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Mean Free Path Calculator — result sheet
Estimate the mean distance and mean time between molecular collisions in a dilute ideal gas.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: λ = kBT/(√2πd²p); vrms = √(3kBT/m); mean free time = λ/vrms.
Mean free path estimates how far a molecule travels between collisions, while the companion speed and time outputs connect that distance with a simple kinetic-theory scale.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Gas temperature — K; minimum 1.0E-6; maximum 1000000
- Absolute pressure — Pa; minimum 1.0E-6; maximum 1000000000000
- Molecular collision diameter — m; minimum 1.0E-12; maximum 0.001
- Molecular mass — kg; minimum 1.0E-33; maximum 1.0E-18
Worked example
| Input | Value |
|---|---|
| Gas temperature | 300 |
| Absolute pressure | 101325 |
| Molecular collision diameter | 3.7E-10 |
| Molecular mass | 4.65E-26 |
The mean free path is about 6.8×10⁻⁸ m; the ideal rms speed is about 517 m/s.
Assumptions and limits
- The gas is dilute and ideal, with a single effective collision diameter and molecular mass.
- Temperature and pressure are absolute and use SI units.
- Molecular-shape effects, mixtures, wall collisions, nonideal gas behavior, and transport coefficients are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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