Name______1
219: Energy and the Environment
Second Exam: May6, 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?
a)(3 pts) PE = mgh = 5400000 m3 x 1000 kg/m3 x 9.8 m/s2 x 800 m = 42 x 1012 J = 42 Terajoules
b)(1 pt) 0.7 x 0.8 = 0.56
c)(2 pts) Because it still costs less to store energy during off-peak times from a large coal or nuclear power plant and get it back during peak times (even with the 56% efficiency) than to run the plant at a higher level and throw away the extra energy produced during off-peak times.
d)(1 pt) Answer to (a) times 80% = 34 x 1012 J = 34 Terajoules.
e)(2 pts) Because energy is lost to heat when the air is compressed. That heat goes into the walls of the salt cavern (or out the compressor).
9 pts
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 whathas 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?
a)(2 pts) 1/8 of the C14 is 3 half lives. 3 x 5730 = about 17200 years
b)(1 pt) The missing mass was the binding energy – it was converted into radiated energy during the nuclear fusion.
c)(3 pts) Alpha decay – a helium nucleus (2 protons and 2 neutrons) leaves the atomic nucleus. The isotope has less mass - two fewer protons and neutrons.
Beta decay – a neutron separates into a proton and electron (which leaves). One element higher (gains a proton), but the mass is the same.
Electron capture – an electron combines with a proton to form an additional neutron. One element lower (loses a proton), but the mass is the same.
d)(2 pts) because the strong nuclear force, which holds the protons together, only acts over short distances, so it becomes harder to hold the nucleus together.
e)(1 pt) Because the U-238 is not fissile, and it hinders the fission reactions.
f)(1 pt) It can be used to make bombs and is therefore a terrorism risk.
10 pts
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?
a)(3 pts) 200 W/m2 x 24 hr = 17.28 Megajoules = ~16,400 Btu/m2 per day
b)(3 pts) 20,000 Btu/hr is 4,800,000 Btu per day
Divided by 16,400 Btu/m2 per day = 29 m2 (assuming 100% efficiency)
Accounting for the 1/3 efficiency: 29 m2 x 3 = 88 m2 = ~950 ft2
c)(1 pt) Example: 30 ft x 40 ft = 1200 ft2. [Students answer will vary] But the point is that the required square footage is of the order of the average house roof.
d)(1 pt) [Answers will vary] The main reason is that the cost of a large flat plate collector system is quite expensive.
8 pts
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.
a) (2 pts) sediment will accumulate behind the dam, and will need to be routinely dredged.
b) (2 pts) it does not block the main river channel (which can then be used for river transport, fish migration, etc.)
c) (2 pts) lots of evaporation off the increased surface leads to a loss of water
d) (1 pt) with global warming, some parts of the world are getting less precipitation, so there would be less water for hydro power.
e) (2 pts) During “spring tides,” when the tidal effects of the moon and sun combine, there will be more tidal power available. During neap tides, the tidal effects of the moon and sun partially cancel, and there will be less tidal power available.
9 pts
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?
a)(2 pts) because these people use very little energy. Most of the world’s energy consumption is by a small total of the world’s population.
b)(2 pts) Several possible choices. Full credit if they give 2 answers. Possible choices include:
- The plant is only growing for part of the year
- Sunlight only directly hits a small portion of growing leaves
- Only about half of this is in a spectrum that is usable by the leaves
- Only a small portion is converted into stored energy
- Some of this energy is lost by photorespiration or used to sustain the plant
c)(2 pts) Full credit for 2 answers. Possible choices include:
- Provides jobs for local farmers
- Reduces the cost of gasoline for consumers
- Reduces dependence on foreign oil
- Fewer CO2 emissions compared to coal or natural gas
- [other answers possible]
d)(2 pts) Full credit for 2 answers. Possible choices include:
- Most biomass plants are in violation of the Clean Air Act for pollution
- Black carbon (soot) is a huge contributor to global warming
- Can lead to bad haze and smog (especially in Asia)
- Drives up the cost of food
- More expensive than natural gas, nuclear, etc.
- Is barely break-even in terms of energy
- Heavily subsidized by the government
- Requires large amounts of pesticides and herbicides
- Quickly removes nutrients from the ground, so needs lots of fertilizer.
e)(2 pts) Biomass: went from 3.26 quadrillion Btu in 2006 to 4.26 quadrillion Btu in 2010 – an increase of 1.0 quadrillion Btu
f)(2 pts) Second-fastest growing is wind: went from 0.266 quadrillion Btu in 2006 to 0.88 quadrillion Btu in 2010 – an increase of 0.61 quadrillion Btu (only 60% of the increase in biomass.
12 pts
6) a) How can you producegeothermally 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 idealsustainable 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?
a)(2 pts) You can use a binary cycle system where the warm water heats a solvent with a low boiling point, and the solvent expands to a vapor, driving the turbine.
b)(2 pts) For deeper depths, the vertical temperature gradient is too small. For shallower depths, the temperature is too low.
c)(1 pts) It is the radioactive decay of isotopes (such as of uranium, potassium, and thorium) that provides the heat inside Earth.
d)(2 pts) Residential geothermal is based on taking advantage of differences in temperature between the outside air/water and the temperature of the ground. During the spring and fall, that temperature difference is very small.
7 pts
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 themaximum 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 105MWh/y annual average electric power. What is its capacity factor (the ratio of actual average power to maximum possible power)?
a) (2 pts) 1. Winds are faster at greater alititudes. 2. Longer rotors require higher turbines.
b) (2 pts) 1. It increases with about the square of the turbine blade diameter (power is about 4x greater each time the diameter doubles). 2. It increases even faster as a function of wind speed (by about a factor of about 8 each time the wind speed doubles)[they could also say that the power is proportional to the cube of the wind speed]
c) (1 pt) This is an exercise in estimating. The correct answer is around 90, but give them full credit if their answer is between 80 and 100.
d)(3 pts) In one year, 146 MW => 146 MW x 3.15569 x 107 s = 4.6 x 1015 j
In a year, the wind farm produces 4 x 105MWh = 4 x 105 x (3.61 x 109 j) = 1.44 x 1015 j
The ratio of 1.44 x 1015 j / 4.6 x 1015 j = ~0.3, so the capacity factor is 30% (or .3)
8 pts
8) The table gives data on different modes of urban transport
Motorcycle / 1,642 / 2 / 75%
Auto / 3,850 / 5 / 25%
Personal truck / 4,698 / 4 / 35%
Transit bus / 24,982 / 44 / 25%
Light rail / 46,397 / 100 / 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?
a)(3 pts) The different vehicles are:
- motorcycle = 1095 kJ/passenger-km
- auto = 3080
- truck = 3355
- bus = 2271
- rail = 1160
b)(1 pt) Rail
c)(2 pts) i. 40 x 21/2= 57 mph
ii. 40 x 31/2= 69 mph
6 pts
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
a)Yes – sunlight to plant biomass via photosynthesis, to ethanol (via various means of processing)
b)Yes – sunlight to plant biomass via photosynthesis, buried long ago, compressed and heated within the earth to become coal
c)Yes – sunlight to marine phytoplankton, buried on the sea floor beneath many other sediments, compressed and heated within earth to break down to become petroleum
d)No
e)No
f)Yes – sunlight drives the water cycle, evaporating water off of the ocean, driving air circulation that lifts the air (gravitational potential energy), allowing rain to fall on the land and flow back to the sea (kinetic energy)
g)Yes – sunlight causes differential heating of Earth’s surface, which helps to drive air circulation and winds
h)Yes (partly) – part of tidal energy is from the sun’s gravity
8 pts
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?
a)(3 pts) Summer – the overhang prevents sunlight from directly entering the house. Vents allow hot air to rise up and leave the house.
Winter – Sunlight (because the sun is lower in the sky) directly enters the house through the lower and upper windows, warming the house.
b)(2 pts) The concrete or stone floor helps absorb and retain the sunlight so it stays warm during the night.
c)(2 pts) On the roof is a flat plate collector, which warms water (or another fluid) which flows through pipes in the floor, helping to warm the floor.
7 pts
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?
a)(1 pt) If the marginal cost of oil becomes very expensive, then other kinds of energy will begin to be developed. If the cost is low, no investment goes into alternative energy sources.
b)(3 pts) Energy sources that have a large capitol cost would be less expensive. Because Solar PV has the highest capitol cost, its total cost would drop the most.
c)(2 pts) Coal would be considered more costly than most other sources of energy.
d)(2 pts) [Answers will vary. Full credit if they give a reasonable explanation for one other source.] Biomass would go up some. Nuclear would go up a lot. Combined cycle would go up the most.
8 pts
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?
a)(2 pts) Because the ownership of the hydrocarbons is uncertain (countries can have different laws for offshore limits)
b)(2 pts) [answer varies]
c)(2 pts) 1/3 of all oil passes through there, and Iran is threatening to blockade it
d)(2 pts) because everyone has sunlight.
8 pts