Joseph Gay-Lussac, a French scientist, is often credited with the discovery of the pressure-temperature law in the early 1800s even though Guillaume Amontons, another French scientist had conducted a similar experiment earlier on with the same conclusion. Gay-Lussac’s experimental apparatus involves immersing a gas-filled, fixed-volume bulb-like copper container in a temperature controlled water bath. The container is connected to a pressure gauge, which measures the pressure of the gas in the container at various temperatures (see diagram below).

Both Gay-Lussac and Amontons found that the relationship between the pressure of a gas and its temperature in Celsius is linear at constant volume.

where *m* is the gradient of the function and *c* is the intercept the function makes with the vertical axis.

Furthermore, the function extrapolates to -273.15^{ o}C at zero pressure regardless of the gas investigated (see graph above). Similar to the way a Celsius-based expression is derived from Jacques Charles’ experimental data, the Celsius-based formula for Gay-Lussac’s experiments is:

where *p _{0 }*is the pressure of the gas at zero degrees Celsius and .

By changing the units of the horizontal axis from Celsius to Kevin (see diagram above), the relationship between pressure and temperature becomes directly proportional:

where *k _{3}* is the proportionality constant.

Eq11 is known as the ** Gay-Lussac’s law** (or

*Amontons’ law*), which states:

**The pressure of a given mass of gas is directly proportional to its absolute temperature (K) at constant volume**

Note that eq10 is also called the *Gay-Lussac’s law* (or *Amontons’ law*) with *T* in Celsius. Since *p _{1}* =

*k*

_{3}*T*and

_{1}*p*=

_{2}*k*

_{3}*T*,

_{2}*Gay-Lussac’s law*can also be expressed as

Gay-Lussac also experimented on other properties of gases and discovered the ** law of combining volumes**, which states:

**Volumes of gases that react with one another are in the ratios of small whole numbers at a given pressure and temperature.**

For example, two volumes of hydrogen gas react with one volume of oxygen gas to form two volumes of water: