A solid metallic sphere of diameter 20 cm and mass 10 kg is heated to a temperature of `327^@C` and suspended in a box in which a constant temperature of `27^@C` is maintained. Find the rate at which the temperature of the Sphere will fall with time. Stefan's constant`=5.67xx10^-8W//m^(2)//K^(4)` and specific heat of metal `=420J//kg//^(@)C`.

Options

A. `0.55^(@)C//sec`
B. `0.66^(@)C//sec`
C. `0.44^(@)C//sec`
D. `0.03^(@)C//sec`

Answer

B

Explanation

`(-(dT)/(dt)) = (sigmaeA)/(mS) [T^(4)-T_(S)^(4)]`
Rate of temperature fall will be maximum when `(T^(4) -T_(S)^(4))` has mass value i.e. `T` has max. value
`(-(dT)/(df))_(max) = (sigma eA)/(mS) [500^(4)-300^(4)]` Put all values & get answer.