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 90°C and 0 ° C , 0°C, respectively. Let T T be the temperature of the contact surface between the two rods. Let Q 1 Q_1 and Q 2 Q_2 be the quantities of heat passing through the cross sections of the copper and aluminium rods, respectively. What are the temperature T T and the relative values of Q 1 Q_1 and Q 2 ? Q_2? (The thermal conductivity of copper is twice as large as that of aluminium.)

T = 60 ° C T=60°C and Q 1 > Q 2 Q_1>Q_2 T = 45 ° C T=45°C and Q 1 = Q 2 Q_1=Q_2 T = 60 ° C T=60°C and Q 1 = Q 2 Q_1=Q_2 T = 30 ° C T=30°C and Q 1 < Q 2 Q_1<Q_2

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