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Question

A copper sphere is suspended in an evacuated chamber maintained at 300 K. The sphere is maintained at a constant temperature of 500 K by heating it electrically. A total of 300 W of electric power is needed to do it. When half of the surface of the copper sphere is completely blackened, 600 W is needed to maintain the same temperature of the sphere. Calculate the emissivity of copper.

A
e=12
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B
e=13
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C
e=14
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D
e=15
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Solution

The correct option is B e=13

Applying <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Stefan-Boltzmann's Law,
P=eσA(T4T4s)
Ts=300 K, T=500 K
300=σeA[50043004] (1)
After half surface is blackened,
600=σeA2[50043004]+σA2[50043004] (2)
[e for black surface =1]
Dividing (2) by (1),
2=(e2+12)e2e=e2+12
or e=13

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