A large cylindrical rod of length L is made by joining two identical rods of copper and steel of length ( 2 L ) each. The rods are completely insulated from the surroundings. If the free end of copp

Question

A large cylindrical rod of length L is made by joining two identical rods of copper and steel of length ( 2 L ​ ) each. The rods are completely insulated from the surroundings. If the free end of copper rod is maintained at 10 0 ∘ C and that of steel at 0 ∘ C then the temperature of junction is (Thermal conductivity of copper is 9 times that of steel)

TestHub · Accepted Answer

Let conductivity of steel K steel ​ = k then from question Conductivity of copper K copper ​ = 9 k ​ θ copper ​ = 10 0 ∘ C θ steel ​ = 0 ∘ C l steel ​ = l copper ​ = 2 L ​ ​ From formula temperature of junction; θ ​ = K copper ​ l steel ​ + K steel ​ l copper ​ K copper ​ θ copper ​ l steel ​ + K steel ​ θ steel ​ l copper ​ ​ = 9 k × 2 L ​ + k × 2 L ​ 9 k × 100 × 2 L ​ + k × 0 × 2 L ​ ​ = 2 10 k L ​ 2 900 ​ k L ​ = 9 0 ∘ C ​

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