A copper sphere is suspended in an evacuated chamber maintained at 300K. 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. The emissivity of copper is ____ $\times 10^{- 1}$ .

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Detailed Solution

If emissivity of the body is ‘e’,

then power required = Radiation rate

$P = σ e A (T^{4} - T_{0}^{4})$ ………….(1)

For black body: $P_{B} = σ A (T^{4} - T_{0}^{4})$ ……….(2)

Eq (1) and (2) gives,

$\frac{P}{P_{B}} = e$

$\Rightarrow e = \frac{210}{700} = 0.3 = 3 \times 10^{- 1}$

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