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Matter: Very Simple

The kinetic theory of ideal gases

  • 3 things to know
  • Components 01, 02 and 03

Overview

Recall questions on the assumptions of kinetic theory, perfectly elastic collisions and steady pressure, pV = ⅓Nm⟨c²⟩ and its one third, root mean square speed and why it is used, calculating it for three particles, nitrogen and a gas of known density, ½m⟨c²⟩ = 3/2 kT, helium against nitrogen, p = ⅓ρ⟨c²⟩, and real gases at high pressure.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Key term

In pV = ⅓Nm⟨c²⟩, what does each symbol represent?

Key term

Why must collisions be elastic if a gas is to exert a steady pressure?

Key term

Explain how the random motion of particles gives a steady pressure on a container wall.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State the three assumptions kinetic theory makes about the particles of an ideal gas.

    Model answer

    The particles occupy a negligible part of the volume, all their collisions are perfectly elastic, and there are no forces between them except while they are colliding.

  2. 2

    What does a perfectly elastic collision mean in the kinetic theory of gases?

    Model answer

    No kinetic energy is lost in the collision, so the total kinetic energy of the particles is unchanged by it.

  3. 3

    Why must collisions be elastic if a gas is to exert a steady pressure?

    Model answer

    If kinetic energy were lost the particles would gradually slow, so the pressure would fall away even at constant temperature.

  4. 4

    Explain how the random motion of particles gives a steady pressure on a container wall.

    Model answer

    Enormous numbers of particles strike the wall each second and each delivers a small momentum change, so the average rate of momentum transfer per unit area is constant.

  5. 5

    In pV = ⅓Nm⟨c²⟩, what does each symbol represent?

    Model answer

    p is the pressure, V the volume, N the number of particles, m the mass of one particle and ⟨c²⟩ the mean square speed of the particles.

  6. 6

    Why does a factor of one third appear in the kinetic theory equation?

    Model answer

    The motion is random in three dimensions, so on average only one third of the mean square speed belongs to motion along any one axis.

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