The total power consumption by all humans on earth is approximately 10 W. Let\'s

Question

The total power consumption by all humans on earth is approximately 10 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/m^2. The earth's radius is 6.37 times 10^6 m. What is the total solar power received by the earth? Express your answer to two significant figures and include the appropriate units. By what factor does solar power received by the earth exceed the total human power consumption? Express your answer using two significant figures.

Explanation / Answer

Given

total power consumption by the humans is P_h = 10^12 W

intensity of radiation received by the earth is I = 1380 W/m^2

the earth radius R = 6.37*10^6 m

PArt A

the total solar power received by the earth is P = I*A

surface area of the earth is A = 4pi*R^2

           A = 4pi(6.37*10^6)^2 m^2

           A = 5.1*10^14 m2

the power P = I*A = 1380 W/m2 *5.1*10^14 m^2 = 7.038*10^17 W

       P_total = 7.038*10^17 W

PArt B

   the ratio of Ptotal to Phuman consumption is

  
   => P_total /P_human = 7.038*10^17 / 10^12 = 703800 = 7.038*10^5

the total power of solar radiation received is 7.038*10^5 times greater than the consumption of the humans on the earth

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