Relation of pressure with mean-free-path

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SUMMARY

The relationship between gas pressure and mean-free-path is defined by the principle that lower gas pressure results in a higher mean-free-path. This occurs because, at lower pressures, gas molecules are less densely packed, allowing them to travel greater distances before colliding with one another. The mean-free-path is quantitatively influenced by the density of the gas; as density decreases, the mean-free-path increases. This concept is fundamental in understanding gas behavior at the molecular level.

PREREQUISITES
  • Understanding of gas laws and behavior
  • Familiarity with molecular dynamics
  • Basic knowledge of pressure and density concepts
  • Knowledge of statistical mechanics principles
NEXT STEPS
  • Study the kinetic theory of gases
  • Explore the mathematical derivation of mean-free-path
  • Learn about the impact of temperature on gas density
  • Investigate applications of mean-free-path in real-world scenarios
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Students of physics, researchers in thermodynamics, and professionals in fields involving gas dynamics will benefit from this discussion.

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My textbook says "The lower the gas pressure, the higher the mean-free-path".
But it does not explain why.

Can someone please explain it briefly? Thank you very much.
 
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The mean free path is the average length a gas molecule travels before bumping into another gas molecule.

Other factors being equal, lower pressure means a molecule will travel further before hitting another molecule.
 
Dr. Courtney said:
The mean free path is the average length a gas molecule travels before bumping into another gas molecule.

Other factors being equal, lower pressure means a molecule will travel further before hitting another molecule.

But how does it related with the pressure? Why is the mean-free-path high when the pressure is lower? How to explain it in term molecular level?
 
Better statement: the lower the density, the longer the mean free path.
 

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