What is the volume of a flexible air-filled container at the surface if it measures 10 cu ft at a depth of 100 feet of sea water?

To determine the volume of a flexible air-filled container at the surface when it measures 10 cubic feet at a depth of 100 feet of seawater, we must consider the effects of pressure on the volume of gases as described by Boyle's Law.

Boyle's Law states that, at a constant temperature, the pressure and volume of a gas are inversely proportional. As you descend underwater, the pressure increases due to the weight of the water above you. At a depth of 100 feet, the pressure is significantly higher than at the surface, leading to a decrease in the volume of the air-filled container.

At 100 feet in seawater, the pressure is approximately 4 atmospheres (1 atmosphere for the surface and about 3 additional atmospheres due to the water column above). According to Boyle's Law, as the pressure increases, the volume decreases:

[ P_1 \times V_1 = P_2 \times V_2 ]

Where:

• P1 is the pressure at the surface (1 atmosphere),

• V1 is the volume at the surface (what we're trying to find),

• P2 is the pressure at 100 feet of seawater (approximately 4 atmospheres),

• V2