I am going to be teaching this topic to my 11th graders soon. I have a
question about the definition of energy. I know that the "ability to do
work" definition runs into trouble when you consider heat, engines and 2nd
law issues. But what if I turn the definition around. Instead of saying
"energy is the ability to do work", I want to say:
Work is defined to be the product of force and displacement (in the same
direction). Then, in different contexts, you can show that work = delta
(some quantity). Any such quantity is referred to as [blank] energy. Fill
in the blank with an adjective that fits the context.
So "energy" is not the ability to do work, but energies are the quantities
that are changed by work.