Thermodynamics & Heat
Intermediate

Gay-Lussac's Law

Pressure is proportional to temperature at constant V.

Formula

P1T1=P2T2\frac{P_1}{T_1} = \frac{P_2}{T_2}

Variables

PPressure
TTemperature

How it works

Gay-Lussac's Law applies to a fixed amount of gas kept at constant volume: if the temperature increases, the pressure rises in direct proportion because gas molecules move faster and hit the container walls more forcefully and more often. The relationship works with absolute temperature, so values must be in kelvin rather than Celsius. It is one of the gas laws that follows from the ideal gas law when volume and amount of gas do not change.

When to use it

Use this law for sealed, rigid containers such as aerosol cans, pressure cookers, gas cylinders, or laboratory vessels where the volume stays constant. It is also useful in chemistry and physics problems asking how pressure changes when a gas is heated or cooled without changing its container size.

Worked example, step by step

A rigid steel tank contains gas at 150 kPa when the temperature is 290 K. The tank is heated until the gas reaches 435 K. Since volume is constant, use P1/T1 = P2/T2. Substitute: 150/290 = P2/435 Solve for P2: P2 = 150 × 435 / 290 P2 = 22500 / 290 P2 = 77.6? Wait, check the arithmetic carefully: 150 × 435 = 65250 65250 / 290 = 225 kPa Final answer: the new pressure is 225 kPa.

Common mistakes to avoid

  • Using Celsius instead of kelvin
  • Applying the law when the container volume changes
  • Cross-multiplying incorrectly or solving for the wrong pressure value

Did You Know?

Gay-Lussac's law is why an aerosol can warns against fire: heat raises the internal pressure until it bursts.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026