Question

A spherical air bubble is formed inside a liquid (like water). The radius of the bubble is 0.5 mm, and the surface tension of the liquid is 0.072 N/m. What is the pressure inside the bubble relative to the outside pressure?

• A. \(1.44 \times 10^3 \, \text{Pa}\) more
• B. \(1.44 \times 10^2 \, \text{Pa}\) more
• C. \(2.88 \times 10^3 \, \text{Pa}\) more
• D. \(2.88 \times 10^2 \, \text{Pa}\) more

Hint:

For a spherical air bubble, the pressure inside the bubble is higher than the outside pressure due to the surface tension. Use the formula \(\Delta P = \frac{4 \gamma}{r}\) to calculate the pressure difference.

Answer 1

The Correct Option is D

The pressure differential across a bubble's surface is determined by the equation: \[ \Delta P = \frac{4 \gamma}{r} \] With the following parameters: - \(\gamma = 0.072 \, \text{N/m}\) (surface tension), - \(r = 0.5 \, \text{mm} = 0.5 \times 10^{-3} \, \text{m}\) (bubble radius). Upon substitution of these values: \[ \Delta P = \frac{4 \times 0.072}{0.5 \times 10^{-3}} = \frac{0.288}{0.5 \times 10^{-3}} = 2.88 \times 10^2 \, \text{Pa} \] Consequently, the internal pressure of the bubble exceeds the external pressure by \(2.88 \times 10^2 \, \text{Pa}\).