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.
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.
As an aside: I assume when they say energy "consumed"
they mean energy /dissipated/. The law of conservation
of energy insists that the physics energy cannot be
created or "consumed". Another possibility is that
they're not talking about the physics energy at all,
but rather some other energy-like notion, which would
be very odd given that the title of the article and
the topic sentence firmly indicate we are talking
about physics.
c) The article gives examples including the burning of
coal and the BTU rating of a refrigerator. This requires
yet a third definition, because neither of those examples
is consistent with definition (a) or definition (b).
You might be able to make (c) consistent with (b) if
you interpret "consumed" as /any/ kind of energy transfer
or transformation ... but that seems like a stretch.
Obviously no critical reasoning has been applied to this
wikipedia article. It seems odd that people with so little
understanding would presume to write articles telling other
people how to define things.
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Now moving beyond wikipedia, it seems that the conventional
textbook definition is mechanical work per unit time. You
can find this in sophisticated texts as well as (shall we
say) somewhat less-sophisticated texts:
*) http://www.feynmanlectures.caltech.edu/I_13.html#Ch13-S1-p9
*) Hewitt, section 9.2
It must be emphasized that I do not want to argue over
definitions. I say people should be free to define things
however they like, within reason. All I ask is:
a) Choose what you like, but recognize that others may
choose differently.
b) OTOH, be consistent with yourself. Say what you mean,
and mean what you say.
===========
This is what we euphemistically call an "opportunity for
improvement". It seems to me that the educational system
could do a much better job at
*) Teaching people to think clearly about "power" in particular.
*) Teaching people to think clearly in general, such as
always being on the lookout for inconsistencies.