Two bodies A and B at temperatures `T_(1)K and T_(2)K` respectively have the same dimensions. Their emissivities are in the ratio of `1 : 3`. If they radiate the same amount of heat per unit area per unit time, then the relation between their temperatures is given by

Options

A. `T_(1)/T_(2)=1/3`
B. `T_(1)/T_(2)=81/1`
C. `T_(1)/T_(2)=3^(1//4):1`
D. `T_(1)/T_(2)=9^(1//4):1`

Answer

C

Explanation

According to Stefan's law of radiation,
`(dQ)/(dt)=e(sigmaAT^(4))` where e is its emissivity
For both bodies, A and `(dQ)/(dt)` are the same.
`thereforee_(1)T_(1)^(4)=e_(2)T_(2)^(4)`
`therefore(T_(1)/T_(2))^(4)=(e_(2)/e_(1))=3/1`
`thereforeT_(1)/T_(2)=4sqrt3=3^(1//4):1`