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 an - Physics MCQ AIEEE 2007 2026 | ExamTest.live

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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:

Solution & Step-by-step Explanation

In steady state, the rate of heat flow Q / t through both sections must be the same.Let T be the interface temperature. \frac{k _{1} A ( T _{1} - T )}{l _{1}} = \frac{k _{2} A ( T - T _{2} )}{l _{2}} \frac{k _{1}}{l _{1}} (T_{1} - T) = \frac{k _{2}}{l _{2}} (T - T_{2}) k_{1} l_{2} T_{1} - k_{1} l_{2} T = k_{2} l_{1} T - k_{2} l_{1} T_{2} k_{1} l_{2} T_{1} + k_{2} l_{1} T_{2} = T (k_{1} l_{2} + k_{2} l_{1}) T = \frac{k _{1} l _{2} T _{1} + k _{2} l _{1} T _{2}}{k _{1} l _{2} + k _{2} l _{1}}

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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:

(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_{1} 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})

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