and we somehow let air flow from one room to the other. Now in what relation are: the time it takes for rooms’ pressures to equalize and the difference between the two pressures.
The size of opening will also matter.
You need to consider the pressure, volume, and temperature of each room, as well as the size of the opening between the two rooms. The pressure, volume, and temperature of each room will tell you how much total gas (air) you have in each room, which you can then use to figure out what the ending pressure and temperature will be for both rooms combined. The size of the opening will determine how much gas can flow from one room to the other, which is going to decrease with time (follows an exponential decay curve) since the pressure differential will be decreasing as the gas (air) flows.
Yeah, I know that all those variables matter. But still without knowing their exact values you can tell that for example time is directly proportional to the pressures difference or it is directly proportional to the square of that difference or it is independent of it at all. That’s all I wanna know…
The pressure differecnce gets smaller and smaller the longer you wait. Whether or not the initial pressure difference affects the equalization time depends on your definition of equalized. If you require the pressure difference to be 1 percent of the initial difference, the equalization time is independent of the difference. If you require the pressures to be equal to within 1% of atmospheric pressure, then it takes less time if you start with a smaller difference.
In the simplest model, the pressure will decay exponentially from the initial value to the final value with a time constant that is independent of the pressure difference. A convenient way to quantify this is the half time (or half life). It will take one half time for the pressure difference to be half the original difference, and two half times to be one-quarter of the original pressure difference, and so on. The half time depends on all the details like the size of the hole and the volume of the rooms, but does not depend on the pressure difference.