Question

6) (a) The United States, with a population of 2.2×10^8 people, consumes 5×10^19 J per year. What is the per capita consumption in watts? (b) The sun's radiation provides the earth with 1000 W/m^2. Assuming solar energy can be converted to electrical energy with a 20% efficiency, how much area is needed to serve the energy needs of each U.S. citizen?

Answer 1

6)Given,

n = 2.2 x 10^8 ; E = 5 x 10^19 J

P = E/t = 5 x 10^19/(365 x 24 x 60 x 60) = 1.6 x 10^12 W

per capita Power consumtion will be:

P' = 1.6 x 10^12/(2.2 x 10^8) = 7.27 x 10^3 W

Hence, P' = 7.27 x 10^3 W

b)I = 1000 W/m^2 ;

I = P/A

P = 0.2 x 1.6 x 10^12 = 3.2 x 10^11 W

A = P/I

A = 3.2 x 10^11/1000

A = 3.2 x 10^8 m^2