Gay-Lussac's Law Calculator
Solve P₁/T₁ = P₂/T₂ for any missing pressure or temperature at constant volume. Leave one field blank, enter the other three, and get an instant result with full step-by-step working.
Gay-Lussac's Law Solver
What Is Gay-Lussac's Law?
Gay-Lussac's Law is the mirror image of Charles' Law: instead of holding pressure fixed and letting volume respond to temperature, it holds volume fixed and lets pressure respond instead. Lock a gas inside a rigid, sealed container and heat it. The molecules move faster and strike the walls harder and more often, and because the walls cannot move outward, that extra force shows up entirely as increased pressure.
The relationship, P₁/T₁ = P₂/T₂, is a direct proportion just like Charles' Law, and it must also use absolute (Kelvin) temperature for the same reason. Graphed as pressure against temperature, it produces a straight line that would reach zero pressure at absolute zero.
Gay-Lussac's Law is the constant-volume case of the combined gas law. When volume also changes, use the full combined gas law calculator instead.
Pressure rises in a straight line with absolute temperature while volume is held fixed.
Real-World Examples of Gay-Lussac's Law
A sealed rigid container cannot expand, so rising temperature shows up entirely as rising pressure.
Aerosol cans carry explicit warnings not to expose them to heat or store them near flames. Because the can's steel shell barely flexes, any temperature rise converts directly into a pressure rise inside, and past a certain point the can can rupture or explode.
A pressure cooker also demonstrates Gay-Lussac's Law: its rigid, sealed body keeps the internal volume fixed while heat is applied, so pressure builds steadily, allowing water to boil at a higher temperature and cook food faster.
Engineers designing gas cylinders, propane tanks, and pressurized industrial vessels use Gay-Lussac's Law to calculate the maximum safe temperature a sealed container can reach before internal pressure exceeds its rated limit.
How the Calculator Works
Worked Example: Gay-Lussac's Law in Practice
Problem: A rigid gas cylinder reads 12.0 atm at 18°C. What pressure would it reach if left in direct sun and heated to 55°C?
A relatively modest 37°C temperature swing raises pressure by over 1.5 atm. Proportionally small compared to the aerosol-can example on this page, but still a meaningful safety margin to account for when storing pressurized cylinders. This is why compressed gas cylinders are rated well above their typical operating pressure and are kept away from direct heat sources.
Common Mistakes When Applying Gay-Lussac's Law
As with Charles' Law, the most frequent error is using Celsius or Fahrenheit directly in P₁/T₁ = P₂/T₂ instead of converting to Kelvin first. Because this is another direct proportion, an unconverted temperature produces a badly wrong pressure ratio. Always apply K = °C + 273.15 (or the Fahrenheit-to-Rankine equivalent) before substituting.
A second mistake is assuming a container is perfectly rigid when it actually has some flexibility. A plastic bottle or a balloon, for instance, will bulge slightly under rising internal pressure rather than staying at truly constant volume, introducing a small error if Gay-Lussac's Law is applied too strictly. For genuinely rigid containers like steel gas cylinders, the approximation is accurate enough to treat as exact.
A third pitfall is forgetting that Gay-Lussac's Law says nothing about volume. A problem that mentions any change in the container's size, even a small one, needs the combined gas law instead, since Gay-Lussac's Law only works for a perfectly sealed, unchanging volume.