The figure shows a system of two concentric spheres of radii r₁ and… | JEE Main 2005 (AIEEE)

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Heat Conduction

The figure shows a system of two concentric spheres of radii $r_1$ and $r_2$ are kept at temperatures $T_1$ and $T_2$ , respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to

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Answer: (d)

A thin shell of radius $r$ and thickness $dr$ : $H = -K(4\pi r^2)\dfrac{dT}{dr}$ , same $H$ through every shell.
$H\int_{r_1}^{r_2}\dfrac{dr}{r^2} = 4\pi K(T_1-T_2) \Rightarrow H\left(\dfrac{1}{r_1}-\dfrac{1}{r_2}\right) = 4\pi K(T_1-T_2)$
$H = \dfrac{4\pi K r_1 r_2 (T_1-T_2)}{r_2-r_1}$
So the answer is (d) $H \propto \dfrac{r_1 r_2}{r_2-r_1}$ .

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Heat Conduction question from JEE Main 2005 (AIEEE)

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