A) A nice round number for the ANNUAL energy consumption for the entire US is 10

Question

A) A nice round number for the ANNUAL energy consumption for the entire US is 10E20 Joules. That’s EVERYTHING. Gasoline, coal, solar, etc. This figure was valid in the year 2000, so maybe it’s around 1.5E20 joules now. What average power (in Watts) does this represent? B) You can measure the maximum intensity of sunlight as about 1300 watts per square meter, but since the sun is not always directly overhead, you should use about 700 watts per square meter as a representative average during the daylight hours the sun is up. Assume 12 hours per day as a yearly average. How much energy in Joules of sunlight falls on a one-square meter patch of area in a year?C) Now suppose a solar-to-electric converter is 20.0 percent efficient. Find the amount of useful (electric) energy a 1-square meter cell will produce in one year. This number is the amount of Joules per square meter an array can be expected to produce. If you now multiply this by the Area A of an array (in square meters) you get the total energy for this array in a year. What area A is needed to give the yearly amount of energy from part A of this problem? Convert this to square km. If you take the square root of this last number, you get the length of one side of this square array.

Explanation / Answer

A)

E = energy consumed = 1.5 x 1020 J

t = time = 1 yr = 365 days = 365 x 24 x 3600 sec

Power is given as

P = E/t = (1.5 x 1020)/(365 x 24 x 3600) = 4.8 x 1012 watts

B)

A = 1 m2

t = time duration = 12 x 365 = 12 x 3600 x 365 sec

I = intensity = 700

energy is given as

E = I t A

E = 700 x 12 x 3600 x 365 x 1

E = 1.1 x 1010 J

C)

Euseful = 0.20 E = 0.20 x 1.1 x 1010 = 1.1 x 1010 = 2.2 x 109 J

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