"Energy is the capacity to do work."
"A vegetable is a potato."
"Energy can be unavailable for doing work."
"A vegetable might not be a potato."

Energy is necessary for doing work, but something else is needed, too.  There's a trouble maker lurking about which can render energy unavailable for doing work. That essential "something else" is that we get rid of the trouble maker.

"trouble maker" is entropy.
There's another kind of trouble maker here too, but this is one that occasionally lurks in the logic we use.  It's the confusion of necessity with sufficiency.  To define energy as "capacity to do work," we must show both necessity and sufficiency.  However, while energy is necessary for doing work, it is not sufficient.  Those textbook authors who define energy as capacity for doing work are making the logical error of confusing necessity and sufficiency.  (That's an improperly inverted implication.)A short lecture, with exemplar; ("Back" to return).

One person might easily sense when this error is being made; another person might not.  Meet one of each; ("Back" to return.)

Use "Back" to return.