A black ened metal sphere of radius 7 cm is encllosed in as evacuated chamber maintained at a temperature of `27^(@)C`. At what rate must energy be supplied to the sphere so as to keep its temperature constant at `127^(@)C` ?
`sigma=5.7xx10^(-8) W m^(-2) K^(-4)`.

Answer

`[61.44 watt]`

Explanation

Here, `r=7 cm = 0.07 m`,
`T_(0)=27+273=300 K`,
`T=127+273=400 K`.
Energy supplier per second to shere to keep its temperature constant
`E 4 pi r^(2) = sigma (T^(4)-T_(0)^(4)) 4 pi r^(2)`
`=(5.7xx10^(-8))[(400)^(4)-(300)^(4)xx4xx(22)/(7)xx(0.07)^(2) ]= 61.44 W`