Gay-Lussac's Law Calculator

Gay-Lussac's Law states that the absolute pressure of a fixed amount of gas is directly proportional to its absolute temperature, provided the volume remains constant. It is expressed as P₁/T₁ = P₂/T₂, where pressures and temperatures must be in absolute units (Pascals and Kelvin). This law is one of the three fundamental ideal gas laws alongside Boyle's Law and Charles's Law.

To apply Gay-Lussac's Law, use the formula P₁/T₁ = P₂/T₂. Rearrange to solve for the unknown: if solving for final pressure, use P₂ = P₁ × T₂ / T₁; if solving for final temperature, use T₂ = T₁ × P₂ / P₁. Always convert temperatures to Kelvin (K = °C + 273.15) and use absolute pressure values before calculating.

Gay-Lussac's Law requires absolute temperature because it describes a directly proportional relationship between pressure and temperature. Celsius and Fahrenheit scales have arbitrary zero points, so ratios between values are meaningless. Kelvin starts at absolute zero (the point of no thermal energy), making it the only scale where the direct proportionality holds true.

Gay-Lussac's Law is evident in many everyday scenarios. Pressure cookers build up pressure as temperature rises inside the sealed vessel. Car tyres and bicycle tyres increase in pressure on hot days. Aerosol cans warn against exposure to heat because rising temperature increases internal pressure, which can cause the can to burst.

Gay-Lussac's Law applies most accurately to ideal gases — theoretical gases where molecules have no volume and no intermolecular forces. Real gases approximate ideal behavior well at low pressures and high temperatures. At very high pressures or near the boiling point of the gas, deviations from Gay-Lussac's Law can be significant.

An isochoric process (also called an isovolumetric process) is one in which the volume of the gas remains constant throughout. Gay-Lussac's Law specifically describes gas behavior during isochoric processes. Rigid containers such as sealed metal tanks or pressure cookers are practical examples where gas undergoes isochoric transformations.

If a pressure cooker starts at atmospheric pressure (101,325 Pa) and room temperature (25°C = 298.15 K) and its pressure doubles to 202,650 Pa, you can solve for T₂: T₂ = T₁ × P₂ / P₁ = 298.15 × 2 = 596.3 K, which is approximately 323°C. This illustrates why pressure cookers are designed with safety valves.

Gay-Lussac's Law relates only pressure and temperature at constant volume (P₁/T₁ = P₂/T₂). The Combined Gas Law merges Boyle's Law, Charles's Law, and Gay-Lussac's Law into a single formula: (P₁V₁)/T₁ = (P₂V₂)/T₂, which accounts for changes in pressure, volume, and temperature simultaneously. Gay-Lussac's Law is essentially the Combined Gas Law with volume held constant.