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Practice Questions
1. Given that 1 kcal of heat is required to increase the temperature of 1 kg of water by 1°C:
a. How many kcals would be required to heat 200 kg of water by 20°C for a bath?
b. How many joules is this?
c. How many Btus?
d. If your water heater can supply 50 kBtu/h, how long will it take to heat this water?

2. a. Given that 1 kWh = 3.6 MJ and that 1 Btu = 1055 J, show that 1 kWh = 3412 Btu.
b. Why would it be incorrect to use this conversion factor directly to determine the amount of coal required to generate electricity in a power plant?

3. A typical home in the northern U.S. might require 120 MBtu of heat for the average winter.
a. If this heat were supplied by a natural gas furnace operating at 50 percent efficiency, how many cubic feet of gas would need to be purchased?
b. At a cost of $0.90/ccf, what would it cost to heat this house for one season?
c. If a new 80 percent efficient furnace could be installed at a cost of $4,000, how long would it take to pay back the cost of this furnace assuming gas prices remained the same?

4. Suppose the house in question 3 is located in Cleveland where the annual average solar flux is 160 W/m22. If 15 m2 of solar panels operating at 20 percent efficiency were installed on this house to collect and store solar energy in the form of hot water:
a. How much energy could be gained in one year in this manner?
b. What fraction of the annual heating requirement is this?
c. Using the hot-water heating requirements for a bath from question 1(c), how many hot baths would this energy supply in one year?

5. The annual average solar flux in Tucson is 250 W/m2. Suppose 10 m2 of solar electric panels operating at 15 percent efficiency were installed on a home there.
a. How many kWh of electricity could be collected by these panels in one year?
b. What fraction of the annual electrical requirement of 10,000 kWh for the average home does this represent?
c. How many square meters of solar panels would be required to supply 10,000 kWh per year?

6. Solar energy is converted naturally into wood biomass with an efficiency of about 0.1 percent. Suppose a wood lot of 100 hectares (106 m2) is located in Missouri, where the average annual solar flux is 200 watts/m2. Given that the heat value for wood is 12 MBtu/ton, how many tons of wood can be produced by this property each year?

7. With moderate winds, a modern large wind turbine can generate about 500 kW of electricity, whereas a large nuclear power plant can generate 1,000 MW.
a. How many wind turbines would be required to give the same output as one nuclear power plant?
b. Discuss some of the advantages and disadvantages to providing electrical power by each method.

8. Batteries are usually rated in terms of ampere-hours, indicating the current that the cell is capable of delivering for a specified time. A typical D-cell flashlight battery, for instance, might be rated at 3 ampere-hours. The total electrical energy available from such a battery is found by multiplying the ampere-hour rating by the battery voltage. Thus this same 1.5 volt D cell could deliver 4.5 watt-hours of electrical energy.

Convert this energy to kWh and compare the cost of electrical energy derived in this manner to that of standard "grid-based" electricity. Assume that the battery costs $1.00 and that electricity from the power company is available at $0.15/kWh.

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Lowell Bailey

Bedford-North Lawrence High School
595 N. Stars Boulevard
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