# Energy math.notebook February 26, Energy Practice Problems for APES. ***last weeks math problems

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1 Energy Practice Problems for APES ***last weeks math problems

2 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."

3 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

4 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

5 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 \$ \$760.64= \$225.07/year \$4650/\$225.07/year = 20.7 years

6 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.

7 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 1000w = \$24 \$96 \$24=\$72 savings

8 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

9 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 hours where only 1 fluorescent is needed to that time. \$12 \$8= \$4 savings for fluorescent bulbs

10 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.

11 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? 3000 ft 2 x 80,000 BTU s x 1 ft 3 ft BTU = 240,000 ft 3

12 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? 240,000 ft 3 = 300,000 ft 3.80 efficient 300,000 ft 3 x \$5 = \$ 1, ft 3 Or 240,000 ft 3 x \$5 = \$12, ft 3.80 efficient = \$1,500

13 B.Discuss two environmental impacts of natural gas use, one positive and one negative. Advantages Disadvantages Contains fewer impurities and emits almost no sulfur dioxide or particulates When unburned, methane escapes into the atmosphere Emits only 60% as much carbon dioxide as coal Exploration of natural gas has the potential of contaminating groundwater

14 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

15 Electric Power from Sun and Wind Fridays review problems

16 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)

17 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 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)

18 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

19 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 \$

20 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.\$ bill \$/yr (years)

21 A grid connected 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 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, 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/m 2 /day. Calculate the average amount of solar energy incident on the PV array each day. 50m 2 x 5 kwh/m 2 /day= 250 (kwh/day)

22 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)

23 3. Calculate the average amount of electric energy produced by this system each year. 25kWh/day x 365days/year= 9125 (kwh/year)

24 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

25 5. Calculate the cost of installing these residential PV systems. 16 mill systems x \$50,000= 800 bill (\$)

26 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)

27 Practice FRQ from Fridays assignment

28 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

29 (b) Assume that the electricity used to power the refrigerator comes from a coal burning 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 one third 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 8140kWh/ton =. 81 tons

30 (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

31 (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.

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