Physics 12: Homework #3: due April 26

In addition to the problems assigned from the book, do these required problems as well. Many are adaptations of problems in the book (Chapter 2) to reduce the pain of gratuitous unit conversions. A few supplemental questions on basic energy calculations are included to help keep you practiced and sharp.

  1. (modified from Q&P 2.11) How many Joules of energy does it take to raise one barrel of oil 4,000 meters from underground? How much is this energy in terms of the heat energy content, in equivalent barrels of oil? Assume that one barrel of oil has 6.1×109 J of energy, and a mass of 650 kg.

  2. (modified from Q&P 2.12) It has been estimated that a person can perform continuous manual labor at a power of 50 watts for an 8-hour working day. How many kilograms of coal contain the energy equivalent of the useful physical labor a person can perform in this time period? How many gallons of oil? See the useful energy equivalents in the front of the book.

  3. (modified from M.C. 2.13) How many barrels of oil does the United States import each year?

  4. (modified from M.C. 2.15) At what rate does the United States use liquid petroleum? Express the answer in barrels per day and barrels per year.

  5. (modified from M.C. 2.17) At our present rate of use, how long will the estimated total remaining recoverable petroleum of the United States supply our needs if we rely 100% on domestic oil? Use estimates of the remaining resource from the book/lecture.

  6. A hot tub containing 1000 liters of water has an electric heater rated at 4184 Watts (funny it should be exactly this!). When running the heater at this rate, how many degrees per hour will the temperature of the water climb. Express your answer in degrees Celsius, Kelvin, and Fahrenheit. Don't be alarmed if two of them are the same. For reference, 1 liter of water has a mass of 1 kg.

  7. The same hot tub is observed to lose 1 °C every eight hours when the heater is off. What is the rate at which heat energy is escaping (in Watts)?

  8. Assuming that the previous rate of heat loss is the average power that must be supplied to the hot tub to maintain temperature at a set point (and this is valid reasoning), how much will it cost per day if the electricity costs 15¢ per kWh? How much does it cost per month?

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