Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surface and have very high thermal conductivity The first and third plates are maintained at temperatures `2T` and `3T` respectively Find the temperature of the middle (i.e second) plate under steady state .

Options

A. `((65)/(2))^(1//4)`
B. `((97)/(4))^(1//4)`
C. `((97)/(2))^(1//4)`
D. `(97)^(1//4)T`

Answer

C

Explanation

In steady state, energy absorbed per second by middle plate is equal to energy released per second by middle plate.

`sigmaA(3T)^(4)-sigmaa(T)^(4)=sigmaA(T')^(4)-sigmaA(2T)^(4)`
`(3T)^(4)-(T)^(4)=(T)^(4)-(2T)^(4)`
`2(T')^(4)=(16+81)T^(4),T'=((97)/(2))^(1//4)T