Three identical large metal plates are kept parallel and close to each other. Each plate can be trea

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Three identical large metal plates are kept parallel and close to each other. Each plate can be treated as an ideal black body and has very high thermal conductivity. The first and third plates are maintained at high temperature T1 = 3T and T3 = 2T. The temperature T2 of the middle (i.e. second) plate under steady state condition is :-

Accepted Answer

[Key Concept: In steady state the net radiant power received by the middle black plate from plate 1 equals that it passes to plate 3.]

For equilibrium,

$$\begin{matrix} & P_{12} = P_{23} \\ & \sigma eA\left( {\text{ }T}_{1}^{4} - T_{2}^{4} \right) = \sigma eA\left( {\text{ }T}_{2}^{4} - T_{3}^{4} \right) \\ & \ \Rightarrow T_{2}^{4} = \frac{1}{2}\left( {\text{ }T}_{1}^{4} + T_{3}^{4} \right) \\ & \ \Rightarrow T_{2} = \left( \frac{97}{2} \right)^{1/4}\text{ }T \end{matrix}$$

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