[Phys-L] energy versus "thermal energy"

[John Denker <jsd@av8n.com>]

On 02/08/2014 07:25 AM, Paul Lulai wrote:
> Second, you state calling it thermal energy is not useful. Energy is
> energy. How is calling this thermal energy different from terms like
> kinetic energy or elastic energy?

As I understand it, elastic energy is just the potential
energy associated with some springy ("elastic") object.
So that's just terminology.  Not a problem.

For any particular object, if there were any such thing as
"thermal energy", it would be impossible to distinguish that
from the energy of the microscopic particles that make up 
the object.  The microscopic energy most definitely includes
both kinetic and potential energy;  for an ordinary chunk
of metal, to an excellent approximation, half of the heat 
capacity is explained by PE and the other half by KE.

So, the first problem is that any notion of "thermal energy" 
totally overlaps with KE and PE.  This makes it tricky to
evaluate the so-called "thermal energy", because of the risk
of double-counting.  This is a minor problem.

A far deeper problem is that it is impossible to distinguish
the "thermal" part of the energy from the "non-thermal" part.
Consider for example an air spring (i.e. gas in a cylinder 
with piston).  Let's talk about the energy in the air spring.
You cannot tell whether that energy resulted from applying 
"heat" to the gas or by doing "work" on the gas.  You can't 
tell and you don't care.

Let's make a few simplifying assumptions, so that we can
write the useful expression
   dE = - P dV + T dS

If you want to call the RHS "work" plus "heat" that's OK in 
this context.  That's one of the many disparate definitions
of "heat" and it's no worse than the others.

In any case, this does *NOT* allow you to define a notion of 
"heat content" aka "thermal energy content".  That's because 
T dS is not the gradient of any potential.  If it were a gradient,
you could integrate it and thereby define a notion of thermal
energy content, but it isn't so you can't ... except possibly
in trivial cases.

The picture you want to have in mind is the Escher waterfall.
  http://www.av8n.com/physics/thermo-forms.htm#fig-escher-waterfall
It has a well-defined slope everywhere, but you cannot integrate 
the slope to obtain any globally well-defined notion of height.

Everybody who has tried to learn thermodynamics has tried to
define a notion of "thermal energy content" but none have 
succeeded, and none ever will.  The sad part is that many of
them /think/ they have succeeded, even though they haven't.

This connects to our recent discussion of the fact that voltage
is not necessarily a potential.  There are lots of non-potential
voltages in this world.  There are lots of electrical fields that
are not the gradient of any potential.  Some resources that may
help explain this can be found at
  http://www.av8n.com/physics/non-grady.htm
  http://www.av8n.com/physics/voltage-intro.htm
  http://www.av8n.com/physics/kirchhoff-circuit-laws.htm
  http://www.av8n.com/physics/thermo-forms.htm