A frame made up of metallic wire enclosing a surface area A is covered with a soap film. If the area of the frame of metallic wire is reduced by 25% the energy of the soap film will be changed by

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The initial surface energy of the soap film is $E_{1} = T \times 2 A$ , where $T$ is the surface tension and $A$ is the area of the frame. The factor of $2$ accounts for the two free surfaces of the soap film.

When the area is reduced by $25%$ , the new area becomes $A_{2} = A - 0.25 A = 0.75 A$ .

The new surface energy is $E_{2} = T \times 2 A_{2} = T \times 2 (0.75 A) = 0.75 (T \times 2 A) = 0.75 E_{1}$ .

The change in energy is $Δ E = E_{1} - E_{2} = E_{1} - 0.75 E_{1} = 0.25 E_{1}$ .

The percentage change in the energy of the soap film is $\frac{Δ E}{E _{1}} \times 100% = 0.25 \times 100% = 25%$ .

Answer: $25%$

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