Gas laws

Physics · The particulate nature of matter. 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

An ideal gas is a model: a huge number of tiny molecules in random motion, with negligible volume, no forces between them except in collisions, and elastic collisions. Pressure comes from the molecules hitting the walls. Each collision changes a molecule's momentum, so it exerts a force on the wall.

For a fixed mass of gas, pressure, volume and kelvin temperature are linked. Change one and at least one of the others must change. The ideal gas equation covers every case, including a change in the amount of gas.

The internal energy of an ideal gas is only kinetic energy, so it depends only on the temperature and the amount of gas. Real gases behave ideally at low pressure and high temperature.

Rules to remember

Common mistake

Students use temperatures in °C in the gas laws. Always convert to kelvin first: doubling a temperature from 20 °C to 40 °C does not double the pressure or the volume.

Worked example

A flask of volume 2.0 × 10−3 m3 holds an ideal gas at a pressure of 1.5 × 105 Pa and a temperature of 300 K. How many molecules are in the flask? (kB = 1.38 × 10−23 J K−1)

  1. Use pV = NkBT, so N = pV ÷ (kBT).
  2. pV = 1.5 × 105 × 2.0 × 10−3 = 300 J.
  3. kBT = 1.38 × 10−23 × 300 = 4.14 × 10−21 J.
  4. N = 300 ÷ (4.14 × 10−21) = 7.2 × 1022.

Answer: About 7.2 × 1022 molecules.

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