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One end of a thermally insulated rod is kept at a temperature T 1 and the other at T 2 . The rod is composed of two sections of lengths l 1 and l 2 and thermal conductivities K 1 and K 2 respectively. The temperature at the interface of the two sections is

Options

  1. A( K 1 l 1 T 1 + K 2 l 2 T 2 ) ( K 1 l 1 + K 2 l 2 )
  2. B( K 2 l 2 T 1 + K 1 l 1 T 2 ) ( K 1 l 1 + K 2 l 2 )
  3. C( K 2 l 1 T 1 + K 1 l 2 T 2 ) ( K 2 l 1 + K 1 l 2 )
  4. D( K 1 l 2 T 1 + K 2 l 1 T 2 ) ( K 1 l 2 + K 2 l 1 )

Correct answer

D. ( K 1 l 2 T 1 + K 2 l 1 T 2 ) ( K 1 l 2 + K 2 l 1 )

Step-by-step solution

k 1 A l 1 T 1 - T = k 2 A l 2 T - T 2 k 1 l 2 + k 2 + l 1 T = k 1 l 2 T 1 + k 2 l 1 T 2 Or T = k 1 l 2 T 1 + k 2 k l 2 T 2 k 1 l 2 + k 2 l !

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