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If deep-sea divers rise to the surface too quickly, nitrogen bubbles in their blood can expand and prove fatal. This phenomenon is known as the bends. If a scuba diver rises quickly from a depth of 25.0 m in Lake Michigan (which is fresh water), what will be the volume at the surface of an N2 bubble that occupied 1.00 mm3 in his blood at the lower depth?

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MechEngineer

Answer:

3.42 cubic mm

Explanation:

Let density of fresh water be [tex]\rho_w = 1000 kg/m^3[/tex]

And atmospheric pressure at the water surface be [tex]P_a = 101325 Pa[/tex]

Let g = 9.8 m/s2. The pressure at the dept of h = 25 m is

[tex]P = P_a + \rho_wgh = 101325 + 1000*9.8*25 = 346325 Pa[/tex]

Using ideal gas law and assume constant temperature, we have the following equation to calculate the volume at the water surface [tex]V_a[/tex], knowing that the volume at the lower depth V = 1 mm3:

[tex]P_aV_a = PV[/tex]

[tex]V_a = PV/P_a = 346325*1/101325 = 3.42 mm^3[/tex]

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