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