A copper sphere is suspended within an evacuated chamber kept at 300 K . The sphere is kept at a constant temperature of 500 K by heating it electrically, which requires 210 W of electric power. Once the surface of the copper sphere is completely blackened, 700 W is required to maintain the sphere at the same temperature. Determine the emissivity of copper.

Step-by-step solution

According to the Stefan-Boltzmann law, the net rate of heat loss by radiation from a body is given by P = e A (T^4 - T₀^4) . For the copper sphere, the power required to maintain its temperature is: P₁ = e A (T^4 - T₀^4) = 210 W When the sphere is completely blackened, it behaves as a black body with an emissivity of 1 . The power required is: P₂ = (1) A (T^4 - T₀^4) = 700 W Dividing the equation for the copper sphere by the equation for the blackened sphere, we get: e = P₁ P₂ = 210 700 = 0.3 Thus, the emissivity o