Model travel using pressure, temperature, and diameter inputs. Compare methods with number density and cross-section. Review outputs quickly with tables, downloads, and interactive plots.
| Gas | Temperature (K) | Pressure (kPa) | Diameter (nm) | Molar Mass (g/mol) | Approx. Mean Free Path |
|---|---|---|---|---|---|
| Air | 300 | 101.325 | 0.365 | 28.97 | About 67 nm |
| Nitrogen | 300 | 101.325 | 0.364 | 28.01 | About 68 nm |
| Helium | 300 | 101.325 | 0.260 | 4.00 | About 133 nm |
The calculator applies the hard-sphere kinetic theory model. Two equivalent routes are supported, depending on the data you already know.
Route 1: Mean free path from pressure and molecular diameter
λ = kT / (√2 × π × d2 × p)
Route 2: Mean free path from number density and cross-section
λ = 1 / (√2 × n × σ)
Supporting relations:
σ = πd2
n = p / (kT)
Average molecular speed = √(8RT / (πM))
Collision frequency = average speed / mean free path
Mean time between collisions = mean free path / average speed
This model assumes ideal-gas behavior and effective hard-sphere molecular collisions. It works well for educational analysis, gas dynamics estimates, and quick benchmark calculations.
It is the average distance a particle travels before colliding with another particle. Gas pressure, temperature, and molecular size strongly affect it.
Higher pressure packs more particles into the same space. That raises collision probability, so the average travel distance between collisions becomes shorter.
Larger molecules have a larger collision area. A bigger effective diameter increases collision chances and decreases the mean free path.
At fixed pressure, yes. Higher temperature raises the numerator in the ideal-gas expression, giving a longer mean free path.
It estimates how often one molecule collides per second. It depends on both mean free path and molecular speed.
You can use it as a first estimate. Accuracy decreases when real-gas effects, strong interactions, or dense conditions become important.
Use pressure and diameter when gas properties are known. Use number density and cross-section when microscopic collision data is available.
Mean free path calculations often involve very large or very small values. Scientific notation keeps the displayed results clear and compact.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.