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Following up on John Clement's comments about gasoline and
oxygen, I found when teaching a distance education version of
Matter & Interactions for in-service high school physics
teachers that many of them were surprised to discover that
they had been carrying around a view of binding energy that
was basically backwards, with the wrong sign. The view was
something like "there is energy stored in the bonds in the
gasoline molecules which we can use" instead of "in
combustion the molecules transition to a lower energy state
and become more bound". To put it another way, they seemed to
have thought that "more" in the bonds (more binding) meant
more "bond" energy was available, instead of more bonding
being associated with lower energy, not higher.
I'll admit I can't express the issue very clearly, but the
teachers themselves were convinced that useful energy
resulting from transitions to lower energy levels (greater
binding) was a new idea for them.