Gay-Lussac's Law Calculator
This Gay-Lussac's Law calculator helps you analyze the relationship between gas pressure and temperature during an isochoric (constant-volume) process. Enter any three of the four parameters — initial pressure (p₁), initial temperature (T₁), final pressure (p₂), or final temperature (T₂) — and the calculator instantly computes the missing value.
Gay-Lussac's Law Definition
Gay-Lussac's Law (also known as the pressure law) describes the relationship between the pressure and temperature of a gas when the volume and amount of gas remain constant. The law states that the absolute pressure of a fixed amount of gas in a rigid container is directly proportional to its absolute temperature.
For Gay-Lussac's gas law to hold true, the container must be rigid so that the volume of the gas cannot change. In other words, Gay-Lussac's law describes the behavior of an ideal gas during an isochoric (constant-volume) process.
Gay-Lussac's Law Formula
The standard form of Gay-Lussac's law formula is:
p₁ / T₁ = p₂ / T₂
where:
- p₁ — initial (absolute) pressure of the gas
- T₁ — initial absolute temperature (in Kelvin)
- p₂ — final (absolute) pressure of the gas
- T₂ — final absolute temperature (in Kelvin)
This can also be written as:
p₁ / p₂ = T₁ / T₂
The ratio of initial and final pressures equals the ratio of initial and final absolute temperatures.
Important: Temperature must always be expressed in an absolute scale (Kelvin or Rankine) for Gay-Lussac's law to work correctly. The calculator automatically converts °C and °F to Kelvin for you.
Solving for Each Parameter
Using Gay-Lussac's Law, you can solve for any one of the four parameters if you know the other three:
- p₂ = p₁ × T₂ / T₁ — find the final pressure
- T₂ = p₂ × T₁ / p₁ — find the final temperature
- p₁ = p₂ × T₁ / T₂ — find the initial pressure
- T₁ = p₁ × T₂ / p₂ — find the initial temperature
Supported Units
Pressure Units
- kPa — Kilopascal (metric, default)
- Pa — Pascal (SI base unit)
- MPa — Megapascal
- atm — Atmosphere
- bar — Bar
- mmHg — Millimeter of mercury (Torr)
- psi — Pound per square inch (US customary / imperial)
Temperature Units
- K — Kelvin (absolute, metric)
- °C — Celsius (metric)
- °F — Fahrenheit (US customary / imperial)
- °R — Rankine (absolute, imperial)
Gay-Lussac's Law Examples
Example 1: Finding Final Pressure
A sealed steel tank contains gas at a pressure of 100 kPa and a temperature of 300 K. The tank is heated to 600 K. What is the final pressure?
Using p₂ = p₁ × T₂ / T₁:
p₂ = 100 × 600 / 300 = 200 kPa
Example 2: Finding Final Temperature (°F)
A car tire has a pressure of 32 psi at 68 °F (20 °C). After a long drive, the pressure rises to 36 psi. What is the tire temperature?
T₁ = 68 °F = 527.67 °R (absolute Rankine). T₂ = 36 × 527.67 / 32 ≈ 593.6 °R ≈ 134 °F
Example 3: Using atm and Celsius
A rigid container holds gas at 1 atm and 27 °C (300 K). It is cooled to −73 °C (200 K). What is the final pressure?
p₂ = 1 × 200 / 300 ≈ 0.667 atm
Gay-Lussac's Law in Real Life
- Car tires: Tire pressure increases as the tires heat up during driving — a direct application of Gay-Lussac's law.
- Pressure cookers: The sealed pot builds up pressure as the temperature inside rises.
- Aerosol cans: Warning labels say "do not incinerate" because increased temperature raises pressure and can cause the can to burst.
- Autoclave sterilizers: Medical and laboratory autoclaves use high temperature to generate high-pressure steam for sterilization.
- Fire extinguishers: Stored in cool environments because heat increases internal pressure.
- Hot air balloons: Heated air inside the balloon has higher pressure, which helps keep the volume constant while the balloon rises.
- Engine cylinders: Combustion rapidly raises temperature and pressure in a nearly constant-volume environment before the piston moves.
Frequently Asked Questions
What is Gay-Lussac's Law?
Gay-Lussac's Law states that the pressure of a fixed amount of gas in a rigid container is directly proportional to its absolute temperature: p / T = constant, or p₁ / T₁ = p₂ / T₂.
Who discovered Gay-Lussac's Law?
The law is named after French chemist and physicist Joseph Louis Gay-Lussac, who first published it in 1809, although Guillaume Amontons had observed the relationship earlier around 1702. It is sometimes called Amontons' Law.
Why must temperature be in Kelvin?
Gay-Lussac's law requires absolute temperature because pressure is proportional to the average kinetic energy of the gas molecules, which is zero at absolute zero (0 K). Using Celsius or Fahrenheit would produce incorrect results because these scales have arbitrary zero points.
What is an isochoric process?
An isochoric process (also called an isovolumetric process) is one in which the volume of the gas remains constant. Gay-Lussac's law applies specifically to isochoric processes.
How does Gay-Lussac's Law relate to other gas laws?
Gay-Lussac's Law is one of the three classical ideal gas laws: Boyle's Law (pressure–volume at constant temperature), Charles' Law (volume–temperature at constant pressure), and Gay-Lussac's Law (pressure–temperature at constant volume). Combined, they form the Combined Gas Law, and with Avogadro's Law, the Ideal Gas Law: pV = nRT.
What is the difference between metric and imperial pressure units?
Metric units include Pascal (Pa), kilopascal (kPa), and bar. The standard imperial unit for pressure is psi (pounds per square inch), commonly used for tire pressure and hydraulic systems in the United States. 1 psi ≈ 6.895 kPa.