# How does kinetic molecular theory explain the Charles' law?

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Feb 1, 2016

Kinetic theory explains why the volume of a container must expand when the temperature of the gas inside increases in order for the pressure to remain constant.

#### Explanation:

Charles' law: for a fixed mass of gas at constant pressure the volume is directly proportional to the temperature.

Analysis of a gas when its temperature increases according to kinetic theory:

• The temperature has increased therefore the molecules have more kinetic energy, so they move with a greater velocity.¹

• If the container's dimensions do not change the molecules will travel across the container between the walls in less time (because they are moving faster and covering the same distance between the container walls). This will increase the rate of collisions, which would increase the pressure.²

• But if the dimensions of the container increased then the molecules would cover a larger distance faster thereby maintaining a constant rate of collisions. This would maintain a constant pressure.

¹ This is due to the relationship between temperature and mean molecular kinetic energy: $E = \frac{3}{2} k T$. Where E is the kinetic energy, k is the Boltzmann constant and T is the absolute temperature (i.e. temperature in kelvins).

² The pressure on the container will also increase due to the greater change of momentum of the molecules when they collide with the wall. The increased temperature increased their kinetic energy, so when their momentum perpendicular to the wall is reversed it has a larger value.
To keep pressure constant due to this effect the volume would need to increase further to reduce the rate of collisions.

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