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Here is some evidence that people define power one way and
use it another.
Note that I use wikipedia as a reflection of how the
general population thinks, not as a source of objective
facts about the subject matter. I have been told by
wikipedia officials that this is how they /want/ it to be.
Let's look at the wikipedia article on power
http://en.wikipedia.org/wiki/Power_%28physics%29
a) In the first sentence, it explicitly defines power as
the rate of doing work (where work is F•dx).
b) In the second sentence, it asserts that this is equivalent
to energy consumed per unit time. This is wildly inconsistent
with the previous definition, as you can see by considering
something like a refrigerator, where the energy dissipated
is not anywhere close to the F•dx work done.