Question

A soap bubble of diameter $7$ cm, its diameter is increased to $14$ cm. If change in its surface energy is $(15000 - x)\,\mu$J, find $x$. (Given surface tension = $0.04$ N/m)

• A. $208$
• B. $216$
• C. $432$
• D. $512$

Hint:

For soap bubbles, always remember that there are two surfaces contributing to surface energy.

Answer 1

The Correct Option is B

Step 1: Formula for change in surface energy of a soap bubble.
A soap bubble has two surfaces, hence change in surface energy is given by:
\[ \Delta E = 2T \times \Delta A \]
Step 2: Change in surface area.
\[ \Delta A = 4\pi(r_2^2 - r_1^2) \]
Therefore,
\[ \Delta E = 8\pi T (r_2^2 - r_1^2) \]
Step 3: Substituting given values.
\[ r_1 = \dfrac{7}{2} \times 10^{-2}\,\text{m}, \quad r_2 = 7 \times 10^{-2}\,\text{m} \]
\[ \Delta E = 8 \times \dfrac{22}{7} \times (49 - \dfrac{49}{4}) \times 10^{-4} \times 0.04 \]
Step 4: Calculating change in surface energy.
\[ \Delta E = 14784\,\mu\text{J} \]
Step 5: Finding value of $x$.
\[ 15000 - x = 14784 \Rightarrow x = 216 \]