Mittelwert Free Path Rechner — Formel

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.

    Lösungsbeispiel

    N₂ molecules (d = 3.7 × 10⁻¹⁰ m) at 298 K and 101325 Pa.

    1. λ = kT / (√2 × π × d² × P)
    2. λ = (1.38×10⁻²³ × 298) / (1.414 × 3.14159 × (3.7×10⁻¹⁰)² × 101325)
    3. λ = 4.11×10⁻²¹ / (1.414 × 3.14159 × 1.369×10⁻¹⁹ × 101325)
    4. λ ≈ 6.6 × 10⁻⁸ m = 66 nm