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Two cylindrical conductors of identical length but unequal radii are joined end to end (in series) between two reservoirs maintained at T1 = 300 K and T2 = 100 K. The larger cylinder has a radius twice that of the smaller cylinder. Their materials have thermal conductivities K1 (smaller) and K2 (larger). In the steady state the junction temperature is found to be 200 K. Determine the ratio K1/K2.

1. 1
2. 2
3. 4
4. 0.5

Correct answer: 4

Solution

Equal heat current means K1*A1*(300-200)/L = K2*A2*(200-100)/L. The temperature drops are equal (100 K each), and the larger cylinder has 4x the cross-sectional area (radius doubled). For equal heat flow with equal drops, K1*A1 = K2*A2, so K1 = K2*(A2/A1) = 4*K2.

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