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Question

Two slabs A and B of different materials but of the same thickness are joined as shown in figure. The thermal conductivities of A and B are k1 and k2 respectively. The thermal conductivity of the composite slab will be



Solution

The correct option is D


The thermal resistance of a slab of length l,area A and thermal conductivity kis given by

R=lkAFor slab A:    R1=12k1AFor slab B:R2=12k2A

Since the slabs are joined in series, the thermal resistance of the composite slab is

Rc=R1+R2

Or    1kcA=12k1A+12k2AOr    1kc=12(1k1+1k2)Which gives  kc=2k1k2(k1+k2)

Hence the correct choice is (d).

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