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Pressure plays a crucial role in understanding how gases behave underwater. When dealing with deep-sea diving, it's important to calculate the pressure experienced at different depths. At a depth of 25 meters, the diver encounters pressure from the water and the atmosphere. Water pressure increases by roughly 0.1 atmospheres (atm) for every meter of water depth, as calculated by the formula: \( P = \rho \cdot g \cdot h \).

• \( \rho \) is the density of fresh water: 1000 kg/m³
• \( g \) is the acceleration due to gravity: 9.8 m/s²
• \( h \) is the depth: 25 m

The atmospheric pressure at sea level is approximately 1 atm. By summing the atmospheric pressure and the water column pressure, the total pressure at 25 meters is around 3.5 atm. Understanding this helps explain why gas bubbles, like nitrogen in the blood, can behave unpredictably when these pressures change as a diver ascends.

The behavior of gas bubbles under pressure changes can be explained using Boyle's Law, which states that the product of pressure and volume for a gas remains constant, as long as the temperature is stable. This is expressed as \( P_1 V_1 = P_2 V_2 \).In the diver's scenario, we know:

• Initial pressure \( P_1 \) is 3.5 atm
• Initial volume \( V_1 \) is 1 mm³
• Final pressure \( P_2 \) is 1 atm

To find the final volume \( V_2 \), rearrange the formula to get \( V_2 = \frac{P_1}{P_2} \cdot V_1 \). This gives us a final expanded volume of 3.5 mm³ upon reaching the surface. Such expansions can have dramatic effects, as gas bubbles grow significantly larger, potentially causing dangerous blockages in blood vessels.

Decompression sickness, commonly known as "the bends," occurs when a diver ascends too quickly. It's caused by the rapid expansion of gas bubbles, particularly nitrogen, in the bloodstream. At greater depths, the pressure forces more nitrogen to dissolve in the blood. As the diver ascends, the decrease in pressure allows the gas to expand. If the ascent is too abrupt, these expanding bubbles can grow too large and form blockages in small blood vessels, leading to symptoms that range from joint pain to paralysis or even death. To prevent this, divers should make gradual ascents and sometimes include decompression stops, allowing their bodies time to safely eliminate excess nitrogen. Educating divers about these preventive measures, as well as the underlying physics, is crucial for their safety.