A black body is heated from 7,^oC to 287,^oC. | vedclass

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(A) According to the Stefan-Boltzmann law,the power radiated by a black body is proportional to the fourth power of its absolute temperature: $E \prop

Vedclass · Accepted Answer

$1:16$

Vedclass · Answer

(A) According to the Stefan-Boltzmann law,the power radiated by a black body is proportional to the fourth power of its absolute temperature: $E \propto T^4$.Given temperatures in Celsius: $T_1 = 7\,^oC$ and $T_2 = 287\,^oC$.Convert these to Kelvin: $T_1 = 7 + 273 = 280\,K$ and $T_2 = 287 + 273 = 560\,K$.The ratio of radiation emitted is $\frac{E_1}{E_2} = \left(\frac{T_1}{T_2}\right)^4$.Substituting the values: $\frac{E_1}{E_2} = \left(\frac{280}{560}\right)^4 = \left(\frac{1}{2}\right)^4 = \frac{1}{16}$.Thus,the ratio is $1:16$.

$A$ black body is heated from $7\,^oC$ to $287\,^oC$. The ratio of radiation emitted is

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