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- What equation do I use to work out the time it takes for a 1000m3 volume of air at 285K to reach ambient air temp (290K at 1 atm).

I have a cube with a volume of 1000m3 at an initial temp of 290K. The bottom side (10m by 10m) is open to the ambient air. I put this cube into a huge fridge and cool the whole volume by 5K. I close the open side by placing a cover on it. This cube has now got a volume of air at a temperature of 285K inside. I then take the cube out of the fridge and suspend it in mid air with the face with the cover facing down. The ambient air that it is placed in is much larger than the volume of 1000m3, is at 1 atm and is at a temp of 290K. I then remove the cover opening the bottom side to the ambient surrounding air at 290K.

1. What I would like to know is what equation I can use to calculate how long the volume in the cube will take to equal 290K once the cover is removed. I am assuming (is the assumption right?) that as soon as the cover is removed due to the cold air being more dense than the ambient air it will "fall" (or be displaced), with ambient air replacing it. What equation can I use to show the length of time it takes for the volume of air to reach 290K. We can neglect any heat transfer through the other closed sides of the volume.

2. If this cold volume of air does "fall" how long will it take for it to equalise to the ambient air temp?

3. How do the equations change if I turn the cube so the open face is facing upwards?

If there is further information needed please let me know and I will add.

1. What I would like to know is what equation I can use to calculate how long the volume in the cube will take to equal 290K once the cover is removed. I am assuming (is the assumption right?) that as soon as the cover is removed due to the cold air being more dense than the ambient air it will "fall" (or be displaced), with ambient air replacing it. What equation can I use to show the length of time it takes for the volume of air to reach 290K. We can neglect any heat transfer through the other closed sides of the volume.

2. If this cold volume of air does "fall" how long will it take for it to equalise to the ambient air temp?

3. How do the equations change if I turn the cube so the open face is facing upwards?

If there is further information needed please let me know and I will add.