If a scuba diver fills his lungs to full capacity of 5.5LL when 8.2mm below the surface, to what volume would his lungs expand if he quickly rose to the surface? Assume he dives in the sea, thus the water is salt.

Answer 1

Assume diver is 8.2 m below surface (and not 8.2mm), and at the surface, P=101.3 kPa.

Pressure below surface
=ρgh
=1000 kg/m² * 9.8 * 8.2 + 101.3
= 80.36+101.3 kPa
= 181.66 kPa

Assuming temperature below water and at the surface are identical, use Boyles law:
P1V1=P2V2
where
P1=101.3 kPa
V1=?
P2=181.66 kPa
V2=5.5 L
Solve for V1 to get
V1=P2V2/P1
=181.66*5.5/101.3
= 9.863 L
= 9.9 L approx.