Pressure & volume
Boyle's Law
Boyle's law: at constant temperature, the pressure and volume of a fixed quantity of gas are inversely proportional (P₁V₁ = P₂V₂). On a breath-hold dive the gas in your lungs, mask, and air spaces is essentially a closed system — ambient pressure rises on descent so those volumes shrink, and they expand again as pressure falls on ascent.
Demo A
Volume vs. pressure
P₁V₁ = P₂V₂
State 1 · Surface
100% surface volume
State 2 · 0 m
100% of surface volume
The formula
Double the absolute pressure and the gas volume halves, if temperature and the amount of gas stay constant. In seawater, ambient pressure rises by about 1 bar for every 10 meters, so at 10 m (2 bar absolute) compressible lung gas is roughly 50% of surface volume; at 20 m (3 bar) about 33%; at 30 m (4 bar) about 25%; at 60 m (7 bar) about 14%. The demo uses this ideal curve. In real tissue, blood shifts into the chest and residual volume (RV) sets a floor — the lungs cannot empty completely — so measured lung volume stops following the pure Boyle line at depth. That is thoracic squeeze territory, not a failure of the law but a limit of anatomy.
Fixed gas on a breath-hold
What stays constant is the number of gas molecules you took in on your last breath — not the volume. As you descend, rising water pressure compresses the same gas into a smaller space; the gas is denser but the quantity is unchanged. On ascent the process reverses: pressure drops, volume grows back toward what you inhaled at the surface. Boyle's law describes that mechanical compression and re-expansion. It does not, by itself, explain oxygen consumption, CO₂ rise, or blackout — those are separate physiology (Dalton, Bohr, metabolism).
Equalization connection
Any air space connected to the surface only through a narrow path behaves the same way. Middle-ear volume shrinks on descent; equalizing opens the Eustachian tubes and pushes a small volume of air in to match rising ambient pressure. Mask air compresses too — most freedivers add a little air from the lungs into the mask on the way down. Sinuses with blocked drainage cannot equalize and become a Boyle problem (squeeze). Ears, mask, and lungs all follow P₁V₁ = P₂V₂; the difference is whether you can actively add gas to the space.
Descent · compression and squeeze
Working depth is often limited by how far gas volume can fall before the chest wall and diaphragm resist further compression. Below that point, effort increases sharply — the feeling of thoracic squeeze. Shallow, relaxed dives stay on the comfortable part of the curve; deep dives push toward RV and blood shift. The ghost outline in the demo shows surface volume for reference: at depth you are living in the compressed fraction, not losing gas to the water.
Ascent · re-expansion
Falling ambient pressure re-expands lung gas toward the volume you took at the surface. That re-expansion is normal Boyle behaviour on a single breath. Ascent barotrauma risk rises when starting volume was pushed above a normal inhale — glossopharyngeal packing adds extra gas that must re-expand on the way up — or when lung tissue is already compromised. A standard surface breath re-expanding to surface volume is expected, not pathological.