Question

Calculate the average power that the surface of Earth facing the Sun receives from the Sun. Assuming that the Earth is a blackbody and radiates the same amount of power that it absorbs from the Sun, calculate the average surface temperature of the Earth. Does your answer make sense compared to your experience? The Sun’s surface temperature is 5800 K, its radius is 6.96x108 m, the distance between Earth and the Sun is 1.5x1011 m, and the radius of the Earth is 6,400 km.

Answer 1

P_radiated by sun = sigma A T^4

= (5.67 x 10^-8)(4 x pi x (6.96 x 10^8)^2)(5800^4)

= 3.906 x 10^26 W

intensity at the location of earth,

I = P / (4 pi r^2)

I = (3.906 x 10^26) / (4 x pi x (1.5 x 10^11)^2)

I = 1381.5 W/m^2

P_absorbed = I (pi Re^2) = 1.778 x 10^17 W

and P_abosrbed = sigma A T^4

I ( pi Re^2) = sigma (4 pi Re^2) T^4

(1381.5 / 4) = (5.67 x 10^-8) T^4

T = 279 K Or 6.4 deg C