Average Speed of Gas Molecules (v_avg = √(8kBT/πm) = √(8RT/πM))
jee-mainjee-advanced
v_avg = √(8kBT/πm) = √(8RT/πM)
What each symbol means
| Symbol | What it stands for |
|---|---|
| M | Molar mass in kg/mol |
| R | Universal gas constant = 8.314 J mol⁻¹ K⁻¹ |
| T | Absolute temperature (K) |
| m | Mass of one molecule (kg) |
| kB | Boltzmann constant = 1.38 × 10⁻²³ J K⁻¹ |
| π | Pi = 3.14159... |
| v_avg | Average (mean) speed of gas molecules (m/s) |
When to use this
Derived by integrating the Maxwell-Boltzmann speed distribution: v_avg = ∫₀^∞ v·f(v)dv. The factor 8/π arises from the integral. v_avg = v_rms × √(8/3π) ≈ 0.921 × v_rms. Always: v_mp < v_avg < v_rms.