Pressure vs. Temperature
Gay-Lussac's Law states that the pressure of a fixed mass of gas is directly proportional to its absolute temperature, provided that the volume of the gas remains completely constant.
When a gas is heated in a rigid, sealed container, the molecules gain kinetic energy. Since the container cannot expand (constant volume), the rapidly moving molecules smash into the walls of the container much more frequently and with much greater force. This manifests macroscopically as a severe increase in internal pressure.
The Danger of Sealed Containers
This law explains several highly dangerous everyday phenomena:
- Aerosol Cans: This is why every can of hairspray, spray paint, or deodorant has a stern warning: "Do not store near heat or incinerate." If an aerosol can is tossed into a fire, the temperature skyrockets, and because the metal can is a fixed volume, the internal pressure will eventually breach the tensile strength of the steel, causing a massive explosion.
- Firearms: When gunpowder burns inside the chamber of a gun, it rapidly creates a massive amount of incredibly hot gas. Because the chamber volume is momentarily fixed, the temperature spike creates an immense pressure spike that violently forces the bullet down the barrel.
- Pressure Cookers: By trapping steam inside a rigid pot, the pressure increases. This high pressure artificially raises the boiling point of water above $100^\circ\text{C}$, allowing food to cook significantly faster without drying out.
The Formula
Example Calculation
A rigid steel scuba tank is left in the trunk of a car on a blazing hot summer day. In the cool morning ($300 , \text{K}$), its pressure was $20,000,000 , \text{Pa}$ (roughly $3000 , \text{PSI}$). In the afternoon trunk, it heats up to $330 , \text{K}$.
- Divide Initial Pressure by Initial Temp ($P_1 / T_1$): $20,000,000 / 300 = 66,666.66...$
- Multiply by New Temp ($T_2$): $66,666.66... \cdot 330 = 22,000,000 , \text{Pa}$.
The pressure has spiked to $22 , \text{MPa}$ ($3200 , \text{PSI}$). SCUBA tanks have burst disks designed to safely vent the gas before this pressure increase causes the entire cylinder to detonate.