Two thin metallic spherical shells of radii r1 and r2 (r1 < r2) are… | JEE Main 2021 (31 Aug, Shift 2)

Q42JEE Main 2021 · 31 AUG · SHIFT 2Difficult

Heat Conduction

Two thin metallic spherical shells of radii r1 and r2 (r1 < r2) are placed with their centres coinciding. A material of thermal conductivity K is filled in the space between the shells. The inner shell is maintained at temperature $\theta$ 1 and the outer shell at temperature $\theta_2 (\theta$ 1 < $\theta$ 2). The rate at which heat flows radially through the material is :-

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Answer: (a)

Thin spherical shell: $H = K(4\pi r^2)\dfrac{d\theta}{dr}$ , constant through all shells.
Integrate from $r_1$ to $r_2$ : $H\left(\dfrac{1}{r_1}-\dfrac{1}{r_2}\right) = 4\pi K(\theta_2-\theta_1)$
$H = \dfrac{4\pi K r_1 r_2(\theta_2-\theta_1)}{r_2-r_1}$
So the answer is (a).

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Heat Conduction question from JEE Main 2021 (31 Aug, Shift 2)

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