Question

A frame made 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 $50\%$, the energy of the soap film will be changed by

• A. $100\%$
• B. $75\%$
• C. $50\%$
• D. $25\%$

Answer 1

Answer: (C)

Surface energy = Surface tension $\times$ surface area
$E=T\times 2A$ (Since the soap film has two surfaces)
$A^{\prime }=[A-\frac{50A}{100}]=\frac{A}{2}$
$\therefore E^{\prime }=T\times 2\left(\frac{A}{2}\right)$
$E^{\prime }=T\times A$
Percentage decrease in surface energy
$=\frac{E-E^{\prime }}{E}\times 100$
$=\frac{2TA-TA}{2TA}\times 100$
$=\frac{1}{2}\times 100$
$=50\%$