Question

The amount of radiant power produced by the sun is approximately 3.9 ✕ 1026 W. Assuming the sun to be a perfect blackbody sphere with a radius of 6.96 ✕ 108 m, find its surface temperature (in kelvins).

Answer 1

Answer:

T=5797.8  K

Explanation:

Given that

Power P = 3.9 x 10²⁶ W

Radius ,r= 6.96 x 10⁸ m

We know that ,From Plank's law

P = σ A T⁴

σ = 5.67 x 10 ⁻⁸

A= Area ,T= Temperature ( in Kelvin)

$T=\left (\dfrac{P}{\sigma A} \right )^{\dfrac{1}{4}}$

Now by putting the values

$T=\left (\dfrac{P}{\sigma A}\right )^{\dfrac{1}{4}}$

$T=\left (\dfrac{3.9\times 10^{26}}{5.67\times 10^{-8}\times 4\times \pi \times (6.96\times 10^8)^2} \right )^{\dfrac{1}{4}}$

T=5797.8  K

The temperature of surface will be 5797.8 K