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Question
A rectangular wireframe of size 2 cm x 2 cm, is dipped in a soap solution and taken out. A soap film is formed, if the size of the film is changed to 3 cm x 3 cm, Calculate the work done in the process. The surface tension of the soap film is 3 x 10-2 N/m.
Solution 1
Given:
A1 = 2 × 2 cm2 = 4 × 10-4 m2,
A2 = 3 × 3 cm2 = 9 × 10-4 m2,
T = 3 × 10-2 N/m
To find:
The work done in the process
Solution:
As the film has two surfaces, the work done is
W = 2T(A2 - A1)
= 2(3 × 10-2)(9 × 10-4 - 4 × 10-4)
= 3 × 10-5J
Solution 2
Given:
A1 = 2 cm × 2 cm = 4 × 10−4 m2 ,
A2 = 3 cm × 3 cm = 9 × 10−4 m2 ,
T = 3 × 10−2 N/m
To find:
Work done (W)
Formula:
W = (T dA)
Calculation:
As the rectangular film has two surfaces,
dA = 2(A2 − A1)
From formula,
W = 3 × 10−2 × 2 × (9 × 10−4 − 4 × 10−4)
= 6 × 10−2 × 5 × 10−4
∴ W = 30 × 10−6
= 3 × 10−5 J
The work done in increasing film is 3 × 10−5 J.
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