What this calculator does
Gay-Lussac's Law describes what happens to the pressure of a fixed amount of gas held in a fixed volume as its temperature changes: pressure and absolute temperature rise and fall together. It is written as p1/T1 = p2/T2, with temperature always measured in kelvin, and applies whenever the container's volume cannot change, such as a sealed rigid vessel.
This calculator solves Gay-Lussac's Law for either the final pressure or the final temperature, given the initial state and one final value. It sits alongside two other classic gas laws: Boyle's Law, which holds temperature constant, and Charles' Law, which holds pressure constant. Gay-Lussac's Law is the constant-volume case.
The formula
Gay-Lussac's Law states that p1/T1 equals p2/T2 at constant volume, provided temperature is in kelvin (add 273.15 to a Celsius reading). Solving for a final pressure multiplies the initial pressure by the ratio of final to initial temperature; solving for a final temperature multiplies the initial temperature by the ratio of final to initial pressure.
| Term | Meaning |
|---|---|
| p1, p2 | Initial and final pressure of the gas. |
| T1, T2 | Initial and final temperature, in kelvin. |
| Constant volume | The condition Gay-Lussac's Law assumes: the container the gas sits in does not expand or contract. |
The inputs explained
| Field | What to enter |
|---|---|
| Initial pressure (p1) (kPa) | The starting pressure of the gas, before the temperature change. |
| Initial temperature (°C) | The starting temperature, entered in Celsius and converted to kelvin automatically. |
| Solve for | Choose whether you know the final temperature and want the final pressure, or the reverse. |
| Final temperature (used when solving for p2) (°C) | The final temperature, used only when solving for final pressure. |
| Final pressure (used when solving for T2) (kPa) | The final pressure, used only when solving for final temperature. |
When to use it
A sealed gas canister heating up
A rigid, sealed canister left in a hot environment cannot expand, so its internal pressure climbs in direct proportion to its absolute temperature.
Checking a pressure vessel rating
Working out the pressure a sealed vessel would reach at a given temperature helps confirm it stays within its rated limits before that temperature is ever reached in practice.
Comparing the three gas laws
Gay-Lussac's Law is the constant-volume counterpart to Boyle's Law (constant temperature) and Charles' Law (constant pressure), useful when a rigid container rules out any volume change.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Final pressure at a range of final temperatures
Starting at atmospheric pressure and 20°C, the pressure reached at a range of final temperatures.
| Final temperature | Final pressure |
|---|---|
| 20°C | 101.325 kPa |
| 40°C | 108.238 kPa |
| 60°C | 115.151 kPa |
| 80°C | 122.064 kPa |
| 100°C | 128.976 kPa |
| 150°C | 146.258 kPa |
Questions
What is Gay-Lussac's Law?
It states that for a fixed amount of gas held at constant volume, pressure divided by absolute temperature stays constant: p1/T1 = p2/T2. Raise the temperature and the pressure rises in step, and vice versa.
How is Gay-Lussac's Law different from Boyle's and Charles' Laws?
Boyle's Law holds temperature constant and relates pressure to volume. Charles' Law holds pressure constant and relates volume to temperature. Gay-Lussac's Law holds volume constant and relates pressure to temperature.
Why must temperature be in kelvin?
The law depends on temperature being measured from absolute zero, the point at which gas pressure would theoretically fall to nothing. Celsius has an arbitrary zero point, so it has to be converted to kelvin (add 273.15) before the ratio means anything.
Does this apply to a container that can expand?
No. Gay-Lussac's Law only holds if the volume genuinely stays fixed. A container that can expand or a gas that is free to escape needs a different approach, such as the combined or ideal gas law.
For the constant-temperature case, see the Boyle's Law calculator. For the constant-pressure case, see the Charles' Law calculator.