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Question

A hollow metallic sphere of radius 20 cm surrounds a concentric metallic sphere of radius 5 cm. The space between the spheres is filled with a material of thermal conductivity k. The inner and outer spheres are maintained at 50C and 10C respectively and it is found that 100 J of heat passes from the inner to the outer surface per second. Find the value of k.

A
1 Wm1C1
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B
0.5 Wm1C1
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C
2 Wm1C1
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D
3 Wm1C1
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Solution

The correct option is D 3 Wm1C1
Given that,
r1=0.05 m
r1=0.20 m
Rate of heat flow H=100 J/s

Rate of heat flow through a concentric shell is given by
H=k4πr1r2(θ1θ2)r2r1
100=k×4×3.14×5×20×40×10415×102
k=2.9853 Wm1C1


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