thermodynamics - Expansion of an ideal gas in an evacuated bottle having nonconducting walls

In the free expansion of ideal gas in a vacuum $dW = 0$ as $p_{ext} = 0$ and $dU = 0$ therefore there is no change in temperature of the ideal gas also. what i want to know that can the following situation also classify as a free expansion of a ideal gas and if no why ? the situation is as follows-

" An evacuated bottle with nonconducting walls is connected through a valve to a large supply of gas, where the pressure is $P_0$ and the temperature is $T_0$. The valve is open slightly, and helium flows into the bottle until the pressure inside the bottle is $P_0$. "

is the process also quasi static. As the bottle is a vacuum it seems that the process is free expansion but i dont think it is.

Answer

The question whether or not it is a free expansion relates to what you choose as your thermodynamic system. Here are two choices, both applicable to the situation you describe.

1. 
   

   We suppose the 'large supply of gas' is itself large but finite, and we suppose it is contained in a large vessel with rigid walls. Let the thermodymamic system under study be this gas. No heat enters or leaves, and since the walls are rigid no work is done on the system, so this system undergoes a process of free expansion as the gas expands into the bottle.

   
   


2. 
   

   Alternatively, take as your thermodynamic system just that part of the gas which ends up in the bottle. You could imagine a thin flexible bag around it if you like. Now the process is not a free expansion, because the rest of the gas does work on your system as it pushes against the bag and this bag (or boundary) moves.