Impulse-momentum theorem and kinetic theory of gases

In summary, the textbook is discussing the concept of collisions between molecules and the walls of a container. The time interval for these collisions is calculated as 2d/v_x, where d is the distance between the walls and v_x is the velocity of the molecule. The average force during these collisions is equal to -2mv_x. However, the textbook clarifies that this is not the time interval for a single particle, but rather the average time between collisions for all particles.
  • #1
member 392791
Hello,

I am reading through my textbook and cannot wrap this idea around my head yet

Basically, when a molecule hits the wall of the container, it is reflected back.
ΔP = -mv_x -mv_x = -2mv_x = FΔt_collision

Then they say the collision occurs every 2d/v_x because that's the time it takes for the molecule to hit one side of the wall then come back. The time interval for this is Δt.

then they say that the average force over the time interval, and they say the change in momentum for this time interval us te same as that for the short duration of the collsion,

FΔt = -2mv_x

I don't understand why they say the time interval it takes for the molecule to go from one side of the wall to the other side and back is the same as the time interval of the collision.
 
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  • #2
No, that is not said. However, you have many particles, colliding all the time. So you are not interested in the time-dependence of the momentum transfers of a single particle - it is sufficient to calculate its average. And that is ("momentum transfer") / ("time between collisions").
 

1. What is the impulse-momentum theorem?

The impulse-momentum theorem states that the change in momentum of an object is equal to the net force acting on the object multiplied by the time interval over which the force is applied. It is a fundamental principle in classical mechanics and is often used to analyze collisions and other dynamic situations.

2. How does the impulse-momentum theorem relate to the kinetic theory of gases?

The kinetic theory of gases explains the behavior of gases in terms of the motion and interactions of individual particles. The impulse-momentum theorem is used in this theory to describe the transfer of momentum between gas particles during collisions, which is essential in understanding gas pressure and other properties.

3. Can the impulse-momentum theorem be applied to all types of collisions?

Yes, the impulse-momentum theorem can be applied to all types of collisions, including elastic and inelastic collisions. In elastic collisions, both momentum and kinetic energy are conserved, while in inelastic collisions, only momentum is conserved. The impulse-momentum theorem allows us to calculate the change in momentum in both cases.

4. Is the impulse-momentum theorem only applicable to gases?

No, the impulse-momentum theorem can be applied to any type of system, including solids and liquids. In fact, it is commonly used in analyzing the motion of objects in fluids, such as in fluid dynamics and aerodynamics.

5. How is the impulse-momentum theorem different from the conservation of momentum?

The impulse-momentum theorem is a specific application of the more general principle of conservation of momentum. While the impulse-momentum theorem deals with the change in momentum over a specific time interval, the conservation of momentum states that the total momentum of a closed system remains constant in the absence of external forces. The impulse-momentum theorem is a useful tool for analyzing individual collisions or interactions within a system, while the conservation of momentum applies to the system as a whole.

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