Re: Entropy and states of matter

["John S. Denker" <jsd@MONMOUTH.COM>]

"Malot, Woody" wrote:
> I need to find a good way to explain that entropy increase is not violated
> when a material goes from a liquid or gas (disorder) to a solid (highly
> ordered).  Any ideas?  This years class does not seem to accept the normal
> explaniations that I have used in the past.

It sounds like you've got several problems all
bundled together.

1) You need to state the law 100% correctly before
deciding whether there is a violation.  Do not assume
that a small change in the wording produces small
violations;  it commonly produces huge, categorical
violations.

In this case I assume the law in question is the second
law of thermodynamics.  It states that entropy obeys
a local law of nondecrease.  Specifically, that means
that the entropy in a region X cannot decrease _except_
by entropy-flow across the boundary of region X.

For a precise definition of entropy, see
  http://www.monmouth.com/~jsd/physics/thermo-laws.htm
especially
  http://www.monmouth.com/~jsd/physics/thermo-laws.htm#sec-second-law
and for a discussion of what I mean by "flow", see
  http://www.monmouth.com/~jsd/physics/conservative-flow.htm

In particular, if the question is, does the entropy
of the H2O molecules decrease when water freezes, the
answer is yes!  The entropy decreases.  The entropy
of some adjacent object(s) simultaneously increases,
so the genuine law is upheld.

==============================

2) There needs to be some discussion of ground rules.
Physics questions are not settled by PbBA (Proof by Bold
Assertion).  Students are not allowed to boldly assert
that the second law is violated.  By the same token, the
teacher is not allowed to boldly assert that the second
law is upheld.  The question must be settled by the
methods of physics, namely a combination of experiments
and calculations.

=============================

3) This leads to the question, what are the appropriate
experiments?  Try this:

Freeze some reasonably-pure water.  Tap water will do.
Call this sample A.

Also freeze some water to which you have added enough
ethylene glycol so that the freeze/melt transition
is depressed significantly (but not so depressed that
you can't get it to freeze).  Call this sample B.

For definiteness, let's assume a 10C depression.
Arrange it so the two samples have the same mass, say
about 4 ounces in a 6-ounce styrofoam cup.  Stick
a small immersion heater in each cup, then freeze them.
Let's assume your freezer can get them to -15C.

Measure how much electrical heat it takes to get
each sample to -5C.  I predict it will take much,
much less heat to warm the pure ice, because it
won't melt.  We see that getting a water-based
sample warm is _not_ sufficient to get it to
melt;  if you want to melt it you need to supply
a lot of energy corresponding to the latent heat.

The same thing works in reverse, although it is
harder to measure.  If you put the two -5C samples
back in the freezer, the freezer will have to work
much harder to refreeze sample B than it will to
simply cool the still-unmelted sample A.

For the next level of detail, draw the curves
representing the temperature (for each sample)
as a function of added energy.  Colored chalk
may help here.

                          /
                         /
             /~~~~~~~~~~/
            /          /
           /----------/
          /
         /
        /

The heat capacity of the two solids is about
the same.  The heat capacity of the two liquids
is about the same.  The latent heat of melting
is about the same.  The big difference is that
the melting occurs at a different temperature.
The plateau corresponds to the physical process
of sucking the entropy out during freezing, and
dumping entropy in during melting.

It is nontrivial to accurately measure these curves,
because ice is a fairly poor heat conductor.  But
the students ought to accept that the experiment
could be done, and the result must come out pretty
much as shown.

The argument is incomplete at this point, because
we've been measuring the energy, not directly
measuring the entropy.  So we must show the
connection.

To repeat:  We agree that the entropy of the
H2O decreases when it freezes.  The only way
to allege a violation of the (correctly-stated)
second law would be to allege that this
decrease is not accompanied by a simultaneous
adjacent corresponding increase in the entropy
of something else (in this case, the refrigerator
mechanism).

  Note: Terminology:  I will speak of "a battery"
  as shorthand to represent any device that stores
  energy with very little entropy.

Nobody has ever built a refrigerator that simply
removes the energy from the H2O as it freezes
and stuffs the energy into a battery.  To freeze
water you need to extract a lot of entropy.
This requirement is in addition to the requirement
to exract energy.

There are imaginary machines that could freeze the
water allegedly without themselves suffering an
increase in entropy.  Maxwell demons for instance.
But every alleged machine in this category has been
shown to not work.  There are excellent theoretical
reasons to believe that no such machine can possibly
work.

If the students allege a violation of the second law,
the burden of proof is on the students to explain
how their demonic machine works.  It is very common
for students to overlook or miscalculate the amount
of entropy transferred to the refrigerator mechanism.

The second law makes many, many correct predictions.
To date, nobody has ever observed an incorrect
prediction.  Miscalculations don't count.