Gay-Lussac's Law Calculator
Gay-Lussac's Law describes how the pressure of a fixed amount of gas at constant volume changes in direct proportion to its absolute temperature. Enter any three of the four variables - initial pressure, initial temperature, final pressure, or final temperature - and this calculator solves for the missing one. Choose from six pressure units (Pa, kPa, atm, bar, mmHg, psi) and three temperature units (K, C, F). The step-by-step panel shows every conversion and arithmetic step so you can check your work.
Formula
Worked example
A sealed aerosol can contains gas at 101.325 kPa at 20 C (293.15 K). When heated to 50 C (323.15 K): P2 = P1 x T2 / T1 = 101.325 x 323.15 / 293.15 = 111.71 kPa. The pressure rose by about 10.3%, which is why aerosol cans warn against heating above 50 C.
What is Gay-Lussac's Law?
Gay-Lussac's Law (also called Amontons' Law) states that the pressure of a fixed amount of gas held at constant volume is directly proportional to its absolute temperature. In equation form: P1/T1 = P2/T2, where pressures can be in any consistent unit and temperatures must be in Kelvin (the absolute scale). The law was formulated in 1808 by French chemist Joseph Louis Gay-Lussac, building on earlier work by Guillaume Amontons. It is one of the simple gas laws that, together with Boyle's Law (pressure vs. volume) and Charles's Law (volume vs. temperature), form the Combined Gas Law and ultimately the Ideal Gas Law PV = nRT.
Why temperatures must be in Kelvin
Gay-Lussac's Law requires absolute temperature because the relationship P1/T1 = P2/T2 is only linear when zero on the temperature scale truly means zero molecular kinetic energy. The Celsius and Fahrenheit scales are offset from absolute zero (0 K = -273.15 C = -459.67 F), so using them directly gives wrong answers. Always convert Celsius to Kelvin by adding 273.15, or Fahrenheit to Kelvin using T(K) = (T(F) - 32) x 5/9 + 273.15. This calculator performs those conversions automatically before applying the formula.
Real-world applications
Gay-Lussac's Law explains many everyday phenomena. Tire pressure: a car tire inflated to 35 psi at 20 C will read about 38-40 psi after a long drive at 60 C because the air inside heats up and cannot expand. Aerosol cans: heating a sealed spray can raises internal pressure, which is why they carry warnings against temperatures above 50 C. Pressure cookers: the sealed vessel lets pressure rise with temperature, raising the boiling point of water above 100 C for faster cooking. Autoclave sterilizers: hospitals use the same principle to reach temperatures that kill microorganisms. Scuba tanks: a filled tank brought into the sun can reach pressures 10-15% above its rated cold fill.
Limitations and ideal gas assumptions
Gay-Lussac's Law assumes ideal gas behavior: molecules have no volume of their own and exert no intermolecular forces. Real gases deviate from this model at very high pressures (above roughly 10 atm) or at temperatures close to the gas's condensation point, where molecular interactions become significant. Under normal laboratory and engineering conditions - moderate temperatures and pressures well above the liquefaction point - the law provides accurate results. For more extreme conditions, use the van der Waals equation or other real-gas equations of state.
Common gas pressure reference values
| Scenario | Typical pressure | Temperature range |
|---|---|---|
| Standard atmosphere (sea level) | 101.325 kPa / 14.696 psi | 0-40 C |
| Car tire (cold, recommended) | 220-250 kPa / 32-36 psi | Ambient |
| Car tire (hot, after driving) | 240-280 kPa / 35-41 psi | 50-80 C |
| Pressure cooker | 120-200 kPa absolute | 100-120 C |
| Bicycle tire (road) | 700-1100 kPa / 100-160 psi | Ambient |
| Scuba tank (full) | ~20,000 kPa / ~3000 psi | Ambient |
| Aerosol can (room temp) | 270-450 kPa / 40-65 psi | 20-50 C |
| Earth atmosphere at 10 km altitude | ~26.5 kPa / 3.84 psi | -50 C |
Standard reference pressures for common scenarios where Gay-Lussac's Law applies.
Frequently asked questions
What does Gay-Lussac's Law state?
Gay-Lussac's Law states that the pressure of a fixed amount of gas in a constant-volume container is directly proportional to its absolute temperature (in Kelvin). If the temperature doubles, the pressure doubles; if the temperature halves, the pressure halves. The mathematical form is P1/T1 = P2/T2.
Why do you have to use Kelvin for temperature?
Because Gay-Lussac's Law is based on a direct proportionality: P is proportional to T. That proportionality only holds when T is measured from absolute zero, which is 0 K (-273.15 C). Using Celsius or Fahrenheit would give incorrect results because their zero points are arbitrary offsets, not true zero energy. The calculator converts your Celsius or Fahrenheit input to Kelvin automatically.
Why does tire pressure increase when driving?
Friction between the tire and the road generates heat, which raises the temperature of the air inside the tire. Because the tire volume is essentially constant, Gay-Lussac's Law applies: the higher temperature produces higher pressure. A tire inflated to 35 psi (241 kPa) at 20 C (293 K) will reach approximately 38.5 psi (265 kPa) at 60 C (333 K), an increase of about 10%. That is why tire manufacturers specify cold inflation pressures.
What is the difference between Gay-Lussac's Law and the Ideal Gas Law?
Gay-Lussac's Law is a special case that applies only when volume and the amount of gas are both fixed. The Ideal Gas Law (PV = nRT) is the complete relationship covering all four variables: pressure (P), volume (V), moles of gas (n), and temperature (T), with R being the universal gas constant. If you need to account for a changing volume or varying amounts of gas, use the Ideal Gas Law or the Combined Gas Law.
Can Gay-Lussac's Law be used for liquids or solids?
No. Gay-Lussac's Law describes ideal gas behavior. Liquids and solids are nearly incompressible and do not follow the same pressure-temperature relationship. For liquids, the temperature dependence of vapor pressure follows the Clausius-Clapeyron equation rather than a simple linear ratio.
How do I solve for temperature instead of pressure?
Rearrange the formula: T2 = T1 x P2 / P1. For example, if a gas at 300 K and 100 kPa is compressed to 150 kPa at constant volume, the new temperature is T2 = 300 x 150 / 100 = 450 K (177 C). In this calculator, select 'Final temperature (T2)' from the 'Solve for' dropdown and enter P1, P2, and T1.