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Thermodynamics

The kinetic theory equation and its derivation

  • 2 things to know
  • Papers 2 and 3

Overview

Recall questions on pV = ⅓Nm⟨c²⟩ and what each symbol means, the four assumptions of the model, and the steps from one molecule in a cube to the pressure on a wall.

What you need to know

Answer each one before you reveal it.

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Numbers

What is the kinetic theory equation relating pressure and volume to molecular motion, and what assumptions does the ideal gas model make?

Numbers

How is pressure defined, and how does a molecule bouncing between the faces of a cube give rise to a force?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State the kinetic theory equation relating the pressure and volume of a gas to the motion of its molecules:

    Model answer

    The equation is pV = ⅓Nm⟨c²⟩.

  2. 2

    In pV = ⅓Nm⟨c²⟩, what do N, m and ⟨c²⟩ each represent?

    Model answer

    N is the number of molecules, m is the mass of one molecule and ⟨c²⟩ is the mean square speed of the molecules.

  3. 3

    What four assumptions does the kinetic theory model of an ideal gas make?

    Model answer

    Molecules are in rapid random motion; their own volume is negligible compared with the volume of the container; all collisions are perfectly elastic; and there are no forces between molecules except during collisions.

  4. 4

    State the equation that defines pressure in terms of force and area:

    Model answer

    Pressure is given by p = F/A, the force acting normally per unit area.

  5. 5

    In the derivation, how does a single molecule bouncing off a wall give rise to a force?

    Model answer

    The molecule's momentum changes by 2mc, so by Newton's second law the rate of change of momentum is the force the wall exerts on the molecule; by Newton's third law the molecule exerts an equal and opposite force on the wall.

  6. 6

    For a molecule moving between opposite faces of a cube of side l, what is the time between successive impacts on the same face?

    Model answer

    The molecule travels a distance 2l between impacts, so the time is 2l/c.

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