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EPS219 – Energy and the Environment
Homework#7 – Due in class, Thursday, March 26, 2015
1) (10 pts) Ch 11, #P2 (A small transformer used for a doorbell steps down the voltage
from 120 V and 0.5A to 12 V. What is the current flow to the doorbell?)
Vin x Iin = Vout x Iout, so (120V)(0.5A) = (12V)(Iout), and Iout = 5A
2) (5 pts) Explain why you couldn’t determine the age of a dinosaur fossil using Carbon-14.
Answer: Because the last dinosaur lived 65 million years ago and the half-life of C-14 is
5730 years. There would be no C-14 left to measure.
3) (10 pts) a) Ch 14, #Q1 (Why doesn’t uranium undergo spontaneous chain reactions in
nature?)
The percentage of U235 is too small (the uranium is mostly U238, which is not fissile).
b) How is the answer to (a) related to the answer to Ch 14, #Q7 (Why is a conventional
nuclear reactor not able to explode as a bomb?)?
Similar reason. The enrichment of U235 in a
reactor is about 3%, which is far less than the
90% needed for a bomb.
4) (10 pts) Look at the accompanying diagram at
the right, from “Class15_Nuclear2.” What is going
on here? Explain why the “Total” curve is not a
simple curve, but has several bumps in it. [Hint: A
related question would be “where does the Th229 come from?”]
Answer: The different nuclides have different
decays rates, and as the initial set of nuclides
decay, they convert to other nuclides that all
have different half-lives, so there is a
progression over time of different dominant
nuclides that are decaying and emitting
energy.
5) (10 pts) Why are some of the best places to generate solar power located about 30°
north or south of the equator, and NOT at the equator?
2 parts:
1. Even though the sun is more directly overhead at the equator, it tends to be very cloudy
at the equator, so solar power is less efficient than it might otherwise be.
2. At about 30deg north and south the global air circulation patterns tends to have cold dry
air descending, so there are few clouds (and many deserts!), making for good places for
solar panels.
6) (20 pts) Suppose that you wanted to supply the world’s total energy needs (18 TW) with
solar panels. Imagine that your solar panels were 15% efficient. Imagine that you only put
them in places that had good solar potential, getting 250 W/m2.
a) What is the total area of solar panels that would be needed?
Answer: 480 x 109 m2, or 480,000 km2
[Area x (250 W/m2) x (0.15) = 18 TW)]
b) What percentage of the world’s total surface area is this?
Answer: 0.09%
[480,000 = C x [4π (6371)2], so C = 0.0009 or 0.09%]
c) If you used crystalline silicon cells that are 200 microns thick (2 x 10-4 m), given that
the density of silicon is 2330 kg/m3, how much silicon would you need?
Answer: 224 x 109 kg, or 224 trillion kg, or 224 billion tons
[Mass = volume x density = (480,000,000,000 m2) (2 x 10-4 m) x ( 2330 kg/m3)]
d) Silicon is a highly reactive element – you never find it occurring naturally as pure
silicon. Where does all the silicon for solar panels come from?
Rocks like quartz, which is SiO2. Common beach sand is mostly quartz, so you can get
your silicon from beach sand.
7) (10 pts) An architecture firm says they have the most efficient building design for
photovoltaic panels mounted flat on the roof. If they are advertising the exact same
building design in both New Orleans and Chicago, how do you know they are lying?
For a roof to have an efficient solar panel mounting, the tilt of the roof has to be
perpendicular to the average direction of incoming sunlight. Because this angle will change
with latitude, a design that is optimal in New Orleans will not be optimal in Chicago (or vice
versa).
8) (10 pts) Explain why off-shore wind turbines needs to be able to regularly pivot to
handle winds blowing both toward and away from shore.
During the daytime there is a dominant sea breeze (wind coming toward land) because the
land heats up faster than the ocean (because the heat capacity of water is much more than
that of rock and soil) and warm land air rises, pulling in air from the ocean. During the
night time there is a dominant land breeze (wind going from land to ocean) because the
land cools down so the ocean is warmer, and the process reverses.
9) (15 pts) Suppose a wind turbine has blades with a radius of 50 m, and the wind is
blowing at 8 m/s. What is the theoretical maximum power that that turbine could capture?
What happens to the theoretical maximum power if you increase the wind speed by 50%?
Answer: (Can be done 2 different ways)
If you just use E= (½)mv2:
Power = E/s = 0.5 x A x rho x v3 = (0.5)(pi)(50m)2(1.2 kg/m)(8 m/s)3
= 2.4 MW
If you change the wind speed to 12 m/s, the power goes up to 8.1 kW (it increases by
(1.5)3, or a factor of 3.375
Or, If you use the “Betz limit” equation from the book:
Power = 2.83 x 10-4 D2v3 kW = (2.83 x 10-4)(100m)2(8m/s)3 = 1.4 MW
If you change the wind speed to 12 m/s, the power goes up to 4.9 MW
(again, increasing by a factor of (1.5)3, or 3.375)