Two spheres of same material have radius $1m$ and $4 m$ and temperature $4000K$ and $2000K$ respectively. The energy radiated per second by the first sphere is
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(c) Energy radiated per sec $\frac{Q}{t} = P = A\varepsilon \sigma {T^4}$
$P \propto {r^2}{T^4} \Rightarrow \frac{{{P_2}}}{{{P_1}}} = \frac{{r_2^2}}{{r_1^2}}.\frac{{T_2^4}}{{T_1^4}} = \frac{{{4^2}}}{{{1^2}}} \times {\left( {\frac{{2000}}{{4000}}} \right)^4} = 1$
$P \propto {r^2}{T^4} \Rightarrow \frac{{{P_2}}}{{{P_1}}} = \frac{{r_2^2}}{{r_1^2}}.\frac{{T_2^4}}{{T_1^4}} = \frac{{{4^2}}}{{{1^2}}} \times {\left( {\frac{{2000}}{{4000}}} \right)^4} = 1$
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