The total rate at which power is used by humans world- wide is approximately 15

Question

The total rate at which power is used by humans world- wide is approximately 15 TW (terawatts). The solar flux av eraged over the sunlit half of Earth is 680 W/m2 (assuming no clouds). The area of Earth's disc as seen from the Sun is 1.28 x 1014 m2. The surface area of Earth is approximately 197,000,000 square miles. How much of Earth's surface would we need to cover with solar energy collectors to power the planet for use by all humans? Assume that the solar en- ergy collectors can convert only 10% of the available sun- light into useful power.

Explanation / Answer

15 TW = 1.5 x 1013 W
680 W / m2

1.5 x 1013 W divided by 680 W / m2 = 2.205 x 1010 m2 (at 100% efficiency)

at 10% efficiency, we need

2.205 x 1010 m2 / 0.1 = 2.205 x 1011 m2

Think of 197,000,000 square miles as a rectangle with these dimensions:

197,000,000 miles by 1 mile

Now, we need to find out how many meters are in one mile:

1 mile = 1609.34 m

Replace mile in the following:

197,000,000 miles by 1 mile

like this:

(197,000,000 miles x 1609.34 m / mi) by (1 mile x 1609.34 m / mi)

317039980000 m by 1609.34 m

510225121413200 m2 = 5.10225 x 1014 m2

Now, for the answer:

(2.205 x 1011 m2 / 5.10225 x 1014 m2 ) * 100 = 0.0432 %

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