Ideal-gas equation
At fixed volume, adding particles or raising the temperature increases the pressure.
Thermodynamics · molecular motion
Kinetic Theory
How do random collisions settle into a steady pressure, temperature and speed distribution? By averaging. No single collision is predictable, but the average over enormous numbers of them hardly fluctuates. The speeds settle into the Maxwell-Boltzmann distribution, and pressure and temperature come out the same every time you measure.
Hard spheres bounce elastically off one another and off all six walls of the box. Each collision looks random, but the speeds settle toward the 3D Maxwell-Boltzmann distribution, which the live histogram follows.
Particles170
Temperature1.00
Pressure0.00
Mean speed0.00
Physics tutorial
Ideal gas: how macroscopic laws emerge from collisions
BackgroundA gas is made of many particles that keep colliding. Temperature sets the scale of their average energy, and pressure comes from the momentum they hand to the container walls.
Why it mattersIt shows that a statistical distribution can predict the behavior of the whole gas without tracking every particle.
Start with the essentials
- Focus question
- Why do random collisions produce stable, repeatable pressure and temperature?
- One-sentence intuition
- Individual collisions are unpredictable, but averages over many independent events become stable.
Core mathematical model
Mean translational energy in 3D
Each of the three translational degrees of freedom contributes one half of the Boltzmann constant times the temperature.
Common difficulties
Temperature is not the speed of each particle
Typical misconceptionAll particles at one temperature move equally fast.
Better mental modelTemperature sets the energy scale of the distribution, and individual speeds still spread over a wide range.
Pressure does not come from particles repelling each other
Typical misconceptionGas pressure mainly comes from particles pushing each other apart.
Better mental modelIn an ideal gas, pressure is the steady flow of momentum from particles striking the walls.
Run the experiment
- 01
Watch the statistics settle
Choose Warm and let the histogram settle.
What to observe: Each bin keeps fluctuating, but the overall distribution settles down. - 02
Change only the temperature
Hold the particle count fixed and heat the gas.
What to observe: The distribution shifts to higher speeds and spreads out, and the mean speed and the pressure rise. - 03
Change only the particle count
Hold the temperature fixed and add particles.
What to observe: The mean speed stays about the same while the pressure goes up.
Related experiments and articles
Heat and collective behaviour · Reading path
What a gas can tell us about atoms
Articles on this path that use this experiment, followed by the other experiments they suggest.