Scuba Diver
August 23, 2009 
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If a scuba diver fills his lungs to full capacity of 5.0 L when 10 m below the surface, to what volume would h
If a scuba diver fills his lungs to full capacity of 5.0 L when 10 m below the surface, to what volume would his lungs expand if he quickly rose to the surface?
_____________L
Boyle's law: PV = const, then
PbVb = PsVs. Where Pb,Vb are 10m below, Ps, Vs is at the surface. Where Vb= 5.0L, Ps= 1atm, then,
Vs = Vb Pb/Ps,
The pressure change under water can be found using P = ρgh, where ρ is the density, and h is the depth.
P = 1000kg/m^3 * 9.81 m/s^2 * 10 m = 98100 Pa = 0.97 atm. (one atmosphere is about 1.01 *10^5 Pa). The pressure at 10m depth is then this amount, plus the atmospheric pressure.
So Pb = 1.97 atm. Then,
Vs = 5.0L * (1.97 atm/ 1 atm)
Vs = 9.9 L
The air in his lungs roughly doubles. Note that I used the density of pure water (1000kg/m^3), not the density of salt water (1027kg/m^3).
Scuba Diving With Dolphins
