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Question:

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

(972)14T

(652)14T

(974)14T

(97)14T

Solution:

Let the area of each plate be A. Total power absorbed by plate 2 is Pabs = P1 + P3 ∴ Pabs = σAe(2T)^4 + σAe(3T)^4 Total power radiated by plate 2 is Prad = P2 + P2 ∴ Prad = 2P2 = 2σAe(T')^4 At steady state, Prad = Pabs ∴ 2σAe(T')^4 = σAe(2T)^4 + σAe(3T)^4 Or 2(T')^4 = (2^4 + 3^4)T^4 ⟹ T' = (97/2)^(1/4)T