Question

A soap bubble of radius $1$ cm has surface tension $0.03$ N/m. Excess pressure inside is:

• A. $3$ Pa
• B. $6$ Pa
• C. $12$ Pa
• D. $24$ Pa

Hint:

Always remember the difference between a liquid drop ($\frac{2T}{R}$) and a soap bubble ($\frac{4T}{R}$). The "double surface" of the soap bubble doubles the excess pressure compared to a drop of the same size and surface tension.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Due to surface tension, the pressure inside a curved surface is always greater than the pressure outside.
A liquid drop has only one free surface (liquid-air interface).
However, a soap bubble is a thin film of liquid with air on both sides, meaning it has two free surfaces (inner and outer).
This "double surface" effect means that the force exerted by surface tension is doubled compared to a simple drop.
Step 2: Key Formula or Approach:
The excess pressure (\(\Delta P\)) inside a soap bubble is:
\[ \Delta P = \frac{4T}{R} \]
(For a liquid drop, it is \(\frac{2T}{R}\)).
Step 3: Detailed Explanation:
Identify the variables from the question:
- Surface tension (\(T\)) = 0.03 N/m.
- Radius (\(R\)) = 1 cm = 0.01 m (must convert to SI units to get pressure in Pascals).
Apply the formula:
\[ \Delta P = \frac{4 \times 0.03}{0.01} \]
\[ \Delta P = \frac{0.12}{0.01} \]
\[ \Delta P = 12 \text{ Pa} \]
If the object were a liquid drop of the same radius, the answer would have been 6 Pa. The factor of 4 is the defining characteristic of a soap bubble.
Step 4: Final Answer:
The excess pressure inside the bubble is 12 Pa.