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 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.

Answer 1

Given

Sphere constant temperature , T = 500K

Chamber temperature, $T_o$ = 300K

Using Stephen's law

$Power=eA\sigma (T^4-T_o^4)$

$\to 210=eA\sigma ({500}^4-{300}^4)$ ....(1)

When the copper sphere surface is completely blackened, it takes 700 W to maintain sphere temperature. To a black body,

e = 1

$\to 700=1.A\sigma ({500}^4-{300}^4)$ ....(2)

By dividing eq. (1) and (2) , we get,

$\frac{210}{700}=\frac{e}{1}$

$\to e=0.3$

So, the emissivity of copper is 0.3