CHAPTER 5 RENEWABLE ENERGY SOURCES II: ALTERNATIVES
Questions and Problems
1. Calculate the pressure in Newtons per square centimeter at the bottom of a static column of water300metershigh.
1 ATM = 760 mm Hg; ρHg = 13.6 g/cc, ρH20 = 1 g/cc
2.
a) How much electricenergycan be generated by the water in a lake2000meterswide by8000meterslong by100metersdeep if all the water falls through a vertical distance of500meters? Assume that the generator is 90% efficient. Express your answer in joules.
b) What would the electricpoweroutput be if the lake were drained over a period of one year? (in megawatts)
c) How large a community would this serve at the typical rate of1MWeper 1000 people (per year)?
d) At$0.05/ KWhr, what is the value in dollars of this electrical energy?
3. BONUS
a) Calculate the energy in joules made available when1kgof water falls30metersif 90% of the energy can be converted to a useful form.
b) Calculate the energy in joules made available when1kgof water is cooled by 2°C if 3% of this energy can be converted to a useful form.
c) Compare these two numbers. Does this say something about the relative amounts of water that must pass through a hydroelectric plant and an OTEC plant?
4. BONUS If a windmill produces23kWof electric power at a wind velocity of10milesper hour, how much power will it produce at a wind velocity of 20 miles per hour?
5. A windmill has a diameter of2meters. It converts wind energy to electrical energy at an efficiency of 60%of the theoretical maximumwhen connected to an electrical generator.
a) What is the electric power output at a wind velocity of (1)10mph? (2)20mph? (3)30mph?
b) How many60wattlightbulbs can be supplied with electricity under conditions of (1), (2), and (3)?
6. How much thermal energy in joules is made available by cooling1cubic meterof rock from 240°C to 100°C? The specific heat is2.4J/cm3⋅°C.
7. BONUS A geothermal-powered steam turbine operates between a steam temperature of 210°C and an environmental temperature of 25°C. What is its maximum (ideal) efficiency? What percentage of the total steam energy must be discharged as a waste heat?
8. Calculate the overall efficiency of an OTEC plant that operates with the ideal Carnot efficiency between the temperatures of 20°C and 5°C, but which uses two-thirds of the energy extracted to run pumps and make up other losses.
9. BONUS
a) Starting from the results ofExamples 5.4and5.5, estimate the number of cubic meters of water that would flow each second through an OTEC plant large enough (1000MWe) to provide electricity for Miami. Use the approximation of an ideal heat engine as in the examples.
b) If this water flows at a velocity of4m/s, what would be the necessary diameter of the pipes?
10. A tidal basin with an area of 14 square kilometers and a depth of 12 meters empties in 6 hours with the water passing through turbines.
a) How many cubic meters per second must flow on average during this six-hour period?
b) How many square meters of cross-sectional area must the turbine pipes have if the flow velocity is 7m/s?
11. Estimate the number of Btu that would be generated annually in the United States if all the municipal waste were incinerated. Assume1000poundsper year per person of burnable waste at4300Btu/lb. How does this compare with the total energy consumption of the United States?
12. BONUS Estimate the forest area needed to supply fuel continuously for a 1000MWe power plant. Note that this requires about three times as much thermal power as electric power.
Multiple Choice Questions
1. BONUS Fifteen kilograms of water 90 meters above a generator represents ___ joules of potential energy.
a) 2102
b) 60
c) 980
d) 9.8
e) 29,160
f) 1350
g) 1380
h) 13,230
2. If a 90-meter high waterfall has a flow rate of 15 kg per 0.1 sec, what is the power in watts in the stream of water as it hits the bottom?
a) 210.2
b) 600
c) 98
d) 9.8
e) 291,600
f) 135
g) 13,800
h) 132,300
3. Hydroelectricity accounts for approximately ___ percent of the electrical energy consumption in the United States.
a) 1
b) 7
c) 40
d) 70
4. How much electric power could be obtained from a small hydroelectric station if the elevation change was 150 meters and if 10,000 kg of water passed through the turbines every second, with the overall efficiency being 85%?
a) 1.3 MWe
b) 25 MWe
c) 12.5 MWe
d) 12.5 kWe
5. A windmill system which produces 5 kW of electric power when the wind is blowing at 3 m/s, will produce ___ kilowatts when the wind is at 9 m/s.
a) 1.67
b) 15
c) 45
d) 135
6. BONUS A wind of 30 m/s produces ___ times as much power per square meter as does a wind of 10 m/s.
a) 27
b) 9
c) 3
d) 36
7. If the wind blows for one year at a steady 10 m/s, the energy we could get in this year per square meter of cross section through the use of a windmill would be about ___ kWh.
a) 2200
b) 600
c) 200
d) 60
8. A modern windmill can extract about ___% of the power in the wind.
a) 1
b) 10
c) 20
d) 40
e) 60
f) 65
g) 70
h) 90
9. Of the total kinetic energy content of a one square meter cross section of wind, one might expect to convert ___ to electricity with a modern windmill.
a) 1%
b) 40%
c) 10%
d) 99%
10. In the OTEC plants envisioned, the colder water is at a temperature of ___, and is drawn in from a depth of ___.
a) 5°C,1000ft
b) 5K,1000ft
c) 5K,1000m
d) 25°C,1000ft
e) 25°F,1000m
f) 5°C,1000m
g) 20°C,500m
h) 20K,5000m
11. BONUS Ocean thermal gradient heat engines operate between temperatures of ___
a) 75°C and 45°C
b) 15°C and −10°C
c) 25°C and 5°C
d) 50°C and 20°C
12. The following is true of geothermal energy:
a) It will easily supply all the energy needs of the United States.
b) Since it basically comes from the sun, it is renewable.
c) It has its origins in the earth's radioactivity, and it can be exhausted locally.
d) The Geysers in California has a capacity of 512 GWe.
13. A geothermal-powered steam turbine operates between a steam temperature of 210°C and an environmental temperature of 25°C. What is its maximum (ideal) efficiency?
a) 13%
b) 18%
c) 23%
d) 28%
e) 33%
f) 38%
g) 43%
h) 48%
14. The normal geothermal gradient is _____
a) 3°C/km
b) 30°C/km
c) 3°C/m
d) 30°C/m
e) 3°C/1000ft
f) 1/16W/cm2
g) 16W/m
h) 3K/m
15. Tidal energy has its origin in _____
a) the phase of the moon.
b) just the oceans sloshing back and forth.
c) the decay of primordial radioactive nuclei within the earth.
d) the kinetic and gravitational potential energy of the earth–moon–sun system.
e) trade winds acting on the earth's surface.
f) the hydrologic cycle.
g) the Carnot dynamics of ideal heat engines.