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 thired plates are maintained at temperatures `2T` and `3T` respectively Find the temperature of the middle (i.e second) plate under steady state .

Explanation

Let `T_(1)` is the temperature of the middlte plate Under steady rate of emission =rate of absorption
`sigma (2A) (T_(1))^(4) =sigma A (2T)^(4) + sigma A (3T)^(4)`
`2T_(1)^(4) = 16T^(4) + 81T^(4) rArr T_(1) = ((97)/(2))^(¼) T`
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