MOL-005 · Molecular-kinetic theory Sample material

Maxwell and Boltzmann distributions

The Maxwell distribution of molecular speeds and the characteristic speeds, Stern's experiment, the barometric formula, the Boltzmann distribution of particles in an external field, the mean free path and the collision frequency of molecules.

Estimated time: 3 h 3 activities

Learning objective

Understand the meaning of the Maxwell distribution function, its graph and its dependence on temperature and molar mass.
Learn to calculate the most probable, mean and root-mean-square speeds.
Know the idea and result of Stern's experiment.
Learn to derive and apply the barometric formula and the Boltzmann distribution, and to estimate the mean free path.

Expected outcomes

Calculates $v_p$, $\langle v\rangle$ and $v_{rms}$ for a given gas and temperature and explains their ratio.
Estimates the fraction of molecules in a narrow speed interval.
Calculates the decrease of atmospheric pressure and density with altitude.
Finds the mean free path and collision frequency from the gas pressure and temperature.

Interactive modelMaxwell speed distribution
Interactive modelBarometric formula and the Boltzmann distribution

Activities

Lecture
Lecture · 1 h 20 min · required
Problem solving on the topic "Maxwell and Boltzmann distributions"
Practice · 1 h 20 min · required
Final test
Test · 20 min · required · pass ≥ 70%

Completion conditions

  • Lecture
  • Problem solving on the topic "Maxwell and Boltzmann distributions"
  • Final test — at least 70%