Temperature of two identical balls are `200^(@)C` and `400^(@)C`. Both are kept in surroundings of `27^(@)C`. The ratio of their rate of radiation energy is . .. . . . .

Options

A. `(1)/(16)`
B. `1/4`
C. `1/2`
D. `((473)^(4)-(300)^(4))/((673)^(4)-(300)^(4))`

Answer

D

Explanation

From Stefan - Boltzmann.s law,
`(dQ)/(dt)" e "sigma" A "(T^(4)-T_(s)^(4))`
where `T_(1)=273+200=473^(@)C`
`T_(2)=273+400=673^(@)C`
and `T_(s)=273+27=300^(@)C`
`:.((dQ)/(dt))_(1)/((dQ)/(dt))_(2)=(esigmaA(T_(1)^(4)-T_(s)^(4)))/(esigmaA(T_(2)^(4)-T_(s)^(4)))`
`=(T_(1)^(4)-T_(s)^(4))/(T_(2)^(4)-T_(s)^(4))`
`:.(((dQ)/(dt))_(1))/(((dQ)/(dt))_(2))=((473)^(4)-(300)^(4))/((673)^(4)-(300)^(4))`