Two spheres S_1 and S_2 have same radii but t | vedclass

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(B) The emissive power $E$ of a body is given by $E = e \sigma T^4$,where $e$ is the emissivity,$\sigma$ is the Stefan-Boltzmann constant,and $T$ is t

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$\sqrt{2}: 1$

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(B) The emissive power $E$ of a body is given by $E = e \sigma T^4$,where $e$ is the emissivity,$\sigma$ is the Stefan-Boltzmann constant,and $T$ is the absolute temperature.Given that the emissive power is the same for both spheres,we have $E_1 = E_2$.Therefore,$e_1 \sigma T_1^4 = e_2 \sigma T_2^4$.Since $\sigma$ is a constant,we get $e_1 T_1^4 = e_2 T_2^4$.Rearranging the terms,we get $\frac{T_1^4}{T_2^4} = \frac{e_2}{e_1}$.Given the ratio of emissivities $e_1: e_2 = 1: 4$,we have $\frac{e_2}{e_1} = \frac{4}{1}$.Thus,$\frac{T_1^4}{T_2^4} = 4$.Taking the fourth root on both sides,$\frac{T_1}{T_2} = (4)^{1/4} = (2^2)^{1/4} = 2^{1/2} = \sqrt{2}$.So,the ratio $T_1: T_2$ is $\sqrt{2}: 1$.

Two spheres $S_1$ and $S_2$ have same radii but temperatures $T_1$ and $T_2$ respectively. Their emissive power is same and emissivity in the ratio $1:4$. Then the ratio $T_1: T_2$ is

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