Gay-Lussac's Law
At constant volume, pressure of a gas is proportional to absolute temperature.
Formula
Variables
Example
A sealed spray can heated in a fire builds pressure and can burst.
How it works
Gay-Lussac's Law says that if a gas is trapped in a rigid container so its volume cannot change, raising its absolute temperature makes the pressure rise in the same ratio. This happens because hotter gas particles move faster, so they collide with the container walls more often and with greater force. The law uses Kelvin temperature, not Celsius, because pressure is directly proportional to absolute thermal energy.
When to use it
Use this law for gases in sealed, rigid containers such as pressure tanks, aerosol cans, or closed metal vessels when the volume stays fixed. It is also useful in chemistry and physics problems where temperature and pressure are compared for the same gas sample.
Worked example, step by step
A gas in a fixed container has a pressure of 120 kPa at 300 K. If it is heated to 450 K, what is the new pressure? Given: P1 = 120 kPa, T1 = 300 K, T2 = 450 K Use Gay-Lussac's Law: P1/T1 = P2/T2 Substitute: 120/300 = P2/450 Cross-multiply: 120 × 450 = 300 × P2 Solve: P2 = (120 × 450) / 300 P2 = 180 kPa Final answer: the new pressure is 180 kPa.
Common mistakes to avoid
- Using Celsius instead of Kelvin for temperature
- Using the law when the volume is not constant
- Mixing up which values are initial and final when solving for the unknown
Did You Know?
A sealed can heated in a fire can explode because pressure rises with temperature.
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