# Gay-Lussac's law

Gay-Lussac's law states that the pressure of a given amount of gas varies directly with the absolute temperature of the gas, when the volume is kept constant (isochoric process).

In diving, we refer to the context of an isochoric process shown here as Gay-Lussac's law. In physics, this relationship is referred to as the Amontons's law. The Gay-Lussac's law describes there an isobaric process, i. e. the change in gas volume depending on the temperature at a constant pressure. However, this is only of very little relevance in diving.

## Basic knowledge for Open Water Diver* (OWD*)

You can observe the gas law by putting a empty, closed plastic bottle from a normal heated room into the freezer: The bottle will contract. The temperature of the trapped air inside the bottle drops. According to Gay-Lussac's law, the pressure in the bottle is reduced and it is compressed by the higher ambient pressure.

The same thing happens with your scuba gear: If you measure the pressure of a warm diving cylinder (e. g. after filling or if it was in the sun for a while), then the pressure is unusual high. As soon as you go into the water with it, the air inside the cylinder cools down and the pressure drops down.

Therefore, never leave your scuba set in the blazing sun. Be aware that you have less air available than you think if you go into the water with a warm diving cylinder. Although the pressure decrease during cooling can be calculated, for practical issues the hand test is sufficient: Put your hand on the cylinder. If it is warm, then you can subtract about 20 bar from the measured pressure.

## Knowledge for Experienced Diver** (ED**)

To calculate the cooling effect you need to use the Kelvin temperature scale. The temperature scale starts with zero (also known as absolute zero) at about -273°C, at which temperature each molecular movement comes to a standstill. A temperature of 0°C corresponds to 273 K.

The pressure $p$ after cooling calculates as:

$p_\text{cold} = \frac{p_\text{warm} \cdot T_\text{cold}}{T_\text{warm}}$

Example: Cylinder temperature 40°C, cylinder pressure 240 bar, water temperature 10°C

$p_\text{cold} = \frac{240\ \text{bar} \cdot (10 + 273)\ \text{K}}{(40 + 273)\ \text{K}} = 217\ \text{bar}$

The pressure change upon heating of the gas can be calculated analogously to the above equation:

$p_\text{warm} = \frac{p_\text{cold} \cdot T_\text{warm}}{T_\text{cold}}$

## Knowledge for experts (DM***)

The Gay-Lussac's law is a special case of the basic equation for ideal gases. Since particle number and volume remain constant in a closed container, the following can be applied:

$\frac{p_\text{warm}}{T_\text{warm}} = \frac{p_\text{cold}}{T_\text{cold}}$

Using Gay-Lussac's law, one could also calculate the pressure increase in the respiratory gas when it reaches the lungs and has been heated to 37°C body temperature there. However, the result has no practical relevance, since one would additionally have to consider the adiabatic cooling and the Joule-Thomson effect when relaxing the gas at the regulator.