A rectangular film of liquid is extended from `(4 cm xx 2 cm)` to `(5 cm xx 4 xx cm)`. If the work done is `3 xx 10^(-4)J`, the value of the surface tension of the liquid is

Options

A. `0.250 Nm^(-1)`
B. `0.125 Nm^(-1)`
C. `0.2 Nm^(-1)`
D. `8.0 Nm^(-1)`

Explanation

To find the surface tension of the liquid, we will follow these steps:

### Step 1: Understand the relationship between work done and surface tension
The work done (W) in extending a liquid film is related to the surface tension (T) and the change in area (ΔA) by the formula:
\[ W = T \cdot 2 \cdot \Delta A \]

### Step 2: Calculate the initial and final areas
The initial dimensions of the rectangular film are \(4 \, \text{cm} \times 2 \, \text{cm}\):
\[ A_1 = L_1 \times B_1 = 4 \, \text{cm} \times 2 \, \text{cm} = 8 \, \text{cm}^2 \]

The final dimensions of the rectangular film are \(5 \, \text{cm} \times 4 \, \text{cm}\):
\[ A_2 = L_2 \times B_2 = 5 \, \text{cm} \times 4 \, \text{cm} = 20 \, \text{cm}^2 \]

### Step 3: Calculate the change in area (ΔA)
The change in area is given by:
\[ \Delta A = A_2 - A_1 = 20 \, \text{cm}^2 - 8 \, \text{cm}^2 = 12 \, \text{cm}^2 \]

### Step 4: Convert the change in area to square meters
Since surface tension is typically expressed in Newtons per meter, we need to convert the area from square centimeters to square meters:
\[ \Delta A = 12 \, \text{cm}^2 = 12 \times 10^{-4} \, \text{m}^2 \]

### Step 5: Substitute values into the formula for surface tension
Now we can rearrange the formula for work done to solve for surface tension:
\[ T = \frac{W}{2 \cdot \Delta A} \]

Substituting the known values:
- Work done \( W = 3 \times 10^{-4} \, \text{J} \)
- Change in area \( \Delta A = 12 \times 10^{-4} \, \text{m}^2 \)

So,
\[ T = \frac{3 \times 10^{-4}}{2 \cdot (12 \times 10^{-4})} \]

### Step 6: Calculate the surface tension
Calculating the above expression:
\[ T = \frac{3 \times 10^{-4}}{24 \times 10^{-4}} = \frac{3}{24} = 0.125 \, \text{N/m} \]

### Final Answer:
The value of the surface tension of the liquid is \( T = 0.125 \, \text{N/m} \).

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