MYTUTOR SUBJECT ANSWERS

355 views

How can the average speedx of a gas molecule be derived?

To start with, some assumptions must be made to simplify the problem. Firstly the N molecules are assumed to have no size, be identical and not interact with each other. The second assumption is that the molecules move randomly and collide elastically with the container which is a cube of side length L.

When a particle collides with the container in the x direction, it rebound in the opposite direction at the same speed meaning the change in momentum is 2mvx. The momentum change of n particles is therefore 2nmvx.

The force exerted on the wall F=Impulse/Time so next we need to find the number of particles colliding with the wall per second. To do this, consider that all particles less than v metres from the wall will collide before one second. This means that any particle in the volume vxL2 will collide. However, only half the particles will be travelling towards the wall so a factor of 1/2 is needed. The number of particles in this volume is vxL2/2*N/L3=vxN/2L. This means F=2mvx+vxN/2L=mNvx2/L. As all directions are equivalent, v2=vx2+vy2+vz2=3vx2 so F=mNv2/3L.

The pressure is therefore P=F/L2=mNv2/3L3=mNv2/3V. This means that PV=Nmv2/3. Also, PV=NkBT so NkBT=Nmv2/3 so kBT=mv2/3. The average speed can now be found in terms of temperature and mass only: v=sqrt(3kBT/m).

Zac T. A Level Chemistry tutor, A Level Further Mathematics  tutor, A...

9 months ago

Answered by Zac, an A Level Physics tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

89 SUBJECT SPECIALISTS

£24 /hr

Rachel H.

Degree: Physics and Astronomy with a Year Abroad (Bachelors) - Durham University

Subjects offered:Physics, Science+ 3 more

Physics
Science
Maths
German
Chemistry

“Hey, I'm Rachel and I'm a fourth year Physics Student at Durham University. My best subjects at school were always science and maths and really enjoyed using my knowledge to help my friends to understand the topics better, if they were...”

£20 /hr

Jakub K.

Degree: Physics and Astronomy (Masters) - Durham University

Subjects offered:Physics, Maths

Physics
Maths

“About meHi! My name is Jakub and I'm studying Physics and Astronomy at Durham University. I have been interested in sciences for as long as I can remeber and I really enjoy sharing thatpassion with others, be it through tutoring or a...”

£26 /hr

Samuel C.

Degree: Physics (Bachelors) - Durham University

Subjects offered:Physics, Maths+ 2 more

Physics
Maths
Further Mathematics
Chemistry

“Hi, I'm Sam Crawford. I'm studying Maths and Physics at Durham University, with an offer from Cambridge for next year, and I absolutely love both subjects.”

About the author

Zac T.

Currently unavailable: until 03/10/2016

Degree: Natural Sciences (Bachelors) - Cambridge University

Subjects offered:Physics, Science+ 4 more

Physics
Science
Maths
Further Mathematics
Chemistry
Biology

“About me I am a student at the University of Cambridge where I study Natural Sciences, a course which allows me to maintain my interest in multiple areas of science and maths. I take modules in Chemistry, Physics, Earth Science and Ma...”

MyTutor guarantee

You may also like...

Posts by Zac

Find the shortest distance between the line L: x=1+t, y=1+2t, z=1-t and the point A: (2,3,4)

How can the average speedx of a gas molecule be derived?

Integrate (x+4)/(x^2+2x+2)

Why are transition metal complexes coloured?

Other A Level Physics questions

How to solve horizontally-launched projectile motion problems using equations of motion?

What does the double slit experiment tell us about light?

What is the optimum angle to throw a snowball for maximum horizontal displacement? (Ignore air resistance, assume the snowball is thrown level with the ground. The angle is measured from the ground up)

Find the magnitude of the force on an electron that is travelling with velocity 2 x 10^4 ms^(-1) in the x direction through a uniform magnetic field of strength 2T in the y direction.

View A Level Physics tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok