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 length $l_1$ and $l_2$ and thermal conductivities $K_1$ and $K_2$ respectively. The temperature at the interface of the two section is
AIEEE 2007, Medium
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$\frac{{{K_1}A\left( {{T_1} - T} \right)}}{{\ell .}} = \frac{{{K_2}A\left( {T - {T_2}} \right)}}{{{\ell _2}}},$
$\therefore T = \frac{{{K_1}{T_1}{\ell _2} + {K_2}{T_2}{\ell _1}}}{{{K_2}{\ell _1} + {K_1}{\ell _2}}} = \frac{{{K_1}{\ell _2}{T_1} + {K_2}{\ell _1}{T_2}}}{{{K_1}{\ell _2} + {K_2}{\ell _1}}}.$
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