How does kinetic molecular theory explain the Charles' law?

Question

Lily Adams · Accepted Answer

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.

Charles' law states that the volume is directly proportional to the temperature for a fixed mass of gas at constant pressure. Analysis of a gas using kinetic theory as its temperature rises: Because of the rise in temperature, the molecules have more kinetic energy and are moving faster. The molecules will travel across the container between the walls in less time if the container's dimensions remain unchanged because they are moving faster and covering the same distance between the walls. This will increase the rate of collisions, which will raise the pressure. However, if the container's dimensions were increased, the molecules would travel farther more quickly, which would keep the rate of collisions constant and the pressure constant. ¹ This is due to the relationship between temperature and mean molecular kinetic energy: #E= 3/2 kT#. Where E is the kinetic energy, k is the Boltzmann constant and T is the absolute temperature (i.e. temperature in kelvins). The increased temperature increased the molecules' kinetic energy, so when their momentum perpendicular to the wall is reversed, it has a larger value. ³ The greater change of momentum of the molecules when they collide with the wall will also cause the pressure inside the container to increase. The volume would need to increase further to reduce the rate of collisions in order to keep the pressure constant due to this effect.

Isabella Alvarez · Answer

undefined Kinetic molecular theory explains Charles' law by stating that as temperature increases, the average kinetic energy of gas molecules increases, causing them to move faster and collide with the container walls more frequently and with greater force, leading to an increase in pressure.