A) 4
B) 16
C) 32
D) 64
Correct Answer: D
Solution :
From Stefan's law, the energy radiated by the sun is given by\[P=\sigma eA{{T}^{4}},\]assuming\[e=1\]for the sun. In 1 st case, \[{{P}_{1}}=\sigma e\times 4\pi {{R}^{2}}\times {{T}^{4}}\] In 2nd case, \[{{P}_{2}}=\sigma e\times 4\pi {{(2R)}^{2}}\times {{(2T)}^{4}}\] \[=\sigma e\times 4\pi {{R}^{2}}\times {{T}^{4}}\times 64=64{{P}_{1}}\] The rate at which energy received at the earth is, \[E=\frac{P}{4\pi R_{SE}^{2}}\times {{A}_{E}}\] where,\[{{A}_{E}}=\]area of the earth, \[{{R}_{SE}}=\]distance between the sun and the earth. So, In 1st case, \[{{E}_{1}}=\frac{{{P}_{1}}}{4\pi R_{SE}^{2}}\times {{A}_{E}}\] \[{{E}_{2}}=\frac{{{P}_{2}}}{4\pi R_{SE}^{2}}\times {{A}_{E}}=64{{E}_{1}}\]
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