A spherical air bubble originating from a scuba diver at a depth of 18.0 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)1.7 cm

Question

Quizplus · Accepted Answer

The pressure at a depth of 18.0m is 2.8 atm. According to Boyle's law, at a constant temperature, pressure and volume have an inverse relationship. So, as the bubble rises to the surface, the pressure decreases and the volume increases. Therefore, the bubble's diameter will increase. The ratio of the initial volume to the final volume is given by:
(initial diameter)^3 / (final diameter)^3 = (initial pressure) / (final pressure)
(1.0 cm)^3 / (final diameter)^3 = 2.8 atm / 1 atm
final diameter = (1.0 cm) / (2.8)^(1/3) = 1.4 cm (approx.)

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