Question

The amount of energy required to form a soap bubble of radius 2 cm from a soap solution is nearly: (surface tension of soap solution = 0.03 Nm^-1)

• A. 50.1 x 10^-4 J
• B. 30.16 x 10^-4 J
• C. 5.06 x 10^-4 J
• D. 3.01 x 10^-4 J

Answer 1

The Correct Option is D

To determine the energy required to form a soap bubble, we must understand the concept of surface tension and how it relates to the energy of a bubble. A soap bubble has two surfaces, both an inner and an outer surface. Therefore, the energy required to create a soap bubble can be calculated using the formula for surface energy:

\(E = 4\pi r^2 \times T \times 2\)

where:

• \(r\) is the radius of the bubble,
• \(T\) is the surface tension of the soap solution,
• The factor of 2 accounts for the two surfaces (inside and outside) of the bubble.

Given:

• Radius \(r = 2\, \text{cm} = 0.02\, \text{m}\) (conversion from centimeters to meters)
• Surface tension \(T = 0.03\, \text{Nm}^{-1}\)

Putting these values into the formula:

\(E = 4\pi \times (0.02)^2 \times 0.03 \times 2\)

Calculating the above expression:

\(E = 4 \times \pi \times 0.0004 \times 0.03 \times 2\)

\(E = 4 \times \pi \times 0.000024\)

Approximating \(\pi \approx 3.14\):

\(E \approx 4 \times 3.14 \times 0.000024\)

\(E \approx 0.00030144\, \text{J} = 3.0144 \times 10^{-4}\, \text{J}\)

Thus, the energy required to form a soap bubble of radius 2 cm is approximately \(3.01 \times 10^{-4}\, \text{J}\). Hence, the correct answer is \(3.01 \times 10^{-4}\, \text{J}\).