A black body radiates energy at the rate of $1 \times 10^5 J / s \times m^2$ at temperature of $227^o C$. The temperature to which it must be heated so that it radiates energy at rate of $1 \times 10^9J/s m^2$, is
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(a) $\frac{{{E_2}}}{{{E_1}}} = {\left( {\frac{{{T_2}}}{{{T_1}}}} \right)^4}$
==> $\frac{{{T_2}}}{{{T_1}}} = {\left( {\frac{{{E_2}}}{{{E_1}}}} \right)^{1/4}} = {\left( {\frac{{{{10}^9}}}{{{{10}^5}}}} \right)^{1/4}} = 10$
==> ${T_2} = 10{T_1} = 10 \times (273 + 227) = 5000\,K$
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