About Gay-Lussac's Law
Gay-Lussac's Law describes how the pressure of a gas changes with temperature when volume and the amount of gas are held constant. Formulated by French chemist Joseph Louis Gay-Lussac in the early 1800s — the same pressure-temperature proportionality had also been observed earlier by Guillaume Amontons, so it is sometimes called Amontons's Law — it states that pressure and absolute temperature are directly proportional: P₁/T₁ = P₂/T₂. This calculator uses your initial pressure and temperature, plus a target final temperature, to find the resulting final pressure.
Understanding the formula
Gay-Lussac's Law falls out of the ideal gas law, PV = nRT. If volume (V) and the number of moles (n) do not change, then P/T = nR/V is a constant, so P₁/T₁ must equal P₂/T₂. Rearranging for the unknown gives the final pressure directly: P₂ = P₁ × (T₂ / T₁). Because the ratio only means something physical when temperature is measured from absolute zero, every temperature is converted to Kelvin before the calculation runs (K = °C + 273.15, or K = (°F − 32) × 5/9 + 273.15).
Working with temperature units
Enter your initial and final temperatures in Kelvin, Celsius, or Fahrenheit — the calculator converts whichever you pick into Kelvin internally, since Celsius and Fahrenheit both have zero points that are not physically meaningful for a gas's pressure. Double-check that a "below zero" entry is still a valid physical state: 0 K (-273.15°C, -459.67°F) is absolute zero, and no real or ideal gas can exist below it, so the calculator rejects any temperature that converts to 0 K or less.
Knowing the limits
Gay-Lussac's Law assumes an ideal gas at constant volume in a sealed, rigid container and a fixed amount of gas — it does not apply if the container can expand or contract, or if gas is added or released during the process (use the combined gas law, P₁V₁/T₁ = P₂V₂/T₂, instead). It is a good approximation for common gases like air or propane at everyday temperatures and pressures — think of a pressure cooker building pressure as it heats, or an aerosol can becoming dangerously pressurized if left in a hot car. Near a gas's condensation point or at very high pressure, real-gas effects make the ideal relationship less accurate.