Re: [Phys-L] heat content

[John Denker <jsd@av8n.com>]

I wrote:
> >  As a corollary, we know that "thermal energy" is the same as "energy".

On 02/11/2014 01:15 PM, Jeffrey Schnick wrote:

> And yet you do, or used to, call it thermal energy.  See:
> http://www.phys-l.org/archives/2008/12_2008/msg00024.html 

OK, good point.

On 02/11/2014 01:06 PM, LaMontagne, Bob wrote:
> > In this definition of temperature, E is just the internal energy of
> > the substance whose temperature is being stated. Gross kinetic and
> > potential energies are not included.

OK, good point.

Both of those points are similar to each other, and to the point
that Bob S. made yesterday.

I need to think about this some more.  I need to clean up my
thinking about systems with subsystems.

Here's the case that I have not handled well in the past.
Let's see if I can do better today:  We have a system.  Within 
the system we have subsystem A.  To make things interesting, 
imagine that subsystem A is "most" of the system.  We also 
have subsystem B.  This might be spatially separated from 
subsystem A, but often it is not;  often it is some subset
of the modes, some subset of the degrees of freedom.  We need
to consider the case where subsystem B is not in equilibrium
with subsystem A.

The case of the cold, fast-moving bullet is a good example.  If
we think of the heat capacity in terms of thermal phonons, the
gross "external" kinetic energy of the bullet is one of the
phonon modes, a very special mode, namely the zero-frequency
infinite-wavelength mode.  This mode is not in equilibrium
with the other 99.999999% of the modes.  There is no way it can 
come into equilibrium, because of conservation of momentum.

The temperature of subsystem B is essentially infinite.  The
inverse temperature ∂S/∂E for this mode is zero, since the 
mode has energy but no entropy.

Similar words apply to an ordinary capacitor.  Subsystem A has
a temperature and a heat capacity and all that stuff, whereas
subsystem B is the electrical mode, the single mode associated 
with gorging and disgorging the capacitor.  To a good approximation, 
the two subsystems are completely decoupled.

This sort of thing is common enough that I can understand why
people would want to call subsystem A "thermal" and subsystem
B "non-thermal".

On the other hand, there is something about this that worries
me.  I reckon this ought to be a solvable problem, but at the
moment I don't have a good solution.  I worry that the distinction
between "thermal" and "non-thermal" is not particularly fundamental.
It is the sort of thing that sometimes works and sometimes doesn't.
This is relevant to the present discussion because there are lots 
of gray areas, i.e. cases where subsystem A is "thermal" at one 
temperature and subsystem B is "thermal" at some other temperature.

I see the notion of subsystem as fundamental.  Labeling one
subsystem as "thermal" and the other as "non-thermal" seems
like a special case ... a common but treacherous special case.

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

As a related point, this may help explain why what I've been 
saying is imperfect but not entirely crazy:

*IF* we restrict attention to subsystem A alone, then there 
is no way of distinguishing its "thermal" energy from its
overall energy.  The possible presence of subsystem B does
not change this.

  OTOH I do need to clean up my explanations to make it clear
  that I am talking about subsystem A alone.  I apologize for
  being sometimes unclear and sometimes inconsistent about 
  this in the past.