Two rigid, thermally insulated compartments of equal volume \(V\) are connected by a closed valve. The left compartment contains \(1.0\text{ mol}\) of helium gas at temperature \(T_0\), and the right compartment contains \(1.0\text{ mol}\) of argon gas at temperature \(T_0\). The valve is opened, allowing the two distinct ideal gases to mix completely within the total volume \(2V\) while remaining thermally isolated from the environment. Which of the following correctly describes the mixing process once equilibrium is reached, along with a valid justification?