I have a mono-atomic ideal gas, expanding from a smaller volume V1 to a larger volume V2, inside a piston. If the expansion is done slowly, so the process is reversible, I understand how to calculate the work done, etc., for a system that is either thermally isolated or connected to a reservoir.
However, I'm having some difficulty understanding how an irreversible process of expansion takes place, if the gas just expands from V1 to V2 due to the removal of a partition connecting to the gas to a vacuum of volume V2-V1. If there is no heat reservoir, I understand there is no work done, so the final and initial temperatures are the same, with increasing entropy. We do not worry about the intermediate states, as our normal rules don't apply anyway.
What happens if during the expansion of the gas into the vacuum, the system is connected to a reservoir, maintained at the same temperature T as the initial temperature of the gas? Does it make sense to say the presence of the reservoir makes no difference to the previous case? The way I see it, there is still no heat transfer, so the system's behaviour is essentially identical to normal free expansion. Is this accurate?