Question
Download Solution PDFThe work done in increasing the size of a soap film from 10 cm × 6 cm to 10 cm × 11 cm is 3 × 10-4 joule. The surface tension of the film is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
Surface Tension
Surface tension is a property of liquids that makes them acquire the least surface area possible. It is the force per unit length acting along the surface of a liquid.
The work done in increasing the surface area of a liquid film is given by the product of the surface tension and the change in surface area.
EXPLANATION:
Let's calculate the surface tension of the soap film:
The initial dimensions of the soap film are 10 cm × 6 cm. Hence, the initial area (A1) is:
A1 = 10 cm × 6 cm = 60 cm2
The final dimensions of the soap film are 10 cm × 11 cm. Hence, the final area (A2) is:
A2 = 10 cm × 11 cm = 110 cm2
The change in area (ΔA) is:
ΔA = A2 - A1 = 110 cm2 - 60 cm2 = 50 cm2
The work done (W) in increasing the size of the soap film is given as 3 × 10-4 joule.
The surface tension (γ) is calculated using the formula:
W = γ × ΔA
Rearranging the formula for γ gives:
γ = W / ΔA
Substitute the values:
γ = (3 × 10-4 joule) / (50 cm2)
Note: 1 cm2 = 10-4 m2, so 50 cm2 = 50 × 10-4 m2
γ = (3 × 10-4 joule) / (50 × 10-4 m2)
γ = (3 / 50) N/m
γ = 0.06 N/m
Therefore, the correct answer is option 2: 3.0 × 10-2 N/m.
Last updated on Jun 6, 2025
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