A copper sphere is suspended in an evacuated chamber maintained at `300 K`. The sphere is mantained 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 copper sphere is completely blackened, `600W` is needed to maintain the same temperature of the the sphere. Calculate the emissivity of copper.

Explanation

Applying Stefan's Law
Initially `T=300K` and `T_(s)=500K`
`300=sigma e A[500^(4)-300^(4)]`……`(1)`
afterwords half of the surface of sphere is completely blackened
`600=(sigma e A)/(2)[500^(4)-300^(4)]+(sigmaA)/(2)[500^(4)-300^(4)]`.........`(2)`
dividing `(2)` by `(1)`
`2=(((e)/(2)+(1)/(2)))/(e)implies2e=(e)/(2)+(1)/(2)impliese=(1)/(3)`