ATM S 211 Climate and Climate Change

Assignment 2: Exponential Growth and Energy exercises Due 14 October 1999

1. Should solar energy be considered the ultimate source of the energy in fossil fuels? State why or why not.

2. In the period 1990-95, the following were rates of population growth in the indicated regions in % per year.

a) World - 1.68%; b) Africa - 2.91%; c) China - 1.44%; d) India - 1.91%,

e) U.S. - 1.03%, f) Europe 0.27%

In each of these regions, if we start in 1995, what is the year in which the population would double its 1995 value, if the rate of population growth remains fixed at the values given above in each case?

3. a) How much energy does it take to move a kilogram of water from sea level to the top of Mount Everest, which is 8,848 meters above sea level? b) How does this compare with the amount of energy required to evaporate a kilogram of water? c) Why do you suppose it is important for the climate system that the second number is bigger than the first? Explain thoroughly.

4. World annual energy consumption in 1996 is approximately 400 megateraJoules from Fig. 1.9 in the class notes (4x1020Joules per year). a) Convert this power to Watts. b) If you wanted to build a solar panel that would absorb this much power (assuming perfect absorption and 100% efficiency), how big an area would the solar panel need to have? c) If it is square, what is the length of one side of this panel in kilometers? d) How does this linear dimension compare with the radius of Earth, which is 6.37x106m? e) How does this square compare with the size of Washington State, which has an area equivalent to a square with sides 430km long. Hint: First convert the power into Watts using the fact that 1 year has ~365 days and one day has 86,400 seconds. Assume that the solar flux at the panel is 1,380 Watts per square meter. Ignore nighttime, seasons, etc.

5. a) How big is the solar panel in part 4, if you can only convert 10% of the insolation into electrical energy, and still want to provide the worlds 1995 energy usage of 4x1020Joules per year? b) Is this a feasible project? c) How does the rate at which power is supplied to the Earth today by the sun compare with the rate at which we are currently extracting fossil fuel energy?