Re: [Phys-L] ?conservation of _internal_ energy

[John Denker <jsd@av8n.com>]

In the context of:

> > The distinction between U and E is significant in fluid dynamics.
> > Maybe I'm missing something, but AFAICT the «internal energy» is
> > not conserved.  To see this, consider the contrast:
> >   a) One parcel expands in such a way as to compress a neighboring
> >    parcel.  U is conserved in this situation.  So far so good.
> >   b) One parcel expands in such a way as to /lift/ a neighboring
> >    parcel.  It seems to me that U is not conserved.


On 01/14/2016 06:58 AM, Lulai, Paul wrote:

> If parcel one is a gas, parcel one would lose energy as it lifted parcel 2.
> Parcel 2 would gain gravitational potential energy if the earth is in the
> system.

Gravity seems to be an unhelpful complication here.  Also
on 01/13/2016 01:31 AM, David Bowman defined «internal energy»
to exclude center-of-mass kinetic energy, without mentioning
gravity at all.

Therefore it may be helpful to look at a non-gravitational
example.  Consider the situation shown here:
  https://www.av8n.com/physics/img48/internal-energy-noncon.png

There are two jack-in-the-box mechanisms.  We focus attention on
the blue one, on the left side of the diagram.  
 -- The top row shows the initial situation.  Each box is stationary,
  pushing against its mirror-image partner.  
 -- The bottom row shows the later situation.  Each box has pushed
  off and is now moving away from the centerline.

If you want to make this look more classically thermodynamical,
you can replace each spring by some gas molecules under pressure.
The idea is the same either way.

It should be obvious by symmetry that no energy crossed the boundary
of the blue system.  (Some momentum crossed the boundary, but that's
the answer to a different question.)

The plain old energy E is conserved.  Some energy that was stored in
the spring has been converted to KE ... more specifically, converted
to KE associated with motion of the center of mass.

However, U is not conserved.  The stored energy counts toward U,
whereas the center-of-mass KE does not.


On 01/14/2016 04:21 AM, Diego Saravia wrote:

> > Its obvious for me that any kind of energy, as internal energy is,  It 's
> > not conserved.

If it's obvious to you, that's commendable ... but it's not an
explanation.  Non-conservation of U is evidently not obvious to
everybody.  Smart people have argued in favor of conservation,
and it took me the better part of a week to come up with decent
pedagogical counterexamples.

A lot of things are obvious in retrospect.

A big part of pedagogy consists of /making/ things obvious,
things that were nowhere near obvious initially.