Calculating Pressure and Volume Increase on Rising from Depth d

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SUMMARY

The discussion focuses on calculating the expansion factor of a diver's lungs when ascending from a depth d without exhaling. The key equations utilized are the ideal gas law (P1V1 = P2V2) and the pressure relationship (P2 = P1 + pgd). The derived formula for lung volume expansion is V1 = V2Patm / (1 - pgd), where Patm represents atmospheric pressure, ρ is the density of seawater, g is the acceleration due to gravity, and d is the depth. The solution is confirmed to be correct based on the provided equations.

PREREQUISITES
  • Understanding of the ideal gas law (P1V1 = P2V2)
  • Knowledge of hydrostatic pressure principles (P2 = P1 + pgd)
  • Familiarity with basic physics concepts such as pressure, volume, and density
  • Ability to manipulate algebraic equations for problem-solving
NEXT STEPS
  • Study the implications of Boyle's Law in gas behavior under varying pressure conditions
  • Research the effects of rapid ascent on human physiology, particularly in diving
  • Explore the relationship between pressure, volume, and temperature in gases
  • Learn about the specific effects of seawater density on buoyancy and pressure calculations
USEFUL FOR

This discussion is beneficial for physics students, diving instructors, medical professionals dealing with decompression sickness, and anyone interested in the physiological effects of pressure changes during diving.

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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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