rms vs average speed

Question

Correct order for speeds: v_rms, v_avg, v_mp (most probable) is:

RankGuru · Accepted Answer

For a Maxwell-Boltzmann distribution of speeds:
1. **Most Probable Speed** ($v_{mp}$): $\sqrt{\frac{2 R T}{M}} \approx 1.41 \sqrt{\frac{R T}{M}}$
2. **Average Speed** ($v_{avg}$): $\sqrt{\frac{8 R T}{\pi M}} \approx 1.60 \sqrt{\frac{R T}{M}}$
3. **RMS Speed** ($v_{rms}$): $\sqrt{\frac{3 R T}{M}} \approx 1.73 \sqrt{\frac{R T}{M}}$
Therefore, the order is $v_{rms} > v_{avg} > v_{mp}$. Memory trick: **RAM** (RMS > Avg > Most probable).

Rank Guru

rms vs average speed

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