The kinetic theory of gases and the gas laws

Kinetic theory/ideal gas

We can understand the behaviour of gases using a very simple model, that of an “ideal” gas.

The model makes a few simple assumptions;

Ideal gas assumptions

• The particles of gas (atoms or molecules) obey Newton’s laws of motion.

Please tell me you remember!

Ideal gas assumptions

• The particles in a gas move with a range of speeds

Ideal gas assumptions

• The volume of the individual gas particles is very small compared to the volume of the gas

Ideal gas assumptions

• The collisions between the particles and the walls of the container and between the particles themselves are elastic (no kinetic energy lost)

Ideal gas assumptions

• There are no forces between the particles (except when colliding). This means that the particles only have kinetic energy (no potential)

Ideal gas assumptions

• The duration of a collision is small compared to the time between collisions.

Pressure – A reminder

Pressure is defined as the normal (perpendicular) force per unit area

P = F/A

It is measured in Pascals, Pa (N.m-2)

Pressure – A reminder

What is origin of the pressure of a gas?

Pressure – A reminder

Collisions of the gas particles with the side of a container give rise to a force, which averaged over billions of collisions per second macroscopically is measured as the pressure of the gas

Change of momentum

Explaining the behavior of gaseshttp://phet.colorado.edu/sims/ideal-gas/gas-properties.jnlp

When we heat a gas at constant volume, the pressure increases. Why?

Explaining the behavior of gases

When we heat a gas at constant volume, the pressure increases. Why?

Increased average kinetic energy of the particles means there are more collisions with the container walls in a period of time and the collisions involve a greater change in momentum.

Explaining the behavior of gases

When we heat a gas a constant pressure, the volume increases. Why?

Explaining the behavior of gases

When we heat a gas at constant pressure, the volume increases. Why?

Increasing the volume reduces the chance of particles colliding with the container walls, opposing the effect of the particles increased kinetic energy.

Explaining the behavior of gases

When we compress (reduce the volume) a gas at constant temperature, the pressure increases. Why?

Explaining the behavior of gases

When we compress (reduce the volume) a gas at constant temperature, the pressure increases. Why?

A smaller volume increases the likelihood of a particle colliding with the container walls.

Explaining the behavior of gases

In this way we are explaining the macroscopic behaviour of a gas (the quantities that can be measured like temperature, pressure and volume) by looking at its microscopic behaviour (how the individual particles move)

Temperature and KE

KEave = (3/2) kBT

KEave – Average Kinetic Energy

kB – Boltzmann constant 1.38 x 10-23 J/K

T – Temperatue (K)