• # question_answer The earth receives at its surface radiation from the sun at the rate of $1400\,\,\text{W/}{{\text{m}}^{\text{2}}}.$ the distance of centre of sun from the surface of earth is $1.5\times {{10}^{11}}m$ and the radius of sun is $7.0\times {{10}^{8}}M.$ what is approximately the surface temperature of the sun treating the sun as a black body? A) 3650 K             B) 4500 KC) 5800 K             D) 6150 K

Temperature of the Sun, ${{T}_{s}}={{\left[ \frac{{{L}^{2}}{{G}_{s}}}{{{r}^{2}}\sigma } \right]}^{1/4}}$ Where L = mean distance between the sun and the Earth $=1.5\times {{10}^{11}}m$ r = radius of the Sun $=7\times {{10}^{8}}m$ ${{G}_{s}}=$ rate of radiation from the sun $=1400\,\text{W/}{{\text{m}}^{\text{2}}}$ $\sigma \,\,=$ Stefan-Boltzmann constan $=5.675\times {{10}^{-\,8}}\,\text{W/(}{{\text{m}}^{\text{2}}}\text{.K)}$ ${{T}_{s}}={{\left[ \frac{{{(1.5\times {{10}^{11}})}^{2}}\times 1400}{{{(7\times {{10}^{8}})}^{2}}\times 5.675\times {{10}^{-\,8}}} \right]}^{1/4}}$ = 5800 K $=900w/{{m}_{2}}$