Let's consider a ballon, such that it has an adiabatic wall, and there is no exchange of heat with the surroundings. Now, let the balloon wall be completely impermeable to the movement of matter across the boundary. If so, then the ballon is theoretically an isolated system. However, if we stretch the balloon, to increase its volume, then the temperature of the air inside the balloon will decrease. Will that mean work is done by the system on the surroundings, despite it being isolated?
Here I thus feel that the concept of isolation is actually a consequence and highly bound by definition. The balloon continues to remain isolated unless, some work is done on it, leading to it losing its property of isolation if some work is done on it.
Is my argument correct?