Published by Patrick Mutisya · 14 days ago
Describe the pressure and the changes in pressure of a gas in terms of the motion of its particles and their collisions with a surface.
Pressure (\$p\$) is defined as the force (\$F\$) exerted per unit area (\$A\$) of a surface:
\$p = \frac{F}{A}\$
In a gas the force comes from the change in momentum of particles when they strike the container walls.
When a gas particle collides with a wall, it exerts a force during the very short contact time. The cumulative effect of many such collisions over the whole surface creates a measurable pressure.
The kinetic theory of gases relates pressure to three main variables:
Ideal‑gas equation (useful for IGCSE level):
\$pV = nRT\$
From kinetic theory, pressure can also be expressed as:
\$p = \frac{1}{3}\,N\,m\,\overline{v^{2}}\,\frac{1}{V}\$
where \$N\$ is the number of particles, \$m\$ is the mass of one particle, and \$\overline{v^{2}}\$ is the mean square speed.
| Change Made | Effect on Particle Motion | Resulting Change in Pressure |
|---|---|---|
| Increase temperature (while \$V\$ and \$n\$ constant) | Particles move faster → higher \$\overline{v^{2}}\$ | Pressure increases (directly proportional to \$T\$) |
| Decrease volume (while \$T\$ and \$n\$ constant) | Same number of particles in a smaller space → more collisions per unit area | Pressure increases (inversely proportional to \$V\$) |
| Increase amount of gas (more moles, \$n\$, at constant \$T\$ and \$V\$) | More particles → more collisions | Pressure increases (directly proportional to \$n\$) |
| Decrease temperature (while \$V\$ and \$n\$ constant) | Particles move slower → lower \$\overline{v^{2}}\$ | Pressure decreases |
| Increase volume (while \$T\$ and \$n\$ constant) | Particles have more space → fewer collisions per unit area | Pressure decreases |
• Higher temperature → faster particles → more frequent and more forceful collisions → higher pressure.
• Smaller volume → particles hit walls more often → higher pressure.
• More gas (more particles) → greater number of collisions → higher pressure.
• Lower temperature or larger volume → opposite effects, reducing pressure.