Question:
If the work done in increasing the area of a thin soap film from $A$ to $3A$ is $W$, then the surface tension of the soap solution is
If the work done in increasing the area of a thin soap film from $A$ to $3A$ is $W$, then the surface tension of the soap solution is
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Logic Tip: The phrase "soap film" or "soap bubble" is a trap specifically designed to test if you remember to multiply the area by 2. If it were a water drop or a liquid surface in a cup, there would only be 1 free surface, and the answer would be $\frac{W}{2A}$.
Updated On: Apr 27, 2026
- $\frac{W}{A}$
- $\frac{W}{4A}$
- $WA$
- $2WA$
- $\frac{W}{3A}$
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The Correct Option is B
Solution and Explanation
Concept:
The work done ($W$) in stretching or creating a liquid film is stored as surface potential energy and is given by the product of the surface tension ($T$) and the change in surface area ($\Delta S$): $$W = T \cdot \Delta S$$ Crucially, a thin soap film suspended in air has two free surfaces (a front surface and a back surface) in contact with the air. Therefore, the actual surface area is twice the geometric area of the film.
Step 1: Calculate the initial and final surface areas.
Let the initial geometric area be $A_1 = A$. Because a soap film has two surfaces, the initial total surface area is: $$S_1 = 2 \cdot A_1 = 2A$$ Let the final geometric area be $A_2 = 3A$. The final total surface area is: $$S_2 = 2 \cdot A_2 = 2(3A) = 6A$$
Step 2: Calculate the change in total surface area ($\Delta S$).
$$\Delta S = S_2 - S_1$$ $$\Delta S = 6A - 2A = 4A$$
Step 3: Calculate the surface tension (T).
Using the work-surface energy relation: $$W = T \cdot \Delta S$$ Substitute the change in area: $$W = T \cdot (4A)$$ Solve for surface tension $T$: $$T = \frac{W}{4A}$$
The work done ($W$) in stretching or creating a liquid film is stored as surface potential energy and is given by the product of the surface tension ($T$) and the change in surface area ($\Delta S$): $$W = T \cdot \Delta S$$ Crucially, a thin soap film suspended in air has two free surfaces (a front surface and a back surface) in contact with the air. Therefore, the actual surface area is twice the geometric area of the film.
Step 1: Calculate the initial and final surface areas.
Let the initial geometric area be $A_1 = A$. Because a soap film has two surfaces, the initial total surface area is: $$S_1 = 2 \cdot A_1 = 2A$$ Let the final geometric area be $A_2 = 3A$. The final total surface area is: $$S_2 = 2 \cdot A_2 = 2(3A) = 6A$$
Step 2: Calculate the change in total surface area ($\Delta S$).
$$\Delta S = S_2 - S_1$$ $$\Delta S = 6A - 2A = 4A$$
Step 3: Calculate the surface tension (T).
Using the work-surface energy relation: $$W = T \cdot \Delta S$$ Substitute the change in area: $$W = T \cdot (4A)$$ Solve for surface tension $T$: $$T = \frac{W}{4A}$$
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