A spherical air bubble originating from a scuba diver at a depth of 30.0 m has a diameter of 1.0 cm.What will the bubble's diameter be when it reaches the surface? (Assume constant temperature. )
A) 0.7 cm
B) 1.0 cm
C) 1.4 cm
D) 1.6 cm

Question

Quizplus · Accepted Answer

According to Boyle's Law, the volume of a gas is inversely proportional to the pressure. As the bubble rises, pressure decreases, causing the volume to increase. Since volume is proportional to the cube of the diameter, the diameter increases by the cube root of the pressure ratio. At 30 m, pressure is 4 atm (1 atm surface + 3 atm water), and at the surface, it's 1 atm. The diameter increases by a factor of (4/1)^(1/3) ≈ 1.587, so the new diameter is approximately 1.6 cm.

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