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Re: [Phys-l] teaching energy



On 09/28/2006 03:53 PM, Rauber, Joel wrote:

| | Here is an excellent article ...

Robin Millar, "Teaching about energy"
http://www.york.ac.uk/depts/educ/ResearchPaperSeries/Paper%2011%20Teaching%20about%20energy.pdf

Yes, I like it, with isolated exceptions.

| I notice that in the reference below, the concept of the
| energy that an object possesses is equated to the amount of
| work that an object is capable of doing.
|
| This has been much criticized on this list.

Criticized indeed. The Millar paper gets this point wrong.
It's frustrating, because the paper gets within one sentence,
arguably within one word, of getting this point exactly right,
and then blows it.

In fact:
-- work can be transformed into any other form of energy
-- not every form of energy can be transformed into work.

Equating energy with doable work is just not correct. This is
not a nitpick; the distinction sheds light on the meaning of
the first law, and is central to the meaning of the second law.

The paper correctly emphasizes the conservation of energy. If
it had chosen almost anything *other* than 'doable work' as the
anchor point of the argument, it would have been great. Viable
choices could have been the PE of an object on a high shelf, the
KE of a moving object, the electrostatic energy of a capacitor,
... almost any form of energy.

Footnote 3 in the paper is bogus, too. The fundamental laws
of thermodynamics apply always; they apply just fine to
cycles and non-cycles alike. Of course there are some nice
corollaries that apply only to cycles, but if the corollaries
don't apply the fundamental laws still do. The example of
the two-potato heat engine is still valid, whether or not the
heat engine carries out complete cycles.
http://www.av8n.com/physics/thermo-laws.htm#sec-workability

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

More generally, when teaching about energy, there are a number of
points that ought to be made. High on the list are:
A) Local conservation of energy,
B) The example of energy in an applied gravitational field, and
C) Universal gravitation.

Item (A) is more important, but let's discuss item (B) first.

The important thing is making correct predictions. It is not
necessary to discuss the details of /how/ the gravitational
field does what it does. This focus on predictions goes back
to Galileo (1638) and was adopted by Newton, as reflected in
the immortal words "hypotheses non fingo".

At the introductory level -- and several levels beyond that --
the venerable and sensible approach is to duck the question of
_where_ the gravitational energy resides. All we need to know
"the energy", i.e. the energy of the whole system. We can make
correct predictions without knowing where the energy resides
(in the objects and/or in the field).

AFAIK, this approach is good enough for all terrestrial practical
purposes.
-- The energy is the energy of the /system/.
-- Don't worry about details beyond what is needed to make
correct predictions. Hypotheses non fingo.
-- We can see that the Newtonian law upholds global conservation
of energy.
-- We will /assume/ that if we looked closely enough, it
would also uphold local conservation of energy. There
is certainly no evidence against this assumption. A more
detailed check of this assumption is beyond the scope of
the course.

To say the same thing another way: Newtonian gravity is very simple.
The formulas work in the appropriate limit. Alas, they don't tell
you what gravity "is" or /how/ it works. If you try to look beyond
the Newtonian theory to see how things work, à la Flamamarion,
http://upload.wikimedia.org/wikipedia/commons/thumb/8/87/Flammarion.jpg/350px-Flammarion.jpg
things get very complicated very fast. Such workings are usually
beyond the scope of the course, unless it is a general relativity
course.

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

People who are not interested in details can stop reading now.

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

Returning to item (A): Local conservation of energy _requires_ that
there be energy residing in the field, and flowing via the field, as
we can see from the following argument.

Consider the following situation:

Region 1 | Region 2 | Region 3
| |
eee | |
eeeee | |
eeeee | | m
eee | o |
| |
Earth | Observer | Moon
| |


Obviously you can raise the energy of the earth/moon gravitational
system by raising the moon in the earth's gravitational potential,
i.e. by doing work on it by pulling it against the gravitational
force.

You can also raise the energy of the system by relocating the earth,
moving it to the left in the diagram above, i.e. raising the earth
in the gravitational potential of the moon, i.e. doing work on it
by pulling it against the gravitational force.

We are already risking trouble at this point, because if we blindly
apply the energy formula
E = G m M / r
we are at risk for double-counting: if we count the energy of the
moon in the earth's potential *and* the energy of the earth in the
moon's potential, we will have overestimated the energy by a
factor of two.

It is traditional and convenient from a /laboratory/ point of view
to speak of the gravitational energy "of" an object when it is subject
to an applied gravitational field ... as if the energy "belonged" to
the object. For example, we speak of the GPE "of" a book on a high
shelf. However, from the point of view of /universal/ gravitation,
this is highly problematic. For starters, equation [1] is symmetric
w.r.t the roles of (m) and (M), and attributing the energy to just
one of the objects would break this symmetry.

Broken symmetry may sound merely inelegant, but the problems are
deeper than that. If you think that the gravitational energy (or
even any /part/ of the gravitational energy) "belongs" to the moon,
it is peculiar that you can change the energy of the moon by
relocating the earth. The observer can see that after you move
the earth, the moon is bound in a less-deep potential. Work done
in Region 1 affects the energy of an object in Region 3. This is
an example of "action at a distance" and it is inconsistent with
item (A) on our list above: /local/ conservation of energy.

Local conservation demands that any decrease in energy in any region
must correspond with a simultaneous increase in energy in some
_adjacent_ region(s). Energy cannot magically disappear from one
region and magically reappear in some distant region. Energy is
conserved right here, right now.
http://www.av8n.com/physics/thermo-laws.htm#sec-energy-con
http://av8n.com/physics/conservative-flow.htm
In our example, local conservation of energy demands that if work done
in Region 1 is going to affect Region 3, the energy must flow through
Region 2.

So, unless you want to overthrow the most fundamental principles
of physics, we have to assume that there is energy flowing in the
field in Region 2. (The energy must be in the _field_, because
there isn't anything else in Region 2.) The details of how to
check this assumption are beyond the scope of the course, but
it is safe to say that there is no evidence against this assumption.
We can also say that the law of local conservation of energy has
been checked in numerous situations (usually involving fields
other than gravity, but sometimes even gravity) and in all cases
where it has been checked, the law is upheld. The more closely
you look, the more precisely the law is upheld.

We have not proved that all of the energy of the system must be
attributed to the field, only that *some* of it must be.