What is the work done in blowing to from a soap bubble of surface area `40 cm^2`? Take surface tension of the soap solution as `0.03 Nm^(-1)`.

Options

A. `2.4 xx 10^(-4) J`
B. `1.2 xx 10^(-2) J`
C. `3.6 xx 10^(-4) J`
D. `4.2 xx 10^(-4) J`

Explanation

To find the work done in blowing a soap bubble with a surface area of \(40 \, \text{cm}^2\), we can use the formula for work done in creating a surface area in the context of surface tension. The work done \(W\) is given by:

\[ W = 2 \Delta S \cdot T \]

where:
- \(\Delta S\) is the change in surface area,
- \(T\) is the surface tension of the liquid.

### Step 1: Convert the Surface Area
First, we need to convert the surface area from cm² to m².

\[ \Delta S = 40 \, \text{cm}^2 = 40 \times 10^{-4} \, \text{m}^2 = 4 \times 10^{-3} \, \text{m}^2 \]

### Step 2: Identify the Surface Tension
The surface tension \(T\) is given as:

\[ T = 0.03 \, \text{N/m} \]

### Step 3: Substitute Values into the Work Done Formula
Now, we can substitute the values of \(\Delta S\) and \(T\) into the work done formula:

\[ W = 2 \Delta S \cdot T = 2 \times (4 \times 10^{-3} \, \text{m}^2) \times (0.03 \, \text{N/m}) \]

### Step 4: Calculate the Work Done
Now we perform the calculation:

\[ W = 2 \times 4 \times 10^{-3} \times 0.03 \]
\[ W = 8 \times 10^{-3} \times 0.03 \]
\[ W = 0.00024 \, \text{J} = 2.4 \times 10^{-4} \, \text{J} \]

### Conclusion
The work done in blowing the soap bubble of surface area \(40 \, \text{cm}^2\) is:

\[ W = 2.4 \times 10^{-4} \, \text{J} \]