kinetic theory of gases - assumption

Watch
o_reo
Badges: 17
Rep:
?
#1
Report Thread starter 10 months ago
#1
one of the assumptions is:
forces that act during collisions last for a much a shorter time than time between collisions.
In my textbook it is rewritten as:
each collision with the container surface is of a much shorter duration than the time between impacts

I still dont get it... what does it mean? doesnt it contradict itself?
0
reply
lordaxil
Badges: 10
Rep:
?
#2
Report 10 months ago
#2
There is no contradiction in either sentence, although I think the reason it is written as "collision with container surface" in the last one is to emphasize that in kinetic theory, the particles do not interact with each other, only the walls of the container.

The reason this assumption is necessary is to split up the motion of gas particles into two separate parts: a slow motion between each collision where they do not interact with any other particle, and a fast (essentially instantaneous) collision during which a single particle exchanges momentum with the container wall. The continual impact of many particles on the wall gives rise to a pressure.

Under the above assumption, the pressure can be calculated explicitly using kinetic theory, and turns out to be related to the temperature and density of the gas particles, as expected from the ideal gas laws. Without the assumption of short collisions, the calculation is much harder, but can be done with methods like molecular dynamics (a numerical simulation technique) and leads to a similar answer.
0
reply
Smokestar
Badges: 17
Rep:
?
#3
Report 10 months ago
#3
I struggled with this concept too but here is how I thought of it. Feel free to correct me if I am wrong.
So here we go,
The total time is the time taken to travel towards the container and the time taken for the gas molecule to collide with the container. Now what the assumption is assuming is that the time taken for the gas molecule to collide is negligible.
However the time taken to travel towards the molecule is not negligable. You will notice in that the derivation for the mean Ke equation it uses ideas of newtons 2nd law.
Force=Ma=change in momentum per second
Now pressure is force/area. The change in momentum is -2mu/t
t which is the time in between collisions. The time if you check in the derivation does not include the time for collisions to occur.
I hope this helps.
0
reply
o_reo
Badges: 17
Rep:
?
#4
Report Thread starter 10 months ago
#4
(Original post by lordaxil)
There is no contradiction in either sentence, although I think the reason it is written as "collision with container surface" in the last one is to emphasize that in kinetic theory, the particles do not interact with each other, only the walls of the container.

The reason this assumption is necessary is to split up the motion of gas particles into two separate parts: a slow motion between each collision where they do not interact with any other particle, and a fast (essentially instantaneous) collision during which a single particle exchanges momentum with the container wall. The continual impact of many particles on the wall gives rise to a pressure.

Under the above assumption, the pressure can be calculated explicitly using kinetic theory, and turns out to be related to the temperature and density of the gas particles, as expected from the ideal gas laws. Without the assumption of short collisions, the calculation is much harder, but can be done with methods like molecular dynamics (a numerical simulation technique) and leads to a similar answer.
wait if particles dont interact with each other then what is the duration of collision with the container surface shorter than?
(Original post by Smokestar)
I struggled with this concept too but here is how I thought of it. Feel free to correct me if I am wrong.
So here we go,
The total time is the time taken to travel towards the container and the time taken for the gas molecule to collide with the container. Now what the assumption is assuming is that the time taken for the gas molecule to collide is negligible.
However the time taken to travel towards the molecule is not negligable. You will notice in that the derivation for the mean Ke equation it uses ideas of newtons 2nd law.
Force=Ma=change in momentum per second
Now pressure is force/area. The change in momentum is -2mu/t
t which is the time in between collisions. The time if you check in the derivation does not include the time for collisions to occur.
I hope this helps.
so the force exerted by the particle on the container is of a shorter duration than time between particle collisions with other particles? is that what the assumption means?
0
reply
Smokestar
Badges: 17
Rep:
?
#5
Report 10 months ago
#5
(Original post by m.s124)
wait if particles dont interact with each other then what is the duration of collision with the container surface shorter than?

so the force exerted by the particle on the container is of a shorter duration than time between particle collisions with other particles? is that what the assumption means?
Yes that what I assume it means. No where in the derivations does it include the time for a collision to occur as the collisions are assumed to be elastic. If they weren't elastic then id assume that there was contact time between the container and gas molecule where it would lose some energy via thermal pathway.
0
reply
Smokestar
Badges: 17
Rep:
?
#6
Report 10 months ago
#6
(Original post by m.s124)
wait if particles dont interact with each other then what is the duration of collision with the container surface shorter than?

so the force exerted by the particle on the container is of a shorter duration than time between particle collisions with other particles? is that what the assumption means?
No the time for the collision to occur between the gas molecule and the container is negligible. Its insignificant. If it wasn't an assumption then the collisions woudnt be elastic as there would be contact time between the container and the molecule which would means some thermal energy lost as of result making the collision inelastic.
1
reply
o_reo
Badges: 17
Rep:
?
#7
Report Thread starter 10 months ago
#7
(Original post by Smokestar)
No the time for the collision to occur between the gas molecule and the container is negligible. Its insignificant. If it wasn't an assumption then the collisions woudnt be elastic as there would be contact time between the container and the molecule which would means some thermal energy lost as of result making the collision inelastic.
I get it now, thank you so much!!!
1
reply
Smokestar
Badges: 17
Rep:
?
#8
Report 10 months ago
#8
(Original post by m.s124)
I get it now, thank you so much!!!
Happy to help!
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Feeling behind at school/college? What is the best thing your teachers could to help you catch up?

Extra compulsory independent learning activities (eg, homework tasks) (2)
5.71%
Run extra compulsory lessons or workshops (7)
20%
Focus on making the normal lesson time with them as high quality as possible (4)
11.43%
Focus on making the normal learning resources as high quality/accessible as possible (3)
8.57%
Provide extra optional activities, lessons and/or workshops (11)
31.43%
Assess students, decide who needs extra support and focus on these students (8)
22.86%

Watched Threads

View All