Explaining the 2 in Δt = 2L/vx in Kinetic Theory

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SUMMARY

The discussion centers on the equation Δt = 2L/vx from the kinetic theory of gases, specifically in the context of deriving pressure (P). The factor of 2 in Δt is relevant when analyzing the collision of gas molecules with a wall of a container. However, in the subsequent equation F = Δp/Δt = mvx²/L, the factor of 2 cancels out due to the relationship between momentum change and the time interval, leading to a simplified expression for force. This cancellation is crucial for understanding the derivation of pressure in kinetic theory.

PREREQUISITES
  • Understanding of kinetic theory of gases
  • Familiarity with momentum and force equations
  • Basic knowledge of calculus and differential equations
  • Concept of pressure in thermodynamics
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  • Study the derivation of pressure in kinetic theory using the ideal gas law
  • Learn about the relationship between momentum and force in classical mechanics
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Students of physics, researchers in thermodynamics, and anyone interested in the mathematical foundations of kinetic theory will benefit from this discussion.

MathewsMD
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http://en.wikipedia.org/wiki/Kinetic_theory#Pressure_and_kinetic_energy

Based on the derivation for P in the above link, one of the early steps was:

Δt = 2L/vx

which is fine since it is analyzing one specific wall of the container, but then in the next step:

F = Δp/Δt = mvx2/L

And the 2 seems to disappear completely. Could anyone please explain why it is gone?
 
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The 2 cancels with the expression for the change in momentum (1st line).
 

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