Problem 2.250

Two chunks of metal with heat capacities \(C_{1}\) and \(C_{2}\) are interconnected by a rod of length \(l\) and cross-sectional area \(S\) and fairly low heat conductivity \(x .\) The whole system is thermally insulated from the environment. At a moment \(t=0\) the temperature difference between the two chunks of metal equals \((\Delta T)_{0} .\) Assuming the heat capacity of the rod to be negligible, find the temperature difference between the chunks as a function of time.