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A spherical ball of radius 1 cm coated with a metal having emissivity e=0.3 is maintained at 1000 K temperature and suspended in a vaccum chamber whose walls are maintained at 300 K. Find the rate at which electrical energy is to be supplied to the ball to keep its temperature constant. [σ=5.67×108 Wm2K4]

A
56.1 W
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B
72 W
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C
122 W
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D
21.19 W
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Solution

The correct option is D 21.19 W
Rate of heat radiated :
dQdt=Aeσ(T4T04)
We know that, for constant temperature,
Rate of heat radiated = Rate of heat supplied
dQdt=0.3×(4×3.14×0.012)×5.67×(108)×[100043004]
=21.19 W
Thus, option (d) is the correct answer.

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