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A Closer Look: Mass-Energy Conservation
Vinegar is poured into a beaker
containing baking soda. |
Why is conservation so important?
The fact that certain measurable quantities
are “conserved” is
one of the most powerful ideas in physical science. It is useful because
it is one of the major ways to make quantitative predictions about the
changes that take place so often in the real world. For example, we know
from the video that, if we combine 45 grams of vinegar and five grams
of baking soda in a closed system, the resultant carbon dioxide and water
will weigh 50 grams, even if we can’t see them. This is the principle
of conservation of mass. Many other quantities (like energy, momentum,
charge, etc.) are conserved in a “closed system” (i.e., a
system that no outside forces or influences can affect).
How is matter
converted into energy?
This concept of conservation of matter evolved
as scientists found that it seemed to hold true in every situation where
it could be tested — e.g.,
if you capture all the water vapor generated from boiling water and
find a way to measure its mass, you find it is the same as the original
mass
of the water.
The situations that caused people to question this idea
were the ones that didn’t seem to be “normal.” In
particular, when it became possible to weigh an individual proton or
neutron, the
component particles
that make up the nuclei of all atoms, it was found that adding
the mass of six protons and six neutrons resulted in more mass than
one carbon
nucleus,
which is made of six protons and six neutrons stuck together. The
sum of the mass of 6 protons and 6 neutrons is 12.0956 atomic mass
units (amu),
while the mass of the carbon nucleus is 12.0000 amu. Therefore,
the mass of a carbon nucleus is less than the sum of its parts.
Because
the principle of conservation of matter is so valuable,
scientists were hesitant to try to start from scratch to explain
this phenomenon
of “lost” mass.
Eventually, it was proposed that since these particles were bound
together, some of the mass had been used in “binding” the
particles together. It is this “binding energy” that
is given by Einstein’s
famous equation E = mc^2, which says that the amount of energy
you get by completely converting mass (m) can be predicted by
multiplying it by
the speed of light (c) squared.
This idea has been tested in
many different contexts. Thus, we must refine our principle
of conservation of mass to be one of
conservation
of mass
and energy because, under certain extreme conditions, they
can transform into each other.
An example of binding energy
In nuclear power plants, in a process called
nuclear fission, the nuclei of uranium atoms are bombarded by neutrons
and
split into
the nuclei
of several smaller atoms. The combined weight of these
smaller atoms is less
than the weight of the original uranium atoms. This loss
of mass has, in fact, been released as energy. This energy is
sometimes
in the form
of
photons of high frequency light, known as “gamma
rays.”
The fission of one gram of uranium releases
the same amount of energy as burning three tons of coal
or 600 gallons
of fuel oil.
In the video, vacuum engineer Bob Childs is
shown working at the MIT Plasma and Fusion Center. In nuclear fusion,
particles of a
lighter element are
transformed into new particles of a heavier element.
Fusion also releases
energy when these particles are bound together. If you
add all the mass and energy that's around before and
after either
nuclear
fusion
or fission,
you'll find that the totals come out to be exactly the
same.
Where is the equivalence of mass and energy important?
Changes
where the loss of mass is significant, like the above examples,
typically happen only in the extreme
conditions of nuclear reactors
or inside stars, like the Sun. However, any time we change
the way particles
are arranged, we are binding them in a different way,
so very small amounts of binding energy are still being
used.
Therefore,
the
water vapor in
the above example would weigh slightly more than the
15 grams
of our original
water because there is slightly less energy in the more “loosely
bound” water vapor.
Typically, this difference
is so small as to be undetectable, so the principle
of conservation of matter is good enough
for everyday situations. (In fact, in any physical
change, the difference in mass is about one part in a billion,
which is smaller than can be measured
by even the most sensitive balances.)
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