Ok i'm lost here....?

Question

the amount of radiant power produced by the sun is approximately 3.9 x 10^26 W. Assuming the sun to be a perfect blackbody sphere with a radius of6.69 x 10^8 m, find its surface temp in Kelvins. I think the answer is about 5800 K. But I have no idea how the answer was reached. can anyone help? thanks

Answer 1

Power = e* sigma * 4piR^2* T^4
sigma = stefan's constant= 5.67 x 10-8 W m-2 K-4
e = 1=emmissivity of perfect BB
T^4 = W/sigma * 4piR^2
T^4 = 3.9 x 10^26 / 5.67*10-8* 4*3.14*6.69^2*10^16
T^4 = 1223.60* 10^12
T = [1223.60* 10^12]^0.25
T = 5914 K

Answer 2

It looks like you need to use the Stefan-Boltzmann law here:

j = s T^4

where j is the energy radiated per square meter per second, s is the Stefan-Boltzmann constant, and T is the temperature in Kelvins. You figure J from the given radiated power and from the surface area of the sun (4 pi r^2).

Answer 3

you use the luminosity equation.

L = Area * stefan-boltzmann constant * Temperature^4

L = radiant power = 3.9 * 10^26 W
Area of a sphere = 4*pi*r^2
Stefan-Boltzmann constant = 5.67 * 10^-8 W*m^-2*K-4

solve for temperature