Question

A scuba diver fills her lungs to capacity (6.0 L) when 10.0 m below the surface of the water and begins to ascend to the surface. Assume the density of the water in which she is swimming is 1000 kg/{eq}m^3 {/eq} and use g = 10 m/{eq}s^2 {/eq}
A. Assuming the temperature of the air in her lungs is constant, to what volume must her lungs expand when she reaches the surface of the water?
B. What effect would the warming of the air in her lungs have on the volume needed when she surfaces?
C. Assuming the temperature of the air in her lungs is constant, what effect does her ascent have on the vrms of the air molecules in her lungs?

Answer 1

The lungs of a scuba diver should expand to a volume of 12 L, the volume of air in her lungs will grow with an increase in surface air temperature, and the rms speed of the air velocity in her lungs won't change.

It is stated that water has a density of 1000 kg/m3. The diver's 6L lung capacity allows her to descend 10m under the sea. We may suppose that the water's temperature is constant.

A. The pressure P₁ at the surface of water is 100000 Pa.

So, the pressure at the depth of 10m in water will be given by,

P₂ = 1000x10x10 + P₁

P₂ = 100000 + P₁

P₂ = 200000 Pa

Now, we can write,

P₁V₁ = P₂V₂

Putting values,

6 x 200000 = V₂ x 100000

V₂ = 12L.

Her lungs should thus enlarge to 12L.

B. Because of the continuous pressure at the surface, the air warming will further increase the amount of air in the lungs.

C. The Vrms are provided by,

Vrms = √(3RT/M)

The Vrms won't change if the temperature stays constant since the air's mass will remain constant.

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