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…

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

MARKS Content Team · Accepted Answer

Correct answer: (A) (l_1+l_2k_1k_2)/(k_2l_1+k_1l_2). 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, ⇒(kAT_1-T_2)/(l_1+l_2)=(k_1AT_1-T_Jl_1=k_2AT_J-T_2l_2, first, calculate the junction temperature by the idea, H_1=H_2=k_1AT_1-T_Jl_1=k_2AT_J-T_2l_2⇒T_J=k_1T_1l_1+k_2T_2l_2)/(k_1l_1+k_2l_2) it means, (kT_1-T_2)/(l_1+l_2)=(k_1T_1-k_1T_1l_1+k_2T_2l_2k_1l_1+k_2l_2l_1⇒k=l_1+l_2k_1k_2)/(k_2l_1+k_1l_2)

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

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Relevant Questions

Two rods whose lengths are l1 and l2 with heat conductivity co-efficients k1 and k2 are placed end to end. The heat conductivity coefficient of a uniform rod of length l1+l2 whose conductivity is same as that of the system of these two rods is

Solution

Relevant Questions

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