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Question

The figure shows a system of two concentric spheres of radii r1 and r2 and kept at temperatures T1 and T2, respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to

A
r1r2(r1r2)
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B
(r2r1)
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C
(r2r1)(r1r2)
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D
In (r2r1)
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Solution

The correct option is A r1r2(r1r2)
Consider a concentric spherical shell of radius r and thickness dr as shown in fig.


The radial rate of flow of heat through this shell in steady state will be H=dQdt=KAdTdr=K(4πr2)dTdr
r2r1drr2=4πKHT1T1dt
Which on integration and simplification gives
H=dQdt=4πKr1r2(T1T2)r2r1dQdtr1r2(r2r1)

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