" of a completely "run dowm" Universe)?

I see the source of your confusion- the entropy of a system depends on a lot more than just the temperature. The entropy of a crystal is indeed lower than that of a fluid, but that's partially due to the difference in temperature, and partially due to the volume available to each particle, and partially due to the freedom each particle has to move- I can exchange two particles in a fluid and you would never know, but if I change particles around in a crystal (like a binary alloy, or a spin lattice), I need to be more careful. In terms of statistical mechanics, the entropy is related to the number of (un-measurable) 'microstates' which all give the same (measureable) 'macrostate'.

A uniform vapor has a high entropy because the macrostate (a volume of vapor) corresponds to an untold number of microstates (specifying the position and velocity of each particle in the vapor), not because it is 'hot'.

Does that help?

--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
.

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