Energy Problems – You must show your set-up, units, and work to receive credit.
Scientific Notation:
1. Convert the following into scientific notation:
a. 727 = ______________________________________
b. 0.000984 = ______________________________________
c. 0.014 = ______________________________________
d. 172000 = ____________________________________
e. 20000000.0 _____________________________________
f. 256000000000 = _______________________________________
2. Convert the following into decimal form:
a. 1.56 x 104 = ___________________________________
b. 7.367 x 109 = ___________________________________
c. 2.75 x 10-10 = _____________________________________
d. 3.6 x 10-2 = ______________________________________
e. 5.90 x 105 = _____________________________________
3. Write the following numbers out, and then in scientific notation:
a. 1 billion =__________________________________=_________________________________
b. 5 million= __________________________________=_________________________________
c. 3 thousand = _______________________________=___________________________________
d. Two hundred seventy three thousand = _____________________________=____________________
e. 114 million = __________________________________=___________________________________
f. 3 hundred = ________________________________=__________________________________
g. One fourth = __________________________________=_________________________________
h. Zero point zero, zero, zero one three = _________________________=__________________________
i. Zero point eight, seven, three, one, nine = ________________________=________________________
Graphing Data:
a. A clam farmer has been keeping records concerning the water temperature and the number of clams
developing from fertilized eggs. The data is recorded below.
b.
c.
d.
e.
Water Temperature in °C
Number of developing clams
15
75
20
90
25
120
30
140
35
75
40
40
45
15
50
0
Make a line graph of the data.
What is the dependent variable?
What is the independent variable?
What is the optimum temperature for clam development according to the chart?
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You must show your set-up, units, and work to receive credit. Box in your answers
1) You own a car that gets 20 miles per gallon (MPG) and you drive an average of 10,000 miles each year.
a) How many gallons of gas do you use in a year?
b) At $3.50 per gallon, how much will you spend on gasoline for the year?
c) If the combustion of each gallon of gasoline produces 20 lbs of CO2, how much CO2 does your car
produce each year?
d) If you traded your car in and bought one that got 25 MPG, how much gasoline would you save in one
year?
e) How much money would you save?
f) How much less CO2 would be emitted into the atmosphere from your improved car?
2) The 2012 Toyota Prius gets 50 MPG city and 40 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 20 MPG highway. The average
American drives 12,000 miles per year. Assume that most people do ¾ of their driving in stop & go city
traffic, and ¼ in freeway traffic.
a) How many gallons of gas would be saved per person by driving a Prius over the F-150? How much
money saved?
b) Assume that every gallon of gas burned contributes approximately 20 lb of CO2 to the atmosphere. How
many extra lbs 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
2012. Sales totaled about 750,000 trucks for the year. Calculate how many gallons of gas and lb 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 CO2 is saved over the life
of the vehicle? How much money is saved? (Assuming gas still costs $3.50 a gallon.)
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3) 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.
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?
Useful Information for questions 5-7:
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•
•
•
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Formula to find electrical energy is: Energy = power x time
TECO Power charges about 10¢ per kWh.
1 ton of coal produces an average of 2500 kWh of electricity.
Each kWh of electricity generated from coal produces 1.5 lbs of CO2.
1 gallon of gasoline produces about 20 lbs of CO2 when burned.
4) Assume that the lights in your kitchen use 300 watts:
a) How much energy and how much does it cost to leave the lights on 24 hours a day for a week?
b) For a month (assume 30 days/month)?
c) For a year?
5) Air Conditioner:
a) How much energy and how much money do you use to run your window air conditioner rated at 1500
watts continuously for the month of July?
b) If you assume that coal was used to produce the electricity for your air conditioner, how much coal was
burned to produce the electricity used?
c) How much CO2 was produced by the electricity used to run your air conditioner?
6) An average incandescent light bulb has a life expectancy of 1,000 hours.
a) How much energy would a typical 60 watt bulb use in a lifetime, assuming it lasts for 1,000 hours?
b) At 10¢/kWh, how much would it cost over its lifetime?
c) A compact fluorescent bulb uses 15 watts and has a life expectancy of 10,000 hours. How much energy
and how much would it cost to use a compact fluorescent for 10,000 hours?
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7) Consider a wind turbine that is rated at 1.5 MW. This means that with sufficiently high winds, it will
produce 1.5 MW or 1,500 kW of power. The installed cost of this turbine is $1.5 million.
a) If this turbine runs at its rated power 100 percent of the time for a full year, how much energy (million
kWh/year) would it produce in a year?
b) This wind turbine has a capacity factor equal to 0.38. This means that over a year, it will produce only
38 percent of its theoretical maximum energy production. How much energy (in million kWh/year) does
this turbine actually produce in a year?
c) Over the next 20 years, U.S. annual electric energy consumption is projected to increase by 1.5 trillion
kWh/year. How many 1.5 MW wind turbines would be needed to supply 10 percent of this additional
energy?
d) Calculate the cost ($) of installing these wind turbines.
e) Assuming the electric energy produced by these turbines is worth 10 cents per kilowatt-hour, these
turbines would generate electric energy worth $15 billion per year. Calculate the simple payback period
for these turbines. (Payback period is the time it takes for a system’s net benefits to equal its cost in
years.)
8) A grid-connected residential PV system is placed on the roof of a 2,000-square-foot suburban house. The
PV array with an area equal to 50 square meters (about 500 square feet) covers half of the south-facing part
of the roof. The power rating of this PV system is 5.0 kW, meaning that it will produce 5.0 kW under peak
sunlight conditions. The installed cost of this system is $50,000.
a) The PV system is operating in a location where the annual average daily incident solar energy (the
insolation) on the array equals 5.0 kWh/m2/day. Calculate the average amount of solar energy incident
on the PV array each day in millions kWh/year.
b) The efficiency of the PV system equals 10 percent (that is, 10 percent of the solar energy incident on the
array is transformed into useful electric power). Calculate the daily average electric energy produced by
this system in millions kWh/year.
c) Calculate the average amount of electric energy produced by this system each year in kWh/year.
d) Over the next 20 years, U.S. annual electric energy consumption is projected to increase by 1.5 trillion
kWh/year. How many rooftop PV systems would be needed to supply 10 percent of this additional
energy?
e) Calculate the cost of installing these residential PV systems.
f) Assuming the electric energy produced by these PV systems is worth 10 cents per kilowatt-hour, these
residential systems would generate electric energy worth $15 billion/year. Calculate the simple payback
period for these PV systems. (Payback period is the time it takes for a system’s net benefits to equal its
cost in years.)
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Wind
Geothermal
Photovoltaic
Passive/Active
Solar
Biomass (Waste)
Biomass (Fuelwood
& Biofuels)
Energy
Source
R or NR
How it works
3 Advantages
3 Disadvantages
5
Nuclear fission
Natural gas
Oil
Coal
Tidal & Wave
Hydroelectric
dam
Energy
Source
R or NR
How it works
3 Advantages
3 Disadvantages
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