Question

The surface of the Sun has a temperature of about 5800 K. The radius of the Sun is 6.96 x 108 m. Calculate the total energy radiated by the Sun each second. Assume the emissivity of the Sun is 0.965

Answer 1

Given:

$T=\rm 5800\:\rm K$

$R=\rm 6.96*10^8\:\rm m$

$\epsilon=0.965$

$\sigma=5.67*10^{-8}\:\rm W/(m^2\cdot K^4)$

$t=1\:\rm s$

The luminosity (radiation power) of Sun

$$L=\epsilon \sigma T^4A=\epsilon \sigma T^4*4\pi R^2$$

The total energy radiated by the Sun each second

$$E=Lt=\epsilon \sigma T^4*4\pi R^2t$$

$$E=0.965*5.67*10^{-8}*5800^4\\ *4\pi*(6.96*10^8)^2*1=3.77*10^{26}\: \rm J$$