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Five rods of the same dimensions are arranged as shown. They have thermal conductivities k1, k2, k3, k4 and k5. When points A andB are maintained at different temperatures, no heat flows through the central rod. It follows that :(a) k1 = k4 and k2 = k3(b) k1/k4 = k2/k3(c) k1k4 = k2k3(d) k1k2 = k3k4
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For no current flow between C and D (Qt)AC=(Qt)CBÞ K1A(θA−θC)l = K2A(θC−θB)lÞ θA−θCθC−θB = K2K1 ...(i) Also (Qt)AD=(Qt)DBÞK3A(θA−θD)l = K4A(θD−θB)lÞθA−θDθD−θB = K4K3 ...(ii) It is given that θC=θD,hence from equation (i) and (ii) we get K2K1=K4K3Þ K1K4 = K2K3K1K4 = K2K3K1K4=K2K3
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