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Question

Two metal rods with identical length and area of cross-section are connected in series. If σ1 and σ2 are the thermal conductance of material of two rods then equivalent conductance of combination is equal to

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Solution

Thermal resistance for both the rods are:
R1=Lσ1A and R2=Lσ2A
Since, rods are connected in series:
Rnet=R1+R2=LA(1σ1+1σ2)

It must be equivalent to, Rnet=2LσA

So, 2LσA=LA(1σ1+1σ2)

σ=2σ1σ2σ1+σ2

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