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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/mC. If the temperature of inner surface is kept at 120C and of the outer surface at 40C. 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 66.66C
Radius of spherical body (b)=4 m
Radius of spherical cavity (a)=2 m
Thermal conductivity of material (K)=100π W/mC
Inner surface temperature (T1)=120C
Outer surface temperature (T2)=40C

At r=3 m
Heat current H1 = Heat current H2
(ΔT)PMRPM=(ΔT)MQRMQ ...(1)
We know that, RPM=14πK(1a1r);RMQ=14πK(1r1b)
From (1)
T1T14πK(1a1r)=TT214πK(1r1b)
120T(1213)=T40(1314)
6(120T)=12(T40)
T=66.66C

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