Energy math.notebook
February 26, 2015
Energy Practice Problems for APES
***last weeks math problems
Energy math.notebook
1. The conventional gas 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."
February 26, 2015
Energy math.notebook
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 $3/gallon)
(47 miles/gallon) = $510.64/year
Hwy Driving Gas Cost: (4000 miles/year x $1.89/gallon)
(48 miles/gallon) = $250/year
Total Gas Cost: $760.64/year
February 26, 2015
Energy math.notebook
February 26, 2015
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 $3/gallon)
(35 miles/gallon) = $685.71/year
Hwy Driving Gas Cost: (4000 miles/year x $3/gallon)
(40 miles/gallon) = $300/year
Total Gas Cost: $985.71/year
Energy math.notebook
C.) How long would it take for the savings in gas costs to offset the increase in the price of the hybrid?
Difference in Car Cost $20, 650 ­$16,000 = $4650
Difference in Gas Cost $985.71­ $760.64= $225.07/year
$4650/$225.07/year = 20.7 years
February 26, 2015
Energy math.notebook
February 26, 2015
Energy Practice Problems for APES
2. One way to conserve energy is to replace incandescent light bulbs with compact fluorescent bulbs. The fluorescent bulb typically uses 25% of the energy of an incandescent bulb of comparable brightness typically lasts about 12 times longer.
Energy math.notebook
February 26, 2015
A. How much would you save by replacing a 100­
watt incandescent bulb with a compact florescent bulb over the 12,000 hour lifetime of the bulb if the electricity cost 0.08$ per kwh (kilowatt hour)?
Incandescent Bulb
100w X 1kw X 12,000 hours X $.08/kwh
1000w = $96
Florescent Bulb
25w X 1kw X 12,000 hours X $.08/kwh
= $24
1000w $96­ $24=$72 savings
Energy math.notebook
February 26, 2015
B. If that bulb was turned on for 12 hours a day, how many months before it needs to be replaced?
12,000 hours X 12 times longer
12 hours/day = 12,000 days
12,000 days =400 months
30 days/month
Energy math.notebook
February 26, 2015
C. If an incandescescent bulb cost $1 and lasts 1,000 hours, and a compact fluorescent bulb costs $8 and lasts 12,000 hours, which bulb has the cost advantage and by how much?
12 incanescent bulbs are needed to last 12000 hours where only 1 fluorescent is needed to that time. $12 ­ $8= $4 savings for fluorescent bulbs
Energy math.notebook
Practice FRQ
3. Answer the questions below regarding the heating of a house in the Eastern United States. Assume the following:
• 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.
February 26, 2015
Energy math.notebook
February 26, 2015
a. Calculate the following, showing all the steps of your calculations, including units.
I. How many of cubic feet of natural gas is required to heat the house for one winter? 3
2 3000 ft x 80,000 BTU’s x 1 ft 2 1000 BTU ft
3 = 240,000 ft Energy math.notebook
February 26, 2015
II. The furnace in the house is only 80% efficient. What would be the cost of heating the house for one winter at this efficiency?
3
3 240,000 ft = 300,000 ft
.80 efficient 3
300,000 ft x $5 = $ 1,500
3 1000 ft
Or
3 240,000 ft x $5 = $12,000
1000 ft3 .80 efficient = $1,500
Energy math.notebook
February 26, 2015
B.Discuss two environmental impacts of natural gas use, one positive and one negative.
Advantages
Disadvantages
Contains fewer When unburned, methane impurities and emits escapes into the almost no sulfur dioxide atmosphere
or particulates
Exploration of natural gas Emits only 60% as much carbon dioxide as has the potential of contaminating coal
groundwater
Energy math.notebook
February 26, 2015
a.Identify and describe three actions the residents of the house could take to conserve heat energy and lower the cost of heating the house.
• Insulation of house, water heater, widows, • Energy efficient water heater
• Lower thermostat when no ones home
• Wear more clothing and use blankets instead of turning up heat
• Close off unused rooms
• Paint rooms darker colors to absorb heat from sun
• Calk of weather strip windows and doors
• Install dual pain window
**Other items are acceptable if they conserve heat/energy
Energy math.notebook
Electric Power from Sun and Wind
Fridays review problems
February 26, 2015
Energy math.notebook
February 26, 2015
Exercise 1: Windpower
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 1500 kW of power. The installed cost of this
turbine is $1.5 million.
1.If this turbine runs at its rated power 100% of the
time for a full year, how much energy would it
produce in a year?
1500kWh ×24hr/day x 365 days/year
13
____________ (million kWh/year)
Energy math.notebook
February 26, 2015
Exercise 1: Windpower
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 1500 kW of power. The installed cost of this
turbine is $1.5 million.
2. This wind turbine has a capacity factor equal to
0.38. This means that over a year, it will produce
only 38% of its theoretical maximum energy
production. How much energy does this turbine
actually produce in a year?
13mill.kwh/year x .38
________________
5 (million kWh/year)
Energy math.notebook
February 26, 2015
Exercise 1: Windpower
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 1500 kW of power. The installed cost of this
turbine is $1.5 million.
3.Over the next 20 years, US annual electric energy
consumption will increase by 1.5 trillion kWh/year.
How many 1.5 MW wind turbines would be needed
to supply 10% of this additional energy?
1.5 trill. kWh x .10= 150 bill. kWh
5 mill. kWh
=30,000 turbines
Energy math.notebook
February 26, 2015
Exercise 1: Windpower
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 1500 kW of power. The installed cost of this
turbine is $1.5 million.
4. Calculate the cost of installing these wind
turbines.
30,000 X 1.5 mill. =
45
mill $
Energy math.notebook
February 26, 2015
Exercise 1: Windpower
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 1500 kW of power. The installed cost of this
turbine is $1.5 million.
5. Assuming the electric energy produced by these
turbines is worth 5 cents per kWh, these turbines
would generate electric energy worth $7.5
billion/year. Calculate the simple payback period for
these turbines. (Payback period is the time it takes for
a system’s net benefits to equal its cost.)
45 bill.$
7.5 bill $/yr
6
__________ (years)
Energy math.notebook
February 26, 2015
A grid­connected residential PV system is placed on the
roof of a 2000 square foot suburban house. The PV array
with an area equal to 50 square meters (about 500 square
feet) covers half of the south­facing 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.
1.The PV system is operating in a location where
the annual average daily incident solar energy (the
insolation) incident on the array equals 5.0
kWh/m2/day. Calculate the average amount of
solar energy incident on the PV array each day.
2
2
50m x 5 kWh/m /day=
250
______________ (kWh/day)
Energy math.notebook
February 26, 2015
2. The efficiency of the PV system equals
10% (i.e. 10% of the solar energy incident
on the array is transformed into useful
electric power). Calculate the daily
average electric energy produced by this
system.
250kWh/day x .10 =
25
__________ (kWh/day)
Energy math.notebook
February 26, 2015
3. Calculate the average amount
of electric energy produced by
this system each year.
25kWh/day x 365days/year=
9125 (kWh/year)
_______
Energy math.notebook
February 26, 2015
4.Over the next 20 years, US annual
electric energy consumption will increase
by 1.5 trillion kWh/year. How many
rooftop PV systems would be needed to
supply 10% of this additional energy?
1.5 trill. kWh/yr x .10=150 bill kWh/year
9125 kWh/year
16 mill systems
________________
Energy math.notebook
February 26, 2015
5. Calculate the cost of installing these
residential PV systems.
16 mill systems x $50,000=
800 bill
____________ ($)
Energy math.notebook
February 26, 2015
6.Assuming the electric energy produced by
these PV systems is worth 10 cents per kWh,
these residential systems would generate electric
energy worth produce $15 billion/year.
Calculate time it takes for you to get back the
money you spent on the system.
$800 bill
$15 bill/year
=
50
___________ (years)
Energy math.notebook
February 26, 2015
Practice FRQ from Fridays assignment
Energy math.notebook
February 26, 2015
Many college students have a mini fridge in their dorm room. A standard mini fridge costs roughly $100, uses about 100 watts of electricity, and can be expected to last for 5 years. The refrigerator is plugged into an electrical socket 24 hours a day, but is usually running only about 12 hours a day. Assume that electricity costs $0.10/kWh. (a) Calculate the lifetime monetary cost of owning and operating the refrigerator. (2 points) 100W x 1kW x 12hr x 365 days x 5 years
1000W day year
$.10= $219 + $100(cost of fridge)=$319
kWh
Energy math.notebook
February 26, 2015
(b) Assume that the electricity used to power the refrigerator comes from a coal­burning power plant. One metric ton of coal contains 29.3 GJ (8,140 kWh) of energy. Because of the inefficiency of electricity generation and transmission, only one­third of the energy in coal reaches the refrigerator. How many tons of coal are used to power the refrigerator during its lifetime? (2 points)
2190kWh x 3=6570 kWh
6570kWh
=. 81 tons
8140kWh/ton
Energy math.notebook
(c) Assume that 15 percent of the mass of the coal burned in the power plant ends up as coal ash, a potentially toxic mixture that contains mercury and arsenic. How many tons of coal ash are produced as a result of the refrigerator’s electricity use over its lifetime? (2 points)
.81 tons x .15= .12 tons
February 26, 2015
Energy math.notebook
February 26, 2015
(d) What externalities does your answer from part (a) not include? Describe one social and one environmental cost associated with using this appliance. (2 points)
Externalities would include all costs not paid by the consumer in the extraction, transportation, and end uses of the coal. Answers will vary, but may include mention of respiratory illness, habitat destruction, and climate change due to increased emissions of carbon dioxide. (e) Describe two ways a college student could reduce the electricity use associated with having a mini fridge in his or her dorm room. (2 points)
Answers will vary, but may include mention of buying an Energy Star certified appliance, sharing a refrigerator with roommates, etc.