In my ongoing saga to understand some simple (?) ideas about ideal gases, I have two questions:
1. Is there a difference between a "classical ideal gas" and an "ideal gas of classical particles"?
My reasoning for thinking the answer might be yes is that it seems to me there are 3 relevant length scales: the thermal de Broglie length (L), the size of a gas particle (R), and the average distance between gas particles (D).
classical ideal gas: one for which D >> L
ideal gas of classical particles: one for which R >> L
2. Is there such a thing as a quantum ideal gas of identical but distinguishable particles?
As a specific example, suppose we are talking about one million atoms of helium-4 and all atoms have their electrons filling the 1s orbital. Thus all atoms are identical. But put these atoms in a cubical box (that is otherwise empty) measuring 100 meters on a side. It seems like each atom will have on average a cubic meter to itself, so I can distinguish atoms (at least for some time) by saying there's one in that cubic meter, one in that cubic meter, etc.
Please comment. What are your answers to these questions?