A) \[{{r}^{2}}_{0}{{R}^{2}}\sigma \frac{{{T}^{4}}}{4\pi {{r}^{2}}}\]
B) \[{{R}^{2}}\frac{\sigma {{T}^{4}}}{{{r}^{2}}}\]
C) \[4\pi {{r}^{2}}_{0}{{R}^{2}}\frac{\sigma {{T}^{4}}}{{{r}^{2}}}\]
D) \[\pi r_{0}^{2}{{R}^{2}}\frac{\sigma {{T}^{4}}}{{{r}^{2}}}\]
Correct Answer: D
Solution :
[d] Energy radiated by sun, according to Stefan's law \[E=\sigma {{T}^{4}}\times (area4\pi {{R}^{2}})\](time) This energy is spread around sun in space, in a sphere of radius r. earth (E) in space receives part of this energy \[\frac{Energy}{Area\,of\,envelop}=\frac{\sigma {{T}^{4}}\times 4\pi {{R}^{2}}\times time}{4\pi {{r}^{2}}}\] \[\therefore \] Power incident per unit area on earth \[=\left( \frac{{{R}^{2}}\sigma {{T}^{4}}}{{{r}^{2}}} \right)\] \[\therefore \] Power incident on earth is \[\pi {{r}_{0}}^{2}\times \frac{{{R}^{2}}\sigma {{T}^{4}}}{{{r}^{2}}}\]
You need to login to perform this action.
You will be redirected in
3 sec
