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

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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 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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