There is an air bubble of radius 1.0 mm in a liquid of surface tension 0.075 N/m and density 1000 kg/m³ at a depth of 10 cm below the free surface. The amount by which the pressure inside the bubble is greater than atmospheric pressure (g=10 m/s²) (in Pa)is

Explanation

The pressure inside the air bubble is influenced by two factors:

1. Hydrostatic Pressure: The pressure due to the liquid column above the bubble.
2. Surface Tension: The additional pressure due to the bubble's surface tension.

Given Data

• Radius of the bubble: r = 1.0 mm = 1.0 × 10^-3 m
• Surface tension: T = 0.075 N/m
• Density of the liquid: ρ = 1000 kg/m³
• Depth: h = 10 cm = 0.1 m
• Acceleration due to gravity: g = 10 m/s²

1. Hydrostatic Pressure:

The pressure exerted by the liquid column is calculated using the formula: 
P_hydrostatic = ρ × g × h

Substituting the values: 
P_hydrostatic = 1000 × 10 × 0.1 = 1000 Pa

2. Excess Pressure Due to Surface Tension:

For an air bubble, the excess pressure due to surface tension is given by:

P_surface = 2 × T / r

Substituting the values:

P_surface = (2 × 0.075) / (1.0 × 10^-3) = 150 Pa

3. Total Pressure Inside the Bubble:

The total pressure inside the bubble is:

P_excess = P_hydrostatic + P_surface

Substituting the calculated values:

P_excess = 1000 + 150 = 1150 Pa

Final Answer

The pressure inside the air bubble is 1150 Pa greater than the atmospheric pressure.