Question

The earth receives at its surface radiation from the sun at the
rate of 1400 Wm$^2$. The distance of the centre of the sun
from the surface of the earth is 1.5 x 10$^{11} $m and the radius of
the sun is 7 x 10$^ 8$ m. Treating the sun as a black body, it
follows from the above data that its surface temperature is
.......K.

Answer 1

Given, $\frac{\sigma T^4}{4\pi R^2}=1400$
$\therefore \, \, \, \, \, T=\bigg(\frac{1400 \times r^2}{\sigma R^2}\bigg)^{1/4}$
$ \, \, \, \, \, \, \, \, \, \, =\bigg[\frac{1400 \times (1.5 \times 10^{11})^2}{(5.67 \times 10^{08}) \times (7 \times 10^8)^2}\bigg]^{1/4}$
=5803 K