Calculating Pressure and Volume Increase on Rising from Depth d

[dimpledur]

Homework Statement

A diver rises quickly to the surface from a depth d. If she did not exhale the gas from her lungs before rising, by what factor would her lungs expand? Assume the temperature to be constant and the pressure in the lungs to match the pressure outside the diver’s body. The density of seawater is ρ. Express your answer in terms of d, ρ, g, and Patm (atmospheric pressure).

Homework Equations

P1V1=P2V2

P2=P1 +pgd

The Attempt at a Solution

P2 (Patm) is a distance d below P1. SO,

P1V1=P2V2
Patm = P1 +pgd
P1 = Patm - pgd
(Patm - pgd)V1=PatmV2
V1 = V2Patm / (1-pgd)

is that right?

 

[dimpledur]

No one can tell?