To calculate the pressure in the body we will use the definition of the hydrostatic pressure for which the pressure of a body at a certain distance submerged in a liquid is defined. After calculating this relationship we will apply the equations of the relationship between the volume and the pressure to calculate the volume in state 2,
[tex]P = P_{atm} + \rho gh[/tex]
Here,
[tex]\rho[/tex]= Density of the Fluid (Water)
g = Acceleration due to gravity
h = Height
[tex]P = P_{atm} + 10^3*9.8*8[/tex]
[tex]P = 1.01*10^{5} +10^3*9.8*8[/tex]
[tex]P = 179400Pa[/tex]
Applying the equations of relationship between volume and pressure we have
[tex]P_1V_1 = P_2 V_2[/tex]
[tex]179400*5.7 = 101000*V_2[/tex]
[tex]V_2 = 10.12L[/tex]
Therefore the volume that would his lungs expand if he quickly rose to the surface is 10.12L
