Thermodynamics
Kinetic theory sandbox
Heat the gas and watch the molecules speed up (v_rms).
Explore kinetic theory with many interacting particles in a sandbox. Watch pressure, temperature, and speed distributions emerge from microscopic collisions.
Kinetic theory
Heat the gas and watch the molecules speed up (v_rms).
Kinetic theory links temperature to average molecular kinetic energy: ½m⟨v²⟩ = (3/2)kT. Heating adds energy that appears as faster random motion. The root-mean-square speed v_rms is what enters the ideal-gas pressure relation and explains why hotter gases exert higher pressure at fixed volume.
- KE_avg = (3/2)kT
- v_rms ∝ √T
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
Temperature is really a measure of average molecular motion. If you double a gas's absolute temperature, does the typical molecular speed also double?
Predictions to weigh
- Molecular speed doubles too, since temperature and speed are directly proportional.
- Molecular speed increases by a factor of √2, not 2, since speed depends on the square root of temperature.
- Molecular speed doesn't depend on temperature.
Variable roles
What you set:
- Temperature T (K)
What you measure:
- Average molecular KE (zJ)
- RMS speed v_rms (m/s)
How the investigation runs
- Open the kinetic-sandbox preset and press Reset. The chamber holds argon gas (M = 0.039948 kg/mol).
- Enable the rms-speed and average-kinetic-energy readouts.
- Set the gas temperature for each trial and record the rms molecular speed.
Governing equation
RMS Molecular Speed — v_rms = √(3·R·T / M)
The root-mean-square speed of gas molecules depends on temperature and molar mass: v_rms = √(3RT/M). Lighter, hotter gases have faster-moving molecules.
Average Molecular Kinetic Energy — KE_avg = 3/2·kB·T
Every ideal-gas molecule, regardless of mass, has the same average translational kinetic energy at a given temperature: KE_avg = (3/2)k_BT. Temperature is fundamentally a measure of this average motion.
What the printable worksheet asks students to work out
- For one trial, compute v_rms = √(3RT/M) using R = 8.314 J/(mol·K) and M = 0.039948 kg/mol. Compare to the table.
- Explain why v_rms grows with the square root of temperature rather than in direct proportion to it.
Where this shows up beyond the lab
- Two gases at the same temperature have the same average kinetic energy, but the lighter gas (smaller M) has a higher v_rms. Explain why, using KE_avg = ½M·v_rms² together with the fact that KE_avg only depends on T.
- Helium (M ≈ 0.004 kg/mol) leaks out of a balloon much faster than the balloon deflates from air alone. Use your v_rms formula to explain why lighter gas molecules escape through tiny pores faster.
- AP Physics 2 — Unit 9: Thermodynamics
- IB Physics — B.3 Gas laws
- General High School Physics — Heat, temperature & gas laws
- NGSS High School Physics — Thermal energy transfer
- Welcome to Kinetic Sandbox
- Select the chamber
- Press Play
- Faster molecules at higher T
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.