Name________________________
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219: Energy and the Environment
Second Exam: May 6, 2013
You have 120 minutes to answer both portions of the test. The test is closed-book,
closed-note. You may use calculators, but not laptops or smartphones. Please put your
name on the top of ALL pages. Answer the questions in the spaces provided. You can go
onto the back if necessary.
1) The Taum Sauk reservoir in Missouri holds as much as 5.4  106 m3 of water and is
800 m above the hydroelectric generating plant at the base of the mountain.
(a) How much greater is the gravitational potential energy of the water in the full
reservoir than that of the same water at the level of the generating plant?
(Gravitational energy is the product of mass, gravity, and height.)
(b) If the pumps that raise the water are 70% efficient and the generating plant is 80%,
what is the overall efficiency of the pumped storage system?
(c) Why would one choose to use pumped storage with this efficiency, which is
considerably less than 100%, instead of just sending the electricity to the consumers
directly?
(d) How much electrical energy is produced by emptying a full reservoir through the
generating plant?
(e) Why is salt-cavern compressed air storage for energy generally much less efficient
than the 70% for pumping water? Where does the lost energy go?
Name________________________
2) a) Radioactive 14C -minus decays to stable 14N with a half-life of 5730 years.
Suppose a piece of wood found on the sand in a southwestern desert has 1/8 of the
amount of 14C relative to what has been present in the atmosphere at the time it
formed. When did the tree that the wood came from die?
b) In class I said that when you assemble a helium nucleus out of two neutrons and two
protons, the masses don’t add up. The masses of the neutrons are 1.00866 amu
(atomic mass units), the masses of the protons are 1.00728 amu, and the mass of the
final helium nucleus is 4.0028 amu. What happened to the missing mass?
c) Explain each of the three different processes represented in this diagram:
d) In terms of fundamental forces, why are large atomic nuclei (many neutrons and
protons) generally less stable than small atomic nuclei?
e) Uranium is naturally found as 99.3% U-238 and 0.7% U-235. Why does the uranium
have to be “enriched” in U-235 for it to be used as fuel for nuclear fission?
f) What is a problem of having fuel that is too enriched in U-235?
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Name________________________
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3) In St. Louis, the typical amount of sunlight falling on a flat plate collector tilted toward
the sun is about 200 W/m2.
a) How much energy, in Btu/m2, is this per day?
b) Suppose that a typical St. Louis house needs 20,000 Btu/hour. How many square feet
of flat plate collectors would be needed to supply the heating needs? (Assume that the flat
plate collectors are 1/3 efficient. 1 m2 = 10.76 ft2.)
c) Estimate (roughly) the dimensions of a typical suburban house, and therefore the
ability of roof-mounted flat plate collectors to supply heating needs.
d) Why do you think it is the case that very few houses have flat plate collectors mounted
on their roofs?
Name________________________
4) a) The amount of sediment that a stream can carry within it varies as a function of
stream velocity. Explain the implication for this in terms of maintenance of a
hydroelectric power plant.
b) What is one advantage of using a diverted “Run of river” channel for a hydroelectric
power plant?
c) What might be a problem resulting from installing a hydroelectric dam in an arid
region with strong demands on water usage?
d) Give an example of how the current global climate change could effect hydroelectric
power production in a particular area.
e) Tidal power will vary in efficiency over the course of a month. Explain why.
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Name________________________
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5) a) If more than half of the world’s people still use traditional biomass “renewable”
energy sources, why is biomass energy such a tiny portion of world’s total energy
supply?
b) The solar energy conversion efficiency for crops are extremely low, about 1% at best.
Explain some of the reasons for this low efficiency.
c) Biomass energy is MUCH less efficient than solar panels or concentrated solar power,
in terms of energy per area. Give two reasons why we still grow crops for biomass energy
(there are lots to choose from).
d) Give two examples of disadvantages (out of many) of using corn to produce biofuels.
e) Using the pie charts on the
right, which US energy source
had the greatest increase (in
total Btu consumption)
between 2006 and 2010?
f) How much more was this
increase compared to the
second-fastest growing
renewable energy source?
Name________________________
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6) a) How can you produce geothermally generated electricity even if the water you are
pumping out of the ground is not hot enough to create steam?
b) In the example that I gave about the ideal sustainable situation of removing heat from
the earth, I said that there was a theoretically optimal depth of 15 km (though not yet
technologically capable) that you would want to drill down to pump water down and then
bring it back to the surface. Explain why there is an optimal depth for this. In other
words, explain the reasons that determine why this would be better than going shallower
or deeper.
c) How is geothermal energy related to nuclear energy?
d) Why would a residential geothermal system be more efficient in the winter than in the
spring or fall?
Name________________________
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7) a) Using the accompanying
table, what are two reasons
why wind turbines have been
getting taller?
b) Using the table, estimate
how the wind power varies as a
function of turbine diameter
and as a function of wind speed
(for example, what happens
when you double either of
these parameters).
c) Estimate the maximum power output would you expect from a wind turbine with a
blade of 37.5-ft diameter in a 25 mph wind.
d) A recent wind farm in Missouri had a maximum output capacity of 146 MW of electric
power. It produces 4.0  105 MWh/y annual average electric power. What is its capacity
factor (the ratio of actual average power to maximum possible power)?
Name________________________
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8) The table gives data on different modes of urban transport
Vehicle
Energy cost (kJ/(vehicle km)) Passenger capacity Load factor
Motorcycle
Auto
Personal truck
Transit bus
Light rail
1,642
3,850
4,698
24,982
46,397
2
5
4
44
100
75%
25%
35%
25%
40%
a) For each mode, using the capacity and load factors given, compute the Energy cost per
passenger-km.
b) Which mode would you recommend for transporting a large number of people? (In
addition to energy cost, consider other factors that may be important.)
c) Air resistance force increases as the square of a vehicle’s speed. Consider the force on
a car traveling at 40 mph.
i. At what speed is the force twice as large?
ii. At what speed is the force three times as large?
Name________________________
9) For each of the following energy sources, explain whether or not it originates as solar
energy. If so, explain the route of transfer of energy.
a) ethanol
b) coal
c) petroleum
d) geothermal
e) nuclear fission
f) hydroelectric
g) wind power
h) tidal power
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Name________________________
10) a) Describe how
this house functions
differently in the
winter and summer?
What role does the
overhang play?
b) The floor is
typically stone or
concrete. Why?
c) What is on the roof,
and why is it
connected to the
floor?
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Name________________________
11) a) Why is the marginal cost of oil so important for the current development of
renewable energy sources?
b) The chart to the right shows
estimated average costs of
different energy sources (in
$/MWhr). (Combined Cycle
sources assume natural gas as the
primary source). All of these
costs are variable. How would
the relative costs of fuel sources
change if capitol costs were
averaged over 40 years instead of
20 years? Which source would it
affect the most?
c) In class I talked about a report
that estimated that including the
hidden costs for coal (such as
health problems and pollution in
mining areas). How would
accounting for these costs in the price of coal power affect market forces for renewable
energy sources?
d) What other sources on this chart would high hidden costs that would significantly
increase the price of power from that fuel source?
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Name________________________
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12) a) Why are many of the geopolitical conflicts areas related to energy sources centered
on hydrocarbons resources that are offshore?
b) Choose an example from among the South China Sea, East China Sea, or Caspian Sea,
and summarize the conflict.
c) Why is there so much global military attention paid to the Strait of Hormuz (at the
mouth of the Persian Gulf)?
d) From the perspective of military costs, why are there benefits of moving from a
petroleum-based economy to a solar energy-based economy?
Name________________________
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Table 3-4d, p. 91