🪲 Gay-Lussac's Law Calculator

Gay-Lussac's Law, formulated by the French chemist Joseph Louis Gay-Lussac in 1809, describes the direct proportionality between the pressure and absolute temperature of a fixed amount of gas at constant volume. The formula is P₁ / T₁ = P₂ / T₂, where temperature must be in Kelvin. When a tire's pressure increases on a hot day, or a pressure cooker builds up steam pressure as it heats, Gay-Lussac's Law explains the physics.

This calculator is useful for chemistry students, automotive mechanics, industrial safety engineers, and anyone working with sealed gas containers. Enter any three of the four values—initial pressure (P₁), initial temperature (T₁), final pressure (P₂), and final temperature (T₂)—and get the fourth instantly. Temperature must be in Kelvin (K = °C + 273.15).

The calculator applies P₁ / T₁ = P₂ / T₂. If you know P₁, T₁, and P₂, it solves for T₂ = (P₂ × T₁) / P₁. If you know P₁, T₁, and T₂, it finds P₂ = (P₁ × T₂) / T₁.

The table below illustrates how the pressure of a gas at 1 atm and 273 K changes with temperature in a sealed container:

Pressure rises linearly with temperature—this is why aerosol cans carry 'Do not incinerate' warnings, and why tire pressure fluctuates between cold mornings and hot afternoons.

1. Convert all temperatures to Kelvin (K = °C + 273.15).
2. Enter any three of P₁, T₁, P₂, and T₂ (T values in Kelvin).
3. Leave the fourth field blank—that is what will be calculated.
4. Click the Calculate button.
5. Review the result and verify it makes physical sense (higher T → higher P).

Why does tire pressure change with temperature?

A car tire is essentially a fixed-volume container. When the air inside heats up (from driving friction or hot roads), the molecules move faster and hit the tire walls harder, raising the pressure proportionally—exactly as Gay-Lussac's Law predicts. A 10 °C increase raises tire pressure by about 1 psi.

Must temperature be in Kelvin?

Yes. Gay-Lussac's Law uses direct proportionality (P ∝ T), which is only valid with absolute temperature. Celsius and Fahrenheit have arbitrary zero points, so their ratios would give wrong results. Use K = °C + 273.15.

What happens to pressure at absolute zero?

Gay-Lussac's Law predicts that pressure reaches zero at 0 K (−273.15 °C). In reality, all gases condense into liquids or solids long before this temperature, so the law no longer applies. Absolute zero is the theoretical limit where molecular motion stops.

Can I use this for pressure cooker calculations?

Yes, approximately. A sealed pressure cooker has a roughly constant volume. Heating water inside generates steam, raising both temperature and pressure. However, the presence of liquid water and steam complicates the pure gas law—real pressure cooker behavior also depends on vapor pressure.

Why are aerosol cans labeled 'Do not incinerate'?

An aerosol can is a sealed container with fixed volume. If you heat it, the gas pressure inside rises proportionally with temperature (Gay-Lussac's Law). At high enough temperatures, the pressure exceeds the can's burst strength and it explodes.

Does this work at very high pressures?

Gay-Lussac's Law is exact for ideal gases. Real gases deviate at extreme pressures where intermolecular forces and molecular volume become significant. For most practical scenarios (tires, pressure cookers, weather), the deviation is negligible.

Always convert temperature to Kelvin before using Gay-Lussac's Law. K = °C + 273.15, or K = (°F − 32) × 5/9 + 273.15. This law assumes constant volume and a fixed amount of gas. If volume changes (e.g. a flexible container), use the combined gas law instead. For automotive tire pressure, remember that a typical tire at 32 psi cold (say 20 °C = 293 K) will read roughly 35–36 psi after highway driving heats it to 50 °C (323 K). Pressure cookers exploit Gay-Lussac's Law: sealing water in a fixed volume and heating it to 120 °C raises the internal pressure to about 2 atm, cooking food faster.