The work done in increasing the size of a soap film from 10 cm ×6 cm to 10 cm ×11 cm is 3 ×1

step 1 My question is the work time increasing the size of a soap film from 10 cm to 10 cm to 10 to 10

The work done in increasing the size of a soap film from 10...

The work done in increasing the size of a soap film from $10 \mathrm{~cm} \times 6 \mathrm{~cm}$ to $10 \mathrm{~cm} \times 11 \mathrm{~cm}$ is $3 \times 10^{-4} J$. The surface tension of the film is $\quad$ [MP PET 1999; MP PMT 2000; AIIMS 2000; JIPMER 2001, 02] (a) $1.5 \times 10^{-2} \mathrm{Nm}^{-1}$ (b) $3.0 \times 10^{-2} \mathrm{Nm}^{-1}$ (c) $6.0 \times 10^{-2} \mathrm{Nm}^{-1}$ (d) $11.0 \times 10^{-2} \mathrm{Nm}^{-1}$

The work done in increasing the size of a soap film from $10 \mathrm{~cm} \times 6 \mathrm{~cm}$ to $10 \mathrm{~cm} \times 11 \mathrm{~cm}$ is $3 \times 10^{-4} J$. The surface tension of the film is $\quad$ [MP PET 1999; MP PMT 2000; AIIMS 2000; JIPMER 2001, 02]
(a) $1.5 \times 10^{-2} \mathrm{Nm}^{-1}$
(b) $3.0 \times 10^{-2} \mathrm{Nm}^{-1}$
(c) $6.0 \times 10^{-2} \mathrm{Nm}^{-1}$
(d) $11.0 \times 10^{-2} \mathrm{Nm}^{-1}$

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Key Concepts

Double-Surface Consideration in Films

In systems like soap films, which consist of two surfaces (front and back), the total energy associated with altering the surface area must account for both sides. This factor is essential when relating the surface tension to the overall work done, effectively doubling the contribution from a single surface.

Area Change Calculation

Calculating the change in area is a key step in applying the concept of surface energy. By determining the difference between the initial and final surface areas, one can directly relate this change to the work done using the surface tension, which quantifies the energy added per unit area.

Surface Tension

Surface tension is a physical property of liquids that arises from cohesive forces among liquid molecules at an interface. It is typically described as the force per unit length or the energy per unit area required to increase the surface area of a liquid, and plays a crucial role in phenomena such as droplet formation and capillarity.

Surface Energy and Work

The work done in modifying a liquid's surface area is directly connected to the surface tension; it represents the energy required to create an additional unit area of the interface. This relationship is used to calculate the energy change during processes such as stretching or compressing a liquid surface.

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