How Does Doubling the Temperature Affect the Mean Free Path in a Gas?

In summary, if the temperature of a gas doubles and the particles travel √2 times as fast, the average distance between particles (mean free path) is unaffected due to the fact that the particles are still moving at the same rate relative to each other. This means that even if the video of the particles is sped up or slowed down, the distance between collisions remains the same.
  • #1
Sarah0001
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Homework Statement
"The mean free path is independent of temperature at constant volume."
Relevant Equations
mean free path inversely proportional to density (=mass of gas/volume)
it is at constant volume density of gas remains same.
Assumption, all N particles in Volume V move with avg speed (rms speed) from avg KE for a given temperature T.
Say Temperature of a gas doubles, I do not understand how the average distance between particles (mean free path) is unaffected if they are traveling √2 times as fast in a fixed volume V. Root 2 as a factor of increase because T*2 --> KE*2 --> V*2 --> Vrms*√2
Is it because relative to one another the if both particles are moving at the same rate then, the distance between them is fixed, regardless of the rate at which distance is covered.
 
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  • #2
Sarah0001 said:
how the average distance between particles (mean free path) is unaffected if they are traveling √2 times as fast
Imagine watching a video of them. If you speed ot up or slow it down the particles will move exactly the same distance between collisions.
 
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Related to How Does Doubling the Temperature Affect the Mean Free Path in a Gas?

What is the mean free path statement?

The mean free path statement is a concept in physics that describes the average distance a particle will travel between collisions with other particles.

How is the mean free path calculated?

The mean free path is calculated by dividing the average distance traveled by the number of collisions that occur within that distance.

What factors affect the mean free path?

Several factors can affect the mean free path, including the density of the medium, the size and shape of the particles, and the temperature and pressure of the system.

Why is the mean free path important in gas dynamics?

The mean free path is important in gas dynamics because it helps to understand the behavior of gases at a microscopic level and can be used to predict macroscopic properties of gases, such as viscosity and thermal conductivity.

How does the mean free path relate to diffusion?

The mean free path is closely related to diffusion, as both concepts involve the movement of particles in a medium. The shorter the mean free path, the more likely it is for particles to collide and diffuse through the medium.

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