Problem 2.247

One end of a rod, enclosed in a thermally insulating sheath, is kept at a temperature \(T_{1}\) while the other, at \(T_{2 \cdot}\). The rod is composed of two sections whose lengths are \(l_{1}\) and \(l_{2}\) and heat conductivity coefficients \(x_{1}\) and \(x_{2} .\) Find the temperature of the interface.