Gas Laws and Diving

Hello! Welcome back to your course on the theory of technical scuba diving.

Introduction

In our last lesson, we focused on the physiological effects of breathing different gas mixtures, using Equivalent Air Depth (EAD) and Equivalent Narcotic Depth (END) to manage decompression and narcosis. Now, we shift our focus from how gases affect the body to the fundamental physical laws that govern their behavior.

Understanding these principles is not just an academic exercise; it is the foundation for comprehending nearly every piece of equipment and every procedure in diving. From the pressure drop in your cylinders as they cool to the life-threatening risk of lung overexpansion, the thermodynamics of gases are always at play.

Lesson 5: Gas Expansion and Compression

Learning Outcome: By the end of this lesson, you will be able to explain the thermodynamic principles governing gas expansion and compression in diving scenarios.

1. The Pressure-Volume Relationship: Boyle's Law

The most fundamental relationship in diving physics is the one between pressure and volume. As you descend, the surrounding water pressure increases, compressing the gas in any flexible space. As you ascend, the pressure decreases, and the gas expands. This is described by Boyle's Law.

To start, let's watch a short video that uses a vivid underwater example to illustrate this core concept.

As the video explains, Boyle's Law states that for a fixed amount of gas at a constant temperature, its volume is inversely proportional to the pressure. Double the pressure, and you halve the volume.

Mathematically, this is expressed as:
$P_1{V}_1=P_2{V}_2$
Where:

• $P_1$ and $V_1$ are the initial pressure and volume.
• $P_2$ and $V_2$ are the final pressure and volume.

This principle has profound implications for divers. To explore these in more detail, please read the following section from the NOAA Diving Manual.

The key takeaway is that the greatest volume change occurs near the surface. Going from 33 feet (2 ATA) to the surface (1 ATA) causes the gas in your lungs to double in volume. This is why a lung-overexpansion injury can occur from an uncontrolled ascent from even very shallow depths.

2. The Influence of Temperature: Charles' and Gay-Lussac's Laws

Pressure and volume are not the only factors; temperature also plays a critical role. Two laws describe its effects:

1. Charles' Law: At a constant pressure, the volume of a gas is directly proportional to its absolute temperature. (e.g., a lift bag's volume changes slightly as it moves through water of different temperatures).
2. Gay-Lussac's Law: At a constant volume, the pressure of a gas is directly proportional to its absolute temperature. (e.g., the pressure inside a rigid scuba cylinder).

This second law is particularly important for divers.

The most common diving application of Gay-Lussac's law relates to scuba cylinders. When a cylinder is filled, the compression of the gas heats it up. After the fill, as the cylinder cools to the ambient temperature, the pressure inside drops. This is why a reputable dive shop will cool the cylinders in a water bath during filling to ensure you get a true, full "cold fill." Conversely, a cylinder left in the sun on a boat deck will show a significant pressure increase.

For a formal definition and the formulas, please review the following resource.

3. The General Gas Law: A Unified View

Boyle's, Charles', and Gay-Lussac's laws can be combined into a single, powerful equation known as the General Gas Law. This law allows you to calculate the final state of a gas when pressure, volume, and temperature all change simultaneously.

The formula is:
$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

This equation is the cornerstone of gas physics in diving. Let's see how it's applied in a realistic scenario.

4. Practical Application: Regulator Freezing

One of the most critical applications of these thermodynamic principles is understanding why a scuba regulator can freeze, even in water that is above freezing temperature.

• When you inhale, the first stage of your regulator must drop the very high pressure from your cylinder (e.g., 200 bar / 3000 psi) down to an intermediate pressure (e.g., ~10 bar / 140 psi).
• According to the gas laws, this massive and rapid drop in pressure (decompression/expansion) causes a correspondingly massive and rapid drop in the gas temperature. This is known as the Joule-Thomson effect.
• The temperature of the gas flowing through the regulator can plummet well below freezing. If there is any moisture in the air from the cylinder or if the regulator is in cold water, ice can form on the internal components, causing it to malfunction—often by "free-flowing" (continuously delivering gas).

This is a primary reason why technical divers use environmentally sealed regulators specifically designed for cold-water environments.

5. Knowledge Check

Let's test your understanding of these laws. Answer the following multiple-choice questions based on the principles we've discussed.

Conclusion

In this lesson, you have explored the fundamental thermodynamic principles that dictate how breathing gases behave under the changing conditions of a dive.

Key Takeaways:

• Boyle's Law ($P_1{V}_1=P_2{V}_2$) describes the inverse relationship between pressure and volume. It is the reason for lung overexpansion risks, buoyancy changes, and the need to equalize air spaces.
• Charles' and Gay-Lussac's Laws describe the direct relationship between temperature and volume/pressure. They explain why cylinder pressures change with temperature.
• The General Gas Law ($P_1{V}_1/T_1=P_2{V}_2/T_2$) combines these principles into a single formula to predict gas behavior when all three variables change.
• These laws have direct, practical consequences, from the danger of regulator freezing to the importance of getting a "cold fill" for your cylinders.

Next Lesson Preview:
Now that we understand how gases behave in bulk, we will zoom in on another of their physical properties: viscosity. In the next lesson, we will analyze the physiological implications of breathing gas viscosity at extreme depths, a critical factor that increases the work of breathing and can limit diver performance.