# Gay-Lussac’s Law – Definition, Formula, Examples

Gay-Lussac’s law or Amonton’s law states that the absolute temperature and pressure of an ideal gas are directly proportional, under conditions of constant mass and volume. In other words, heating a gas in a sealed container causes its pressure to increase, while cooling a gas lowers its pressure. The reason this happens is that increasing temperature imparts thermal kinetic energy to gas molecules. As the temperature increases, molecules collide more often with the container walls. The increased collisions are seen as increased pressure.

The law is named for French chemist and physicist Joseph Gay-Lussac. Gay-Lussac formulated the law in 1802, but it was a formal statement of the relationship between temperature and pressure described by French physicist Guillaume Amonton in the late 1600’s.

Gay-Lussac’s law states the temperature and pressure of an ideal gas are directly proportional, assuming constant mass and volume.

### Gay-Lussac’s Law Formula

Here are the three common formulas for Gay-Lussac’s law:

P ∝ T
(P1/T1) = (P2/T2)
P1T2 = P2T1

P stands for pressure, while T is absolute temperature. Be sure to convert Fahrenheit and Celsius temperature to Kelvin when solving Gay-Lussac’s law problems.

A graph of either pressure versus temperature is a straight line, extending up and away from the origin. The straight line indicates a directly proportional relationship.

### Examples of Gay-Lussac’s Law in Everyday Life

Here are examples of Gay-Lussac’s law in everyday life:

• Tire pressure: Automobile tire pressure drops on a cold day and soars on a hot day. If you put too much air in your tires when they are cold, they could over-pressurize when they heat up. Similarly, if your tires read the proper pressure when they are hot, they will be underinflated when it’s cold.
• Pressure cooker: Applying heat to a pressure cooker increases the pressure inside the device. Increasing pressure raises the boiling point of water, shortening cooking times. Because the container is sealed, flavors aren’t lost to the air with steam.
• Aerosol can: The reason you shouldn’t store aerosol cans under hot conditions or dispose of them by burning is because heating the can increases the pressure of its contents, potentially causing the can to burst.
• Water heater: An electric water heater is a lot like a pressure cooker. A pressure-relief valve prevents steam from accumulating. If the valve malfunctions, heat drives up the steam pressure inside the heater, eventually bursting it.

### Gay-Lussac’s Law Example Problem

#### Example #1

An aerosol deodorant can has a pressure of 3.00 atm at 25 °C. What is the pressure inside the can at a temperature of 845 °C? This example illustrates why you shouldn’t incinerate aerosol cans.

First, convert the Celsius temperatures to the Kelvin scale.
T1 = 25°C = 298 K
T2 = 845 °C = 1118 K

Next, plug the numbers into Gay-Lussac’s law and solve for P2.

P1T2 = P2T1
(3.00 atm)(1118 K) = (P2)(298 K)
P2 = (3.00 atm)(1118 K)/(298 K)
P2 = 11.3 atm

#### Example #2

Heating a gas cylinder to 250 K raises its pressure to 2.0 atm. What was its initial temperature, assuming the gas started out at ambient pressure (1.0 atm)?

P1T2 = P2T1
(1.0 atm)(250 K) = (2.0 atm)(T1)
T1 = (1.0 atm)(250 K)/(2.0 atm)
T1 = 125 K

Note that doubling the absolute temperature of a gas doubles its pressure. Similarly, halving the absolute temperature halves the pressure.

### Other Gay-Lussac’s and Amonton’s Laws

Gay-Lussac stated that all gases have the same average thermal expansivity at constant temperature and pressure. In other words, gases behave predictably when heated. Sometimes this law is also called Gay-Lussac’s law.

Usually, “Amonton’s law” refers to Amonton’s law of friction, which states that the lateral friction between any two materials is directly proportional to the normal applied load, assuming a proportional constant (the friction coefficient).

### References

• Barnett, Martin K. (1941). “A brief history of thermometry”. Journal of Chemical Education, 18 (8): 358. doi:10.1021/ed018p358
• Castka, Joseph F.; Metcalfe, H. Clark; Davis, Raymond E.; Williams, John E. (2002). Modern Chemistry. Holt, Rinehart and Winston. ISBN 978-0-03-056537-3.
• Crosland, M. P. (1961). “The Origins of Gay-Lussac’s Law of Combining Volumes of Gases”. Annals of Science, 17 (1): 1. doi:10.1080/00033796100202521
• Gay-Lussac, J. L. (1809). “Mémoire sur la combinaison des substances gazeuses, les unes avec les autres” (Memoir on the combination of gaseous substances with each other). Mémoires de la Société d’Arcueil 2: 207–234.
• Tippens, Paul E. (2007). Physics (7th ed.). McGraw-Hill. 386–387.