Energy and Human Ambitions on a Finite Planet, 2021a

15 Nuclear <strong>Energy</strong> 272
d) two fragments of distinctly different size will emerge
e) the fission is an alpha decay: a small piece having A 4 is
emitted
24. A particular fission of 235 U + n (total A 236) breaks up. One
140
fragment has Z 54 <strong>and</strong> N 86, making it Xe. If no extra
neutrons are produced in this event, what must the other fragment
be, so all numbers add up? Refer to a periodic table (e.g., Fig. B.1;
p. 375) to learn which element has the corresponding Z value, <strong>and</strong>
express the result in the notation
A X.
25. Follow the same scenario as in Problem 24, except this time two
neutrons are left out of the final fragments. What is the smaller
140
fragment this time, if the larger one is still Xe?
26. Provide three examples of probable fragment size pairs (mass
numbers, A) from the fission of 235 U + n, making up your own
r<strong>and</strong>om outcome while respecting the distribution of Figure 15.15
in determining A values. For the sake of this exercise, assume no
extra neutrons escape the fragments.
27. Paralleling the graphical approach in Example 15.4.3 using Figure
15.10, what total energy would you expect to be released in a fusion
process going from two deuterium (H
2 4
) nuclei to He,inMeV?
Hint: no need to identify elements; just settle
on pairs of A values that add up correctly.
Hint: Don’t forget to count both
2 H.
28. Both nuclear <strong>and</strong> coal electric power plants are heat engines.
What is the fundamental difference between these two, comparing
Fig. 6.2 (p. 90) to Figure 15.12?
29. If a nuclear plant is built for $10 billion <strong>and</strong> operates for 50 years
under an operating cost of $100 million per year, what is the cost
to produce electricity, in $/kWh assuming that the plant delivers
power at a steady rate of 1 GW for the whole time?
30. Since each nuclear plant delivers ∼1 GW of electrical power, at
∼40% thermodynamic efficiency this means a thermal generation
rate of 2.5 GW. How many nuclear plants would we need to supply
all 18 TW of our current energy dem<strong>and</strong>? Since a typical lifetime
is 50 years before decommissioning, how many days, on average
would it be between new plants coming online (while old ones are
retired) in a steady state?
Hint: express the plant power in kW <strong>and</strong>
multiply by hours in 50 years to get kWh
produced.
Hint: how many days will one plant live,
then how many plants per day?
31. Extending Problem 16 toward what actually happens, we know
from Table 15.7 that the change in mass (which was close to 1 kg in
Prob. 16) is only 0.08% of the U Furthermore, a fresh
235 238
fuel rod is only 5% U—the rest being U. So how much total
uranium 85
235
must be loaded into the reactor each year, if all the U
is used up? 86
235
mass. 84 84: 0.185 out of 235 a.m.u.
85: Treat the two isotopes as having the
same mass: the rod has 20 times more uranium
than just the 235U
part.
32. Problem 15 indicated that we need the mass-equivalent of fewer
than 10 tons 87 of material to support the world’s annual energy
86: It’s not, actually, so this answer is a
lower limit on the actual mass that has to
be loaded in. So much for the ∼1 kg answer
from Problem 16.
87: One ton is 1,000 kg.
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.