A rigid, thermally insulated cylinder of total volume \(12 \text{ L}\) is divided into two compartments, A and B, by a thin, frictionless, thermally conducting piston that is initially held fixed in the center so that each compartment has a volume of \(6 \text{ L}\). Compartment A contains \(1.0 \text{ mol}\) of a monatomic ideal gas at an initial temperature of \(300 \text{ K}\), and compartment B contains \(3.0 \text{ mol}\) of the same ideal gas at an initial temperature of \(500 \text{ K}\). The piston is released and the system is allowed to reach mechanical and thermal equilibrium. What are the final equilibrium temperature \(T_f\) of the system and the final volume \(V_A\) of compartment A?