Kinetic theory of gases

Physics · Heat and thermodynamics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

The kinetic theory explains the behaviour of a gas from the motion of its molecules. It assumes: a gas has a very large number of molecules in random motion; the size of a molecule is very small compared with the distance between molecules; molecules exert no forces on each other except during collisions; and collisions are perfectly elastic.

Pressure comes from molecules hitting the walls. Each collision changes a molecule's momentum, and the rate of change of momentum is a force on the wall.

The absolute temperature of an ideal gas is directly proportional to the average translational kinetic energy of its molecules. So all gases at the same temperature have the same average kinetic energy per molecule, though lighter molecules move faster.

Rules to remember

Common mistake

Using °C in the gas laws or in (3/2)kT. Always change to kelvin first: 27 °C to 327 °C is 300 K to 600 K, so the volume doubles at constant pressure; it does not become 12 times as large.

Worked example

The average translational kinetic energy of the molecules of a gas is 8.28 × 10−21 J. Find the temperature of the gas. (k = 1.38 × 10−23 J K−1)

  1. Average kinetic energy = (3/2)kT, so T = (2 × energy) ÷ (3k).
  2. T = (2 × 8.28 × 10−21) ÷ (3 × 1.38 × 10−23) = (1.656 × 10−20) ÷ (4.14 × 10−23).
  3. T = 400 K, which is 127 °C.

Answer: T = 400 K.

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