## Problems

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OM means order of magnitude problem.

1. A snowball, mass = 0.5 kg, is thrown at 10 m/s. How much kinetic energy does it possess? What happens to that energy after you are hit with that snowball?

2. OM: The Chamber of Commerce and the Board of Development are always promoting their city as the place for new industry. If a city has a population of 100,000 and a growth rate of 10% per year, what is the population after five doubling times? How many years is that?

3. What is the doubling time if the growth rate is 0.5%? The world population in 2008 was around 6.7 * 109.

4. OM: If world population is 7 * 109, estimate how many years before the population reaches 28 * 109.

5. OM: How many people will there be on the earth by the year 2100? Assume present rate of growth of world population.

6. OM: If the growth rate of population could be reduced to 0.5% per year, how many years would it take to reach 24 * 109 people?

7. OM: The population of the world is predicted to reach 11 * 109. Mexico City is one of the largest cities in the world at 2 * 107 people. How many new cities the size of Mexico City will have to be built to accommodate this increase in population?

8. OM: The most economical size of nuclear power plants is around 1,000 MW. How many nuclear power plants would have to be built in the United States over the next 50 years to meet the U.S. long-term historical growth of 7% per year in demand for electricity?

9. OM: Assume electricity demand increases by 10% per year over the next 30 years for the world. To meet all that increased demand, how many 1,000 MW nuclear plants would have to be installed by the end of 30 years? What is the total cost for those nuclear plants at \$5,000/kW?

10. OM: If electricity demand increases by 50% over the next 30 years for China, how many 300 MW coal plants would have to be installed by the end of 30 years? What is the total cost for those coal plants at \$2,000/kW?

11. OM: For problem 10, how many metric tons of coal would be needed for that thirtieth year? Assume plants operate at 90% capacity and 40% efficiency.

12. What is the efficiency at a nuclear power plant if the incoming steam is at 700°C and the outgoing steam is at 320°C? Remember, you have to use Kelvin.

13. The Hawaii Natural Energy Institute tested a 100 kW ocean thermal energy conversion (OTEC) system. The surface temperature is 30°C, and at a depth of 1 km the temperature is 10°C. Calculate the maximum theoretical efficiency of an OTEC engine. Remember, you have to use Kelvin.

14. For a binary-cycle, geothermal power plant the incoming temperature is 110°C and the outgoing temperature is 71°C. Calculate the maximum theoretical efficiency of that steam turbine.

15. OM: Use the coal reserves of the United States. At today's rate of consumption, how long would they last for the United States?

16. OM: Assume a growth rate of coal consumption for the United States of 10% per year, because they are going to also use coal for liquid fuels. How long will the U.S. coal last?

17. OM: Assume a growth rate of coal consumption for China of 15% per year. How long will the China coal last?

18. For your home, estimate the power installed for lighting. Then estimate the energy used for lighting for 1 year.

19. Estimate the energy saved if you converted your home lighting from incandescent to compact fluorescent lights. Fluorescent lights are more efficient, more light per watt.

20. What is the maximum power (electrical) used by your residence (assume all your appliances, lights, etc. are on at the same time)?

21. OM: World oil production will peak during 2008 to 2015. Estimated reserves are 2 * 1012 bbl. How long will that last at the present rate of consumption?

22. OM: Same as previous problem, but assume a demand increase of 2.5% per year. How long will the oil last?

23. OM: Calculate how long world coal reserves will last if world demand increases at a rate of 5% per year.

24. OM: The United States now has 200 million cars, which consume 10 million barrels of gasoline per day. Suppose the Chinese government goal is the same ratio of people to cars within 30 years. How many cars will they have and how many barrels of oil will they be consuming per year?

A nuclear power plant uses around 3 * 104 kg of uranium oxide to generate 1 TWH of electricity.

25. OM: How long will U.S. uranium last for the present installed nuclear power plants?

26. OM: Same as problem 25, except assume a 2%/year growth in nuclear power plants.

27. OM: How long will world uranium last for the present world nuclear power plants?

28. OM: Same as problem 27, except assume a 4%/year growth in nuclear power plants.

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## Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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