Three very large plates of same area are kept parallel (in vertical plane) 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

Step-by-step solution

Let the temperature of the middle plate be T₂ . In steady state, the net rate of heat received by the middle plate must be zero. The middle plate receives radiation from the first plate on one side and from the third plate on the other side. It also emits radiation from both of its sides. According to Stefan-Boltzmann law, the net rate of heat transfer per unit area to the second plate is given by: (T₁^4 - T₂^4) + (T₃^4 - T₂^4) = 0 T₁^4 + T₃^4 = 2T₂^4 Given T₁ = 2T and T₃ = 3T , substituting these values: (2T)^4 +