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.