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.

Answer 1

According to Stefan^,s law,
$\mathrm{Power}=\mathit{}eA\sigma \left(T^4-T_0^4\right)$
Temperature difference = 200 K

Let the emissivity of copper be e.

210 = eAσ(500⁴ − 300⁴) ...(1)

When the surface of the copper sphere is completely blackened, 700 W is needed to maintain the temperature of the sphere.
For a black body,
e = 1
700 = 1·Aσ(500⁴ − 300⁴) ...(2)
On dividing equation (1) by equation (2) we have,

$$\begin{gathered} \frac{210}{700}=\frac{e}{1} \\ \Rightarrow e=0.3 \end{gathered}$$