Two rods A and B of different materials are welded together as shown in the figure. If their thermal conductivities are k1 and k2, the thermal conductivity of the composite rod will be
12(k1+k2)
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=k1A(θ1−θ2)d
and Q2=k2A(θ1−θ2)d
where 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−θ2)d
But, Q=Q1+Q2
⇒k(2A)(θ1−θ2)d=k1A(θ1−θ2)d+k2A(θ1−θ2)d⇒k=12(k1+k2)
Hence, the correct choice is (d).