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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 length l1 and l2 and thermal conductivities K1 and K2 respectively. The temperature at the interface of the two section is

1. (K1 l1 T1 + K2 l2 T2)/(K1 l1 + K2 l2)
2. (K2 l2 T1 + K1 l1 T2)/(K1 l1 + K2 l2)
3. (K2 l1 T1 + K1 l2 T2)/(K2 l1 + K1 l2)
4. (K1 l2 T1 + K2 l1 T2)/(K1 l2 + K2 l1)

Correct answer: (K1 l2 T1 + K2 l1 T2)/(K1 l2 + K2 l1)

Solution

The correct option is derived from the principle of thermal equilibrium, where the heat flow through both sections of the rod must be equal at the interface. This equation balances the thermal conductivities and lengths of the two sections with their respective temperatures, ensuring that the heat transfer rates are consistent.

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