What is Gay-Lussac's law?

Gay-Lussac's law states that at constant volume and fixed amount of gas, pressure is directly proportional to absolute temperature: P₁/T₁ = P₂/T₂.

Who discovered Gay-Lussac's law?

Joseph Louis Gay-Lussac formulated the law around 1808 based on the earlier work of Guillaume Amontons (1700s).

What is an isochoric process?

An isochoric (constant volume) process is one in which the gas's volume cannot change. Gay-Lussac's law describes the pressure-temperature behaviour during such a process.

Why must temperature be in Kelvin?

Because the law relates absolute temperature to absolute pressure. Using Celsius or Fahrenheit would give a wrong proportional relationship.

How is Gay-Lussac's law applied in everyday life?

Pressure cookers (heating builds pressure at fixed volume), car tyres in summer (warm tyres show higher pressure), and aerosol cans warning against fire (heating raises internal pressure and risks rupture) all illustrate the law.

Is Gay-Lussac's law accurate for real gases?

Yes, closely, for air and other common gases at moderate pressure and temperature in a rigid container. Deviations grow at very high pressure, where the Van der Waals equation gives a more accurate answer.

Gay-Lussac's Law Calculator

Solve P₁/T₁ = P₂/T₂, the pressure-temperature law at constant volume.

Gay-Lussac's Law Calculator

P₁/T₁ = P₂/T₂ (constant V). Enter 3 values.

P₁

T₁

P₂ (solving for this)

T₂

P₂

1.333 atm

P₂ = P₁T₂/T₁ = 1.333 atm

Gay-Lussac's Law: Pressure at Constant Volume

Gay-Lussac's law captures what happens when a gas is heated or cooled inside a rigid, sealed container. With volume fixed and the amount of gas constant, pressure is directly proportional to absolute temperature: P₁/T₁ = P₂/T₂. Heat the container and the pressure rises in exact proportion to the Kelvin temperature.

This is the third of the three simple gas laws, complementing Boyle's law (P-V at constant T) and Charles' law (V-T at constant P).

Isochoric Process

A constant-volume process is called isochoric (or isovolumetric). All heat added to a gas in an isochoric process goes into raising internal energy and pressure. No work is done because the gas cannot expand. See the dedicated isochoric process calculator for heat and energy quantities.

Worked Example 1: Pressure Cooker

A pressure cooker is sealed at 100 kPa and 295 K. The contents heat to 393 K (120 °C). Final pressure: P₂ = P₁ × T₂/T₁ = 100 × 393/295 = 133 kPa. The cooker reaches about 1.3 atm internally, raising the boiling point of water and speeding cooking.

Worked Example 2: Car Tyre on a Hot Day

A tyre measures 220 kPa at 285 K (about 12 °C). After sun exposure the tyre temperature rises to 320 K (47 °C). New pressure: P₂ = 220 × 320/285 = 247 kPa, a noticeable jump.

Gay-Lussac's Law Formula and Symbols

Symbol	Meaning	Unit
P₁	Initial pressure	Pa, kPa, atm, mmHg, psi
T₁	Initial temperature	Kelvin (K)
P₂	Final pressure	Pa, kPa, atm, mmHg, psi
T₂	Final temperature	Kelvin (K)

The two rearrangements of P₁/T₁ = P₂/T₂ are P₂ = P₁ × T₂/T₁ and T₂ = T₁ × P₂/P₁. As with every gas law on this site, temperature must be in Kelvin before you substitute it. Convert Celsius by adding 273.15; convert Fahrenheit with K = (°F − 32) × 5/9 + 273.15.

Worked Example 3: Aerosol Can Warning Label

An aerosol can is sealed at 250 kPa and 293 K (20 °C). Warning labels tell users not to store cans above 50 °C (323 K). What pressure would the can reach at that temperature? P₂ = P₁ × T₂/T₁ = 250 × 323/293 = 276 kPa. That is only an 11% rise for a 30-degree change, which is why the same labels warn far more urgently against open flame: a can left near a fire can reach several hundred degrees, and Gay-Lussac's law predicts the internal pressure at those temperatures easily exceeds what the thin metal shell can hold.

How It Relates to Charles' Law and Combined Gas Law

Gay-Lussac's law is the constant-volume sibling of Charles' law (constant pressure) and Boyle's law (constant temperature). When more than one variable changes at once, use the combined gas law, or the isochoric process calculator if you also need the heat transferred.