Question

9(e). The diagram illustrates a composite bar of iron and copper, insulated along its sides, with a diameter of 10 mm. The length and thermal conductivity of the iron are 0.15 m and 40 Wm⁻¹K⁻¹ respectively, and those of the copper are 0.05 m and 360 Wm⁻¹K⁻¹ respectively. If the free ends of the iron and copper are kept at 100°C and 0°C respectively, calculate: I. the temperature θ at the interface between the bars; II. the rate of heat flow along the bar.

Accepted Answer

At steady state, the rate of heat flow through both bars is equal: (KA×Δθ/l)iron = (KA×Δθ/l)copper. 40×(100-θ)/0.15 = 360×(θ-0)/0.05. Solving gives θ ≈ 3.6°C.
Rate of heat flow, Q/t = KA(θ_H-θ_C)/l, using the copper section: Q/t = 360×(π×0.01²/4)×(3.6-0)/0.05 ≈ 2.02 W.

WAEC Physics 2021 Theory — Question 18

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