The excess pressure inside a soap bubble of radius R is (S is the surface tension)

Options

A. `2S/R`
B. `4S/R`
C. `S/R`
D. `S/2R`

Answer

To determine the excess pressure inside a soap bubble of radius \( R \) with surface tension \( S \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Excess Pressure**:
- The excess pressure inside a soap bubble arises due to the surface tension of the liquid forming the bubble. A soap bubble has two surfaces (inner and outer) that contribute to the pressure difference.

2. **Formula for Excess Pressure**:
- The formula for the excess pressure inside a soap bubble in air is given by:
\[ \Delta P = \frac{4S}{R} \]
- Here, \( \Delta P \) is the excess pressure, \( S \) is the surface tension of the soap solution, and \( R \) is the radius of the bubble.

3. **Justification for the Formula**:
- When a soap bubble is in air, it has two interfaces (inner and outer surfaces). Each surface contributes to the pressure difference. The total excess pressure is thus derived from the contributions of both surfaces:
- Each surface contributes \( \frac{2S}{R} \), leading to a total of \( 2 \times \frac{2S}{R} = \frac{4S}{R} \).

4. **Final Expression**:
- Therefore, the excess pressure inside a soap bubble of radius \( R \) in air is:
\[ \Delta P = \frac{4S}{R} \]