Two spherical bodies of radii r_1 and r_2 hav | vedclass

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(A) According to the Stefan-Boltzmann Law,the power radiated by a spherical body is given by $P = \sigma A T^4$,where $A = 4\pi r^2$ is the surface ar

Vedclass · Accepted Answer

$(\frac{T_2}{T_1})^2$

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(A) According to the Stefan-Boltzmann Law,the power radiated by a spherical body is given by $P = \sigma A T^4$,where $A = 4\pi r^2$ is the surface area.Given that both bodies radiate the same power,we have $P_1 = P_2$.Therefore,$\sigma (4\pi r_1^2) T_1^4 = \sigma (4\pi r_2^2) T_2^4$.Simplifying the equation,we get $r_1^2 T_1^4 = r_2^2 T_2^4$.Rearranging for the ratio of radii,we get $(\frac{r_1}{r_2})^2 = (\frac{T_2}{T_1})^4$.Taking the square root on both sides,we obtain $\frac{r_1}{r_2} = (\frac{T_2}{T_1})^2$.

Two spherical bodies of radii $r_1$ and $r_2$ have surface temperatures $T_1$ and $T_2$ respectively. They radiate the same power. The ratio $r_1/r_2$ is . . . . . .

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