## The Molecular Model of an Ideal Gas

An ideal gas is a model of a gas that treats the gas molecules as points of infinitesimally small size that obey all Newton's Laws of motion and undergo only elastic collisions with each other and the walls of the container. In detail, the assumptions of the ideal gas model are:

• Newton's Laws apply to molecular behaviour. Conservation of momentum applies, but only to collisions between gas molecules and not to collisions between the gas molecules and the walls of the container – see the bottom bullet point below.

• There are no intermolecular forces apart from when the molecules hit each other.

• The molecules are perfect spheres of zero radius. This means that the whole volume of the container is available for the gas molecules to move around in.

• The molecules are in random motion. There is no preferred direction and no large scale movement of the gas. For a container shaped as a cube, the average number of collisions per second with each wall will be the same. This means – see discussion below – that the pressure exerted on each wall of the container is the same.

• All collisions between molecules and between molecules and the walls of the container are elastic, so kinetic energy is conserved.

• The collisions have no duration, so the time of any collision is zero

• The walls of the container are assumed to be fixed. Because collisions are also assumed to be elastic, the speed of the molecule is unchanged.

• The volume of the gas is equal to the volume of the container, since the gas expands to fill the container.

Each time a gas molecule collides with the wall of the container and rebounds, the momentum of the molecule changes. This implies (Newton's second Law) a force on the wall. The force will actually be equal to the rate of change of momentum of all the gas molecules colliding with the wall. There will be very many collisions each second, so we can assume the force to be constant. Remembering then thatwe can relate this force exerted on the walls of the container to the gas pressure.

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