According to Stefan's law, $\mathrm{E}={\mathrm{\sigma T}}^4$
Total surface area of the sun$=4{\mathrm{\pi R}}_{\mathrm{S}}^2$ .
Therefore, the total energy radiated per second by the sun per unit solid angle

          $=-\frac{{\mathrm{\sigma T}}^4\times 4{\mathrm{\pi R}}_{\mathrm{s}}^2}{4\mathrm{\pi }}={\mathrm{\sigma T}}^4{\mathrm{R}}_{\mathrm{s}}^2$

Let R_es be the distance of earth from the sun. Hence, intensity of radiation of earth

$\begin{array}{l}\mathrm{l}={\mathrm{\sigma T}}^4{\mathrm{R}}_{\mathrm{s}}^2/{\mathrm{R}}_{\mathrm{es}}^2\\ \therefore 1400=\left(5.6\times {10}^{-8}\right){\mathrm{T}}^4{\left[\frac{7.0\times {10}^8}{1.5\times {10}^{11}}\right]}^2\\ \mathrm{T}=5801\mathrm{K}\end{array}$