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(C) According to the Stefan-Boltzmann law,the power radiated by a black body is given by $P = A \sigma T^4$,where $A$ is the surface area,$\sigma$ is

Vedclass · Accepted Answer

$1:4$

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(C) According to the Stefan-Boltzmann law,the power radiated by a black body is given by $P = A \sigma T^4$,where $A$ is the surface area,$\sigma$ is the Stefan-Boltzmann constant,and $T$ is the absolute temperature.Since the spheres are of the same material and at the same temperature,$\sigma$ and $T$ are constant.The surface area of a sphere is $A = 4 \pi r^2$,so $P \propto r^2$.Therefore,the ratio of the emissive power is $\frac{P_1}{P_2} = \frac{r_1^2}{r_2^2}$.Given $\frac{r_1}{r_2} = \frac{1}{2}$,we have $\frac{P_1}{P_2} = (\frac{1}{2})^2 = \frac{1}{4}$.

If the ratio of the radii of two spheres of the same material and at the same temperature is $1:2$,find the ratio of their emissive power.

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