A black body radiates heat energy at the rate of $2\times10^5\, J/sm^2$ at temp. of $127\,^oC$. The temp of black body at which rate becomes $32\times10^5\, J/s-m^2%$ is ....... $^oC$
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$\mathrm{E}=\sigma \mathrm{T}^{4}$ and $\mathrm{T}_{1}=127+273=400 \mathrm{K}$
$\Rightarrow \quad \frac{\mathrm{T}_{2}}{\mathrm{T}_{1}}=\left(\frac{\mathrm{E}_{2}}{\mathrm{E}_{1}}\right)^{1 / 4}$
$\Rightarrow$$ \mathrm{T}_{2}=\left(\frac{32 \times 10^{5}}{2 \times 10^{5}}\right)^{1 / 4} \times 400 $
$=2 \times 400=800 \mathrm{K}=800-273=527^{\circ} \mathrm{C} $
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