Expanded lungs?

Question

A diver rises quickly to the surface from a

5m depth. 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 1.03 x 10^3 kg/m3.

The answer is 1.5 , but I cannot get it. I think you use the equation P=P + (density)(h)(g)

Answer 1

You've got the right idea.  The density of sea water is about 1000 kg/m^3 and g is about 10 m/s^2, so density*g*h is about 50,000 Pa.  Atmospheric pressure is about 100,000 Pa, so in surfacing, the diver goes from 150 kPa to 100 kPa for a reduction in pressure by a factor of 2/3.  PV=nRT=some constant (since temperature is constant), so you want PV=P'V' where the ' indicates after surfacing and the regular variables are before surfacing.  The previous calculation showed that P'=2/3P, so  PV=2/3PV', or V'=3/2V=1.5V