Speed Ratio Relation (v_mp : v_avg : v_rms = √2 : √(8/π) : √3 ≈ 1.414 : 1.596)
jee-mainjee-advanced
v_mp : v_avg : v_rms = √2 : √(8/π) : √3 ≈ 1.414 : 1.596 : 1.732
What each symbol means
| Symbol | What it stands for |
|---|---|
| M | Molar mass (kg/mol) |
| R | Universal gas constant = 8.314 J mol⁻¹ K⁻¹ |
| T | Absolute temperature (K) |
| v_mp | Most probable speed — speed at which Maxwell distribution peaks (m/s) |
| v_avg | Mean (average) speed — arithmetic mean of all molecular speeds (m/s) |
| v_rms | Root mean square speed — √(⟨v²⟩), always the largest (m/s) |
When to use this
Valid for ideal gas obeying Maxwell-Boltzmann speed distribution. Ratio is UNIVERSAL — independent of gas type, temperature, or pressure. Individual speeds depend on T and M, but ratio cancels out. Always: v_mp < v_avg < v_rms.