Calculateur de Van der Waals
Calculez les propriétés des gaz avec l'équation de Van der Waals.
Mean Free Path
0.0000 m
Mean Free Path vs Temperature (T)
Formule
## Mean Free Path ### Formula **λ = kT / (√2 × π × d² × P)** Where: - **λ** = mean free path (m) - **k** = Boltzmann constant = 1.38 × 10⁻²³ J/K - **T** = temperature (K) - **d** = molecular diameter (m) - **P** = pressure (Pa) The mean free path increases with temperature and decreases with pressure and molecular size.
Exemple Résolu
N₂ molecules (d = 3.7 × 10⁻¹⁰ m) at 298 K and 101325 Pa.
- 01λ = kT / (√2 × π × d² × P)
- 02λ = (1.38×10⁻²³ × 298) / (1.414 × 3.14159 × (3.7×10⁻¹⁰)² × 101325)
- 03λ = 4.11×10⁻²¹ / (1.414 × 3.14159 × 1.369×10⁻¹⁹ × 101325)
- 04λ ≈ 6.6 × 10⁻⁸ m = 66 nm
Questions Fréquentes
What is the mean free path?
It is the average distance a gas molecule travels between successive collisions with other molecules. At atmospheric pressure, it is typically tens of nanometers.
How does pressure affect mean free path?
Lower pressure means fewer molecules per volume, so molecules travel farther between collisions. In vacuum chambers, mean free paths can be meters.
Why does molecular diameter matter?
Larger molecules have bigger collision cross-sections, making collisions more frequent and the mean free path shorter.
Apprendre