Question

When you swim underwater, the pressure of the water pushes against your chest cavity and subsequently reduces the size of your lungs. For every 10 m below the water surface, the pressure exerted by the water adds 14.7 psi to atmospheric pressure so 10 m below the surface would have a total pressure of 29.4 psi. If a swimmer has a lung volume of 6 L at sea level (atmo- spheric pressure), what would the volume of he lungs be when she is at the bottom of a pool that is 5 m deep?

Answer 1

The volume of the lungs at 5m deep is 4L

Step-by-step explanation:

Hello!

We can solve this problem considering that the air inside de lungs behave as an ideal gas, and that the temperature is the same at sea leavel and 10 m below the surface, in this case:

P1 V1 = P2 V2 -- (1)

wher P and V stands for pressure and volume, and 1 and 2 for the intial (sea level) and final (5m below) states.

We know that:

P1 = 14.7 psi

V1 = 6 L

And if the pressure exerted by the water adds 14.7 psi to atmospheric pressure so 10 m below the surface, then at 5 m below it must add 14.7/2 psi, therefore:

P2 = (14.7/2) psi + atmospheric pressure = 7.35 psi + 14.7 psi

P2 = 22.05 psi

Solving equation (1) for V2:

V2 = V1 (P1/P2) = 6 L (14.7 psi / 22.05 psi ) = 6 *(2/3) = 4 L

The volume of the lungs at 5m deep is 4L