A) \[\frac{4\pi {{r}^{2}}{{\sigma }^{4}}}{{{R}^{2}}}\]
B) \[\frac{{{r}^{2}}\sigma {{(t+273)}^{4}}}{4\pi {{R}^{2}}}\]
C) \[\frac{16{{\pi }^{2}}{{r}^{2}}\sigma t}{{{R}^{2}}}\]
D) \[\frac{{{r}^{2}}\sigma {{(t+273)}^{4}}}{{{R}^{2}}}\]
Correct Answer: D
Solution :
Power radiated by sun at \[t{}^\circ C\text{ }\,=\,\,\sigma {{\left( t\text{ }+\text{ }273 \right)}^{4}}4\pi {{r}^{2}}\] Power received by a unit surface area \[=\,\,\,\frac{\sigma {{(t+273)}^{4}}\,4\pi {{r}^{2}}}{4\pi {{R}^{2}}}\] \[=\,\,\,\frac{{{r}^{2}}\sigma {{(t+273)}^{4}}}{{{R}^{2}}}\]
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