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Question

# A spherical body of radius 4 m has a concentric cavity of radius 2 m as shown in the figure. Thermal conductivity of the material is 100π W/m∘C. If the temperature of inner surface is kept at 120∘C and of the outer surface at 40∘C. Then, find the temperature T at a distance 3 m from centre. (in ∘C).

A
66.66C
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B
33.66 C
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C
23 C
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D
63.32 C
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Solution

## The correct option is A 66.66∘CRadius of spherical body (b)=4 m Radius of spherical cavity (a)=2 m Thermal conductivity of material (K)=100π W/m∘C Inner surface temperature (T1)=120∘C Outer surface temperature (T2)=40∘C At r=3 m Heat current H1 = Heat current H2 (ΔT)PMRPM=(ΔT)MQRMQ ...(1) We know that, RPM=14πK(1a−1r);RMQ=14πK(1r−1b) From (1) T1−T14πK(1a−1r)=T−T214πK(1r−1b) ⇒120−T(12−13)=T−40(13−14) ⇒6(120−T)=12(T−40) T=66.66∘C

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