[Phys-L] irreversibility and entropy versus energy

[John Denker <jsd@av8n.com>]

On 02/08/2014 07:25 AM, Paul Lulai wrote:
> Do you mean it is more useful to say entropy for a reversible cycle
> (a, b, c, d) is constant at identical points/states in the  cycle?

That's true ... but it's only the tippiest tip of the iceberg.

> This is the direction I am trying to go (just recently trying to
> emphasize this point). I am curious about other aapproaches.

Let's start simple.  Perhaps the simplest and most basic
physics idea is the idea that balls roll downhill.   This
is usually explained in terms of energy.

The problem is, the real physics is otherwise:  In the absence
of friction, if you start the ball at the top of the hill, it
will roll down into the valley, keep going, and roll *up* the
hill on the other side, and so on forever.

If you want it to roll down and *stay* down, you need friction.
You need dissipation.  You need entropy.

If we look more closely at this situation, we can ask about
equilibrium and stability.  The obvious answer is for the
ball to be at rest at the bottom of the valley, but at any
finite temperature that is not the right answer, due to
thermal fluctuations.

Thermal fluctuations may not be super-important for large
physical objects at ordinary temperatures, so this issue
is typically neglected during the first weeks of the
introductory physics class.  OTOH if we look at smaller 
objects the story changes.  Bring to class a two-liter
bottle containing nothing but air.  The lowest-energy
configuration would be for all the air molecules to sit
at the bottom of the bottle.  That is not, however, the
equilibrium situation.  If you tried to put them into 
the minimum-energy configuration, they would immediately
move uphill, doing work against the interatomic potential
and also against gravity.

A big part of chemistry -- the part we call p-chem i.e.
physical chemistry -- revolves around using entropy to
explain equilibrium, reversibility, and spontaneity.

-----------

Bottom line:  If you want to explain the actual physics, you 
need to talk about entropy.

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

Pedagogical remark:  There is a difference between explanation
and motivation.  
  *) The examples given above are in the motivation category.
   They suggest that we ought to care about entropy.  There
   are about 100 other examples.  Some of them are rooted in
   basic mechanics, but most are not.  I recommend the "12
   coins" puzzle and the "20 questions" example:
     http://www.av8n.com/physics/twelve-coins.htm
     http://www.av8n.com/physics/twenty-questions.htm

  *) To actually explain about entropy, I would not start
   with p-chem or with heat engines.  Instead I would define
   entropy in terms of probability and proceed from there.
      http://www.av8n.com/physics/thermo/entropy.html

See also next messages.