A rigid insulator container is divided into two compartments by a thin membrane. The left compartment contains n_ar moles of argon gas (monoatomic), while the right compartment contains n_ni moles of nitrogen gas (diatomic). Two temperature sensors, one placed in the left compartment and one in the right compartment, measure T_ar and T_ni respectively. The membrane prevents any mixing of the gases. Find the final temperature T_f of the system in terms of n_ar, n_ni, T_ar, and T_ni when thermal equilibrium is reached.