Question

If the surface tension at the soap bubble-air interface is 0.09 N/m; then what is the internal pressure in a soap bubble of 24 mm diameter?

• A. $7.5 \frac{N}{m^2}$
• B. $15 \frac{N}{m^2}$
• C. $20 \frac{N}{m^2}$
• D. $30 \frac{N}{m^2}$

Hint:

Remember the "Double Surface" rule for soap bubbles.

• Droplet/Jet: Use $4\sigma/d$.

• Soap Bubble: Use $8\sigma/d$.
Always double the pressure for a bubble because it has two sides of film!

Answer 1

The Correct Option is D

Surface tension causes a pressure difference between the inside and outside of a curved liquid interface. For a soap bubble, which has two surfaces (inner and outer), the formula differs from a liquid droplet. 1. Given Parameters:

• Surface Tension ($\sigma$) = 0.09 N/m

• Diameter ($d$) = 24 mm = $0.024$ m

• Radius ($r$) = 12 mm = $0.012$ m

2. Formula for Soap Bubble: The gauge pressure ($P$) inside a soap bubble is given by: $$P = \frac{8\sigma}{d} \quad \text{or} \quad P = \frac{4\sigma}{r}$$

3. Calculation: Using the diameter formula: $$P = \frac{8 \times 0.09}{0.024}$$ $$P = \frac{0.72}{0.024}$$ $$P = 30 \text{ N/m}^2$$

4. Why the factor of 8? A soap bubble consists of a thin film of liquid with

two interfaces: one with air on the inside and one with air on the outside. Each interface contributes $4\sigma/d$ to the total pressure resistance, resulting in a total of $8\sigma/d$. A solid liquid drop, by contrast, only has one interface and would have a pressure of $4\sigma/d$.