At what depth does a sealed balloon filled with air that has a volume of 6 cubic inches expand to 12 cubic inches?

At what depth does a sealed balloon filled with air that has a volume of 6 cubic inches expand to 12 cubic inches?

• A. 33 feet
• B. 20 feet
• C. 50 feet
• D. 99 feet

Answer: (A)

The expansion of a sealed balloon filled with air is a direct result of the principles of gas laws, particularly Boyle's Law, which states that the volume of a gas is inversely proportional to the pressure exerted on it, assuming the temperature remains constant. As you descend underwater, the pressure increases due to the weight of the water above you. In the scenario provided, a balloon initially has a volume of 6 cubic inches and expands to 12 cubic inches. This indicates that the balloon's volume doubles, which means that the pressure surrounding the balloon must halve for that change to occur. To determine at what depth this happens, we need to calculate how much pressure the balloon experiences underwater. The pressure increases by approximately one atmosphere (atm) for every 33 feet of seawater: 1 atm at the surface, 2 atm at 33 feet, 3 atm at 66 feet, and so on. If the pressure on the balloon is halved, it is inversely related, meaning you would need to be at a depth where the total pressure equals the surface pressure divided by two. At 33 feet, the total pressure is 2 atm (1 atm from the air above plus 1 atm from the water). Thus

The expansion of a sealed balloon filled with air is a direct result of the principles of gas laws, particularly Boyle's Law, which states that the volume of a gas is inversely proportional to the pressure exerted on it, assuming the temperature remains constant. As you descend underwater, the pressure increases due to the weight of the water above you.

In the scenario provided, a balloon initially has a volume of 6 cubic inches and expands to 12 cubic inches. This indicates that the balloon's volume doubles, which means that the pressure surrounding the balloon must halve for that change to occur.

To determine at what depth this happens, we need to calculate how much pressure the balloon experiences underwater. The pressure increases by approximately one atmosphere (atm) for every 33 feet of seawater: 1 atm at the surface, 2 atm at 33 feet, 3 atm at 66 feet, and so on. If the pressure on the balloon is halved, it is inversely related, meaning you would need to be at a depth where the total pressure equals the surface pressure divided by two.

At 33 feet, the total pressure is 2 atm (1 atm from the air above plus 1 atm from the water). Thus