1. How Pressure Comes From Molecular Motion
Gas pressure arises because molecules constantly collide with the container walls. Each collision exerts a tiny force. The combined effect of countless collisions per second produces measurable pressure.
The faster the molecules move, the more forceful the collisions become.
2. Link Between Pressure and Kinetic Energy
Kinetic theory shows a direct relation between pressure and the average kinetic energy of molecules. If molecules move faster, pressure increases (for a fixed volume).
3. Average Kinetic Energy of a Molecule
The average kinetic energy of a molecule is:
E_{avg} = \dfrac{3}{2} k_B T
So if temperature increases, molecular kinetic energy increases.
3.1. Connecting to Pressure
Higher temperature → faster molecules → more forceful and more frequent collisions → higher pressure (if volume is constant).
4. Deriving the Pressure–Energy Relation
Using kinetic theory:
P V = \dfrac{1}{3} m N \bar{c^2}
Replacing the average kinetic energy:
\dfrac{1}{2} m \bar{c^2} = \dfrac{3}{2} k_B T
we get the ideal gas equation:
P V = N k_B T
4.1. Interpretation
This equation shows that pressure is a direct measure of total molecular kinetic energy per unit volume.
5. Physical Meaning of the Relation
Pressure increases when molecules:
- move faster (higher temperature)
- collide more frequently (higher density)
- have higher kinetic energy
5.1. Simple Example
A sealed metal can becomes harder when heated because the faster-moving molecules inside strike the walls more forcefully, increasing pressure.
6. Everyday Applications
- Tyre pressure increases after long driving because air heats up, raising kinetic energy and pressure.
- Pressure cookers work by trapping steam, increasing both temperature and pressure.
- Helium balloons expand in warm places as the gas molecules inside move faster.