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

In summary, the "2" in the equation Δt = 2L/vx in Kinetic Theory represents the average time between collisions of gas molecules. It is derived from the assumption of straight-line motion and constant velocity, and is necessary to account for the distance traveled to and from a collision. This "2" is a fundamental constant that cannot be replaced with another value.
  • #1
MathewsMD
433
7
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?
 
Chemistry news on Phys.org
  • #2
The 2 cancels with the expression for the change in momentum (1st line).
 

1. What is the meaning of the "2" in the equation Δt = 2L/vx in Kinetic Theory?

The "2" in the equation represents the average time it takes for a molecule to travel a distance of L, assuming a constant velocity of vx. It is a constant factor derived from the Kinetic Theory of Gases and is used to calculate the average time between collisions of gas molecules.

2. How is the "2" derived in the equation Δt = 2L/vx in Kinetic Theory?

The "2" is derived from the assumption that gas molecules move in a straight line between collisions and that they travel at a constant velocity. This means that the average time between collisions is equal to the distance traveled (L) divided by the velocity (vx). To account for both the distance traveled to and from a collision, the factor of 2 is included.

3. Is the "2" a constant value in the equation Δt = 2L/vx in Kinetic Theory?

Yes, the "2" is a constant value in this equation. It is a fundamental constant derived from the Kinetic Theory of Gases and is used to calculate the average time between collisions of gas molecules.

4. Why is the "2" necessary in the equation Δt = 2L/vx in Kinetic Theory?

The "2" is necessary in this equation because it accounts for the distance traveled to and from a collision. Without this factor, the equation would only calculate the average time between collisions in one direction, leading to an inaccurate result.

5. Can the "2" in the equation Δt = 2L/vx in Kinetic Theory be replaced with another value?

No, the "2" in this equation is a fundamental constant and cannot be replaced with another value. It is derived from the Kinetic Theory of Gases and is necessary for accurately calculating the average time between collisions of gas molecules.

Similar threads

Kinetic Theory of Gas: F=-2mv/2L/V
    • Mechanics
Replies
10
Views
2K
B Collision time interval of a gas molecule with wall of container
    • Thermodynamics
Replies
6
Views
1K
Can gas kinetic theory explain heat transfer from gas to a container?
    • Thermodynamics
Replies
6
Views
1K
Kinetic theory of gases: rebound speed and force questions
    • Mechanics
Replies
2
Views
2K
Is there a Conceptual problem here? (Pressure in the Kinetic theory of gases)
    • Mechanics
Replies
15
Views
4K
Explain convection heat transfer using kinetic theory
    • Thermodynamics
Replies
1
Views
5K
Kinetic Theory of Gases: Momentum Change & Force
    • Mechanics
Replies
4
Views
2K
Question about kinetic theory
    • Mechanics
Replies
4
Views
1K
# of gas particles hitting one face of a cubic container
    • Introductory Physics Homework Help
Replies
6
Views
1K
I A Bold New Take on Quantum Theory
    • Quantum Interpretations and Foundations
Replies
25
Views
1K

Hot Threads

Recent Insights

Back
Top