If A Scuba Diver Fills His Lungs To Full Capacity Of 5.3 L When 30 M Below The Surface, To What Volume Would H?
If a scuba diver fills his lungs to full capacity of 5.3 L when 30 m below the surface, to what volume would his lungs expand if he quickly rose to the surface?
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The pressure increases linearly as the diver descends, with the difference given by:
ΔP = ρgy, where ρ ~= 10^3 kg/m^3 is the density of the water, g ~= 9.8 m/s^2 is the acceleration of gravity and y is the *depth* (positive axis pointing down) in meters, to give the pressure difference in Pa. If V0 is the volume of air at the surface (in m^3 for SI units), P0 = 1 atm is the surface air pressure (you convert to Pa), and V = 5.3 L = 5.3 * 10^-3 m^3 is the volume at a depth y = 30 m, then you have all you need to solve for V0
P0*V0 = P*V = (P0 + ΔP)V
V0 = V * (1 + ΔP/P0)
V0 = V * (1 + ρgy/P0)
Plug numbers and compute. You should probably convert m^3 back to L for your answer.
For a sanity check, I know from scuba lessons that 33 feet of fresh water is about 1 atmosphere. That’s about 10m per atm, so at 30m the pressure should be 3 atm greater than the 1atm at the surface, so your computed result should be close to 4*5.3 L ~= 21 L