By virtue of some internal mechanism, temperature of spherical shell is maintained in steady state which emits radiation like black body while kept in vaccum and isolated from all radiation. If this shell is enveloped by another shell `B` of same radius, still emitted like a black body, find the ratio of temperatures of shell `B` and shell `A` when it was alone:

Options

A. `(2)^(1//4)`
B. `(3)^(1//4)`
C. `(4)^(1//4)`
D. None of these

Answer

A

Explanation

When shell `A` alone is there
`P_(S) = sigma AT_(0)^(4)`
When there are both the shells
`sigma AT_(1)^(4) = P_(S) = sigma A T_(0)^(4)`
`sigma AT_(2)^(4) -sigma A T_(1)^(4) = P_(S) = sigmaA T_(0)^(4)`
`T_(2)^(4) = 2T_(0)^(4)`
`T_(2)//T_(0) = (2)^(1//4)`.