Energy and Human Ambitions on a Finite Planet, 2021a

15 Nuclear <strong>Energy</strong> 246
15.3 Mass <strong>Energy</strong>
<strong>Energy</strong>—whatever the form—has mass <strong>and</strong> actually changes the weight
of something, although almost imperceptibly. A hot burrito has more
mass than the exact same burrito—atom for atom—when it’s cold. 12 Most
of us are familiar, at least casually, with the famous relation E mc 2 .
More helpfully, we might express it as
ΔE Δmc 2 , (15.1)
where the Δ symbols indicate a change in energy or mass, <strong>and</strong> c ≈
3 × 10 8 m/s is the speed of light. Using kilograms for mass results
in Joules for energy. Because c 2 is such a large number (nearly 10 17 ),
the mass change associated with daily/familiar energy quantities is
negligibly small. Box 15.2 explains why E mc 2 is valid for all energy
exchanges—not just nuclear ones—but generally results in mass changes
too small to measure in non-nuclear contexts. Earlier, we discussed
conservation of energy. More correctly, we observe conservation of massenergy.
That is to say, a system can actually gain or lose net energy if the
mass changes correspondingly. In the case of nuclear energy release, the
“new” energy comes at the expense of reduced mass.
12: The burrito is also ever-so-slightly more
massive if it has kinetic energy, gravitational
potential energy, or any form of energy. A
battery is more massive when charged, even
if no atoms or electrons are added. Incidentally,
charging a battery does not mean
literally adding electrical charges (adding
particles), but amounts to rearranging electrons
among the atoms within the battery.
Box 15.2: E mc 2 Everywhere
Physics is not selective about when we might apply E mc 2 .It
always applies, to every situation. It’s just that outside of nuclear
reactions it does not result in significant mass differences.
For example, after we eat a 1,000 kcal burrito to fuel our metabolism,
we expend the energy 13 <strong>and</strong> lose mass according to Δm ΔE/c 2 .
Since ΔE ∼ 4 MJ (1,000 kcal), we find the associated mass change is
4.6 × 10 −11 kg, which is ten orders-of-magnitude smaller than the
mass of the burrito itself. 14 So we’d never notice, even though it’s
really there.
When we wind up a mechanized toy, coiling a spring, we put energy
into the spring <strong>and</strong> the toy actually gets more massive! But for every
Joule we put in, the mass only increases by about 10 −17 kg. Forgive
us for not noticing. Only in nuclear contexts are the energies large
enough to produce a measurable difference in mass.
13: . . . ultimately given off as thermal energy
to our environment
14: This amount of mass corresponds to
that of a tiny length of hair that is shorter
than it is wide.
Example 15.3.1 Since mass <strong>and</strong> energy are intimately related, it is
common to express masses in energy terms. How would we express
12.0 a.m.u. in MeV (a unit of energy; see Sec. 5.9; p. 78)?
1 a.m.u. is equivalent to 1.66 × 10 −27 kg (last row of Table 15.4), so
12 a.m.u. is 1.99×10 −26 kg. To get to energy, apply E mc 2 , computing
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.