Kinetic Theory of Gases: Momentum Change & Force

[science_world]

The kinetic theory of gas state that p=(1/3)(N)(m)(u^2)/(V).
In one step of its derivative related to change of momentum and force given to the wall (Refer to Cubic Container and molecule movement in x,y,z axes in attachment), the equation is given by:

change in momentum / time = force
delta(p) / (2L/u) = F
2mc / (2L/u) = F
(m)(u^2) / (L) = F

*L= length of cube
m = mass of one molecule
u = velocity of one molecule in x axis

This equation assume that "time" means [time taken for the molecule to move from one side of cube to the other side and back to the first side (2L= distance traveled)] divided by [velocity of molecule = u].

I think this is a wrong assumptions. Time for rate of momentum change actually means the time in which the force take to change the momentum of a particle. This means time in the above equations should be [time when force by wall change the momentum of particle, in other words the collision time] not [time taken to move from one side to another side].

Someone please do explain this. Thank you.

Picture in attachment by Ensmilvideo as seen in Youtube.com

 

[haruspex]

The total force on the wall is the rate of change of momentum of all the particles taken together. That rate will depend on the frequency each particle strikes the wall, on average, and that depends on the time to travel 2L.

 

[science_world]

But, in usual cases, such as calculating forces given by an object to a wall, the time used is time taken in collision, not time taken for the object to move from a point to that wall and back to that point again. Why it doesn't apply here?

Refer to formula: delta p / delta t = F
delta t is collision time. This formula is also used in kinetic theory of gases.

 

[haruspex]

Because what is being calculated is the average force over time. If you could look at a perfectly detailed graph of force v time you'd see it made up of gazillions of separate tiny pulses, but that's not of interest.

 

[PJC01]

I would like to clarify that the equation presented in the content is correct. The time in the equation refers to the time taken for the molecule to move from one side of the cube to the other side and back, which is the time it takes for the molecule to complete one full cycle of motion. This is because in the kinetic theory of gases, molecules are assumed to follow a random motion and collide with each other and the walls of the container.

The equation is derived from the concept of conservation of momentum, which states that the total momentum of a system remains constant unless acted upon by an external force. In this case, the force acting on the molecule is the force exerted by the wall during a collision. The time taken for this collision is the time used in the equation.

I understand the confusion regarding the use of the term "time" in this context, but it is important to note that the equation is derived and used in the context of kinetic theory of gases, where molecules are assumed to have random motion and collisions. This is a simplified model and may not accurately represent the motion of individual molecules, but it provides a good understanding of the behavior of gases at a macroscopic level.

I hope this explanation helps in understanding the concept better. If you have any further questions, please feel free to ask.