Question

The total power consumption by all humans on earth is approximately 1013 W. Let�s compare this to the power of incoming solar radiation. The intensity of radiation from the sun at the top of the atmosphere is 1380 W/m2. The earth's radius is6.37�106 m.

What is the total solar power received by the earth?

By what factor does solar power received by the earth exceed the total human power consumption?

Answer 1

(a) Power = 7.04 * 10^17 W

(b) 7.04 * 10^4

Step-by-step explanation:

Parameters given:

Radius of the earth, R = 6.37 * 10^6 m

Total power consumption = 10¹³ m

Intensity of solar radiation = 1380 W/m²

(a) We can find power by using the formula below:

Power = Intensity * Surface Area

Surface Area is given as:

4 * 3.142 * R²

4 * 3.142 * (6.037 * 10^6)²

S. A. = 5.099 * 10¹⁴ m²

Power = 1380 * 5.099 * 10¹⁴

Power = 7.04 * 10^17 W

(b) Factor by which the solar power received by earth is greater than the power consumed is:

(7.04 * 10^17) / (10^13)

= 7.04 * 10^4

The solar power received by earth is greater than the power consumed by a factor of 7.04 * 10⁴