A) \[\frac{4\pi {{r}^{2}}\sigma {{t}^{4}}}{{{R}^{2}}}\]
B) \[\frac{{{r}^{2}}\sigma {{(t+273)}^{4}}}{4\pi {{R}^{2}}}\]
C) \[\frac{16{{\pi }^{2}}{{r}^{2}}\sigma {{t}^{4}}}{{{R}^{2}}}\]
D) \[\frac{{{r}^{2}}\sigma {{(t+273)}^{4}}}{{{R}^{2}}}\] where \[\sigma \] is the Stefan's constant.
Correct Answer: D
Solution :
From Stefarfs law, the rate at which energy is radiated by sun at its surface is \[P=\sigma \times 4\pi {{r}^{2}}{{T}^{4}}\] [Sun is a perfectly black body as it emits radiations of all wavelengths and so for it\[e=1]\] The intensity of this power at earth's surface (under the assumption\[R>>{{r}_{0}})\]is \[I=\frac{P}{4\pi {{R}^{2}}}\] \[=\frac{\sigma \times 4\pi {{r}^{2}}{{T}^{4}}}{4\pi {{R}^{2}}}\] \[=\frac{\sigma {{r}^{2}}{{T}^{4}}}{{{R}^{2}}}\] \[=\frac{\sigma {{r}^{2}}{{(t+273)}^{4}}}{{{R}^{2}}}\]You need to login to perform this action.
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