Calculate pressure changes with temperature at constant volume using Gay-Lussac's Law (P₁/T₁ = P₂/T₂) for ideal gas behavior.
Gay-Lussac's Law (also called Amontons' Law) states that the pressure of an ideal gas is directly proportional to its absolute temperature when the volume is held constant: P₁/T₁ = P₂/T₂. Heat a sealed container and the pressure rises; cool it and the pressure drops.
This fundamental gas law explains everyday phenomena — why tire pressure increases on a hot day, why aerosol cans warn against heating, and why pressure cookers reach higher temperatures. It is one of the three classical gas laws (along with Boyle's and Charles') that combine into the ideal gas law PV = nRT.
This Gay-Lussac's Law Calculator lets you find the final pressure after a temperature change, the required temperature for a desired pressure, or verify the initial conditions. It supports multiple pressure units (kPa, atm, psi, bar) and temperature scales (°C, K, °F). Preset buttons cover tire inflation, pressure cooker operation, engine combustion, and cryogenic scenarios. A reference table lists thermodynamic properties for common gases.
Use this calculator when you need to estimate how pressure changes in a sealed gas system as temperature rises or falls at constant volume. It is particularly useful for quick safety and operating checks on tires, tanks, cans, and other closed gas volumes. It also helps explain why a moderate temperature change can matter in a confined gas system.
Gay-Lussac's Law: P₁ / T₁ = P₂ / T₂ (constant volume) P₂ = P₁ × (T₂ / T₁) T₂ = T₁ × (P₂ / P₁) All temperatures must be in Kelvin (absolute).
Result: P₂ = 220.45 kPa
Heating a sealed container from 20°C to 50°C raises the pressure from 200 kPa to 220.45 kPa — a 10.2% increase.
Gay-Lussac's law only applies cleanly when the amount of gas and the container volume stay constant. If gas escapes, the vessel flexes, or the gas undergoes phase change, the simple proportionality between pressure and temperature no longer tells the full story.
This is why tire pressures climb after driving, why sealed cans can rupture when overheated, and why pressure vessels are rated with thermal conditions in mind. The law is simple, but it has very practical safety implications whenever a gas is trapped in a fixed volume.
The biggest error is using Celsius or Fahrenheit directly in the ratio instead of absolute temperature. The second is forgetting that gauge pressure and absolute pressure are not the same quantity in thermodynamic calculations.
It assumes an ideal gas at constant volume. Real gases deviate at very high pressures or low temperatures.
The law is a direct proportionality (P ∝ T), which only holds with absolute temperature. Using °C or °F would give wrong results.
The amount of gas (moles) must remain constant. If gas leaks out, the law does not apply directly.
It is a special case of PV = nRT with volume and amount of gas held constant, so pressure varies directly with absolute temperature. If either the gas amount or the container volume changes, the simple two-temperature ratio is no longer enough by itself.
At absolute zero (0 K), an ideal gas would have zero pressure. In practice, all gases liquefy before reaching 0 K.
No. Charles' Law holds pressure constant and relates volume to temperature. Gay-Lussac's holds volume constant and relates pressure to temperature.