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If a scuba diver fills his lungs to full capacity of 5.7 L when 8.0 m 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. Express your answer using two significant figures

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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