Fish contain a collapsible swim bladder containing air that they use to help them maintain buoyancy so they can swim at any level and not sink or float. If a swordfish has a fish bladder with a volume of \(32.7 \mathrm{~L}\) at sea level where the pressure is 755 torr and the temperature is \(28^{\circ} \mathrm{C}\), what will the volume of the swim bladder be if the swordfish dives under the water to catch some mackerel where the pressure is 2577 torr and the temperature is \(12^{\circ} \mathrm{C}\) ?

Gas law calculations are a fundamental component of understanding how gases behave under various environmental conditions. By applying mathematical relationships, these calculations help predict how a gas's volume, pressure, and temperature will change in response to its surroundings. The core concept revolves around the gas laws, which are a collection of scientific laws that describe the behavior of a gas in a closed system.
Temperature is a critical component in these calculations and must always be in Kelvin because the Kelvin scale sets zero as absolute zero, where all molecular motion stops. To convert Celsius to Kelvin, you add 273.15 to the Celsius temperature. Pressure conversion is also vital as it must be consistent throughout the calculations. Commonly, atmospheric pressure (atm) is used, and to convert torr to atmospheres, the conversion factor of 1 atm equals 760 torr is applied.
Understanding these conversions and how to apply them is crucial for accurately determining the behavior of gases. These calculations are useful in various fields, like meteorology, engineering, and even biology—as demonstrated in this exercise where a fish's swim bladder is studied.

The swim bladder is a unique organ found in many fish species, allowing them to control their buoyancy in the water. By adjusting the volume of gas, fish can ascend or descend in the water column without expending much energy. The swim bladder behaves according to the principles of gas laws, expanding, and contracting as pressure and temperature shift.
In the example of the swordfish, understanding how the swim bladder volume changes with depth (and consequently, pressure) and temperature is crucial for predicting the fish's buoyancy. High pressure at greater depths compresses the swim bladder, reducing its volume, while lower sea level pressure allows it to expand. Additionally, temperature changes can lead to variations in volume based on thermal expansion or contraction of gases. Oceanographers, biologists, and even fishermen can benefit from understanding these principles to better comprehend fish behavior and habitat preferences.

Pressure-temperature-volume relationships are at the heart of understanding how gases react to environmental changes. These relationships are described by the Combined Gas Law, which combines Charles's Law, Boyle's Law, and Gay-Lussac's Law into a single equation that shows how pressure, temperature, and volume are interrelated.
This law implies that if the amount of gas and the mass remain constant, as in the case of the swim bladder, the ratio of the initial and final states of pressure, volume, and temperature will remain equal. Therefore, if the temperature and pressure conditions change, the volume will also adjust to maintain the same ratio. These principles are essential for various applications, such as designing pressurized systems, understanding atmospheric phenomena, and even in medical practices where the behavior of respiratory gases is crucial. In the swordfish example, as pressure increases while the temperature decreases during the dive, the volume of the swim bladder shrinks, as predicted by the equation.