The amount of work done in increasing the size of a soap film 10 cm ×6 cm to 10 cm ×10 cm is

step 1 we are given that the initial area initial area initial area of a soft of a soft film is equal t

The amount of work done in increasing the size of a soap...

The amount of work done in increasing the size of a soap film $10 \mathrm{~cm} \times 6 \mathrm{~cm}$ to $10 \mathrm{~cm} \times 10 \mathrm{~cm}$ is (S.T. = $\left.30 \times 10^{-3} \mathrm{~N} / \mathrm{m}\right)$ (A) $2.4 \times 10^{-2} \mathrm{~J}$ (B) $1.2 \times 10^{-2} \mathrm{~J}$ (C) $2.4 \times 10^{-4} \mathrm{~J}$ (D) $1.2 \times 10^{-4} \mathrm{~J}$

The amount of work done in increasing the size of a soap film $10 \mathrm{~cm} \times 6 \mathrm{~cm}$ to $10 \mathrm{~cm} \times 10 \mathrm{~cm}$ is (S.T. =
$\left.30 \times 10^{-3} \mathrm{~N} / \mathrm{m}\right)$
(A) $2.4 \times 10^{-2} \mathrm{~J}$
(B) $1.2 \times 10^{-2} \mathrm{~J}$
(C) $2.4 \times 10^{-4} \mathrm{~J}$
(D) $1.2 \times 10^{-4} \mathrm{~J}$

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Key Concepts

Surface Tension

Surface tension is a physical property of liquids that represents the energy per unit area at the interface between the liquid and another medium (such as air). It arises due to the cohesive forces between liquid molecules and determines how much energy is required to increase the surface area of the liquid.

Work Done in Changing Surface Area

In the context of surface phenomena, work done is the energy required to change the area of a liquid’s surface. This is calculated by multiplying the surface tension by the increase in surface area. This concept links mechanical work to the energetic cost of modifying interfacial boundaries.

Area Change Calculation

Determining the work done requires calculating the difference in areas before and after the change. Understanding how to compute areas and their differences is crucial, as it directly relates to the amount of energy needed to produce the specified change in the system’s configuration.

Double Surface Nature of Soap Films

Soap films have two surfaces (front and back), so when calculating work done in increasing the area of a soap film, it is essential to consider that both surfaces contribute to the overall energy change. This factor effectively doubles the energy required compared to a single surface.

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