The student will be able to use Boyle's Law to solve marine-related pressure and volume problems.
Many of the fishes in the Texas State Aquarium exhibits are collected by fishing with hook and line in the offshore waters of the Gulf of Mexico. Extreme care must be taken when the fishes are brought to the surface as many come from great depths. The atmospheric pressure at the surface is relatively constant and is a standard reference for pressure measurement, referred to as one atmosphere of pressure. However, that pressure increases by one atmosphere for each 33 feet of sea water. The pressure affects the gases in the fishes' bodies, decreasing the volume occupied by the gases with each increase in depth. Conversely, as a fish rises in the water column, the decreasing pressure causes the volume of the gases in the body, primarily the swim bladder, to increase. If the rise occurs too rapidly, tissue and organ damage will kill the fish.
The change in pressure and volume can be easily predicted using a basic law of physics. Boyle's Law states that the volume and the pressure of a gas are inversely related. If P1 = initial pressure, V1 = initial volume, P2 = new pressure, and V2 = new volume, then
P1V1 = P2V2
For example, if a fish at 66 feet (3atm) had a swim bladder that occupies 0.25 liters, you can determine the size of the swim bladder at the surface as follows:
P1 = 3 atm
V1 = 0.25 liters
P2 = 1 atm
P1V1 = P2V2
V2 = P1V1/P2
= (3 atm)(0.251)/(1 atm)
- A large red snapper hooked at 198 feet has a surface swim bladder size of .94 liters. How big was the swim bladder at the time it was hooked?
- A grouper had a swim bladder size of 0.15 liters when hooked at 99 feet. How big was the swim bladder at the surface?
- If a jewfish had a swim bladder size of 0.17 liters at the point it was hooked, and 1.02 liters at the surface,m how deep was the fish when it was hooked?
- A grey tiger fish hooked at 175 feet has a surface swim bladder size of 0.66 liters. How big was the swim bladder at the time it was hooked?
- An amberjack had a swim bladder size of 0.2 liters when hooked at 110 feet. How big was the swim bladder at the surface?
- A barracuda had a swim bladder size of 0.15 liters at the point it was hooked, and 1.1 liters at the surface, how deep was the fish when it was hooked?