Question

The sun has a radiated power of 3.9 · 1026 W, a surface temperature of 5800 K and a radius of 6.96 · 108 m. Examine whether the sun radiates like a black body?

Answer 1

Radiation energy Q emitted by an object in time t, object has surface area A, emissivity e and kelvin temperature T is:

$Q=e \sigma T^4At \\ \sigma = 5.87 \times 10^{-8} \;J/(s \times m^2 \times T^4) \\ Q = 3.9 \times 10^{26} \;W \\ r = 6.96 \times 10^8 \;m \\ T = 5800 =5.8 \times 10^3\;K \\ t = 1 \;s$

The sun is an spherical shape object. The surface area of the sun is

$A = 4 \pi r^2 \\ = 4 \pi (6.96 \times 10^8)^2 \\ = 6.087 \times 10^{18} \;m^2 \\ e = \frac{Q}{\sigma T^4At} \\ = \frac{3.9 \times 10^{26}}{5.87 \times 10^{-8} \times (5.8 \times 10^3)^4 \times 6.087 \times 10^{18} \times 1} \\ = \frac{3.9 \times 10^{26}}{4.04 \times 10^{26}} \\ = 0.965 ≈ 1$

e = 1 for black body

So, the sun radiates like a black body.