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JEE Main2007PhysicsThermal Properties of MatterActual

One end of a thermally insulated rod is kept at a temperature T₁ and the other at T₂ . The rod is composed of two sections of lengths ₁ and ₂ and thermal conductivities k₁ and k₂ respectively. The temperature at the interface of the two sections is

Options

  1. A( k ₂ ₂ T ₁+ k ₁ ₁ T ₂ ) / ( k ₁ ₁+ k ₂ ₂ )
  2. B( k ₂ ₁ T ₁+ k ₁ ₁ T ₂ ) / ( k ₂ ₁+ k ₁ ₂ )
  3. C( k ₁ ₂ T ₁+ k ₂ ₁ T ₂ ) / ( k ₁ ₂+ k ₂ ₁ )
  4. D( k ₁ ₁ T ₁+ k ₂ ₂ T ₂ ) / ( k ₁ ₁+ k ₂ ₂ )

Correct answer

C. ( k ₁ ₂ T ₁+ k ₂ ₁ T ₂ ) / ( k ₁ ₂+ k ₂ ₁ )

Step-by-step solution

( T ₁- T ) k ₁ ₁ = ( T - T ₂ ) k ₂ ₂ ~T = T ₁ k ₁ ₂+ T ₂ k ₂ ₁ k ₁ ₂+ k ₂ ₁

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