A black body at a high temperature T K radia | vedclass

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(D) According to the Stefan-Boltzmann law,the energy radiated per unit area per unit time by a black body is proportional to the fourth power of its a

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$E/16$

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(D) According to the Stefan-Boltzmann law,the energy radiated per unit area per unit time by a black body is proportional to the fourth power of its absolute temperature: $E \propto T^4$.Let $E_1 = E$ at temperature $T_1 = T$.Let $E_2$ be the energy radiated at temperature $T_2 = T/2$.Using the ratio: $\frac{E_2}{E_1} = \left( \frac{T_2}{T_1} \right)^4$.Substituting the values: $\frac{E_2}{E} = \left( \frac{T/2}{T} \right)^4 = \left( \frac{1}{2} \right)^4 = \frac{1}{16}$.Therefore,$E_2 = E/16$.

$A$ black body at a high temperature $T \ K$ radiates energy at the rate $E \ W/m^2$. When the temperature falls to $(T/2) \ K$,the radiated energy will be:

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