Consider two containers separated by a removable wall, each side of which is a perfect mirror for the gas in the respective container. Also the walls of the containers are ideal mirrors. In each container the gas is the same, it is ideal and in thermodynamic equilibrium, therefore the distributions of the energies of the molecules is the Maxwell-Boltzmann law. The gas in the container A has temperature $T_A$, and the gas in the container B has temperature $T_B$, with $T_A$ > $T_B$.
It is known that when the wall is removed, each gas expands into the other container and in the end, all the gas reaches thermodynamic equilibrium, at some intermediate temperature $T_C$, i.e. $T_A$ > $T_C$ > $T_B$.
In there a way to calculate the final parameters, temperature, pressure, entropy, from the two initial distributions of energies (velocities) + volumes of containers and initial pressures in them?