Re: good and bad thermo concepts

[John Denker <jsd@MONMOUTH.COM>]

At 06:54 PM 2/2/01 +1100, Brian McInnes quoted Callen:
> " A certain
> gentleman owns a little pond, fed by one stream and drained by
> another.  The pond also receives water from an occasional rainfall and
> loses it by evaporation, which we will consider as "negative rain".
> In the analogy we wish to pursue the pond is our system, the water
> within it is the internal energy, water transferred by the streams is
> work, and water transferred as rain is heat."  Callen develops the
> analogy for the best part of a page -the first point is that no
> examination of the pond at any time can indicate how much of the water
> came from the streams and how much by rain.

This is a fine analogy.  I think we all agree that there are two main
concepts in play here:
  a) The total amount of water in the pond, and
  b) the transfer of water in the form of rain.

The analogy to thermodynamics is clear:
  a) The total amount of thermal energy in a given body, and
  b) The transfer of energy from one body to another due to
     an infinitesimal difference in temperature.

Let us postpone any discussion of which of these should be called
"heat".  That is just a name.  The first order of business is to understand
what _concepts_ we want to emphasize.  Usually people devise names for good
concepts;  only very rarely does good terminology or good notation arise in
the absence of good concepts.

Clearly one should not talk about the amount of rain in the pond.  For
present purposes, water in the pond is just water;  we do not care whether
it entered the pond via the rain-process or the stream-process.

But we can talk about the amount of water in the pond.

Again I emphasize that I do not wish to discuss what concepts, if any,
should be called "heat".  That's just a name.  To avoid confusion, let's
define new terms:
  FOO:  The total amount of thermal energy in a given body.
  BAA:  The transfer of energy from one body to another due to
        an infinitesimal difference in temperature.

Clearly one should not talk about the amount of baa in a system.  For
present purposes, foo in the system is just foo;  we do not care whether it
entered the system via the baa-process or some other process.

But we can talk about the amount of foo in the system.

It seems clear that foo (thermal energy) is a very important concept.  It
seems equally clear that baa (temperature-driven transfer) is a much less
important concept.

If the only thermodynamics problem you are ever going to address is an
idealized external-combustion engine, then you might think that baa
deserves a lot of attention.  But what about the rest of the field?
  -- What about an external-combustion engine that is not idealized,
     i.e. that is not quasi-isothermal, i.e. where things are not
     restricted to the _infinitesimal_ temperature differences required
     by the definition of baa?
  -- What about the foo that is used in _internal_ combustion engines,
     including piston engines, turbojets, and others?
  -- What about the foo that is produced by metabolism in the
     tissues of living creatures?
  -- What about the foo that is produced when we expose butter
     to microwaves?
  -- What about the foo that is produced when we run an electric
     current through NiChrome?
  -- What about the foo that is produced when somebody scrapes an iron
     baa against a piece of brass in a lathe?
     http://dbhs.wvusd.k12.ca.us/Chem-History/Rumford-1798.html
  -- What about the cooling (_negative_ transference of foo) when a
     suitable object (atom) is placed in a laser-cooling apparatus
     http://www.nobel.se/physics/laureates/1997/
     especially in view of the fact that a trivial retuning of the
     laser will change this to a _positive_ transference of foo?

I stand by my assertion that focusing on "temperature-driven transference"
is a bad idea, no matter what name you give it.

You can write
        dE = dQ - dW
if you like.  Whether or not this equation means anything important depends
on how you interpret the symbols.  If you interpret Q to be "baa"
(temperature-driven transfer), then this is _not_ a fundamental equation at
all.  It applies only to a certain type of idealized quasi-isothermal
external combustion engines, and a few other things like that.

At this point the question is, why bother?  Why bother to introduce the
concept of "baa" at all?  The students come into class not caring about
external-combustion engines.  The instant they leave class they will stop
caring about external-combustion engines.  Why burden them with a concept that
 -- is of no use to people who don't work in the field,
    such as homeowners and office workers, and
 -- is also of no use to people who _do_ work in the field,
    such as HVAC contractors, or researchers in the low-temp
    physics lab, et cetera.

The concept of "baa" is vastly less useful than the concept of
"rain".  Rain, even though it takes a back seat to the primary concept of
"water", remains a useful concept in many parts of the world.

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

Here are some constructive counter-proposals.

First of all, rather than writing
        dE = dQ - dW                            (1)
write instead
        E = E_nonthermal + E_thermal            (2)
and hence
        dE = dE_nonthermal + dE_thermal         (3)

Note that equations (2) and (3) are obviously correct.  In cases where
equation (1) means anything, equation (3) is equally useful.  In other
cases, equation (3) remains useful even when equation (1) is inapplicable
because of the very narrow definition of Q.

===

Also, rather than bothering your students with "baa", teach them something
useful.  Teach them about entropy.  The concept of entropy has many uses:
  a) Librarians talk about the entropy when books get mis-filed.
  b) Cryptographers talk about entropy.
  c) Communication engineers talk about entropy.
  d) Machine-learning / AI folks talk about entropy.
  e) Real-world engine designers use the concept of entropy,
     even though they can't use the concept of "baa".
  f) You can discuss the entropy budget of a foo-exchanger
     even when there is a non-isothermal exchange of foo.

Don't define entropy via  dS=dQ/T or anything like that.  Entropy exists
even in the absence of temperature;  examples (a) through (d) above are
essentially zero-temperature examples.

It is relatively easy to teach the basic concept of energy.  Put about 15
coins in a box, all heads-up.  This is a low-entropy state.  Paint the
heads some conspicuous color if it helps the students to see.  Then shake
the box to get a high-entropy state.....

It takes a bit more work to teach the connection between energy and
entropy.  But at least you've got a chance of teaching the connection
between energy and entropy when they understand entropy, as opposed to
trying to teach the connection when they _don't_ already understand entropy.