Two identical black-body plates P and Q are at temperatures Tₚ and Tq, with Tq

Question

Two identical black-body plates P and Q are at temperatures Tₚ and Tq, with Tq < Tₚ. The net radiative power per unit area from P to Q is W₀. Two identical intermediate plates are then inserted between P and Q, and heat transfer occurs only between adjacent plates. In steady state the power per unit area is Wₛ. Find W₀/Wₛ. Image

Physics · Circular Motion

JEE Advanced 2025 Paper 1

G1 Physics · Accepted Answer

Initially, W₀ = σ(Tₚ⁴ − Tq⁴). With two identical intermediate plates, there are three successive radiative gaps. In steady state the same heat flux Wₛ flows through each gap. Adding the three fourth-power temperature drops gives Tₚ⁴ − Tq⁴ = 3(Wₛ/σ). Hence W₀ = 3Wₛ ⇒ W₀/Wₛ = 3.