Kinetic Theory: Temperature and Molecular Speed
1 · Predict
Temperature is really a measure of average molecular motion. If you double a gas's absolute temperature, does the typical molecular speed also double?
- 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.
2 · Set Up
- 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.
3 · Collect Data
| Temperature T (K) | Average molecular KE (zJ) | RMS speed v_rms (m/s) |
|---|---|---|
| 300 | ||
| 600 | ||
| 900 |
Plot v_rms (y-axis) against √T (x-axis) for your three trials. Is the line straight through the origin?
4 · Analyze
- 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.
5 · Extend
- 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.
The Physics Behind This Experiment
RMS Molecular Speed
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
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.