Gay-Lussac's Law
Gay-Lussac's Law states that for a fixed amount of an ideal gas at constant volume, the pressure of the gas is directly proportional to its absolute (Kelvin) temperature — when temperature doubles (in Kelvin), pressure doubles. This isochoric (constant volume) relationship arises because higher temperatures cause gas molecules to collide with the container walls more frequently and with greater force. It explains why sealed aerosol cans or vehicle tyres can burst if overheated, and why pressure cookers build up pressure as the internal temperature rises above 100 °C.
Key Formula
P₁/T₁ = P₂/T₂ (constant n and V)
LaTeX: \frac{P_1}{T_1} = \frac{P_2}{T_2} \quad (\text{at constant } n, V)
| Symbol | Meaning | Unit |
|---|---|---|
| P₁ | Initial absolute pressure | Pa |
| T₁ | Initial absolute temperature | K |
| P₂ | Final absolute pressure | Pa |
| T₂ | Final absolute temperature | K |
Worked Example
Problem
A sealed gas cylinder has a pressure of 300 kPa at 27 °C. If the cylinder is placed in a fire and the temperature rises to 327 °C, what is the new pressure? (Assume constant volume.)
Solution
Step 1: Convert to Kelvin: T₁ = 27 + 273 = 300 K; T₂ = 327 + 273 = 600 K. Step 2: Apply Gay-Lussac's Law: P₂ = P₁ × T₂ / T₁. P₂ = 300 × 600 / 300 = 300 × 2 = 600 kPa.
Answer
P₂ = 600 kPa (pressure doubled as temperature in Kelvin doubled)
Gay-Lussac's Law Data — Gas at Constant Volume
| Temperature (°C) | Temperature (K) | Pressure (kPa) | P/T (kPa K⁻¹) |
|---|---|---|---|
| 27 | 300 | 100 | 0.333 |
| 127 | 400 | 133 | 0.333 |
| 227 | 500 | 167 | 0.333 |
| 327 | 600 | 200 | 0.333 |
| 427 | 700 | 233 | 0.333 |
Interactive Tools
PhET Gas Properties
Heat gas in a rigid container and observe pressure increasing at constant volume.
Open ToolDesmos Gay-Lussac's Law Graph
Plot P vs T (Kelvin) to confirm the direct proportionality at constant volume.
Open ToolKhan Academy: Gay-Lussac's Law
Explanation, examples, and practice problems on the pressure-temperature gas law.
Open Tool
Wikimedia Commons, CC BY-SA
Related Terms
Ideal Gas Law
The Ideal Gas Law is an equation of state for a hypothetical ideal gas, combining the empirical gas laws of Boyle, Charles, and Gay-Lussac into a single relationship between the pressure, volume, amount, and absolute temperature of a gas. It assumes gas molecules have negligible volume and no intermolecular forces, making it an excellent approximation for real gases at low pressures and high temperatures. It is foundational to thermodynamics, chemistry, and engineering, used in everything from weather balloon calculations to industrial gas storage and the analysis of respiratory physiology.
Boyle's Law
Boyle's Law states that for a fixed amount of an ideal gas at constant temperature, the pressure of the gas is inversely proportional to its volume — when volume doubles, pressure halves, and vice versa. Mathematically, the product PV remains constant. This relationship arises because compressing a gas into a smaller volume increases the frequency of molecular collisions with the container walls, thereby raising pressure. It is applied in everyday contexts from tyre pumps and syringes to scuba diving depth calculations and the design of pneumatic systems.
Charles's Law
Charles's Law states that for a fixed amount of an ideal gas at constant pressure, the volume of the gas is directly proportional to its absolute (Kelvin) temperature — when temperature doubles (in Kelvin), volume doubles. This is an isobaric (constant pressure) process, and the ratio V/T remains constant. The law explains why a balloon expands when warmed, why hot air rises in atmospheric convection, and why gas-filled containers must be stored away from heat sources to prevent rupture.
Named after the French chemist and physicist Joseph Louis Gay-Lussac (1778–1850), who published this pressure-temperature relationship in 1809. Gay-Lussac was a prolific experimentalist who also investigated the law of combining gas volumes and made ascents in hydrogen balloons to study the atmosphere.