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Three rods of identical cross-section and identical length are made of three different materials of thermal conductivity K₁, K₂ and K₃ respectively. They are joined end to end in that order to make one long rod. The free end of the K₁ rod is maintained at 100 °C and the free end of the K₃ rod at 0 °C. In the steady state the K₁–K₂ joint is at 70 °C and the K₂–K₃ joint is at 20 °C, and there is no loss of energy from the surface of the rod. The correct relationship between K₁, K₂ and K₃ is

Asked in JEE Main 6th Sept 2nd Shift 2020 · Series and parallel resistance

• (1) K₁:K₃=2:3, K₂:K₃=2:5
• (2) K₁<K₂<K₃
• (3) K₁:K₂=5:2, K₁:K₃=3:5
• (4) K₁>K₂>K₃

Step-by-step solution

Why the other options are wrong

• (2) comes from reading K∝Δθ, the wrong way round. Even that wrong route gives K₁:K₂:K₃=30:50:20, in which K₃ is the smallest, so the chain K₁<K₂<K₃ does not follow from either reading. The true order is K₂<K₁<K₃.
• (3) comes from is built from the same K∝Δθ slip and then mislabelled: that route gives K₁:K₂=30:50=3:5, which is the ratio printed here as K₁:K₃. The correct values are K₁:K₂=5:3 and K₁:K₃=2:3.
• (4) comes from is the reverse ordering, and it fails for the same reason as the option that reverses it: with equal lengths and areas, a rod that carries the same current across a smaller drop must have the larger K, and the smallest drop here is 20 °C across K₃.

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