Heat conduction

A copper rod and an aluminium rod with the same cross sectional areas are joined as above, with the temperatures at each end maintained at \(90°C\) and \(0°C,\) respectively. Let \(T\) be the temperature of the contact surface between the two rods. Let \(Q_1\) and \(Q_2\) be the quantities of heat passing through the cross sections of the copper and aluminium rods, respectively. What are the temperature \(T\) and the relative values of \(Q_1\) and \(Q_2?\) (The thermal conductivity of copper is twice as large as that of aluminium.)

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