Explanation

(b) During clear nights object on surface of earth radiate out heat and temperature falls. Hence option (a) is wrong
The total energy radiated by a body per unit time per unit area $E \propto T^{4}$. Hence option (c) is wrong
Energy radiated per second is given by $\frac{Q}{t} = PA\varepsilon\sigma T^{4}$
$\Rightarrow \frac{P_{1}}{P_{2}} = \frac{A_{1}}{A_{2}}.\left( \frac{T_{1}}{T_{2}} \right)^{4} = \left( \frac{r_{1}}{r_{2}} \right)^{2}.\left( \frac{T_{1}}{T_{2}} \right)^{4} = \left( \frac{1}{4} \right)^{2}\left( \frac{4000}{200} \right) = \frac{1}{1}$
$\because P_{1} = P_{2}$, hence option (d) is wrong
Newton’s law is an approximate form of Stefan’s law of radiation and works well for natural convection. Hence option (b) is correct