Kinetic Theory of Gases
Why does a gas push on its container? Why does pressure rise when you heat it? This lesson answers these questions by watching tiny molecules move, collide and bounce, live on your screen.
Every demo is interactive. Drag the sliders and watch what changes.
1. What is a gas?
A gas is a huge crowd of atoms or molecules that are far apart compared with their own size. They move constantly in random directions. Air in a balloon is a mix of nitrogen, oxygen and other molecules doing exactly this.
2. Live molecule simulator
Each dot is a molecule. Blue is slow, red is fast. Molecules collide with each other like billiard balls. The glowing white dot with a trail is one molecule followed through the crowd. Walls flash when molecules hit them.
This is a simplified two-dimensional model. Real gases move in three dimensions and contain about 10²² molecules per litre.
Speed distribution of this simulation
Molecules do not all move at the same speed. Collisions keep swapping energy between them. The bars show the live count of molecules at each speed, and the line shows the theoretical Maxwell-Boltzmann curve for a 2D gas.
Change the temperature in the simulator above. The whole distribution slides to higher speeds and spreads out.
3. Basic assumptions of an ideal gas
- Molecules are extremely small, so their own volume is negligible.
- They move continuously and randomly in all directions.
- There are no attractive or repulsive forces except during collisions.
- All collisions are perfectly elastic. Kinetic energy is conserved.
- Newton's laws of motion apply.
- The duration of a collision is negligible.
4. How a gas produces pressure
When a molecule hits a wall, its momentum reverses. By Newton's second law, a change of momentum per second is a force. Billions of such hits every second add up to a steady push on the wall.
Derivation (cubical box of side L)
One molecule of mass m moving along x with speed vₓ:
For N molecules, with V = L³:
Motion is random, so average(v²) = 3 × average(vₓ²). Therefore:
5. Temperature and kinetic energy
Temperature is a measure of the average translational kinetic energy of the molecules. Double the absolute temperature and the average kinetic energy doubles. It does not depend on what the gas is.
You can read this live in the simulator above, in the "Average KE" box.
6. Ideal gas lab: Boyle's law and Gay-Lussac's law
Combining all gas laws gives one equation:
The cylinder shows the gas. The graph shows pressure against volume. Grey curves are isotherms (constant temperature) at 200 K, 400 K and 600 K. The amber curve is your current temperature.
Gay-Lussac's law (P₁/T₁ = P₂/T₂): keep volume fixed and change only the temperature. Watch the piston flash faster as molecules speed up.
7. Molecular speeds: most probable, average and RMS
Pick two gases and a temperature. The curves show the real 3D Maxwell-Boltzmann distribution. The area under each curve is 1. The dashed lines mark the three speeds of gas A. Light molecules are far faster than heavy ones at the same temperature.
Race at RMS speed (slowed down enormously)
8. Degrees of freedom, equipartition and heat capacity
A degree of freedom is an independent way a molecule can store energy. The law of equipartition says each active one stores an average of ½kT per molecule.
Translation moves the molecule across the screen, rotation spins it, and vibration stretches its bonds. A monatomic atom can only translate, so f = 3. Diatomic gases usually have f = 5 near room temperature and f = 7 when vibration switches on.
9. Mean free path
The mean free path is the average distance a molecule travels between two collisions.
In real air at room conditions, λ is about 68 nm, roughly 180 times a molecule's diameter. In this 2D demo the matching formula is λ = 1 / (√2 × d × n), where n is molecules per unit area. The white rings mark where the followed molecule collided.
10. Formulas at a glance
| Quantity | Formula |
|---|---|
| Pressure | P = F/A |
| Kinetic pressure equation | P = ⅓ ρ v²rms |
| RMS speed | √(3RT/M) |
| Average KE per molecule | 3kT/2 |
| Ideal gas equation | PV = nRT |
| Mean free path | kT / (√2 π d² P) |
| Energy per mole | fRT/2 |
| Cv and Cp | fR/2 and (f+2)R/2 |
| Specific heat ratio γ | (f+2)/f |
Constants
| Constant | Value |
|---|---|
| Gas constant R | 8.314 J mol⁻¹ K⁻¹ |
| Boltzmann constant k | 1.380649 × 10⁻²³ J/K |
| Avogadro constant NA | 6.022 × 10²³ mol⁻¹ |
| Standard atmosphere | 101325 Pa |
11. Check your understanding
12. Final understanding
- Gas molecules are in continuous random motion.
- Collisions with the walls produce pressure.
- Temperature measures the average translational kinetic energy.
- RMS speed increases with temperature and decreases with molecular mass.
- Pressure, volume and temperature are linked by PV = nRT.
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