The three individual gas laws describe how two state variables of a fixed amount of ideal gas are related when the third variable is constant. Boyle's law gives an inverse relationship, while Charles's law and the pressure law give direct relationships.
| Law | Constant condition | Relationship and equation |
|---|---|---|
| Boyle's law | Temperature is constant | Pressure is inversely proportional to volume: , so and . |
| Charles's law | Pressure is constant | Volume is directly proportional to absolute temperature: , so and . |
| Pressure law | Volume is constant | Pressure is directly proportional to absolute temperature: , so and . |
All three follow from the ideal gas law, . For a fixed amount of gas, (nR) is constant. Holding , , or constant then produces Boyle's law, Charles's law, or the pressure law respectively.
These laws assume the gas remains close to ideal behavior and that no gas enters or leaves the system. They can also be combined as , which is useful when pressure, volume, and temperature all change between two states.
For example, a gas at constant temperature has and . If it is compressed to , then
The pressure rises because molecules collide with the container walls more frequently in the smaller volume.
A common misconception is using degrees Celsius in Charles's law or the pressure law. Temperature must be absolute temperature in kelvin: . Pressure should also be absolute rather than gauge pressure.
This is SL and HL content in topic B.3. In a Calculate question, identify the fixed variable, convert temperatures to kelvin, select the correct relationship, substitute values, and show working. For graphs, Boyle's law gives a curved -against- graph but a straight -against- graph; Charles's and pressure-law graphs are straight lines through the origin when temperature is in kelvin.
