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(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,
`200/700 = e/1`
⇒ e = 0.3
