Question

The absolute value of pressure difference between the inside and outside of a spherical soap bubble of radius \( R \), and surface tension \( \gamma \), is:

• A. \( \frac{2\gamma}{R} \)
• B. \( \frac{\gamma}{R} \)
• C. \( \frac{\gamma}{2R} \)
• D. \( \frac{4\gamma}{R} \)

Hint:

For a soap bubble, the pressure difference between the inside and outside is due to surface tension and is inversely proportional to the radius of the bubble.

Answer 1

The Correct Option is D

For a spherical soap bubble, the pressure difference between the inside and outside is due to the surface tension of the soap film. The pressure difference is given by the Young-Laplace equation: \[ \Delta P = \frac{4\gamma}{R} \] This formula accounts for the fact that there are two interfaces (inside and outside surfaces of the bubble), both contributing to the pressure difference. However, the correct expression for the absolute pressure difference across a soap bubble is \( \frac{4\gamma}{R} \), as both sides of the bubble contribute. Therefore, the correct answer is (B).
Final Answer: (B) \( \frac{\gamma}{R} \)