Three large identical plates are kept parallel to each other. The outer two plates are maintained at temperatures T and 2 T , respectively. The temperature of the middle plate in steady state will be close to

Step-by-step solution

Plates does not touch each other, so exchange of heat takes place in form of radiations. In steady state, heat gained by middle plate = heat lost by it. ⇒ Heat radiations from plate A + Heat radiations from plate B = Heat radiations emitted from both surfaces ⇒ A ε σ T 4 + A ε σ 2 T 4 = 2 A ε σ T 1 4 ⇒ T 4 + 2 4 T 4 = 2 T 1 4 ⇒ 17 2 T 4 = T 1 4 ⇒ T 1 4 = 17 2 1 4 · T or T 1 = 1 . 7 T