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[Phys-l] workable versus unworkable energy



I am reminded of the following wise little poem:

Be very, very careful what you put into that brain,
because you will never, ever get it out again.

-- Paul Jackson


That brings me to the topic of the day, namely the association
of energy with "the ability to do work".

We cannot equate (much less define) energy as the ability to do
work, because that would violate the first or second law of
thermodynamics. For details on this point, see
http://www.av8n.com/physics/thermo-laws.htm#sec-workability

To repeat, we have a choice. We can keep any two of the following
statements:
[1] The first law of thermodynamics, conservation of energy.
[2] The second law of thermodynamics, paraconservation of entropy.
[3] Energy defined as the ability to do work.


Some on this list have argued as follows:
Even though ability-to-do-work is not an exact expression for
the energy, pedagogy has to start somewhere, and this is an
expedient starting-place.
That argument -- /as far as it goes/ -- has some merit, but it
is certainly not the whole story. We need to consider other
starting points, all with various pros and cons.

No matter what starting-point is chosen, we must keep in mind the
Paul Jackson poem.

It appears quite a few authors have been dropping the ball on this
one. It is easy to find references where energy is /defined/ to
be the ability to do work. Not analogized, not exemplified, but
out-and-out /defined/.

Even that wouldn't be so bad, except that there are some professors
out there who prefer [3] to [1] in the list above! I'm not kidding!
-- They teach that "energy" is /defined/ as the ability to do work.
-- As a consequence, their so-called "energy" is not conserved.
This doesn't bother them.
-- They sneer at anyone who suggests that energy should be conserved.

You can't make this stuff up.

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

Action items:

1) Obviously, when something is an example or an approximation, *say*
it is an example or an approximation; don't try to pass it off as a
definition.

That seems like a small thing, but in the case of energy it would
be a tremendous improvement over the status quo, namely:
++ "Everybody knows" energy is defined as the ability to do work.
++ "The dictionary says" energy is defined as the ability to do work.
++ "The encyclopedia says" energy is defined as the ability to do work.
++ "The state-adopted textbook says" energy is defined as the ability to do work.
++ "The testing standard says" energy is defined as the ability to do work.

They make no bones about it; not an example, not an approximation,
not a limiting case ... an out-and-out definition.

When an idea has limited validity, you don't need to get hypertechnical
about the limits, especially in an introductory course. I can live
with anything along the following lines:
"Having the ability to do work is an /example/ of energy."
"In simple cases, energy can be used to do work."
and of course you can get progressively more specific if you want:
"In nonthermal situations, energy can be used to do work."
"High-grade i.e. nonthermal energy can be used to do work."
"One form of energy can be converted to another, subject to the
law of conservation of energy /and/ all the other laws of physics."
etc. etc. etc.

None of those are exactly how I would handle it, but I mention them
to make the point that there are ways to tell the truth without
getting bogged down in undue complexity.


2) In an ideal world, item (1) would suffice ... but in fact we have
to deal with the following scenario:

2a) Student is told "a is an example of b, provided w, x, y, and z."

2b) Student swears under oath he was told "a is defined as b, period".

I haven't got a lot to say about it, except forewarned is forearmed.
Expect it, deal with it. Review and revisit things. Test them on
how well they remember the provisos.

Also I would make a big point about the relative importance of items
[1], [2], and [3] as listed at the top of this note. Given the
choice of keeping conservation of energy versus keeping something else,
you should usually choose conservation of energy.