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 of radius 2 cm, we use the formula for surface energy of a bubble: \(E = 4\pi r^2 \times 2 \times T\), where \(r\) is the radius, and \(T\) is the surface tension. The factor of 2 accounts for the inner and outer surfaces of the bubble.

Given:

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

Substitute these values into the equation:

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

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

\(E = 4 \times 3.1416 \times 0.0004 \times 2 \times 0.03\)

\(E = 1.507 \times 0.00024\) (approximating \(\pi\) as 3.1416)

\(E = 0.00036168\) J

Thus, the energy required is approximately \(3.01 \times 10^{-4}\) J.

Therefore, the correct answer is:

3.01 x 10^-4 J