Which of the following statements is true/correct?

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
\(\frac{Q}{t} =P A \varepsilon \sigma T^{4} \)
\( \Rightarrow \frac{P_{1}}{P_{2}} =\frac{A_{1}}{A_{2}}\left(\frac{T_{1}}{T_{2}}\right)^{4}=\left(\frac{\pi}{r_{2}}\right)^{2} \cdot\left(\frac{T_{1}}{T_{2}}\right)^{4} \)
\( =\left(\frac{1}{4}\right)^{2}\left(\frac{4000}{200}\right)=\frac{1}{1}\)
\(\because P_{1}=P_{2}\), hence option (d) is wrong. Newton's law is an approximate from of Stefan's law of radiation and works well for natural convection. Hence option (b) is correct.