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A large cylindrical rod of length L is made by joining two identical rods of copper and steel of length ( L 2 ) each. The rods are completely insulated from the surroundings. If the free end of copper rod is maintained at 100^ C and that of steel at 0^ C then the temperature of junction is (Thermal conductivity of copper is 9 times that of steel)

Options

  1. A90^ C
  2. B50^ C
  3. C10^ C
  4. D67^ C

Correct answer

A. 90^ C

Step-by-step solution

Let conductivity of steel K_ steel =k then from question Conductivity of copper K_ copper =9 k aligned & _ copper =100^ C & _ steel =0^ C & l_ steel =l_ copper = L 2 aligned From formula temperature of junction; aligned & = K_ copper _ copper l_ steel +K_ steel _ steel l_ copper K_ copper l_ steel +K_ steel l_ copper & = 9 k 100 L 2 +k 0 L 2 9 k L 2 +k L 2 & = 900 2 k L 10 k L 2 =90^ C aligned

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