APES Energy Problems. Practice Problems: 1. How much energy, in kj, does a 75 Watt light bulb use then it is turned on for 25 minutes?

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1 APES Energy Problems Energy: The basic unit of energy is a Joule (J). Other units are calorie, kilojoule, British Thermal Unit (BTU), and therm. 1000J = 1 kj 1000cal = 1kcal 1 cal = J 1 BTU = 1.05 kj 1 therm = 100,000 BTU Power: Power is the rate at which energy is used. (P = E/t) Unit: Watt 1W = 1J/s (1Watt = 1 Joule per second) A 100 Watt bulb uses 100 J/sec of electrical energy. If it is 20% efficient, then the bulb converts 20% of the electrical energy into light and 80% is wasted by being transformed into heat (ever felt a hot light bulb?). What is the example of the First Law of Thermodynamics above? Electric energy transformed into light and heat energy This is the law of the conservation of energy. It states that energy can neither be created, nor can it be destroyed. This means that the total amount of energy in the universe always remains conserved, or constant. However, energy can be changed from one form to another. What is the example of the Second Law of Thermodynamics above? The 20% efficiency (80% waste) increasing disorder This is the law of increasing entropy. It states that the entropy of the universe increases with every physical process (change) that occurs. Entropy refers to the level of disorder, randomness, or chaos, of a system, the higher the randomness of a system, the higher its entropy. The more organized a system, the lower its entropy. Practice Problems: 1. How much energy, in kj, does a 75 Watt light bulb use then it is turned on for 25 minutes? 2. The Kilowatt Hour, or kwh, is not a unit of power but of energy. Notice that kilowatt is a unit of power and hour is a unit of time. E = P x t (rearranged from above). A kilowatt hour is equal to 1 kw delivered continuously for 1 hour (3600 sec). Convert a 1 KWh to KJ s. 3. Assume your electric bill showed you used 1355 kwh over a 30-day period. a.) Find the energy used, in kj, for the 30 day period. b.) Find the energy used in J/day. c) At the rate of $.0749/kwh, what will your electric bill be for this month?

2 4. A 100 Watt light bulb is 20% efficient. 100 W= 100 J/s a.) How much energy does it use in 12 hours of operation? b.) How much energy does the bulb convert to light during 12 hours? c.) Convert total energy use to kwh 5. 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 J and kwh. b.) Find the operating cost for 4 weeks. Assume cost is $.0758/kWh 6. Refrigeration is costly in terms of energy usage. A single-door, manual defrost refrigerator uses 600 kilowatt hours/year (abbreviated kwh/yr). A large, 20 cu ft two-door automatic defrost refrigerator uses 1880 kwh/yr. How many kcal/yr do each type of refrigerator use? 1kWh = 860kcal. 7. 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.) Calculate the total number of kwh used per year. b.) Determine the cost of air conditioning for one year. c.) How many kcal are used per year? d.) How many BTUs are used in one year? 8. Suppose your electric lights use 400 watts per hour and average four hours per day, every day for one year. a.) How many kwh per year does this represent? 400 W= 400 J/s b.) If replacing the lights with a fluorescent bulb would save 60 w per night, what savings in kwh does this represent in one year? c.) If the fluorescent bulb costs $18 but lasts for 10 years, would you consider it a wise investment over incandescent bulbs? Explain your answer.

3 9. Transportation energy is costly. a.) Calculate the gallons of gas use just for going to the supermarket in one year if you take 5 trips to the store per week, traveling 7.5 miles roundtrip, and your car gets 22 miles per gallon. b.) Convert the gallons to kcal/year if there are kcal per gallon. c.) What are some of the other energy uses associated with getting foodstuffs to the consumer other than transportation costs? d.) What suggestions would you make to the average American to help save energy and money relating to the answers you gave in C? 10. From 2013 APES Exam: Battery electric vehicles (BEVs) have been introduced to consumers as an alternative way to reduce the environmental effects caused by use of internal-combustion engine (ICE) vehicles. A comparison of both vehicle types can help determine whether the use of BEVs would be beneficial in the future. Where calculations are required, show your work. (a) Identify THREE strategies that the federal government could implement to encourage the use of BEVs. (b) Assume that the fuel efficiency of the ICE vehicle is 25 miles per gallon (mpg) and that gasoline costs $3.75 per gallon (gal). Calculate the cost of gasoline per mile. (c) The charger supplies energy to the BEV battery at an average rate of 4.0 kilowatts (kw) and fully charges the BEV battery in 7.0 hours. The car will run for 100 miles on a full charge. The cost of electricity is $0.11 per kilowatt-hour (kwh). i. Calculate the cost of the electricity to fully charge the battery. Assume that the battery is not charged to begin with. ii. Calculate the cost of electricity per mile to drive the BEV. When it is driven 100 miles, the ICE vehicle contributes 72.8 pounds (lb) ofco2 from the burning of the gasoline. The drilling, refining, and transportation costs of getting the gasoline to the gas station add an additional 17.7 lb of CO2 per 100 miles. The BEV does not emit anyco2 itself, but the extraction, transportation, and combustion of the coal that produced the electricity at the power plant add 63.6 lb of CO2 for the same 100 miles. (d) Calculate the difference in the amount ofco2 that would enter the atmosphere if both cars were driven 100 miles. (e) Describe TWO economic impacts (excluding costs related to climate change resulting from CO2 emissions or the cost of gasoline at the pump) that result from an increased number of BEVs on the road.

4 11. From 2012 APES Exam: The Fremont School District uses oil to heat school buildings. Go Green! is a new project the district will implement. The superintendent has declared that the district will dedicate itself to reducing its carbon footprint. In addition to taking serious energy-conservation measures, the district is planning to help offset its carbon dioxide emissions by raising money to help conserve a portion of a large tract of forest land adjacent to the high school campus. (a) Describe one alternative energy source that would reduce the carbon footprint of the school district. Discuss one environmental benefit (other than reduced CO2 emissions) and one environmental drawback of using the alternative source instead of fuel oil. (b) Identify TWO ecological benefits provided by intact forest ecosystems (other than reducing CO2 levels in the atmosphere). (c) Use the assumptions below to answer the questions that follow. For each calculation, show all work. The biomass of the forest increases at an annual rate of kg/ha. The forest biomass is 50 percent carbon by mass. Each year the district uses gallons of fuel oil for heating and hot water. 10 kg of CO2 is produced when 1 gallon of fuel oil is burned. 1.0 kg of CO2 contains 0.27 kg of carbon. The cost of putting 1 ha of the forest into conservancy is $12,000. (i) Calculate the mass of carbon, in kg, that is accumulated and stored in 1.0 ha of forest in one year. (ii) Calculate the mass of carbon, in kg, that is emitted by the school as a result of its fuel-oil consumption in one year. (iii) Calculate the number of hectares of forest the school district needs to conserve in order to offset the carbon released in one year by the school burning its fuel oil. (iv) Calculate the amount of money the school district must raise for the conservation project. 12. From 2009 APES Exam: Anaerobic methane digesters have been used for many years to reduce energy costs on farms throughout Europe and on some large farms in the United States. The digesters operate by using anaerobic bacteria to break down animal waste. During the process, which typically uses a tank heated to about 100 F (38ÁC) to speed the reactions, raw manure is broken down and methane is produced. The methane can then be used to generate electricity or produce heat. For a certain dairy farm with 500 cows, the cost of installing a digester is approximately $400,000. Assume that the farm uses 800,000 kilowatt-hours (kwh) of electricity each year at a cost of $0.10 per kwh. The waste from a single cow can produce 3.0 kwh of electricity each day. (a) Describe the steps by which methane produced in the digester can be used to generate electricity. (b) Discuss TWO environmental benefits that may result from the installation of an anaerobic methane digester.

5 (c) Assuming that the cost of electricity remains constant and the farmer starts using the manure from the cows in an anaerobic digester to produce electricity on the farm, calculate: (i) The number of kwh of electricity that can be produced in one year (ii) The amount of money the farmer can save in one year, NOT counting the installation cost of the digester. (You may round your answer to the nearest $1,000.) (iii) The amount of time, in years, that it will take to recover the cost of installing an anaerobic digester on the farm. (You may round your answer to the nearest whole number of years.) (d) Calculate the minimum number of cows the farm would need to produce 800,000 kwh of electricity per year. 13. From 2007 Apes Exam: The Cobb family of Fremont is looking at ways to decrease their home water and energy usage. Their current electric hot-water heater raises the water temperature to 140 F, which requires 0.20 kwh/gallon at a cost of $0.10/kWh. Each person in the family of four showers once a day for an average of 10 minutes per shower. The shower has a flow rate of 5.0 gallons per minute. (a) Calculate the following. Be sure to show all your work and include units with your answers. (i) The total amount of water that the family uses per year for taking showers (ii) The annual cost of the electricity for the family showers, assuming that 2.5gallons per minute of the water used is from the hot-water heater (b) The family is considering replacing their current hot-water heater with a new energy-efficient hot-water heater that costs $1,000 and uses half the energy that their current hot-water heater uses. How many days would it take for the new hot-water heater to recover the $1,000 initial cost? (c) Describe TWO practical measures that the family could take that would reduce their overall water use at home. (d) Describe TWO conservation measures (other than reducing hot water use) that the family could take to reduce the total amount of energy that they use at home. 14. From 2004 APES Exam: West Fremont is a community consisting of 3,00 homes. A small coal-burning power plant currently supplies electricity for the town. The capacity of the power plant is 12 megawatts (MW) and the average household consumes 8,000 kilowatt hours (kwh) of electrical energy each year. The price paid to the electric utility by West Fremont residents for this energy is $0.10 per kwh. The town leaders are considering a plan, the West Fremont Wind Project (WFWP), to generate their own electricity using 10 wind turbines that would be located on the wooded ridges surrounding the town. Each wind turbine would have a capacity of 1.2 MW and each would cost the town $3 million to purchase, finance, and operate for 25 years. (a) Assuming that the existing power plant can operate at full capacity for 8,000 hrs/yr, how many kwh of electricity can be produced by the plant in a year?

6 (b) At the current rate of electrical energy use per household, how many kwh of electrical energy does the community consume in one year? (c) Compare your answers in (a) and (b) and explain why you would or would not expect the numbers to be the same. (d) Assuming that the electrical energy needs of the community do not change during the 25-year lifetime of the wind turbines, what would be the cost to the community of the electricity supplied by the WFWP over 25 years? Express your answer in dollars/kwh. (e) Identify and explain TWO environmental benefits to West Fremont of switching from coal to wind power and TWO environmental costs to West Fremont of switching from coal to wind power. 15. From 1998 APES Exam: The environmental impact of washing a load of dirty dishes in an electric dishwasher differs from that of washing them by hand in a sink. Use the information and data below to answer thee questions that follow. Show your calculations. Assume: i. The dishes all fit in one load. ii. The water coming into the water heater for the sink and into the water heater in the dishwasher is at 50 o F. iii. The water heaters for the sink and the dishwasher are both 100% efficient. iv. In one complete cycle, the electric dishwasher uses 10 gallons of water heated to 140 o F and the dishwasher also uses kwh of electrical energy for its mechanical operation. v. Washing the dishes by hand requires 20 gallons of water heated to 110 o F. Other Information: 1 gallon of water = 8 lb. water 1 BTU = the amount of energy needed to raise the temperature of 1 pound of water by 1 o F. 1 kwh = 3400 BTUs. a. Calculate the total energy (in BTU s) used both to heat the water and run the electric dishwasher to wash a load of dishes. b. Calculate the energy (in BTU s) used to heat the water for washing the load of dishes by hand. c. Discuss the economic and environmental costs and benefits of i. using the electric dishwasher (including its manufacture and disposal) ii. washing the dishes by hand