In the derivation of the pressure exerted by an ideal gas on a container by a single molecule, we consider the time between consecutive collisions on the same wall to understand the frequency of collisions and the force exerted by each collision.
When a gas molecule collides with the wall of the container, it exerts a force on the wall due to the change in momentum. The pressure exerted by the gas is a result of the cumulative effect of these individual collisions by all the gas molecules.
To determine the pressure exerted by a single gas molecule, we need to consider the rate at which it collides with the wall. This collision rate is related to the time between consecutive collisions on the same wall.
By analyzing the motion of a gas molecule, we can determine the time it takes for the molecule to travel from one collision point to the next on the same wall. This time interval is referred to as the mean free time or the average time between consecutive collisions.
The frequency of collisions is inversely proportional to the mean free time. A shorter mean free time indicates a higher collision frequency, which means that the molecule collides with the wall more frequently, exerting a greater force.
In the derivation, we use the concept of the mean free time to calculate the average force exerted by the gas molecule on the wall during each collision. By considering the cumulative effect of all the gas molecules and summing up their individual contributions, we can determine the overall pressure exerted by the gas on the container.
So, by taking into account the time between consecutive collisions on the same wall, we are able to understand the frequency of collisions and the force exerted by each collision, which is crucial in the derivation of the pressure exerted by an ideal gas on a container.