A spherical air bubble originating from a scuba diver at a depth of 15 m has a diameter of 0.8 cm.What will the bubble's diameter be when it reaches the surface? (Assume constant temperature. )

Question

Quizplus · Accepted Answer

This question can be solved using Boyle's Law, which states that the volume of a gas is inversely proportional to the pressure it experiences. As the air bubble rises to the surface, the pressure exerted on it decreases while the volume of the bubble increases.

The pressure at the surface is approximately 1 atm or 101.3 kPa. At a depth of 15 m, the pressure is about 2.5 atm or 253.8 kPa.

Using the formula:

P1V1 = P2V2

where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

We can rearrange the formula to solve for V2:

V2 = (P1/P2) x V1

Plugging in the values:

V2 = (253.8 kPa / 101.3 kPa) x (4/3 x pi x (0.4 cm)^3)

V2 = 1.1 cm

Therefore, the bubble's diameter when it reaches the surface will be approximately 1.1 cm, which is answer choice C.

A Spherical Air Bubble Originating from a Scuba Diver at a Depth