The time it takes for all the air in a room to be completely replaced with fresh air when you have an open door depends on several factors, including the size of the room, the size of the door, the outdoor wind conditions, and the temperature difference between the indoor and outdoor air.
To get a rough estimate, we can use a concept known as air exchange rate. The air exchange rate is the number of times the air in a room is replaced with fresh air in an hour. For natural ventilation (with an open door in this case), the air exchange rate can range from 0.1 to 1 air change per hour (ACH), depending on the factors mentioned above.
Let's take an example where the air exchange rate is 0.5 ACH. It means that half of the air in the room will be replaced with fresh air in one hour.
To calculate the time it takes for all the air to be replaced, you can use the formula:
Time (in hours) = 0.693 / Air Exchange Rate (ACH)
For our example with an air exchange rate of 0.5 ACH:
Time = 0.693 / 0.5 ≈ 1.386 hours
So, in this example, it would take approximately 1.4 hours for all the air in the room to be replaced with fresh air. Keep in mind that this is just an estimate, and actual conditions may lead to faster or slower air exchange rates. Additionally, if there are fans or other factors affecting airflow, the time for air replacement may differ.