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Re: conservation of energy



John Barrer wrote:

My intro students have benefitted
greatly from the approach which focuses on the energy
of a system and examining how that energy may be
changed by various processes - workING, radiatING,
heatING, transportING (ie, adding fresh cells, more
fuel etc), all of which are means to the end of
altering the energy of a system.

That's all good.

But the -ING needs explaining. I don't see why the -ING
forms ought to be emphasized or why they ought to be used
to the exclusion of the non-ING forms (work, radiation,
heat, transport and/or flow, et cetera).

I find it useful to draw an analogy between heat and force.
-- Force has its -ING forms (forcING, shovING) but they
are not considered obligatory or even preferable, are they?
-- Force is sometimes the gradient of a potential, but
not always (e.g. betatron). Correspondingly students are
(alas) strongly tempted to view work as the gradient of some
potential, but it almost never is. This is a deep, serious
pedagogical challenge, but I don't see how the grammatical
device of changing work to workING sheds any real light on
the issue. I find the direct approach, using diagrams of
non-conservative fields, to be more satisfactory:
http://www.av8n.com/physics/non-conservative.htm
http://www.av8n.com/physics/thermo-forms.htm

And yes, I consider work to be a vector, for the same
reasons that force is a vector. The field in a betatron
might be
force = X d(Y) - Y d(X) [1]
where d(...) denotes the exterior derivative, which when
applied to a scalar-valued function produces the gradient
of that function. The same words apply to
work = -P d(V) [2]
I see no reason to require that all vectors have names
ending in -ING.

Note that both of these examples involve non-exact
differentials (except in the highly less-than-general
cases where P can be written as a function solely
of V, X can be written as a function solely of Y, et
cetera). That is, even though d(X), d(Y), and d(V)
are gradients, the force in equation [1] is not the
gradient of any potential, and similarly the work in
[2] is not the gradient of any potential.

So I leave it as a question: what is the problem that
the -ING terminology is supposed to solve, and is it
the best way to solve that problem?