Calculating Pressure and Volume Increase on Rising from Depth d

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A diver rising from depth d experiences a change in lung volume due to pressure differences. The pressure in the lungs must equal the external pressure as the diver ascends, leading to the equation P1V1 = P2V2. The pressure at depth is calculated as P2 = P1 + pgd, allowing for the determination of lung expansion. The derived formula indicates that V1 can be expressed as V1 = V2Patm / (1 - pgd). The discussion seeks validation of this calculation, emphasizing the importance of understanding pressure and volume relationships in diving scenarios.
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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?
 
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