## Problems

2. Ten percent growth rate is a doubling time of 7 years. Five doubling times = 35 years. Can do by doubling times, starting with 100,000:

200,000 400,000 800,000 1,600,000 3,200,000

Or five doubling times = 25 = 32. So number is 32 * 100,000 = 3,200,000 people.

4. You have to assume or obtain a growth rate for population. I chose 1%, which gives a doubling time of 69 years. Round to 70 years.

2010 2080 2150

5. Year 2008 there are 6.7 billion people in the world. You have to assume or obtain a growth rate for population. Growth rate is 1.2%.

To calculate directly, use Equation 2.7, k = 0.012, t = 92, kt = 1.104:

r = 6.7 * 109 * e1104 = 6.7 * 109 * 3.0 = 20 billion people

If you chose a smaller growth rate, 1%, the results are much the same. Estimate using doubling time: DT = 69/1.2 = 57 years.

At 2065, 13.4* 109, and at 2122, 26*10" people, so at 2100, estimate 19 to 20*10" people.

6. Use Equation 2.7 and solve for time: 24 * 109 = 6.7 * 109 * e0005t, then t = 255 years.

Or use doubling times. DT = 138 years. So it would take 2 DTs to reach 24* 109 people, around 270 years.

7. Stabilization point = 11 * 109, increase in population = 4.3 * 109. 4,300 million/20 million = 215 new cities the size of Mexico City.

Can you imagine the infrastructure problems for building that many new cities?

Electric generating capacity in United States = 1,100,000 MW. 50 years is 5 DTs.

1,100,000 2,200,000 4,400,000 8,800,000 17,600,000 35,200,000 MW

Amount of new capacity = 35,200,000 - 1,100,000 = 34,000,000 MW. Number of 1,000 MW plants = 34,000.

Ten percent growth is doubling time of 7 years. For 30 years that would be 4 DTs. 2008 world electrical generating capacity is around 4,000 GW. So by 4 DTs, need 64,000 GW with 60,000 GW of new capacity. Number of 1,000 MW plants = 60,000.

At \$5,000/kW each plant would cost \$5 * 109 and 60,000 plants would cost \$300 * 1012. Electricity demand China = 500,000 MW (2006). In 30 years need 250,000 MW of new capacity; 250,000 MW/300 MW = 830 plants.

830 plants * 300,000 kW/plant * \$2,000/kW = \$500 * 109

11. We need 250,000 MW of new capacity, which we are going to fuel by coal. 90% availability means 0.90 * 2.5 * 108 kW* 8,760 h/year = 1.97 * 1012 kWh/year. Efficiency of the coal plant is 40%, so amount of coal energy needed is 2 * 1012 kWh/year divided by 0.40 = 5 * 1012 kWh/year.

1 metric ton of coal has 2.2 * 1010 J = 6 * 103 kWh.

Tons of coal/year = 5* 1012 kWh/year divided by 6*03 kWh = 8.2* 108 = 820,000,000 metric tons of coal per year just to fuel China power plants.

TH 973

TH 383

15. Coal reserves in the United States = 2.5 * 1011 metric tons. Coal production (20 06) = 1.05* 109 tons/year.

Number of years = 2.5 * 1011 tons/1.05 * 109 tons/year = 238 years. That is without any increase in production.

16. S = 2.5 * 1011 tons, k = 0.10, r0 = 1.05 * 109 tons

V r0

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T = 10 ln (24.8) = 32 years 17. Coal reserves in China = 1.15 * 1011 metric tons. Coal production = 2.38 * 109 tons.

0.15

18. Number of lights in my house = 40, average 100 W, on 4 h/day.

Energy = 4 kW*4 h/day = 16 kWh/day = 500 kWh/month = 6,000 kWh/year.

That is a high estimate, because some of the lamps are smaller and some are fluorescent.

19. Efficiency of incandescent bulbs is 5%. Efficiency of fluorescent bulbs is around four times higher. Produce same amount of light for fewer watts. Therefore, I would use 1,200 kWh/year.

20. Maximum power in my house.

If you use horsepower of a motor, then 1 hp = 0.75 kW.

If you use volts (120 or 240) and current (amps), then P = VI (volts * amps) = watts.

 Use kW Lights 4.0 Hair dryers 3.2 Air conditioner 2.0 Stove, electric 11.7 Clothes dryer, electric 5.6 Toaster 1.0 Irons 1.6 Power tools, drills, etc. 2.0 Microwave 1.0 Other appliances (motors) 1.0 TV, computer, VCR, etc. 2.0 Fans 0.3 Disposal 0.3 Dishwasher 0.8 Refrigerator 0.8 Freezer 0.6 Garage door opener 0.4 Estimated total power 40

21. Oil consumption (20 08) = 86* 106 bbl/day * 365 day/year = 3.1 * 1010 bbl/year.

22. Oil consumption growth of 2.5%.

Can calculate directly form Equation 2.9, Te = 1/k ln(k* S/Ro + 1).

Te = (1/0.025) * ln(0.025 * (2 * 1012/3.1 * 1010) + 1) = 38 years

If no increase in consumption, it would only last 2 * 1012/3.1 * 1010 = 64 years. Could use spreadsheet and increase consumption each year by 2.5% and add to get cumulative numbers. When reach cumulative value of S, that is the number of years.

23. Coal consumption growth of 5%.

Can calculate directly from Equation 2.9, Te = 1/k ln(k* S/Ro + 1)

Te = (1/0.05) * ln (0.05 * [2 * 1012/3.03 * 1010] + 1) = 29 years

24. Population China (2007) = 1,300,000,000 people. Population growth rate = 0.6%. r = 1.3 * 109 * e(0006)(30) = 1.5 * 109 people in China in 30 years.

In United States, 300 million people, so take the ratio of cars to people for United States (2/3) and apply to China. So for China, 1,500 million people * (2/3) = 1,000 million cars. Barrels of gasoline needed = (1,000/200) * 10 million bbl/day = 50 million bbl/day. Since only half of oil is converted to gasoline, China would use 100 million bbl of oil/day. How does that compare to world oil production today?

25. Presently in United States, there are 104 nuclear power plants (106 GW; production, 788 TWH/year).

Amount of uranium oxide needed per year = 788 TWh * 3 * 104 kg/TWh = 2.4 * 107 kg = 2.4 * 104 metric tons. From Table 2.4, resource is 4 * 105 metric tons. Resource will last 4 * 105/2.4 * 104 = 17 years.

26. Can calculate from Equation 2.9, Te = 1/k ln(k* S/Ro + 1).

Te = (1/0.02) * ln (0.02 * [4 * 105/2.4 * 104] + 1) = 14 years

27. World nuclear (365 GW, 2700 TWh/year).

Amount of uranium oxide needed per year = 2,700 TWh * 3 * 104 kg/TWh = 8.1 * 107 kg = 8.1 * 104 metric tons. From Table 2.4, resource is 5 * 106 metric tons. Resource will last 5 * 106/8.1 * 104 = 62 years.

28. Can calculate from Equation 2.9, Te = 1/k ln(k* S/Ro + 1).

Te = (1/0.04) * ln (0.04 * [5 * 106/8.1 * 104] + 1) = 32 years

## Renewable Energy 101

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. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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