范德华方程计算器 — 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.
### 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.
- λ = kT / (√2 × π × d² × P)
- λ = (1.38×10⁻²³ × 298) / (1.414 × 3.14159 × (3.7×10⁻¹⁰)² × 101325)
- λ = 4.11×10⁻²¹ / (1.414 × 3.14159 × 1.369×10⁻¹⁹ × 101325)
- λ ≈ 6.6 × 10⁻⁸ m = 66 nm