Problems
Name_________________
Background:
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Energy is the capacity to do work.
Power is the rate at which energy is used. The basic unit of power is the Watt.
(1 Watt = 1 Joule per second)
Power = Energy
Time
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1 KW = 1,000W
1 MW = 1,000,000W
Energy (in kilowatt-hours) = Power (kilowatts) x Time (hours)
Practice Problems:
1. If an electrical device has been operating at 750 Watts for 4 hours, how many kilowatthours of energy has it produced?
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?
3. A 1.0 watt light bulb in 20% efficient. That means 20% of the electrical energy is
converted into light and 80% is transformed into heat.
a. How many kWh does it use in 12 hours of operation?
b. How much energy does the light bulb convert to light during the 12 hours? How
much to heat?
4. To reheat a piece of cold pizza, you can either heat it in a typical toaster oven (1150
Watts) for 6 minutes or put it in the microwave (1300 Watts) for 1 minute. Which uses
less energy for this process—the toaster or microwave?
5. 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?
6. 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.
7. An electric clothes dryer has a power rating of 4000 W. Assume a family does 5 loads
of laundry each week for 4 weeks. Assume each dryer load takes 1 hour.
a. Find the energy used in kWh
b. Find the operating cost for 4 weeks. Assume cost is $.0758/kWh
8. Assume you use an air conditioner for a total of 137 days, 24 hours per day, at a rate of
7.25 kWh per hour. Assume the cost per kWh is $.0825 and 1 kWh = 3400 BTUs (A British
thermal unit (BTU) is the amount of heat needed to raise the temp. of 1 pound of
water by 1 degree Fahrenheit).
a. Calculate the total number of kWh used per year.
b. Determine the cost of air conditioning for one year.
c. How many BTUs are used in one year?
9. One pound (lb) of bituminous coal contains 12,000 BTUs of energy. 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?
10. How many kWhs of energy could be generated by a coal burning power plant that
burned 250 tons of coal and was 40% efficient? (1 metric ton of standard coal = 2.5 x
107 BTU and 1 kWh = 3,400 BTU)
11. Answer the questions below regarding the heating of a house in the Eastern United
States. Assume the following:
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The house has 3,000 square feet of living space.
80,000 BTUs of heat per square foot are required to heat the house for the winter.
Natural gas is available at a cost of $5.00 per thousand cubic feet.
One cubic foot of natural gas supplies 1,000 BTUs of heat energy.
The furnace in the house is 80% efficient.
Calculate the following, showing all the steps of your calculations, including units.
a. The number of cubic feet of natural gas required to heat the house for one
winter
b. The cost of heating the house for one winter
Efficiency of Travel
12.
Energy expended for different modes of transportation in the United States
Mode
MJ per passenger-kilometer Energy Use
Air
2.1
Passenger car (driver alone)
3.6
Train (Amtrak)
1.1
Bus
1.7
a. Imagine that you had unlimited time and you needed to get from Washington,
D.C., to Cleveland, Ohio. The distance is roughly 600 km (370 miles). For each
mode of transportation, calculate how many megajoules of energy you would
use.
b. If a gallon of gasoline contains 120 MJ, how many gallons of gasoline does it
take to make the trip by car?
13. The conventional gasoline-powered 2016 Honda Civic is one of the best gas-powered
cars in its class for mileage. The conventional Honda Civic gets 31 MPG during city
driving (42 MPG Freeway). When the exact same car is given a hybrid-electric engine,
mileage is 44 MPG city and 47 MPG Freeway. $29,400 is the cost of the Honda Civic
Hybrid, $18,680 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 $2.10 a gallon?
b. How much would you spend on gas for the conventional Civic in a year,
assuming gas cost $2.10 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?
14. The 2016 Toyota Prius gets 53 MPG city and 46 MPG freeway. The "best-selling car in
America" is the Ford F-150 truck. The 4WD version of the F-150 gets 15 MPG city and 21
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?
Energy Star
15. You are about to invest in a 66-inch flat screen TV. These TVs
come in both Energy Star and non-Energy Star models. The
cost of electricity is $0.15 per kilowatt-hour, and you expect to
watch the TV an average of 4 hours per day.
a. The non-Energy Star model uses 0.5 kW. How much will it cost you per year for
electricity to run this model?
b. If the Energy-Star model uses only 40% of the amount of electricity used by the nonEnergy Star model, how much money would you save on your electric bill over 5
years by buying the efficient model?
Efficiency of Light Bulbs
Government regulations took place in January of 2014 to stop businesses in the United
States from manufacturing or importing 60- and 40-watt incandescent light bulbs. It's all
part of a 2007 federal law requiring light bulbs to meet higher energy efficiency
standards. In the past few years, 75-watt and 100-watt bulbs were phased out. Greener
options of LED and CFL (Compact Florescent Light) bulbs use much less power than
regular bulbs and last longer.
Consumer Reports has said that LEDs last the longest, but they are also the more
expensive option to replace incandescent bulbs. However, rebates are making them
more affordable. CFLs don't last quite as long as LEDs, but they are still a more efficient
option and can use up to 70 percent less power.
Energy Costs
Average Life Span
Watts of electricity used
(800 lumens equivalent
to typical 60 watt bulb)
Cost per bulb
Electricity Used (kWh/yr)
Light Emitting
Diodes (LED)
50,000 hours
7 watts
$4.99
Incandescent Light Compact
Bulbs
Fluorescents (CFL)
1,200 hours
10,000 hours
60 watts
14 watts
$.94
$1.60
Annual Operating Cost
Total life time costs
16. Assume a home has 30 bulbs and each bulb is on for an average of 5 hours per
day. Energy costs are $.10/kWh. Calculate the electricity used in one year and
the annual operating costs for each bulb. Calculate the total lifetime costs for
using each type of bulb.