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A composite bar is made of three rods of equal length and equal cross-section joined end to end. Their thermal conductivities are K/2, 5K and K respectively. The ends A and B are kept at fixed temperatures and all heat entering A leaves at B with no loss from the sides. Find the effective thermal conductivity of the bar.

1. 15K/16
2. 6K/13
3. 5K/16
4. 2K/13

Correct answer: 15K/16

Solution

Summing series resistances gives 3/K_eff = (2 + 1/5 + 1)/K, so K_eff = 15K/16.

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