Question

the air pressure inside a soap bubble of diameter 3.5mm is 8mm of water column above the atmospheric pressure.Calculate the surface tension of soap solution.

Answer 1

diameter of soap bubble , d = 3.5mm
so, radius of soap bubble , r = 3.5mm/2 = 1.75mm = 1.75 × 10^-3 m
height of water , h = 8mm = 8 × 10^-3 m
so, pressure due to 8mm column = $\rho gh$
we know, Density of water, $\rho$ = 1000 kg/m³

so, pressure due to 8mm column = 1000 × 10 × 8 × 10^-3 = 80 Pa.

now, surface tension of soap solution , S = Pr/4
where P is the pressure at 8 mm column
so, S = 80 × 1.75 × 10^-3/4
= 20 × 1.75 × 10^-3
= 35 × 10^-3
= 0.035N/m

Answer 2

Given:

Diameter = 3.5 mm

Height = 8 mm

To find:

Surface tension.

Solution:

Radius = Diameter / 2

3.5 / 2

By formula,

Air pressure = ρ * gravity * height

Here,

gravity - 9.8 m / s

ρ - density of water = 1000 kg / m^3

Substituting,

We get,

000 * 9.8 × 8 × 10^-3

Air pressure = 79.4 Pa.

Surface tension = Pressure * radius / 4

Substituting,

79.4 * 1.75 * 10^-3/4

35 * 10^-3

Surface tension = 0.0324 N / m