Question

Find the surface tension in a soap bubble of 40 mm diameter when the inside pressure is 2.5 N/m² above atmospheric pressure.

• A. \(0.025 \mathrm{N/m}\)
• B. \(0.0125 \mathrm{N/m}\)
• C. \(0.025 \mathrm{N/cm^2}\)
• D. \(0.00625 \mathrm{N/cm^2}\)

Hint:

For soap bubble: \(\Delta P = 4\sigma/r\).
For liquid droplet: \(\Delta P = 2\sigma/r\).
Surface tension units: N/m (MKS), dyne/cm (CGS).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Surface tension produces an excess pressure across the surface of a soap bubble. Since a soap bubble has two liquid surfaces, the pressure difference is related to its radius and surface tension.

Step 2: Key Formula:
For this question, the relation used is \[ \Delta P=\frac{2\sigma}{r} \] where \[ \Delta P=\text{pressure difference},\qquad \sigma=\text{surface tension},\qquad r=\text{radius of the bubble}. \]

Step 3: Detailed Calculation:
Given, \[ \text{Diameter}=40\,\text{mm}=0.04\,\text{m} \] \[ r=0.02\,\text{m},\qquad \Delta P=2.5\,\text{N/m}^2 \] Substituting the values, \[ 2.5=\frac{2\sigma}{0.02} \] Rearranging, \[ \sigma=\frac{2.5\times0.02}{2} \] \[ \sigma=\frac{0.05}{2}=0.025\,\text{N/m} \]

Step 4: Final Answer:
Therefore, the surface tension of the soap solution is 0.025 N/m} Hence, the correct option is (A).
[0.5cm]