Question

The earth receives solar radiation at a rate of 8.2 J cm${}^{-2}$ min${}^{-1}$. If the sun radiates as the black bodies, the temperature at the surface of the sun will be (the angle subtended by sun on the earth in suppose 0.53${}^o$ and Stefan constant is $\sigma =5.67\times {10}^{-8}W{m}^{-2}{K}^4$)

• A. 5800 K
• B. 6700 K
• C. 8000 K
• D. 7800 K

Answer 1

The correct option is A 5800 K

As shown in the figure, angle subtended by sun on earth:
$\omega =\frac{D}{R}=0.53\times \frac{\pi }{180}=9.25\times {10}^{-3}radian$

Heat from sun $Q_s$:
$Q_s=\pi D^2\sigma T^4$

This heat is evenly distributed on a sphere of radius R (distance between earth and sun).

So heat ($Q_e$) received at earth surface per unit area.
$Q_e=\frac{\pi D^2\sigma T^4}{4\pi R^2}=\frac{8.2}{60}$

$\frac{\sigma T^4}{4}\frac{D^2}{R^2}=\frac{8.2}{60}$

$\frac{5.67\times {10}^{-8}\times (9.25\times {10}^{-3}{)}^2\times T^4}{4}=\frac{8.2}{60}$

$T=5800K$