# Calculating Mean Free Path Ratios in a Divided Ideal Gas System

• Tachyonprince
Let's try this instead:L ~ Volume / Number of particlesCan't be right: this only applies if target particles aren't movingNo, that refers to the precise expression involving the average velocity of particles. The moving target is corrected for by multiplying the average velocity by a factor of √2. The proportionality to V/N is unaffected.In summary, the conversation discusses the calculation of the ratio of mean free paths in two sections of a box with a dividing wall and a hole. The incorrect idea that the ratio is half is dismissed and the correct answer of 0.7 is explained, taking into account the movement of the target particles.
Tachyonprince
I have a box with a wall in mid dividing it in 2 sections, and the wall has a hole of diameter d. There is ideal gas in both sections at 150 K in one section and at 300 K in another. How am I supposed to calculate ratio of mean free paths in 2 sections.

My attempt: L ~ Volume / Number of particles
=> L ~ Temperature / Pressure

Now, Assuming pressure to be same on both sections, ratio must be half. But that is incorrect. Why? Correct answer is 0.7.

And read the PF guidelines -- they apply to royalty, too..

But what the heck, I'll risk my neck (perhaps I can be knighted posthumously... ):

Tachyonprince said:
L ~ Volume / Number of particles
Can't be right: this only applies if target particles aren't moving

BvU said:
Can't be right: this only applies if target particles aren't moving
No, that refers to the precise expression involving the average velocity of particles. The moving target is corrected for by multiplying the average velocity by a factor of √2. The proportionality to V/N is unaffected.

I agree. Unfortunate Wrong way to put it on my part

## What is the mean free path of an ideal gas?

The mean free path of an ideal gas is the average distance a molecule travels between collisions with other molecules.

## How is the mean free path calculated?

The mean free path can be calculated using the formula: λ = kT/(√2 π d^2 p), where λ is the mean free path, k is the Boltzmann constant, T is the temperature, d is the diameter of the molecule, and p is the pressure.

## What factors affect the mean free path of an ideal gas?

The mean free path is affected by the temperature, pressure, and size of the gas molecules. It also depends on the type of gas and the presence of any external forces, such as gravity or electric fields.

## Why is the mean free path important in gas dynamics?

The mean free path is important because it helps us understand the behavior of gases in different conditions. It is used to calculate the diffusion rate, viscosity, and thermal conductivity of gases, and it also plays a role in gas flow and heat transfer processes.

## How does the mean free path differ from the mean free time?

The mean free path and mean free time are related but different concepts. The mean free path is the average distance a molecule travels between collisions, while the mean free time is the average time between collisions. The mean free path is inversely proportional to the pressure, while the mean free time is directly proportional to the pressure.

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