Two rods A and B of different materials are welded together as shown in Fig. If their thermal conductivities are k₁ and k₂, the thermal conductivity of the composite rod will be

detailed solution

Correct option is D

If the ends of the rods are maintained at temperatures θ1 and θ2 the rate of flow of heat through each rod is given by               Q1=k1Aθ1−θ2dQ2=k2Aθ1−θ2dwhere A is the cross-sectional area of each rod and d is the length of each rod. Now the cross-sectional area of the composite rod is 2A. If k is the thermal conductivity of the composite rod, the rate of heat flow is       Q=k(2A)θ1−θ2dBut Q=Q1+Q2. Therefore k(2A)θ1−θ2d=k1Aθ1−θ2d+k2Aθ1−θ2dor   k=12k1+k2Hence the correct choice is (d).