Stefan’s Law

A black body at a temperature $227°\mathrm{C}$ radiates heat at the rate of $5 \mathrm{cal} {\mathrm{cm}}^{-2} {\mathrm{s}}^{-1}.$ At a temperature of $727°\mathrm{C},$ the rate of heat radiated per unit area is approximately $\underline{ }$ $\mathrm{cal} {\mathrm{cm}}^{-2} {\mathrm{s}}^{-1}$

When the temperature of a body is increased from $27°\mathrm{C}$ to $127°\mathrm{C},$ the radiation emitted by it increases by a factor of ________

Earth receives Sun's radiation at the rate of $\mathrm{P} \mathrm{W} {\mathrm{m}}^{-2}$. Mean distance between the Sun and the Earth is $r m$. Radius of the Sun is $R m$. If Stefan's constant is $\sigma$ (in $\mathrm{SI}$ units), surface temperature of the Sun, in kelvin, is