How many times in a 10 hour flight is the air recirculated in a 747?

Question

How many times in a 10 hour flight is the air recirculated in a 747?

Answer 1

The air is continuously circulated through the use of an Environmental Control System (ACS).

The ECS system simply pressurizes outside air.  Pressurized air rises in temperature, so it is diluted with some cooler air taken from inside the cabin.

The pressure inside the cabin is regulated by an variable size hole in the back of the plane called an outflow valve.  The pressurization is basically "on" or "off" meaning that the pressurization and air conditioning system (they are the same system) just pumps air into the cabin all the time and it is eventually vented overboard through the outflow valve.

Airplanes are not airtight.  Not even close.  The airflow through them circulates continuously.

Edit: adding clarification

Cal is correct, air is recirculated to reduce wear and tear on the ECS system and to reduce fuel burn.  I was simply trying to be brief :)

Answer 2

Jason is correct, but most modern planes do recirculate the air in the cabin because just dumping it out the outflow valve wastes fuel (since the engines have to work harder to keep the cabin filled with pressurized air).  The recirculation system re-filters and heats or cools the air to keep the passengers comfortable without using too much bleed air.

Since the air molecules scatter at random, some air could be recirculated indefinitely until the plane lands.  But there still is quite a bit of air escaping from the outflow valve so most of the air wouldn't be more than an hour in the plane.