Classical statistical mechanics
Maxwell–Boltzmann speed distribution
Explore how temperature and molar mass change molecular speeds, compare the histogram with , and measure .
Equipment
- Ideal-gas sample of 6,000 molecules and a speed histogram
- Temperature and molar-mass controls with a theoretical distribution curve
Procedure
Choose a gas and temperature
Set the molar mass and temperature. Each molecular velocity component is sampled from a thermal Gaussian distribution.
Read the speed histogram
The bars show normalized measured speeds; the smooth curve is the Maxwell–Boltzmann probability density for the selected gas and temperature.
Measure the root-mean-square speed
Compare the sample value with . Draw a new sample and note the finite-sample variation.
Simulation
Experiment history
James Clerk Maxwell derived the distribution of molecular speeds in 1860 while developing the kinetic theory of gases. His result connected a statistical description of many molecules with measurable macroscopic properties such as temperature and pressure.
Ludwig Boltzmann extended the statistical-mechanical foundations during the 1870s, clarifying how molecular probability and the distribution of energy underpin thermodynamic behavior. The modern Maxwell–Boltzmann speed law combines these classical results for a dilute ideal gas in thermal equilibrium.