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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 the copper rod is maintained at 100 °C and that of the steel at 0 °C, then the temperature of the junction is (thermal conductivity of copper is 9 times that of steel)

Asked in JEE Main Online 2012 · Junction temperature

• (1) 90 °C
• (2) 50 °C
• (3) 10 °C
• (4) 67 °C

Step-by-step solution

Why the other options are wrong

• (2) comes from is the average of the two end temperatures. Averaging is correct only when the two halves have equal thermal resistance; here the copper half has one ninth of the steel half's resistance.
• (3) comes from is the same calculation with the two materials swapped, that is, the junction found as though the steel were the good conductor. Almost the whole temperature drop falls across the poor conductor, so the junction must lie near the copper end, not the steel end.
• (4) comes from splitting the 100 °C in the ratio 1:2 instead of 1:9, which is what happens if K_Cu=9Kₛₜₑₑₗ is read as a ratio of 3 somewhere, or if the resistances are taken as √9=3 apart.

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