A spherical air bubble originating from a scuba diver at a depth of 14.0 m has a diameter of 0.8 cm.What will the bubble's diameter be when it reaches the surface? (Assume constant temperature. )
A)1.9 cm
B)1.2 cm
C)1.1 cm
D)0.9 cm
E)1.7 cm

Question

A spherical air bubble originating from a scuba diver at a depth of 14.0 m has a diameter of 0.8 cm.What will the bubble's diameter be when it reaches the surface? (Assume constant temperature. )
A)1.9 cm
B)1.2 cm
C)1.1 cm
D)0.9 cm
E)​1.7 cm

Quizplus · Accepted Answer

The pressure at a depth of 14.0 m is (14.0 m) * (9.81 m/s^2) * (1000 kg/m^3) = 137,340 Pa. Assuming constant temperature and using the ideal gas law, the pressure of the air inside the bubble must also be 137,340 Pa.

When the bubble reaches the surface, the pressure will decrease to atmospheric pressure, which is approximately 101,325 Pa. Using the ideal gas law again, the new volume of the air inside the bubble can be calculated as V = (nRT)/P, where n, R, and T are constants. Since the temperature is constant, the new volume is proportional to 1/P, so V2/V1 = P1/P2. Plugging in the numbers gives:

V2/V1 = 137,340 Pa / 101,325 Pa = 1.356

Therefore, the new diameter of the bubble will be 1.356 times its original diameter:

d2/d1 = (V2/V1)^(1/3) = 1.122

d2 = (1.122)(0.8 cm) = 0.8976 cm, which is closest to choice C) 1.1 cm.

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