Mean Free Path Calculator Formula

Understand the math behind the mean free path calculator. Each variable explained with a worked example.

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Formulas Used

Mean Free Path

mean_free_path = (1.38e-23 * temp) / (1.4142 * pi * pow(diameter_m, 2) * pressure_pa)

Variables

VariableDescriptionDefault
tempTemperature (T)(K)298
pressure_paPressure(Pa)101325
diameter_mMolecular Diameter(m)3.7e-10

How It Works

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.

    Worked Example

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

    temp = 298pressure_pa = 101325diameter_m = 3.7e-10
    1. 01λ = kT / (√2 × π × d² × P)
    2. 02λ = (1.38×10⁻²³ × 298) / (1.414 × 3.14159 × (3.7×10⁻¹⁰)² × 101325)
    3. 03λ = 4.11×10⁻²¹ / (1.414 × 3.14159 × 1.369×10⁻¹⁹ × 101325)
    4. 04λ ≈ 6.6 × 10⁻⁸ m = 66 nm

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