Question

A scuba diver that ascends to the surface too quickly can experience decompression sickness, which occurs when nitrogen that dissolves in the blood under high pressure, forms bubbles as the pressure decreases during the ascent. Therefore an understanding of the gas laws is an important part of a scuba diver\'s training. In fresh water the pressure increases by 1 atm every 34 ft below the water surface a diver descends. If a diver ascends quickly to the surface from a depth of 68 ft without exhaling, by what factor will the volume of the diver\'s lungs change upon arrival at the surface? Assume the atmospheric pressure at the surface of the water is 1 atm.

Answer 1

The factor that the volume of the diver\'s lungs will change upon arrival at the surface is V2/V1 = 3/1.

Step-by-step explanation:

The pressure at 68 ft below the surface will be 1 atm original pressure + 1 atm/34 ft x 68 ft = 2 atm = 3 atm

This way, when the diver reaches 34 ft. the pressure is 2 atm

Assuming a constant temperature, and dealing with Boyle's Law where

P1V1 = P2V2

The pressure goes from 3 atm (P1) to 1 atm (P2), the volume (V2) has to become 3x the volume that it was at 3 atm.

Than, (3 atm)* (V1) = (1 atm) * (V2)

V2/V1 = 3/1 will be the factor the volume of the diver\'s lungs change upon arrival at the surface