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Q.

Three rods of same dimensions are arranged as shown  in figure. They have thermal conductivities K1 , K2 and K3. The points P and Q are maintained at different temperatures for the heat to flow at the same rate along PRQ and PQ. Which of the following options is correct?

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a

K3=12K1+K2

b

K3=K1+K2

c

K3=K1K2K1+K2

d

K3=2K1+K2

answer is C.

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Detailed Solution

Rate of flow of heat along PQdQdtPQ=K3AΔθl …………(i)Rate of flow of heat along PRQdQdtPRQ=KsAΔθ2l Effective conductivity for series combination of two rods of same lengthKs=2K1K2K1+K2So dQdtPRQ=2K1K2K1+K2⋅AΔθ2l=K1K2K1+K2⋅AΔθl  ……(ii) Equating Eqs. (i) and (ii) K3=K1K2K1+K2
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