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Question

# A spherical body of radius b=4π m has a concentric cavity of radius a=2π m as shown in the figure. Thermal conductivity of the material is 100 W/m∘C. If temperature of inner surface is kept at 70∘C and of the outer surface at 30∘C, then find the rate of heat flow. (in kW)

A
16
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B
32
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C
64
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D
40
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Solution

## The correct option is C 64Given, Radius of spherical body (b)=4π m Radius of spherical cavity (a)=2π m Thermal conductivity of material (K)=100 W/m∘C Inner surface temperature (T1)=70∘C Outer surface temperature (T2)=30∘C Then, Rate of heat flow (dQdt)=ΔTR Thermal resistance offered by a spherical shell, having inner radius a and outer radius b is given by (R)=14πK(1a−1b) R=14π×100(π2−π4)⇒R=11600 ∘C/W ∵ΔT=T1−T2=40∘C ⇒dQdt=1600×(40)=64 kW Thus, option (c) is the correct answer.

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