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Why a Gas Exerts a Pressure
Consider the molecules of a gas moving at random in a container, as shown below.
The molecules are continually colliding with each other and with the walls of the container. (On the diagram, only a few paths of molecules have been drawn because...itís a bit tedious drawing them!) It is assumed that all collisions are elastic. (Consider what would happen if the collisions were not elastic.) When a molecule collides with the wall, a change of momentum occurs. The change in momentum is caused by the force exerted by the wall on the molecule. The molecule exerts an equal but opposite force on the wall. The pressure exerted by the gas is due to the sum of all these collision forces.
Why the Pressure Exerted by a Gas Increases as the Temperature Increases
If the temperature of the gas is increased, the average kinetic energy of its molecules increases. Therefore, the molecules hit the wall "harder" and also more frequently. The total force due to the collisions is greater. Therefore the pressure increases.