Question about transient temperature and pressure for air flowing into a box

[Chiel555]

Hi all; i have some ( more) questions:

Imagine a room of 10 meters long, 10 meters wide and 5 meters high, filled with air

and a box of 1 by 1 by 1 meter, completely vacuum; the box is connected to the room and open so the air can flow freely from the room into the box;

both room and box are perfectly insulated on the outside so no heat and no air can escape

now suppose that de room starts with a certain temperature T and pressure P and the box with temperature 0 en pressure 0;

you would expect that in time the room and the box have the same temperature and after a time the same
pressure
what are those times ?; are they the same ?

 

[Baluncore]

... the box is connected to the room and open so the air can flow freely from the room into the box; ...

It will depend on how "free" your "flow freely" actually is. In theory, the time will be infinite, because the temperature and pressure will approach equality asymptotically, as a decreasing exponential rate.

If you change the question to having the walls of the small box disappear in an instant, then the room will be filled with sound waves for some time, as the depression wave fills the vacuum at the speed of sound, and echos between the diagonal corners of the room. The question will then be, how quiet is equilibrium?