How deep must an inverted drinking glass be pushed beneath the surface of water so that the volume of enclosed air is squeezed to half?
A)76 cm
B)10.3 m
C)14.7 m
D)20.6 m
E)29.4 m

Question

Quizplus · Accepted Answer

The depth required can be calculated using Boyle's Law, which states that the pressure of a gas times its volume is a constant for a given amount of gas at constant temperature (P1V1 = P2V2). At the surface, the pressure (P1) is 1 atmosphere and the volume (V1) is the initial volume of the air. To halve the volume (V2 = V1/2), the pressure (P2) must be doubled (P2 = 2P1). Since each 10 meters of water depth adds approximately 1 atmosphere of pressure, the glass must be pushed 10 meters below the surface to double the atmospheric pressure it experiences, thus halving the volume of the enclosed air.

How Deep Must an Inverted Drinking Glass Be Pushed Beneath