Question

Assuming the sum to be spherical body of radius $R$ at a temperature of $T$ $K$, evaluate the total radiant power, incident on Earth, at a distance $r$ from the Sun.
where $r_0$ is the radius of the Earth and $\sigma$ is Stefan's constant.

• A. $\frac{R^2\sigma T^4}{r^2}$
• B. $\frac{{4\pi r_0^{2}R}^2\sigma T^4}{r^2}$
• C. $\frac{{\pi r_0^{2}R}^2\sigma T^4}{r^2}$
• D. $\frac{{r_0^{2}R}^2\sigma T^4}{r^2}$

Answer 1

The correct option is C $\frac{{\pi r_0^{2}R}^2\sigma T^4}{r^2}$

Total power $=\sigma \left(4\pi R^2\right)T^4$
At a distance $r$, power per unit area $=\frac{\sigma \left(4\pi R^2\right)T^4}{\pi r^2}$
Effective earth's area $=\pi r_0^2$

So the total radiant power will be the multiplication of the power per unit area and the effective earth area upon putting the values we will get the answer which is option (c)