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Steel and copper rods are joined end to end between a furnace at 450 C and an ice box at 0 C. With conductivities, lengths and areas satisfying K2/K1 = 9, A1/A2 = 2, L1/L2 = 2 (subscript 1 = steel, 2 = copper), find the steady-state temperature T at the steel-copper junction.

1. 18 C
2. 14 C
3. 45 C
4. 150 C

Correct answer: 45 C

Solution

Equating heat currents gives (450 - T)/T = (K2/K1)(A2/A1)(L1/L2) = 9*(1/2)*2 = 9, so 450 = 10T and T = 45 C.

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