Home / Topics / Kinetic Theory & Statistical Physics
Most probable speed
Advanced
Peak of the speed distribution.
v_p = √(2kT/m)The peak of f(v) is v_p = √(2kT/m).
N₂ at 300 K: 422 m/s.
Smaller than v_rms and the mean.
In more detail
The most probable speed is the speed at which the Maxwell-Boltzmann distribution peaks, v_p = sqrt(2kT/m). It is lower than the mean and rms speeds.
Real-world uses
- Estimating the typical speed of molecules in a gas.
- Comparing gases at the same temperature.
- Engineers use the most probable speed to describe the typical molecular speed in a gas at a given temperature.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Why are there three speeds?
Mean, rms and most probable speeds weight the distribution differently.
Which is largest?
The rms speed is largest, followed by the mean, then the most probable.
Is the most probable speed the average?
No. The most probable speed is the peak of the distribution, which is slightly lower than the average speed.
Related topics in Kinetic Theory & Statistical Physics
Equipartition theorem · Specific heats of gases · Maxwell–Boltzmann distribution · Average, rms and most probable speeds · Law of atmospheres · Diffusion