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.

#### Solution

According to Stefan,s law,

power` = eAσ (T^4 - T_0^4)`

Temperature difference = 200 K

Let the emissivity of copper be* e.*

210 = *eAσ*(500^{4} − 300^{4}) ...(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,

`200/700 = e/1`

⇒ e = 0.3