Three identical rods are thermally connected in series. The left and right rods have conductivity 2K and the middle rod conductivity K. Their outer ends are at 3T and T. If junction temperatures are T₁ and T₂, find T₁/T₂. Image
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Question

Three identical rods are thermally connected in series. The left and right rods have conductivity 2K and the middle rod conductivity K. Their outer ends are at 3T and T. If junction temperatures are T₁ and T₂, find T₁/T₂. Image

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G1 Physics · Accepted Answer

Step 1: The three rods have equal length L and cross-section A. Thermal resistance is R = L/(kA). Step 2: Side-rod resistances are each L/(2KA); middle rod resistance is L/(KA), double a side resistance. Step 3: Total drop is 3T − T = 2T. The three temperature drops are therefore in ratio 1:2:1, so they are T/2, T and T/2. Step 4: Left junction temperature T₁ = 3T − T/2 = 5T/2. Step 5: Right junction temperature T₂ = T₁ − T = 3T/2. Step 6: T₁/T₂ = (5T/2)/(3T/2) = 5/3. Final answer: 5/3, Option…