Gay-Lussac Law
At constant volume, pressure is proportional to temperature.
Formula
Variables
Example
Heated sealed can bursts
How it works
Gay-Lussac’s law says that if a gas is trapped in a container that cannot change volume, raising the gas temperature makes the pressure rise in the same ratio. This happens because warmer gas particles move faster, so they hit the container walls more often and with greater force. The temperatures must be in an absolute scale, so use kelvin rather than Celsius.
When to use it
Use this law for gas problems where the amount of gas and the volume stay fixed, such as a sealed rigid tank or a closed aerosol can being heated or cooled. It is also useful whenever you need to compare pressure changes caused only by temperature change.
Worked example, step by step
A sealed steel cylinder has a pressure of 200 kPa at 300 K. What is the pressure when the gas is heated to 450 K? Use Gay-Lussac’s law: P1/T1 = P2/T2 Substitute: 200/300 = P2/450 Cross-multiply: 200 × 450 = 300 × P2 P2 = 90,000 / 300 P2 = 300 kPa Final answer: the pressure increases to 300 kPa.
Common mistakes to avoid
- Using Celsius instead of kelvin
- Applying the law when the volume is changing
- Mixing up which values are the initial state and which are the final state
Did You Know?
Heating a sealed can raises its pressure fast, the reason spray cans warn against incineration.
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