B.3 · IB Physics
Maxwell–Boltzmann distribution
Molecules in a gas do not share one speed: they spread across a distribution. Heat the gas or change its molar mass and watch the curve shift and flatten while the area under it stays fixed.
Predict first
Start from the default settings (helium at 300 K). Raise Temperature to 1200 K. What happens to the most probable speed vp?
vp = √(2kT ÷ m), so vp ∝ √T. Quadrupling T from 300 K to 1200 K doubles vp, from about 1120 to about 2230 m s⁻¹.
Check it in the model: Move the Temperature slider from 300 K to 1200 K and compare the Most probable speed vp readout.
distribution tail above threshold vrms 300 K reference
vp = √(2kT ÷ m)
mean v = √(8kT ÷ πm)
vrms = √(3kT ÷ m)
mean Ek = (3/2) kT
Try this
- Set Gas to Nitrogen and raise Temperature from 300 K to 1200 K. By what factor do vp and the mean kinetic energy change, and why is the peak lower?
- At 300 K, compare helium, nitrogen and CO₂. Which readout is identical for all three gases, and which one depends on the molar mass?
- Use the Hot helium preset (threshold 2000 m s⁻¹), then change Gas to nitrogen. How does the fraction above the threshold change, and why do light gases escape from atmospheres?
Exam tip: Temperature measures the average kinetic energy, 3/2 kT, but a tail of fast molecules always remains; as T rises the peak moves right and drops because the area, the number of molecules, cannot change.