Re: ENERGY

[Leigh Palmer <palmer@sfu.ca>]

> The text I use (and others) refer to the fact that during even "normal"
> combustion, a small amount of matter is actually converted to entergy
> via E=mc^2.

It is unfortunate that a textbook containing such an incorrect and
confusing statement can come to be used in your school.

> How much matter might be converted when one strikes a match? And what
> matter is it that is converted, an electron or two or a few neutrons?
> What determines what matter undergoes this conversion?

Not one massive particle is created nor destroyed in this process.
The only change is in the *relativistic mass* of the system, not in
the amount of matter as is reckoned from the numbers of electrons
and nucleons. The latter numbers remain the same after as before
the burning takes place provided all oxygen which is consumed in
the flames and all combustion products are collected and retained
afterward. The system itself must be reckoned as containing all
these things from the beginning and retaining them at the end This
might be done by confining the system to a jar.

The energy of the system before the match is struck is calculable
from the familiar Einstein relation E = m*c**2. To carry out this
calculation one must know the gravitational or inertial mass of the
system (they are the same) and that can, in principle, be measured
by a very good bathroom scale. The system should be weighed while
at a uniform temperature. After the match has been burned and the
system has returned to the original uniform temperature by means of
losing its excess heat to the environment, the jar is weighed again.
The difference in weight (far smaller than one could hope to detect
even on the best bathroom scale) can be used to determine the change
in system energy using, again, the Einstein formula. If one believes
in the law of conservation of energy one will see that the energy
change measured in this way is equal to the energy lost by the
system in the process of cooling to the original temperature.

> I look forward to any illumination on this topic about which I know
> little.  Thank you.

I hope I've cast more lumens than a match, but I fear that there is
a conceptual problem that is too difficult to overcome by teaching
in this limited medium. I need reaction to play against; trying to
explain in this way is a little like pushing on a rope.

Let me say one final thing about energy. Energy is a mathematical
abstraction. It is a property solely dependent on the state of an
isolated system. We know lots of ways to calculate energy, and we
know ultimately that one formula alone will suffice, though it is
of restricted practical use. This abstract quality of energy makes
it impossible to separate from a system; there is no such thing as
"pure energy", and energy can't be "transferred" from one system
to another, though Nature behaves in such a way that this is a
useful way to talk about energy. Again: the energy is an abstract
mathematical property of an isolated system and is solely a function
of the state of that system.

I should point out at this point that several other quantities share
this status. Linear and angular momentum, lepton number, electric
charge, baryon number, entropy are all abstract mathematical functions
of the state of an isolated system (though some, like baryon number,
are far less abstract than others).

Leigh