One end of a rod, enclosed in a thermally insulating sheath, is kept at a temperature `T_1` while the other, at `T_2`. The rod is composed of two sections whose lengths are `l_1` and `1_2` and heat conductivity coefficients `x_1` and `x_2`. Find the temperature of the interface.

Explanation

Let `T` = temperature of the interface
Then heat flowing from left = heat flowing into right in equilibrium.
Thus `k_1 (T_1 - T)/(t_1) = k_2 (T - T_2)/(l_2)` or `T = (((k_1 T_1) /(l_1) + (k_2 T_2)/(l_2)))/(((k_1)/(l_1) + (k_2)/(l_2)))`.