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

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SUMMARY

Doubling the temperature of a gas does not affect the mean free path of its particles, despite their increased velocity. When the temperature (T) is doubled, the kinetic energy (KE) also doubles, resulting in a root two increase in the root mean square velocity (Vrms). However, since all particles experience this increase uniformly, the average distance between collisions remains constant. This phenomenon illustrates that the relative motion of particles, rather than their absolute speed, determines the mean free path.

PREREQUISITES
  • Understanding of kinetic theory of gases
  • Familiarity with concepts of temperature and kinetic energy
  • Knowledge of root mean square velocity (Vrms)
  • Basic principles of particle collisions in a fixed volume
NEXT STEPS
  • Study the kinetic theory of gases in detail
  • Explore the relationship between temperature and kinetic energy
  • Learn about the derivation of mean free path in gases
  • Investigate the implications of particle velocity on collision frequency
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Students of physics, researchers in thermodynamics, and anyone interested in the behavior of gases under varying temperature conditions.

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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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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