Scuba Diver's Balloon Volume Change During Dive

How does the volume of the balloon change as the scuba diver descends to a depth of 100 feet?

The volume of the balloon will decrease as the scuba diver descends to a depth of 100 feet. This is because the pressure at this depth is greater than at the surface, and according to Boyle's law, the volume and pressure of a gas are inversely proportional when temperature is constant.

What was the new volume of the balloon when the pressure at a depth of 100 feet was 4.0 atm?

The new volume of the balloon will be 2.50 liters.

Explanation:

Boyle's law states that the pressure and volume of a gas are inversely proportional when the temperature is constant. In this case, the pressure at a depth of 100 feet is 4.0 atm, which is four times greater than at the surface. As a result, the volume of the balloon will decrease to one-fourth of its original volume due to the increase in pressure.

Calculation:

To find the new volume, we can use the equation:

Where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. Rearranging the equation to find V2:

Plugging in the values, we get:

Solving for V2, we find that the new volume of the balloon is 2.50 liters.

Scuba diving involves encountering changes in pressure and volume of gases underwater, which can have significant effects on equipment like balloons used by divers. Understanding the principles of Boyle's law can help predict and explain such changes in volume as divers descend to different depths.

As the scuba diver descends to a depth of 100 feet, the increase in pressure causes the volume of the balloon to decrease. This is a direct application of Boyle's law, which describes the inverse relationship between the pressure and volume of a gas.

By utilizing the formula P1V1 = P2V2 and understanding the concept behind it, we can calculate the new volume of the balloon as the pressure changes at different depths. In this case, the new volume of the balloon is determined to be 2.50 liters when the pressure at a depth of 100 feet is 4.0 atm.

It is crucial for scuba divers to be aware of such changes in volume and pressure during dives to ensure the safety and functionality of their equipment. By applying scientific principles like Boyle's law, divers can better understand and manage the effects of pressure on gases at varying depths.