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