One end of a thermally insulated rod is kept at a temperature T₁ and other at T₂ . rod is compos

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10-2.Transmission of Heat

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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

A

$\left( {{K_2}{l_2}{T_1} + {K_1}{l_1}{T_2}} \right)/\left( {{K_1}{l_1} + {K_2}{l_2}} \right)$

B

$\left( {{K_2}{l_1}{T_1} + {K_1}{l_2}{T_2}} \right)/\left( {{K_2}{l_1} + {K_1}{l_2}} \right)$

C

$\left( {{K_1}{l_2}{T_1} + {K_2}{l_1}{T_2}} \right)/\left( {{K_1}{l_2} + {K_2}{l_1}} \right)$

D

$\left( {{K_1}{l_1}{T_1} + {K_2}{l_2}{T_2}} \right)/\left( {{K_1}{l_1} + {K_2}{l_2}} \right)$

Solution

$\frac{{{k_1}\left( {{T_1} – T} \right)}}{{{l_1}}} = \frac{{{k_2}\left( {T – {T_2}} \right)}}{{{l_2}}}$

Standard 11

Physics

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