This paper focuses on the determination of the final equilibrium state when two ideal gases, isolated from the exterior and starting from preset initial conditions, interact with each other through a piston. Depending on the piston properties, different processes take place and also different sets of equilibrium conditions must be satisfied. Three cases are analysed, namely, when (case 1) the piston is a heat conductor and free to move, (case 2) the piston allows heat conduction but its position is fixed, and (case 3) the piston is free to move but it is adiabatic (so no heat can be exchanged). Cases 1 and 2 have straightforward solutions, but it is shown that case 3 leads to an undeterminable final state. Even though this last situation seems to be strange and difficult, mechanical and thermodynamical analyses are performed. It is shown that the determinability of the final state depends on whether friction is considered or not. Carried out numerically, both analyses provide consistent results and not only do they enable an interesting and useful discussion regarding the concepts of energy, heat, work and entropy, but they also reinforce some ideas which were recently published.