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Question

A spherical ball of radius 1 cm coated with a material having emissivity 0.3 is maintained at 1000 K temperature and suspended in a vacuum chamber whose walls are maintained at 300 K temperature. Find the rate at which electrical energy is to be supplied to the ball to keep its temperature constant.
[Given σ=5.67×108 W m2K4]

A
19.1 W
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B
21.2 W
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C
30 W
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D
8 W
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Solution

The correct option is B 21.2 W
Since the temperature of ball is constant,
Rate at which it is lossing heat = Rate at which heat is supplied to it.
Rate of heat loss =dQdt=eAσ(T4T4s)
=0.3×4π(0.01)2×5.67×108(100043004)
=21.2 watt
Therefore, electrical energy should be supplied at the same rate.

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