Re: A "heat" question

["John S. Denker" <jsd@MONMOUTH.COM>]

Carl Mungan wrote:

> Each iteration of the heat, work, and energy discussions slowly
> evolves my understanding. What a thorny topic. But worthy of
> consideration, not just stubbornly clinging to current notions.

:-)

> Anyhow, for what it's worth, here are some of my current thoughts on
> the topic.
>
> Heat and work are forms of energy transfer, or if you prefer, ways of
> changing the energy of a system. The energy of a system can be
> divided into internal energy and (for want of a better name) bulk
> energy.
>
> Bulk energy certainly includes 0.5MV^2 where M = total mass and V =
> velocity of center of mass. For a system divided into well-defined
> macroscopic parts (blocks, springs, planets, etc) it can also include
> the interactional potential energy between the parts (and probably
> should if you want to make contact with the mechanical energy chapter
> in intro texts).
>
> Internal energy is the kinetic energy intrinsic to the parts (both
> bulk rotational and microscopic translational) plus the potential
> energy due to interactions between particles inside a part. It also
> includes nonmechanical forms such as radiation, magnetic energy,
> field energies, etc.

I'm not sure I buy this distinction between "internal"
and "bulk" energy.

Suppose I have two black boxes.  You are allowed to
measure their thermodynamic properties such as
"heat capacity".  Can you tell how much of the "heat"
you apply in your "heat capacity" measurements is
connected to internal energy inside the boxes, and
how much is connected to "bulk" energy inside the
boxes????

Before you answer, consider some of the things I
might have inside the boxes, including:

1) A weighted piston:

       |           |
       |           |
       |ppppppppppp|
       |ppppppppppp|
       |ppppppppppp|
       |    PPP    |
       |  g PPP g  |
       | g  PPP    |
       |    PPP   g|
       -------------


where "p" symbols indicate the movable piston, and
"g" symbols indicate gas molecules.  The piston has
an extension that rests on the bottom of the cylinder.

Assume the heat capacity of the non-gaseous materials
is negligible compared to the heat capacity of the
gas.
  a) If I have a heavy piston and a low gas pressure,
your experiments will measure Cv, the heat capacity
at constant volume.
  b) If I have a less-heavy piston and a higher gas
pressure, the gas will lift the piston off the bottom,
and you will measure Cp, the heat capacity at constant
pressure.  Some of the energy you apply to the black
box will go into raising the piston, which (if I
understand the intent of the previous definitions)
is "bulk energy".

2) I could have a fluid of atoms with permanent
magnetic dipole moments in an applied magnetic
field.  This system is formally identical to the
previous system, but in this case I think we are
supposed to call all the energy "internal energy".

I find this inconsistency troubling.  I suspect
the suggested definitions are unhelpful when
it comes time to do real-world thermodynamic
engineering.


> It may or may not be possible to divide energy transfer into heat and
> work.

I agree.

> Work is always defined as an integral of force dotted with
> displacement,

I agree.

>  but there are many different kinds, depending on which
> force and which displacement you consider: there is the work which
> equals only the change in the bulk KE (usually called center-of-mass
> or pseudo work),

... from the Greek word "pseudo", meaning deceitful,
fraudulent, lying ...

See http://www.monmouth.com/~jsd/physics/momentum-squared.htm
for why pseudowork is !!not!! equal to the change in
the bulk KE.  It says in part:
       The KE of the center-of-mass (P^2/2M) is a lower
       bound on the total KE. But the change in P^2/2M
       is not a lower bound on the change in the total
       KE, or an upper bound, or anything else.

> there is the kind which changes only the bulk
> kinetic and potential energy (usually called nonconservative particle
> work), there is the kind which appears in the first law of
> thermodynamics, etc.

I still doubt these ideas are useful.

> Heat is the nonadiabatic energy transfer.

Is that meant to be a definition?

It sounds like a really fine definition, until you
realize that "adiabatic" means literally "no (heat)
flowing through" so this seems circular.  We need
an independent definition of adiabatic or an
independent definition of heat.

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

I am struck by the fact that in this entire thread,
nobody has mentioned the word "entropy".

Thermodynamics is about entropy.  That's what sets
thermodynamics apart from mechanics.

As long as people keep trying to define "work" in
mechanical terms, and then define "heat" by means
of the execrable W+Q formula, this is !!guaranteed!!
to be thornier than a cactus and to remain so for
all time.

In every case I know of, rather than asking about
W and/or Q, you can ask about the energy and the
entropy.
 -- You can talk about the energy of system A and
    the energy of system B.  You can talk about the
    delta E_a and the delta E_b when the two systems
    interact, and the two must add up to zero.
 -- You can talk about the entropy of system A and
    the entropy of system B.  You can talk about the
    delta S_a and the delta S_b when the two systems
    interact, and the two must add up to zero or more.

Energy is primary and fundamental.
Entropy is primary and fundamental.
You can't do thermodynamics without entropy.
Entropy is well-defined even when other concepts such
as heat and temperature are not.

This posting is the position of the writer, not that of Attila, Genghis,
or Kublai.

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.