Unit 5 Section 2 The Pressure of an Ideal Gas

• Temperature is related to the kinetic energy of the molecules - as the temperature increases, the average speed of the molecules increases.
• This means the rate of change of momentum of the molecules collidng with the wall of the container increases, and so the force on the walls of the container increases.

If the pressure inside the container remains constant, the volume of the container will increase to compensate for the temperature change for two reasons:

• If the volume is larger, there will be a longer time between molecules-wall collisions, and so the rate of change of momentum will be reduced.
• As the volume increases, the surface area of the walls increases. Pressure is defined as the force per unit area, and so increasing the area decreases the pressure.

If the volume of the container is fixed, this will result in an increased pressure inside the container for two reasons:

• There will be more collisions between the molecules and the walls of the container in a given amount of time.
• On average, a collision will result in a larger change in momentum, and so exert a larger force on the walls of the container.

• All molecules of the gas are identical.
• The gas conatins a large number of molecules.
• The molecules move rapidly and randomly.
• Newtonian mechanics apply - the motion of the molecules follow Newton's laws.
• Collisions between molecules themselves or at the walls of a container are perfectly elastic - kinetic energy is conserved.
• There are no forces between molecules except during collisions (they move with constant velocity in a straight line between collisions).
• The forces that act during collisions are instantaneous.
• The molecules have a negligible volume compared with the volume of the container (i.e. They act as point masses).

A gas obeying these assumptions is called an ideal gas. Real gases behave like ideal gases as long as the pressure isn't too big and the temperature is reasonably high (compared with their boiling point), so they're useful assumptions.