CIE A Level Physics (9702) exams from 2022

Revision Notes

15.2.1 Kinetic Theory of Gases

Assumptions of the Kinetic Theory of Gases

  • Gases consist of atoms or molecules randomly moving around at high speeds
  • The kinetic theory of gases models the thermodynamic behaviour of gases by linking the microscopic properties of particles (mass and speed) to macroscopic properties of particles (pressure and volume)


  • The theory is based on a set of the following assumptions:
    • Molecules of gas behave as identical, hard, perfectly elastic spheres
    • The volume of the molecules is negligible compared to the volume of the container
    • The time of a collision is negligible compared to the time between collisions
    • There are no forces of attraction or repulsion between the molecules
    • The molecules are in continuous random motion
  • The number of molecules of gas in a container is very large, therefore the average behaviour (eg. speed) is usually considered

Exam Tip

Make sure to memorise all the assumptions for your exams, as it is a common exam question to be asked to recall them.

Root-Mean-Square Speed

  • The pressure of an ideal gas equation includes the mean square speed of the particles:


  • Where
    • c = average speed of the gas particles
    • <c2> has the units m2 s-2
  • Since particles travel in all directions in 3D space and velocity is a vector, some particles will have a negative direction and others a positive direction
  • When there are a large number of particles, the total positive and negative velocity values will cancel out, giving a net zero value overall
  • In order to find the pressure of the gas, the velocities must be squared
    • This is a more useful method, since a negative or positive number squared is always positive
  • To calculate the average speed of the particles in a gas, take the square root of the mean square speed:

Root-Mean-Square Speed equation 1

  • cr.m.s is known as the root-mean-square speed and still has the units of m s-1
  • The mean square speed is not the same as the mean speed

Worked example: Root-mean-square speed

Root-Mean-Square_Speed_Worked_Example_-_Root-Mean-Square_Speed_Question, downloadable AS & A Level Physics revision notes

Step 1:            Write out the equation for the pressure of an ideal gas with density

Root-Mean-Square Speed equation Worked Equation 1a

Step 2:            Rearrange for mean square speed

Root-Mean-Square Speed equation Worked Equation 1

Step 3:            Substitute in values

Root-Mean-Square Speed equation Worked Equation 2

Step 4:            To find the r.m.s value, take the square root of the mean square speed

Root-Mean-Square Speed equation Worked Equation 3

Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

Join Save My Exams

Download all our Revision Notes as PDFs

Try a Free Sample of our revision notes as a printable PDF.

Join Now
Go to Top