Two rods whose lengths are l 1 and l 2 with heat conductivity co-efficients k 1 and k 2 are placed end to end. The heat conductivity coefficient of a uniform rod of length l 1 + l 2 whose conductivity is same as that of the system of these two rods is

Question

Two rods whose lengths are l 1 and l 2 with heat conductivity co-efficients k 1 and k 2 are placed end to end. The heat conductivity coefficient of a uniform rod of length l 1 + l 2 whose conductivity is same as that of the system of these two rods is, l 1 + l 2 k 1 k 2 k 2 l 1 + k 1 l 2, l 1 + l 2 k 1 k 2 k 1 l 1 + k 2 l 2, k 1 l 1 + k 2 l 2 l 1 + l 2 k 1 k 2, k 1 l 2 + k 2 l 1 l 1 + l 2 k 1 k 2

MARKS App · Accepted Answer

When two rods are connected in series then the heat flow per unit time is the same across each rod, it means, H = H 1 = H 2 , ⇒ k A T 1 - T 2 l 1 + l 2 = k 1 A T 1 - T J l 1 = k 2 A T J - T 2 l 2 , first, calculate the junction temperature by the idea, H 1 = H 2 = k 1 A T 1 - T J l 1 = k 2 A T J - T 2 l 2 ⇒ T J = k 1 T 1 l 1 + k 2 T 2 l 2 k 1 l 1 + k 2 l 2 it means, k T 1 - T 2 l 1 + l 2 = k 1 T 1 - k 1 T 1 l 1 + k 2 T 2 l 2 k 1 l 1 + k 2 l 2 l 1 ⇒ k = l 1 + l 2 k 1 k 2 k 2 l 1 + k 1 l 2

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