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:

<c2>

  • 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

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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.
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