I just started reading JohnD's interesting essay "The Lows of
Thermodynamics." I have a comment about this section (at the
beginning):
Some well-understood examples of energy include following:
• gravitational energy: m g h
• kinetic energy: ½ m v2
• Hookean spring energy: ½ k x2
• capacitive energy: ½ C V2
• inductive energy: ½ L I2
We generalize this by saying energy is anything that can be converted
to some known form(s) of energy in accordance with the law of
conservation of energy (section 1.2).
Suppose we first define MECHANICAL WORK, as in most textbooks.
This definition is recursive. That is, we can pull our understanding of
energy up by the bootstraps. We can identify new forms of energy as
they come along, because they contribute to the conservation law in the
same way as the already-known examples.
Non-experts sometimes try to define energy as “the ability to do
MECHANICAL work” but this is unhelpful. At best, it would saddle us
with the burden of defining “work” which is no easier than defining
energy. Mechanical work is not difficult to define.
More importantly, though, equating energy with doable work is
inconsistent with thermodynamics:
The term "ability to do work" is not the same thing as "equating energy
with doable work." Yes, I am trying to defend the preliminary
definition by non-experts -- energy as "ability to do mechanical work,"
as in most textbooks. I think that the concept of mechanical work
naturally leads to m*g*h, to 0.5*m*v^2, . . . and to 0.5*L*I^2, in
that order. I think that JohnD is not talking about an introductory
physics course.
• Consider an isolated system containing a hot potato, a cold potato,
and a tiny heat engine. This system has some energy and some ability to
do work.
• Contrast that with a system that is just the same, but instead of a
hot potato and a cold potato, it has two hot potatoes. This system has
more energy but less ability to do work.
Energy is somewhat abstract. There is no getting around that. You just
have to get used to it -- by accumulating experience, seeing how energy
behaves in various situations. As abstractions go, energy is one of the
easiest to understand, because it is so precise and well-behaved.
Ludwik Kowalski
Let the perfect not be the enemy of the good.