Question

The sun is 1.5 1011 m from the earth.
(a) Over what surface area is solar radiation spread at this distance?


(b) What is the total power radiated by the sun? (The sun delivers energy to the surface of the earth at a rate of approximately 1400 W/m2.)


(c) Treating the sun as a body of emissivity 1, estimate its temperature. The sun's radius is 6.96 108 m.
K

Answer 1

a. A = 4•π•r^2 = 4•π•(1.5•10^11)^2 = =9•π•10^22 m^2.

b. Power density is p =1400 W/m^2.
The total power is
P = p•A =1400 • 9•π•10^22 =
=3.96•10^26 W.

c. Stefan-Boltzmann Law
R = σ•T^4,
R =P/A1 = P/(4• π•r1^2), is the black body irradiance,
σ =5.67• 10^-8 W•m^-2•K^-4 is the Stefan-Boltzmann constant,
T =[P/(A1• σ)]^1/4 ={3.96•10^26/[4• π•(6.96• 10^8)^2]}^1/4 = 5800 K.