Respuesta :
Answer:
ΔP = 0.497 10⁵ Pa
Explanation:
All materials are elastic, so they deform for the pressures applied, in bulk module is the deformation spreads for a given pressure, it is defined by
B = - P /(ΔV/V)
Where the negative sign is for the module to be positive, P is the pressure and ΔV/V is the unit volume reduction
Let's apply that equation to our case, let's look at the volumes of the bubbles
In the water
r₁ = 2.9 mm = 2.9 10⁻³ m
V = 4/3 π R3
V₁ = 4/3 π (2.9 10⁻³)³
V₁ = 102.2 10⁻⁹ m³
On the surface
r₂ = 3.8mm = 3.8 10⁻³m
V₂ = 4/3 π (3.8 10⁻³)³
V₂ = 229.8 10⁻⁹ m³
Δv = V₁-V₂
ΔV = (102.2 - 229.8) 10⁻⁹ m³
ΔV = -127.6 10⁻⁹ m³
Let's calculate the pressure
B = - P / (ΔV / V)
P = - B ΔV / V
P = - 1.2 10⁵ (-127.6 10⁻⁹/102.2 10⁻⁹)
P = 1,498 10⁵ Pa
The pressure difference between this depth and the surface is the difference with the atmospheric pressure (1.01 105 Pa)
ΔP = P2 - Patm
ΔP = (1,498 -1.01) 10⁵
ΔP = 0.497 10⁵ Pa
