• # question_answer                 The radiant energy from the sun, incident normally at the surface of earth is $20\,kcal/{{m}^{2}}\,\min$. What would have been the radiant energy, incident normally on the earth, if the sun had a temperature, twice of the present one?                                                                                                                       A)                 $160\,kcal/{{m}^{2}}\,\min$ B)                 $40\,kcal/{{m}^{2}}\min$         C)                 $320\,\,kcal/{{m}^{2}}\,\min$ D)                 $80\,\,kcal/{{m}^{2}}\,\min$

According to Stefan's law, the rate at which an object radiates energy is proportional to the fourth power of its absolute temperature i.e.,                 $E=\sigma {{T}^{4}}\,or\,E\,\propto \,{{T}^{4}}$                 or            $\frac{{{E}_{1}}}{{{E}_{2}}}={{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{4}}$                 Here,  ${{T}_{1}}=T,\,{{T}_{2}}=2T,\,{{E}_{1}}=20\,kcal/{{m}^{2}}$min                 $\therefore \frac{20}{{{E}_{2}}}={{\left( \frac{T}{2T} \right)}^{2}}$                 or            $\frac{20}{{{E}_{2}}}=\frac{1}{16}$                 $\therefore {{E}_{2}}=20\times 16$                 $=320\,kcal/{{m}^{3}}\,\min$