Re: Definition of heat [and S]

[John Denker <jsd@MONMOUTH.COM>]

At 09:46 AM 11/27/99 -0500, Ludwik Kowalski wrote:

> It is true that we never know which part of dU, gained by an
> object, came in the form of d'Q and which came in the form
> of d'W.

One has to be careful here.  Many people *define* dQ to be the amount of
energy transferred by heatflow, and dW to be the amount of energy
transferred by other means.  If one plays by such rules, then one might
well know how much of the energy gain thermal and how much was nonthermal.

But I agree if we look at the system after the process is complete, we do
not know and should not care how the energy got there.

Note that it is possible to define dQ and dW in terms of changes (not
transfers) and thereby escape some horrible pitfalls, as discussed below.

> This is like not knowing which part of water in the
> Atlantic Ocean came from which river. Or like not knowing
> which part of dU came as d'Q from object A and which came
> as d'Q from object B.

I know what you mean.

> Why should this be an argument
> against saying that heat is a form of energy?

It isn't.  The arguments lie elsewhere.

> Should we go one step further and say that mechanical, or
> any other, work is also a form of energy?

Mechanical energy is a form of energy.  It's up to you whether you want to
extend the word "work" to cover mechanical energy per se (as opposed to the
more restrictive definition of a _transfer_ of mechanical energy).

To my ears, "work" (unlike "heat") sounds like an energy transfer.  You can
generalize it if you like, and I'll understand, but others may not.

> My work of 200
> joules done against friction becomes heat and my work of
> 800 joules , done at the same time against gravity, becomes
> potential energy. Exactly 1000 joules of chemical energy
> was lost (step by step) by my body in the process of pulling
> this sled uphill. First it was chemical energy, then it was
> work, and finally it became heat and potential energy. Why
> should this interpretation be rejected? What is wrong with
> saying that work and heat are forms of energy?

The way you use the terms, there is nothing wrong.

The problem is that the same symbols and the same words can be used in
another way.  Specifically, one can write the equation
        total energy = thermal energy + nonthermal energy
which applies to the energy of a particular region of space, or a
particular system.  The LHS and both terms on the RHS are functions of
state, independent of how the system got into that state.

One can go on to write the equation
        change in total energy = change in thermal energy
                               + change in nonthermal energy
which is obviously correct also, and which, again, applies to the energy of
a particular region of space, or a particular system.

Now for the tricky part.

As soon as we start talking about energy _transfer_, we are walking on
eggshells.  We agree that energy itself can be transferred from one system
to another, and is conserved in the process.  OTOH there is no reason to
believe that in general a particular subtype of energy is conserved during
a transfer.

To illustrate this point with the most obvious example:  Consider the
reversible expansion of an ideal gas as it pushes on a piston in a
cylinder.  Whatever external mechanism is connected to the piston undergoes
an increase in nonthermal energy.  But does that mean that the gas
underwent a decrease in nonthermal energy?  NO!!!!  An ideal gas doesn't
have any relevant nonthermal energy!!!  In fact the gas underwent a
decrease in thermal energy.  It cooled as it expanded.

I don't mind defining work to be a subtype of energy _transfer_, and I
don't mind defining heatflow to be a subtype of energy _transfer_ -- the
main problem is not with the words but with the concepts they refer
to.  The problem arises when:
  a) these concepts are given an importance they don't deserve.
  b) these concepts are used to write "laws" that cannot be reconciled
with an accurate physical description of what is going on.

To return to a more positive, constructive approach to things:  The power
of thermodynamics comes from the fact that we can perform a thermodynamic
analysis of a system without knowing *anything* about the innards of the
system.  This is one of the most majestic ideas in all of science.  I have
been fascinated by this idea since childhood.

In particular, consider system X as a black box.  From the outside we can
tell that X comprises a cylinder and a piston, but we do not know whether
the cylinder contains pressurized gas, or a metal spring, or some
arrangement of magnets, or whatever.
  *) From the outside, we can tell that the piston of system X exerts a
force on some other system A in the outside world.  We know that motion of
the piston causes A to undergo a change in nonthermal energy, but we don't
know whether the innards of the box underwent a change in thermal energy,
nonthermal energy, or both.
  *) Similarly, when we connect the black box to heat reservoir B or heat
reservoir C, we can account for the energy changes and entropy changes in B
and C -- again without knowing what is going on inside X.
  *) The wonderful thing is that we can place important bounds on the net
effect on A, B, and C without understanding the innards of the box.

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

To summarize:
  -- It is OK to talk about a given system's total energy, and the change
therein.
  -- It is OK to talk about a given system's thermal energy, and the
change therein.
  -- It is OK to talk about a given system's nonthermal energy, and the
change therein.
  -- It is OK to talk about transferring total energy from one system to
another, because energy is conserved.  dU(A) + dU(B) = 0
  -- In reversible processes, it is OK to talk about transferring entropy
from one system to another.  dS(A) + dS(B) = 0.
  -- For irreversible processes, the concept of transferring entropy from
one system to another is partially useful and partially problematic.  A
more elaborate statement is necessary.  You can safely say system A lost
entropy and system B gained entropy in the process.  dS(A) + dS(B) >
0.  You can perhaps call this a "transfer" of entropy in the amount dS(A)
plus "production" of entropy in the amount dS(B)-dS(A) ... but it's
debatable whether this makes things more clear or less clear.  Certainly
the transfer is not the whole story.
  -- It is a reeeeeally bad idea to talk about transferring subtypes of
energy (e.g. thermal energy or nonthermal energy) from one system to
another, because these subtypes are not conserved.  Note that this warning
applies equally to reversible processes and irreversible processes.  (We
have a huge problem because of the prevalence of textbooks that use such
terms and such concepts.)
  -- As a corollary, it is ridiculous to think that one could calculate
the thermal energy and nonthermal energy in a system by adding up the
thermal and nonthermal transfers thereto.  (Alas, everybody who sees the
equation dU = dW + dQ is tempted to integrate both sides.  If dW and dQ are
defined in terms of transfers, disaster ensues.  So don't do that.)  OTOH
the thermal and nonthermal energy content remain perfectly good functions
of state, and can be calculated by other means.



Simple rule:  If you ever find yourself tempted to talk about the
_transfer_ of a nonconserved quantity, STOP!!!