The total amount of solar energy that arrives at the earth from the sun is 1.74

Question

The total amount of solar energy that arrives at the earth from the sun is 1.74 × 1017 W, and the surface area of the earth is 5.1 × 1014 m2 (assuming the earth's radius is 6.37 × 106 m). (a) If a solar panel is about 20% efficient in converting solar photons into electrical power, how big a solar panel (in area, m2) would be required to run a 70 W light bulb? (b) Humans use approximately 4.87 × 1018 J of electrical energy per year. What fraction of the available solar energy is required to meet this consumption?

Explanation / Answer

(A) Intensity = P / A

I = (1.74 x 10^17 W) / (5.1 x 10^14 m^2 )

I = 341.18 W/m^2

70 = 0.20(341.18 A)

A = 1.03 m^2

(b) time = 1 year = 365 x 24 x 3600s

t = 31.54 x10^6 sec

P_consumption = (4.87 x 10^18) / (31.54 x 10^6) = 1.544 x 10^11 W

fraction = (1.544 x 10^11) / (1.74 x 10^17 )

= 8.88 x 10^-7 ....Ans

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