The temperature of a body is 400^{circ}C. Ass | vedclass

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

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$800K$

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(D) According to the Stefan-Boltzmann law,the energy emitted per unit time by a black body is proportional to the fourth power of its absolute temperature: $E \propto T^4$.Given the initial temperature $T_1 = 400^{\circ}C = 400 + 273 = 673 \ K$.We want to find the temperature $T_2$ such that the emitted energy $E_2 = 2E_1$.Using the ratio: $\frac{E_2}{E_1} = \left( \frac{T_2}{T_1} ight)^4$.Substituting the values: $2 = \left( \frac{T_2}{673} ight)^4$.Taking the fourth root on both sides: $T_2 = 673 	imes 2^{1/4}$.Calculating the value: $2^{1/4} \approx 1.189$.$T_2 = 673 	imes 1.189 \approx 800 \ K$.

The temperature of a body is $400^{\circ}C$. Assume the temperature of the surroundings is negligible. At what temperature will the body emit double the energy?

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