A copper sphere is suspended in an evacuated chamber maintained at 300 K. The sp

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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 210 W of electric power is needed to do it. When the surface of the copper sphere is completely blackened, 700 W is needed to maintain the same temperature of the sphere. Calculate the emissivity of copper.

Options:

A . 0.5

B . 0.4

C . 0.3

D . 0.2

Answer: Option C
:
C
Before painting it black the power needed =

e σ A (T^{4} - T_{0}^{4}) = 210

...(i)
T = 500 K

T_{0}

= 300 K
e

\to

emissivity
After the paint the surface behaves like a black body.

∴ σ A (T^{4} - T_{0}^{4}) = 700

...(ii)
Dividing (i) and (ii)

e = \frac{210}{700}

\Rightarrow

e = 0.3

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