APES Energy Unit
Information & Problems
Energy and Power
Watts (W) are used for measuring power. A one hundred watt light bulb, for example, is rated to
consume one hundred watts of power when turned on. If such a light bulb were on for four
hours it would consume a total of 400 watt-hours (Wh) of energy (or 0.4kWh of energy – see
next paragraph). Watts, therefore, measure instantaneous power while watt-hours measure the
total amount of energy consumed over a period of time.
A megawatt (MW) is one million watts (106) and a kilowatt (kW) is one thousand watts (103).
Both terms are commonly used in the power business when describing generation or load
consumption. For instance, a 100 MW rated wind farm is capable of producing 100 MW during
peak winds, but will produce much less than its rated amount when winds are light. As a result
of these varying wind speeds, over the course of a year a wind farm may only average 30 MW
of power production. Similarly, a 1,000 MW coal plant may average 750 MW of production
over the course of a year because the plant will shut down for maintenance from time-to-time
and the plant operates at less than its rated capability when other power plants can produce
power less expensively.
The ratio of a power plant's average production to its rated capability is known as capacity
factor. In the previous example, the wind farm would have a 30 percent capacity factor (30 MW
average production divided by 100 MW rated capability) and the coal plant would have a 75
percent capacity factor (750 MW average divided by 1,000 MW rated capability). Load factor
generally, on the other hand, is calculated by dividing the average load by the peak load over a
certain period of time. If the residential load at a utility averaged 5,000 MW over the course of a
year and the peak load was 10,000 MW, then the residential customers would be said to have a
load factor of 50 percent (5,000 MW average divided by 10,000 MW peak).
Knowing the peak and average demand of a power system is critical to proper planning. The
power system must be designed to serve the peak load, in this example 10,000 MW. But the
actual load will vary. The load might be 10,000 MW at noon, but only 4,000 MW at midnight,
when fewer appliances are operating. The capacity or load factor gives utility planners a sense
of this variation. A 40 percent load factor would indicate large variations occur in load, while a
90 percent load factor would indicate little variation. Residential homes tend to have low load
factors because people are home and using appliances only during certain hours of the day,
while certain industrial customer will have very high load factors because they operate 24 hours
a day, 7 days a week.
Sample Problem
A water bed is heated every day. If it used its maximum power, it would run at 350 Watts.
The actual annual consumption in this problem is 960 kWh. Is the water bed running at
maximum power?
1. Convert units (either 960 kWh = 960,000 Wh or 350 Watts = 0.350 kW)
2. Calculate the number of hours in a year (365 days x 24 hrs/day = 8760 hours)
3. Calculate the watts (960,000Wh/8760 hrs = 110 Watts)
4. The answer is less than the maximum of 350 Watts (~30% of total)
Part I: Problem Solving
Show your work!!!
Note: ENERGY (in kilowatt-hours) = POWER (in kilowatts) x TIME (in hours)
1. If an electrical device has been operating at 750 Watts for 4 hours, how many kilowatthours of energy has it produced?
Answer: 0.750kW x 4hr
2. Your computer needs 200 Watts of power. If you use the Internet for 3 hours, how many
kilowatt-hours (kWh) of energy have you used?
Answer: 0.200kW x 3hr
3. To reheat a piece of cold pizza, you can either heat it in a typical toaster oven (1150
Watts) for 6 minutes (0.1 hours) or put it in the microwave (1300 Watts) for 1 minute
(0.0167 hours). Which uses less energy for this process – the toaster or microwave?
Toaster: 1.150kW x 0.1hr
Microwave: 1.3kW x 0.0167hr
4. With moderate winds, a modern large wind turbine can generate about 250 kW of
electricity, whereas a large nuclear power plant can generate 1,000 MW. How many wind
turbines would be required to give the same output as one nuclear power plant?
Wind: 250kW = 0.250MW
Nuclear: 1000MW
1000/0.250 =
5. A 1.5-volt D cell battery can deliver 4.5 watt-hours of electrical energy.
Convert this energy to kWh and compare the cost of electrical energy derived from batteries to
that of standard "grid-based" electricity. Assume that the battery costs $1.00 and that electricity
from the power company is available at $0.10/kWh.
Answer: 4.5 wh/1000wh/kWh= .0045kWh for a dollar
.0045kWh x $.10/kWh =
for power company electicity
6. One pound (lb) of bituminous coal contains 12,000 BTUs of energy. A BTU is a British
Thermal Unit, or the amount of heat required to raise the temperature of one pound of
water (one pint) by one degree Fahrenheit. Suppose a coal-fired power plant needs 3,400
BTU's of heat to produce one kilowatt-hour of electricity. This plant has a 1 Megawatt
output. Showing all steps, calculate the following:
A. How much coal is required to produce one kilowatt-hour of electricity?
B. How much coal must be burned to keep the plant at full output for 24 hours?
C. Assuming the coal is 2% sulfur by mass, how many pounds of sulfur would be released in a
24-hour period?
Answer
A. How much coal is required to produce one kilowatt-hour of electricity?
1 lb coal = 12,000 BTU
1 kWh = 3,400 BTU
(3,400 BTU/kWh)/(12,000 BTU/1 lb coal) = 0.28 lb coal/kWh
B. How much coal must be burned to keep the plant at full output for 24 hours?
Full output = 1 MW
Note: Important metric conversion: 1 MW = 1000 kW
(0.28 lb coal/kWh) x (1000 kW) x (24 h) = 6720 lb coal
C. Assuming the coal is 2% sulfur by mass, how many pounds of sulfur would be released in a 24 hour period?
0.02 x 6720 = 134.4 lb sulfur
7. The conventional gasoline-powered 2004 Honda Civic is one of the best gas-powered
cars in its class for mileage. The conventional Honda Civic gets 35 MPG during city
driving (40 MPG Freeway). When the exact same car is given a hybrid-electric engine,
mileage is 47 MPG city and 48 MPG Freeway. $20, 650 is the cost of the Honda Civic
Hybrid, $16,000 is the cost of the Honda Civic conventional, depending on features. You
plan to drive mostly in the city, to and from work and for weekend errands. You expect to
drive 8,000 miles a year in city driving, plus another 4,000 miles in longer trips that would
count as "highway."
A.) How much would you spend on gas for the hybrid Civic in a year, assuming gas cost $1.89
a gallon?
B.) How much would you spend on gas for the conventional Civic in a year, assuming gas cost
$1.89 a gallon?
C.) How long would it take for the savings in gas costs to offset the increase in the price of the
hybrid Civic?
Answer
A.) How much would you spend on gas for the hybrid Civic in a year, assuming gas cost $1.89 a gallon?
City Driving Gas Cost: (8000 miles/year x $1.89/gallon)/(47 miles/gallon) = $321.70/year
Hwy Driving Gas Cost: (4000 miles/year x $1.89/gallon)/(48 miles/gallon) = $157.50/year
Total Gas Cost: $479.20/year
B.) How much would you spend on gas for the conventional Civic in a year, assuming gas cost $1.89 a gallon?
City Driving Gas Cost: (8000 miles/year x $1.89/gallon)/(35 miles/gallon) = $432/year
Hwy Driving Gas Cost: (4000 miles/year x $1.89/gallon)/(40 miles/gallon) = $189/year
Total Gas Cost: $621/year
C.) How long would it take for the savings in gas costs to offset the increase in the price of the hybrid Civic?
Difference in Car Cost = $4650
Difference in Gas Cost = $141.80/year
$4650/$141.80/year = 32.8 years
*Note: If gas were $2.89/gallon, the length of time is reduced to 21.45 years. Probably not a compelling
reason to buy a hybrid. See the next problem for another argument in favor of a hybrid.
8. The 2004 Toyota Prius gets 60 MPG city and 51 MPG freeway. The "best-selling car in
America" is the Ford F-150 truck. The 4WD, V6 version of the F-150 gets 15 MPG city
and 19 MPG highway.
A.) The average American drives 12,000 miles per year. Assume that most people do most of
their driving in stop & go city traffic (75%), and not in freeway traffic (25%). How many
gallons of gas would be saved per person by driving a Prius over the F-150?
B.) Assume that every gallon of gas burned contributes approximately 20 kg of CO2 to the
atmosphere. How many extra kg of CO2 are put into the atmosphere by the F-150 in a year,
when compared to the Prius?
C.) F-Series trucks (all the Ford trucks like the F-150) were the best-selling vehicles in America
for the 22nd consecutive year in 2003. Sales totaled 845,586 trucks for the year. Calculate how
many gallons of gas and kg of CO2 would be saved if all of these truck purchasers bought a
Prius instead (unlikely, and perhaps unreasonable, but let's just see).
D.) If the vehicle is in service (to one owner or another) for 10 years, how much C02 is saved
over the life of the vehicle? How much money is saved? Assume gas still costs $1.89 a gallon,
as it did in 2003.
Answer
A.) The average American drives 12,000 miles per year. Assume that most people do most of their driving in stop
& go city traffic (75%), and not in freeway traffic (25%). How many gallons of gas would be saved per person by
driving a Prius over the F-150?
Prius Gas Consumption
City: (9000 miles/year)/(60 miles/gallon) = 150 gallons/year
Hwy: (3000 miles/year)/(51 miles/gallon) = 58.8 gallons/year
Total: 208.8 gallons/year
Truck Gas Consumption
City: (9000 miles/year)/(15 miles/gallon) = 600 gallons/year
Hwy: (3000 miles/year)/(19 miles/gallon) = 157.9 gallons/year
Total: 757.9 gallons/year
Difference = 549.1 gallons/year saved by driving a Prius
B.) Assume that every gallon of gas burned contributes approximately 20 kg of CO2 to the atmosphere. How many
extra kg of CO2 are put into the atmosphere by the F-150 in a year, when compared to the Prius?
549.1 gallons/year x 20 kg CO2/gallon = 10,982 kg CO2/year
C.) F-Series trucks (all the Ford trucks like the F-150) were the best-selling vehicles in America for the 22nd
consecutive year in 2003. Sales totaled 845,586 trucks for the year. Calculate how many gallons of gas and kg of
CO2 would be saved if all of these truck purchasers bought a Prius instead (unlikely, and perhaps unreasonable, but
let's just see).
845,586 trucks x 549.1 gallons extra/truck = 4.6 x 10 8 gallons extra
4.6 x 108 gallons extra x 20 kg CO2/gallon = 9.3 x 10 9 CO2
D.) If the vehicle is in service (to one owner or another) for 10 years, how much C02 is saved over the life of the
vehicle? How much money is saved? Assume gas still costs $1.89 a gallon, as it did in 2003.
(549.1 fewer gallons/year) x (20 kg CO2/gallon) x 10 years = 109,820 kg CO2
9. APES Exam Energy Question #1
Compare the impact of washing dishes by hand to the impact of washing in an electric washer.
Assume the following:
The dishes all fit in one load. The water going into the water heater for both the sink and the
washer is 50 degrees F. The water heaters are both 100% efficient. The electric washer uses 10
gallons of water heated to 140 degrees F and uses 0.500 kilowatt-hours of electrical for the load.
Washing by hand uses 20 gallons heated to 110 degrees F. One gallon of water weighs 8
pounds. 1 BTU is the amount of energy needed to raise the temperature of one pound of water
by 1 degree F. 1 kilowatt-hour = 3400 BTU.
a. Calculate the total energy in BTU used to heat the water and run the electric washer to wash a
load of dishes.
b. Calculate the energy in BTU used to heat the water for washing a load of dishes by hand.
c. Discuss the economic and environmental costs and benefits of each method.
Dishwasher Solution
a. Mass of water = 10 gals x 8 lbs/gal = 80 lbs water
Energy to heat this water = 80 gals x 90 degrees F x 1BTU/1 lb degree F = 7200 BTU
Energy to run dishwasher = 0.500kWh x 3400 BTU/kWh = 1700 BTU
Total energy = 7200 BTU + 1700 BTU = 8900 BTU
b. Mass of water = 20 gals x 8 lbs/gal = 160 lbs water
Energy to wash by hand = 160 lbs x 60 degrees F x 1 BTU/1 lb degree F = 9600 BTU
c. examples
Dishwasher
Hand wash
Dishwasher
Hand wash
Environmental costs
Pollution from extraction of resources
and transportation, use of resources
when purchased new, energy for
production and transportation.
More water & energy used
Economic costs
Production cost, transportation,
disposal when broken, repair,
purchase cost.
More water & energy used
more time for consumer to
wash dishes
Environmental benefits
Uses less energy & water
(if run full), lasts for a long
time.
No need for resources,
transportation, no need
for landfill space
Economic benefits
Jobs for production,
transportation, sales,
may save time for consumer.
No need for resources,
transportation
10. APES Exam Energy Question #2
Calculate the number of cubic feet of natural gas required to heat a house for one winter, as well
as the cost. Assume the following:
The house has 2000 square feet of living space. 80,000 BTU of heat per square foot are required
to heat for the winter. Natural gas is available at a cost of $5.00 per thousand cubic feet. One
cubic foot of natural gas supplies 1000 BTU of heat energy. The furnace in the house is 80%
efficient.
Home Heating Solution
a. 2000 ft2 x 80,000 BTU/ft2 x 1 ft3/1000 BTU = 160,000 ft3 natural gas
If this represents 80% efficiency, then 160,000 ft3/0.80 = 200,000 ft3
For 160,000 ft3: 160,000 ft3 x $5.00/1000 ft3 = $800
For 200,000 ft3: 200,000 ft3 x $5.00/1000 ft3 = $1000
11. APES Exam Energy Question #3
A large, coal-fired electric power plant produces 12 million kilowatt-hours of electricity each
day. Assume that an input of 10,000 BTU of heat is required to produce an output of 1 kilowatthour of electricity. Show all your work to calculate:
a. BTU of heat needed to generate the electricity produced by the power plant each day.
b. Pounds of coal consumed by the power plant each day, assuming one pound of coal yields
5,000 BTU of heat.
c. Pounds of sulfur released by power plant each day, assuming that the coal contains 1% sulfur
by weight.
d. The EPA standard for power plants like this one is that no more than 1.2 pounds of sulfur be
emitted per million BTU of heat generated. Using your previous answers, determine whether
the power plant meets the EPA standard.
Coal Plant Answer
1MW = 1000kW
1kWh = 10,000 BTU
12 x 106 kWh
1 lb coal = 5,000 BTU
a. (12 x 106 kWh) x 10,000 BTU/1 kWh = 1.2 x 1011 BTU/day
b. (1.2 x 1011 BTU/day) x (1 lb coal/5,000 BTU) = 2.4 x 107 lbs coal = 24 million lbs
c. 24 million lbs coal x 1% = 240,000 lbs sulfur/day = actual produced
d. Allowed: 1.2 lbs sulfur for every 1 million (1 x 106) BTU
(1.2 x 1011 BTU/day) x (1.2 lbs sulfur/1 x 106 BTU/day) = 144,000 lbs sulfur/day = allowed
amount of sulfur produced
*The power plant produces 240,000 lbs sulfur/day. The allowed amount is 144,000 lbs
sulfur/day. The power plant is not in compliance.
Part II: Nonrenewable Resource Use
A. Oil Consumption
1. One barrel of oil holds 42 gallons. All of the energy used by a person each year can be
expressed in what are called oil equivalents. Experts tell us that in the United States, on average,
a person consumes twenty-five barrels each year.
2. Calculate how many barrels of oil your family consumes each year based on the number of
people in your family.
3. Calculate how many barrels of oil are used by the entire class and the families (assume 4
people per family); by the whole school (population 1050); by the whole town (population
50,000); and by the state (population 3 million). Compare your family, class, school and town's
energy consumption to the 11 million gallons of oil spilled in Alaska in the 1989 Exxon Valdez
disaster.
4. Calculate how many barrels of oil were spilled.
5. How long would it take your family/class/school/town to use 11 million gallons of oil?
6. List five ways that you could reduce your oil consumption.
B. Oil Issues (see APES text)
1. What five countries have most of the world’s oil reserves?
2. What percentage of the world’s oil reserves is found in the United States?
3. What percentage of the world’s oil does the United States use?
4. What percentage of the oil used in the United States is imported?
5. How long are known and projected supplies of conventional oil expected to last in (a) the
world and (b) the United States?
6. List the advantages and disadvantages of drilling for oil and natural gas in Alaska’s Arctic
National Wildlife Refuge.
7. What are the advantages and disadvantages of using conventional oil as an energy resource?
8. What are the advantages and disadvantages of using heavy oil from oil sand and oil shale as
energy resources?
Part III: Energy Conservation in the United States
Use the APES textbook
1. How much of the energy used in the United States is wasted? What percentage is wasted
because of the second law of thermodynamics, and what percentage is wasted unnecessarily?
What are three of the least efficient energy-using devices?
2. What do most experts believe is the best way to save energy in transportation? Why isn’t this
being emphasized in the United States?
3. Explain why the real cost of gasoline to consumers in the United States is several times the
price they pay at the pump.
4. List reasons why there is little emphasis on saving energy in the United States, despite its
important benefits.
Part IV: Review Questions for Chapters 17 & 18
See website