Relation of pressure with mean-free-path

In summary, the textbook states that the mean free path of gas molecules is longer when the gas pressure is lower. This means that at lower pressures, gas molecules can travel further before colliding with another molecule. This is because lower pressure results in lower density, allowing molecules to have a longer distance between collisions.
  • #1
fricke
39
3
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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  • #2
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.
 
  • #3
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?
 
  • #4
Better statement: the lower the density, the longer the mean free path.
 

1. What is the relation between pressure and mean-free-path?

The mean-free-path is the average distance a molecule travels before colliding with another molecule. As pressure increases, the number of molecules in a given space also increases, resulting in more frequent collisions. This leads to a decrease in the mean-free-path.

2. How does pressure affect the mean-free-path of gas molecules?

As pressure increases, the mean-free-path decreases. This is because the increased number of gas molecules in a given space leads to more frequent collisions between molecules, reducing the average distance between collisions.

3. Can pressure and mean-free-path be directly proportional?

No, pressure and mean-free-path have an inverse relationship. As pressure increases, the mean-free-path decreases. Similarly, as pressure decreases, the mean-free-path increases.

4. What is the significance of mean-free-path in gas dynamics?

The mean-free-path is an important concept in gas dynamics as it helps determine the ability of gas molecules to travel and transfer energy. It is also used to calculate the viscosity and thermal conductivity of gases.

5. How does temperature affect the relation between pressure and mean-free-path?

Temperature has a direct effect on pressure and mean-free-path. As temperature increases, the pressure also increases, leading to more frequent collisions between molecules and a decrease in mean-free-path. Similarly, a decrease in temperature leads to a decrease in pressure and an increase in mean-free-path.

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