One end of a thermally insulated rod is kept at a temperature T 1 and 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

Question

One end of a thermally insulated rod is kept at a temperature T 1 and 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, ( K 2 l 2 T 1 + K 1 l 1 T 2 ) ( K 1 l 1 + K 2 l 2 ), ( K 2 l 1 T 1 + K 1 l 2 T 2 ) ( K 2 l 1 + K 1 l 2 ), ( K 1 l 2 T 1 + K 2 l 1 T 2 ) ( K 1 l 2 + K 2 l 1 ), ( K 1 l 1 T 1 + K 2 l 2 T 2 ) ( K 1 l 1 + K 2 l 2 )

MARKS App · Accepted Answer

Let temperature at the interface is T . For part AB , Q 1 t ∝ T 1 - T K 1 l 1 For part BC , Q 2 t ∝ T - T 2 K 2 l 2 At equilibrium, Q 1 t = Q 2 t ∴ T 1 - T K 1 l 1 = T - T 2 K 2 l 2 ⇒ T = T 1 K 1 l 2 + T 2 K 2 l 1 K 1 l 2 + K 2 l 1

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