Volume Change of Nitrogen Bubbles in Divers: The Bends Phenomenon

[flip290]

Homework Statement

If deep-sea divers rise to the surface too quickly, nitrogen bubbles in their blood can expand and prove fatal. This phenomenon is known as the bends. If a scuba diver rises quickly from a depth of 23m in Lake Michigan (which is fresh water), what will be the volume at the surface of an N₂ bubble that occupied 1.0 mm³ in his blood at the lower depth?(Assume that the pressure difference is due only to the changing water pressure, not to any temperature difference, an assumption that is reasonable, since we are warm-blooded creatures.)
V= mm³

Homework Equations

p₁V₁=p₂V₂
P=(density)(g)(h)+p
density of water= 1000 kg/m³

The Attempt at a Solution

First, I found the pressure at 23m to be 3.23 atm
Then, I assumed that at the surface the pressure would be 1atm.
Finally using the pv=pv equation i found the V= 3.2mm³. However, this was incorrect. Am I doing this completely wrong?

 

[Chestermiller]

I got the same answer as you. Who says 3.22 mm³ is incorrect? Check and see whether surface tension effect should be included.