Re: [Phys-L] Energy & Bonds

[John Denker <jsd@av8n.com>]

On 11/12/2013 01:19 PM, Ron Mcdermott wrote:

> There is one overriding tendency behind the process of bonding: Forming a
> more stable product; where more stable is more resistant to change.

I would not have said that.

Just the other day, a friend of mine who works for a certain TLA 
(Three-Letter Agency) was mixing up a batch of high explosive,
  1,3,5-Trinitroperhydro-1,3,5-triazine
otherwise known as RDX.  That involved making a lot of bonds, leading
to a product that is *less* stable than what he started with.  Rather
dramatically less stable.  And I know of plenty of stuff even less 
stable than RDX.

There are actually multiple definitions of stability, _none_ of which
correspond to any "overriding tendencies" in the laws of physics.
 -- Mechanical stability has to do with second derivatives of the energy.
 -- Thermodynamic stability has to do with second derivatives of the entropy.

I assume that the phrase "overriding tendency" was intended to allude to
the maximum-entropy principle.  Please do not confuse entropy with the
second derivatives of the entropy.  If you mean entropy, please say
"entropy".  Please don't call it "stability".

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

> Within this overarching tendency are two subtendencies:
> 1, A tendency to lower energy (PE) and...
> 2. A tendency to greater disorder (more modes of freedom in the material
> p>g>l>s).

I wouldn't have said that, either.

First of all:  If you mean entropy, please say "entropy".  Don't call it
"disorder".  Note the contrast:
 *) Entropy is a property of the macrostate, i.e. a property of the ensemble.
  Specifically, it is the ensemble average of the surprisal.
 *) Disorder, to the extent that it can be defined at all, is a property
  of the microstate.

This makes it pretty clear that disorder cannot be a good proxy for entropy.
It is not a good euphemism.  This is a very common mistake, but it is a
mistake nonetheless.

Secondly:  The maximum-entropy principle is not a "subtendency";  it is the
whole story.  I am reminded of the immortal words of David Goodstein, at the
top of his chapter on Variational Principles in Thermodynamics:

        Fundamentally there is only one variational principle in
        thermodynamics.  According to the Second Law, an isolated body
        in equilibrium has the maximum entropy that physics
        circumstances will allow.  However, given in this form, it is
        often inconvenient to use.

In particular, the various rules of thumb about minimizing the energy, or
the free energy, or the Gibbs free enthalpy, or whatever....  Those are all
corollaries -- subtendences if you will -- of the second law, valid under
this-or-that set of restrictions and assumptions.

Do yourself a favor:  If you mean entropy, say "entropy".  If you have to 
teach the students about entropy, just go ahead and do it.  That is waaaay
easier than teaching them a bunch of wrong ideas about "stability" and 
"disorder".  Easier and in every way better.
   http://www.av8n.com/physics/thermo/entropy.html


> By convention, we presume the force between bonding atoms to be attractive,
> so infinite separation is zero PE, and PE is negative in sign; lower
> energy, then, being a more negative PE (explanation covered earlier).

When atoms are far apart, not yet bonded, but about to bond, then
the interaction between them is attractive.  Otherwise they would
never bond.  This is not merely a convention;  it is an observable
physical phenomenon.  Even atoms that will never form a bond within
the IUPAC definition of chemical bond still exhibit some attraction
in the far field.  Hint: van der Waals interactions.

However ... that is not the whole story.  When the atoms are actually
bonded, some of the interactions are attractive (tension), some are
repulsive (pressure), and some are neither (shear).  For example, if
you have a chunk of aluminum with equilibrium volume V, if you increase
*or* decrease the volume, the energy goes up.  This can be readily
understood in terms of the equation of motion:  The electrostatic PE
is not the only contribution.  There are also very significant KE
contributions.  This can be explained without too much difficulty
even at the HS level:
  electron --> de Broglie wave
  particle in a box --> wave in a box
  momentum = ℏ k
  KE = p^2 / (2m)

This is not rocket science.  It's just quantum physics, and at this 
level of detail it's easy.  And it's not wrong.  AFAICT there's nothing 
I just said that will ever have to be unlearned.  Refined, maybe, but 
not unlearned.  For one thing, the atomic potential is not exactly a 
box-like square well, but I don't think that's going to surprise or 
confuse anybody.

The point remains:  Electrostatic PE is not the whole story.  The
atomic KE is really a big deal.  It accounts for the sturdiness and
indeed the very existence of ordinary matter.