By what factor would a scuba diver’s lungs expand if she

Solution 87P

Here we have to find out by what factor would a scuba diver’s lungs expand if she ascended rapidly to the surface from a depth of 125 ft without inhaling or exhaling and if an expansion factor greater than 1.5 causes lung rupture, how far could she safely ascend from 125 ft without breathing.

Step 1

Given :

Density of seawater = 1.04 g/mL

Density of Hg = 13.5 g/mL

Depth = 125 ft

Expansion factor greater than 1.5 may causes lung rupture.

In order to find out the factor by which a diver’s lungs would expand, we have to find out the factor by which P changes from 125 ft to the surface by applying Boyle’s law.

It is known that 1 ft = 12 in, thus we can write the conversion factor,  

Pressure of water can be calculated as,

P (H2O) = 125 ft

= 3.81 104 mm H2O

Now we will calculate the pressure of Hg,

= = =

hHg = 2935.11 mm Hg

Pressure of Hg =  2935.11 mm Hg = 3.861 atm

Total pressure Ptotal = 1 atm + 3.861 atm = 4.861 atm

Now the volume change of the diver’s lungs  can be calculated by using Boyle’s law as follows,

P1V1 = P2V2

=

= = 4.861 atm