APES



Energy Math ProblemsShow all calculations with units – No work shown, no credit on AP ExamPower (watts) = current (amps) x voltage (volts) = Energy (Joules) /time ?1 kWh = 3,600,000 Joules BTU = energy to raise temperature of 1 pound of water by 1oF1 pound of water = 8 pounds1 kWh = 3413 BTU ?????1 kilogram = 2.2 pounds ????1 cubic foot of gas contains 1031 BTUs ?????????1 ton of coal has 2.5E7 BTUR value = [area (ft2) x time (hours) x ΔT (?F)] / BTU1. How many kWh of energy could be generated by a coal power plant that burned 250 tons of coal and was 40% efficient? [7.3E5 kWh]2. How much natural gas must be burned in order to produce 5.2E4 kWh of electricity if the power plant is 65% efficient? [2.6E5 ft3]3. How many pounds of water would raise in temperature 20oF by the 90% efficient burning of 30 cubic feet of natural gas? [1.39E3 pounds]4. The R-value of a hot water heater insulation blanket is 6.7 and covers an area of 25 square feet. a. How many BTUs will it save for every hour that it prevents 1 oF of temperature change? [3.73 BTU]b. How many BTU will it save in one year? [3.3E4 BTU]c. How many cubic feet of gas will that save in one year? [32 cubic feet]5. A gas-burning furnace heats 5000 pounds of water 25 oF by burning 210 cubic feet of natural gas.How many BTU are produced by the burning of the natural gas? [2.2E5 BTU]b. How many BTU are required to heat the water?c. What is the efficiency of a gas-burning furnace? [57%]6. Seven (7) tons of coal are burned to generate 3.6E4 kWh of electricity. ?How many kWh of energy are ideally produced by seven tons of coal? [5.1E4 BTU]b. What is the efficiency of the generator? [71%]7. You replace one 75-watt incandescent light bulb with a fluorescent light bulb that gives the same amount of light but draws only 20 watts. ?You use the light bulb for an average of 4 hours a day.a. How many kWh does the incandescent light bulb use? [0.3 kWh]b. How many kWh does the fluorescent light bulb use? [0.08 kWh]c. How many kWh do you save per year? [80.3 kWh]d. The cost of one kWh is $0.25. ?How much money does the fluorescent bulb save in one year? [$20.08]8. How much power is produced by a solar cell that produces 0.6 amps of current and has a voltage of 0.75 volts? [0.45 W]a. If solar cell only collected sunlight when the solar constant (the amount of energy available per cm3) was 0.08 watts/cm2, how many watts of energy would a solar cell collect if the solar cell has an area of 20 cm2? [1.6 W]b. What is the efficiency of this solar cell? [28%]c. How many of these solar cells would it take to run a 60-watt bulb? [130] 9. The efficiency of a coal power plant is 65%, of energy transmission is 95%, and of an electric stove is 85%. a. How many BTU of heat could be produced after 0.50 tons of coal have been burned? [1.25e7]b. How many BTU of heat are produced by the electric stove? [6.6E6 BTU]10. The temperature of a 200,000 gallon pool is raised from 60oF to 75oF? a. How many BTU are required to heat the pool? [1.9E7 BTU]b. How many cubic feet of gas must be burned by an 80% efficient pool heater to heat the pool? [1.8E4 ft3] ................
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