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Average, rms and most probable speeds
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Ordered v_p < v_avg < v_rms.
Ordering: v_p : v_avg : v_rms = 1 : 1.128 : 1.225. They differ because the distribution is skewed.
For O₂ at 300 K: 395, 446, 484 m/s.
Use the one that fits the question: v_rms for energy.
In more detail
For a Maxwell-Boltzmann gas, the most probable speed, mean speed and rms speed are in the ratio 1 : 1.128 : 1.224. The ratios are fixed by the shape of the distribution.
Real-world uses
- Physics courses use these ratios to test understanding of distributions.
- Gas chemistry uses them to estimate speeds from measurements.
- Physicists compare the three typical molecular speeds to describe the spread of velocities in a gas.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
How do I remember the ratio?
Remember the order: most probable, then mean, then rms.
Do the ratios depend on temperature?
No, the ratios are the same at any temperature.
What is the order of the three speeds?
The most probable speed is lowest, then the average speed, then the rms speed, which is the highest of the three.
Related topics in Kinetic Theory & Statistical Physics
Specific heats of gases · Maxwell–Boltzmann distribution · Most probable speed · Law of atmospheres · Diffusion · Fick's law