范德华方程计算器
使用范德华方程计算实际气体的状态参数。
Mean Free Path
0.0000 m
Mean Free Path vs Temperature (T)
公式
## 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.
计算示例
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
常见问题
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.
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