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
Answer: Option A
:
A
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=−4πKH∫T1T1dt
Which on integration and simplification gives
H=dQdt=4πKr1r2(T1−T2)r2−r1⇒dQdt∝r1r2(r2−r1)
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:
A
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=−4πKH∫T1T1dt
Which on integration and simplification gives
H=dQdt=4πKr1r2(T1−T2)r2−r1⇒dQdt∝r1r2(r2−r1)
Was this answer helpful ?
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