- #1
Dyon
- 30
- 2
I have reviewed recently the demonstration of the formula for the pressure of a gas by using the kinetic theory and it seems that there is a terrible flaw in it, which I will describe below. Can anyone comment on it, please?
In all textbooks, the pressure of a gas is proven to be proportional to the mean square speed of its molecules. The demonstration starts with the observation that the pressure of a gas is due to the ellastic collision of molecules with the walls of the container. Therefore, it calculates the change in the momentum arising from the elastic collision of one molecule with the wall, which is
Δp = 2mv (where v is the component of the molecule velocity perpendicular to that wall)
Nothing wrong up to here.
However, when calculating the force produced by this collision, instead of dividing this change in momentum to the time during which this collision takes place (Newton's second law), the authors divide the change in the momentum by the time taken by the particle to travel to the opposite wall and back 2L/v (where L is the length of the box perpendicular to the wall). They write
F = change in momentum / time taken = 2mv / (2L/v)
I contend that there is a serious problem here because the two time intervals obviously refer to different things.
You can see this here http://en.wikipedia.org/wiki/Kinetic_theory but is in fact in every textbook.
Don't you think that there is something wrong with this derivation?
Waiting for your comments. Thanks
In all textbooks, the pressure of a gas is proven to be proportional to the mean square speed of its molecules. The demonstration starts with the observation that the pressure of a gas is due to the ellastic collision of molecules with the walls of the container. Therefore, it calculates the change in the momentum arising from the elastic collision of one molecule with the wall, which is
Δp = 2mv (where v is the component of the molecule velocity perpendicular to that wall)
Nothing wrong up to here.
However, when calculating the force produced by this collision, instead of dividing this change in momentum to the time during which this collision takes place (Newton's second law), the authors divide the change in the momentum by the time taken by the particle to travel to the opposite wall and back 2L/v (where L is the length of the box perpendicular to the wall). They write
F = change in momentum / time taken = 2mv / (2L/v)
I contend that there is a serious problem here because the two time intervals obviously refer to different things.
You can see this here http://en.wikipedia.org/wiki/Kinetic_theory but is in fact in every textbook.
Don't you think that there is something wrong with this derivation?
Waiting for your comments. Thanks