Problem 2.248

Two rods whose lengths are \(l_{1}\) and \(l_{2}\) and heat conductivity coefficients \(x_{1}\) and \(x_{2}\) are placed end to end. Find the he at conductivity coefficient of a uniform rod of length \(l_{1}+l_{2}\) whose conductivity is the same as that of the system of these two rods. The lateral surfaces of the rods are assumed to be thermally insulated.