Solving Ideal Gas Law Model Homework

[Andy123]

Homework Statement

My problem is with the last line of the derivation. Usually, we take the rate of change of momentum (force) to be change of momentum divided by the impact time. But this slide of pp showed that the traveling time of the particle in the box is used but not the impact time. Why is it? Appreciate any comment on this. Thank you!

Homework Equations

The Attempt at a Solution

I realized that if the impact time is used. The force will be very large since the impact time is likely to be very small.

 

[SteamKing]

Homework Statement

My problem is with the last line of the derivation. Usually, we take the rate of change of momentum (force) to be change of momentum divided by the impact time. But this slide of pp showed that the traveling time of the particle in the box is used but not the impact time. Why is it? Appreciate any comment on this. Thank you!

Homework Equations

The Attempt at a Solution

I realized that if the impact time is used. The force will be very large since the impact time is likely to be very small.

Do you think the impact time of a gas molecule will be a significant fraction of the travel time of that molecule after it rebounds?

 

[Andy123]

No, it should be a very small fraction.