Question

The Earth has an average temperature of 58.3˚F, and radius of 6.38 x 106 m, and an emissivity of 0.986. The Sun has an average temperature of 9941˚F, and radius of 6.09 x 1012 m, and an emissivity of 0.986. Calculate the energy emitted by the Earth and the Sun in one day.

Answer 1

from stefans Boltzman law

rate of eenry trnasfer = H = Q/t =    A e sigma T^4

Energy Q = A e sigma T^4 * t

here A   = 4pi r^2

sigma = 5.67 *10^-8

t = 24 hrs = 24 * 60* 60 s

so

for earth :

r = 6.38 *10^6 m

T = 58.3 F = 287.761 K

e = 0.986

so energy E of earth = (4 *3.14 * (6.38*10^6)^2*0.986* 5.67 *10^-8 * 287.76^4) * (24* 60*60)

Energy of earth = 1.69 *10^22 Joules for each second

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for Sun:

r = 6.09 *10^12 m

e = 0.986

T = 9941 F = 5778.15 K

Eenrgy E = (4 *3.14 * (6.09*10^12)^2*0.986* 5.67 *10^-8 * 5778.15^4) * (24* 60*60)

E of Sun for each second = 2.5 *10^39 Joules