# What are some examples of the kinetic theory of gases?

Mar 13, 2017

This is an explanation of the pressure law according to kinetic theory.

#### Explanation:

Gas pressure increases for a fixed mass of gas as temperature is increased at constant volume.

Explanation with reference to the following quantities and dimensions of gas container:
1. Kinetic energy of gas molecules. Kinetic energy of gas molecules is related to temperature by the equation: ${E}_{K} = \frac{3}{2} k T$
2. Change in momentum per collision with the container wall.
3. Length/width/height of container.

As temperature increases the (average) kinetic energy of gas molecules increases (seen by equation ${E}_{K} = 3 / 2 k T$).
Velocity of gas molecules increases.
The change of momentum during a collision with a wall of the container increases due to the increased initial velocity.
This causes an increase in the rate of change of momentum for each collision.

The volume remained constant so the distances between the walls of the container remained constant.
The velocity of molecules increased, so they travel between walls in a shorter time (according to $t = \frac{s}{v}$).
As molecules reach walls more frequently the number of collisions per unit time increases.
Thus the rate of change of momentum (across each wall in total) increases due to this fact also.

The increased rate of change of momentum increases the average force exerted on the walls of the container. So the pressure increases according to ($p = F / A$).