Respuesta :
Answer:
The number of air molecules in her lung compared with the number she had in a full breadth at the surface is;
C. Twice as many
Explanation:
The depth at which the scuba diver fills her lungs with air, d = 10 m
Pressure of fluid = Density, ρ × Acceleration due to gravity, 'g' × Depth, 'd'
Where;
ρ = 970 kg/m³
g ≈ 9.81 m/s²
∴ The pressure of the water of the 10 m water column = 970 kg/m³ × 9.81 m/s² × 10 m = 95,157 Pa
The atmospheric pressure, P₁ = 101,325 Pa
The total pressure at the 10 m depth = The atmospheric pressure + The pressure of the water of the 10 m water column
∴ The total pressure at the 10 m depth, P₂ = 95,157 Pa + 101,325 Pa = 196,482 Pa
By the combined gas law, we have;
P₁·V₁/n₁ = P₂·V₂/n₂
Where;
P₁ = The atmospheric pressure
P₂ = The pressure at 10 m depth
V₁ = V₂ = The volume of her lungs
n₁ = The number of air molecules at the surface that fills her lungs
n₂ = The number of air molecules that fills her lungs at the 10 m depth
Therefore, we have;
P₂/P₁ = n₂/n₁ × V₁/V₂
From V₁ = V₂, we have;
P₂/P₁ = n₂/n₁ × V₁/V₁ = n₂/n₁ × 1
∴ P₂/P₁ = n₂/n₁
P₂/P₁ = 196,482/101,325 ≈ 2
∴ P₂/P₁ = n₂/n₁ ≈ 2
n₂ ≈ 2 × n₁
The number of air molecules that fills her lungs at the 10 m depth, n₂ is approximately 2 times (twice) as many as the number of air molecules at the surface that fills her lungs, n₁
Therefore the correct option is twice as many molecules as she had in a full breath at the surface is required to fill her lungs at the 10 m water depth.
This question involves the concepts of pressure, the equation of state, and the number of molecules.
The number of molecules in hr breathe are "C. twice as many" as compared to the number of molecules in her lungs when she had a full breath at the surface.
According to the equation of state:
[tex]\frac{P_1V_1}{n_1}=\frac{P_2V_2}{n_2}[/tex]
where,
n₁ = no. of molecules in lungs at surface
n₂ = no. of molecules in lungs at depth
P₁ = Pressure at surface = Atmospheric Pressure = 101325 Pa
P₂ = Pressure at depth = 101325 Pa + ρgh
P₂ = 101325 Pa + (1000 kg/m³)(9.81 m/s²)(10 m) = 199425 Pa
V₁ = V₂ = V = Volume of lungs
Therefore,
[tex]\frac{(101325\ Pa)V}{n_1}=\frac{(199425\ Pa)V}{n_2}\\\\[/tex]
n₂ = 2 n₁
Learn more about the equation of state also known as general gas law here:
https://brainly.com/question/14906240?referrer=searchResults
