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If a black body emits $0.5 \mathrm{~J}$ of energy per second when it is at $27^{\circ} \mathrm{C}$, then the amount of energy emitted by it when it is at $627^{\circ} \mathrm{C}$ will be
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The correct answer is:
$40.5 \mathrm{~J}$
According to Stefan's law.
$E \propto T^{4}$
$\frac{\mathrm{E}_{1}}{\mathrm{E}_{2}}=\left[\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\right]^{4}$
$\frac{\mathrm{E}_{1}}{0.5}=\left[\frac{273+627}{273+27}\right]^{4}$
$\mathrm{E}_{1}=0.5\left(\frac{900}{300}\right)^{4}$
$\Rightarrow \quad \mathrm{E}_{1}=40.5 \mathrm{~J}$
$E \propto T^{4}$
$\frac{\mathrm{E}_{1}}{\mathrm{E}_{2}}=\left[\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\right]^{4}$
$\frac{\mathrm{E}_{1}}{0.5}=\left[\frac{273+627}{273+27}\right]^{4}$
$\mathrm{E}_{1}=0.5\left(\frac{900}{300}\right)^{4}$
$\Rightarrow \quad \mathrm{E}_{1}=40.5 \mathrm{~J}$
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