Describe the pressure and the changes in pressure of a gas in terms of the forces exerted by particles colliding with surfaces, creating a force per unit area

Cambridge IGCSE Physics 0625 – Topic 2.1.2: Particle Model

Objective

Describe the pressure and the changes in pressure of a gas in terms of the forces exerted by particles colliding with surfaces, creating a force per unit area.

1. The particle model of matter

The particle model assumes that all matter is made up of tiny particles (atoms or molecules) that are in constant motion. In a gas the particles:

• are far apart compared with their size,
• move rapidly in straight lines until they collide with another particle or with the walls of the container,
• collisions are perfectly elastic (no loss of kinetic energy), and
• the average kinetic energy of the particles is proportional to the absolute temperature.

2. What is pressure?

When a gas particle strikes a surface it exerts a force on that surface. The cumulative effect of many such collisions over an area \$A\$ gives the pressure \$P\$:

\$P = \frac{F}{A}\$

where \$F\$ is the total force exerted by the particles on the surface and \$A\$ is the area of that surface.

3. How particle collisions produce pressure

Each collision changes the particle’s momentum. By Newton’s second law, a change in momentum over a time interval \$\Delta t\$ produces a force:

\$F = \frac{\Delta p}{\Delta t}\$

Summing the forces from all particles that strike the surface each second gives the total force, and dividing by the area yields the pressure.

4. Factors that affect the pressure of a gas

The pressure of a gas changes when any of the following variables are altered:

1. Temperature (\$T\$) – Raising the temperature increases the average kinetic energy of the particles, so they strike the walls more often and with greater force, increasing pressure.
2. Volume (\$V\$) of the container – Reducing the volume brings the walls closer together, so particles collide with the walls more frequently, raising pressure (Boyle’s law).
3. Amount of gas (moles \$n\$) – Adding more particles increases the number of collisions per unit time, increasing pressure.
4. Nature of the gas – For ideal gases the particle size and intermolecular forces are negligible; real gases deviate at high pressures or low temperatures.

5. Key relationships

\$\displaystyle \frac{V1}{T1} = \frac{V2}{T2}\$

6. Explaining pressure changes with the particle model

Consider a sealed container:

• Heating the gas – Particles move faster, each collision transfers more momentum, so \$F\$ on the walls increases → \$P\$ rises.
• Compressing the gas – The same number of particles now have a smaller distance to travel before hitting a wall, increasing the collision frequency → \$F\$ rises → \$P\$ rises.
• Adding more gas – More particles mean more collisions per unit time, increasing \$F\$ and thus \$P\$.

7. Summary

Pressure is the result of countless microscopic collisions of gas particles with a surface. It can be expressed as a force per unit area, \$P = F/A\$. Changes in temperature, volume, or amount of gas alter the speed, frequency, or number of these collisions, leading to predictable changes in pressure as described by Boyle’s, Charles’s, Gay‑Lussac’s, and the ideal‑gas equations.