The work done by a boy in making a soap bubble of diameter 1.4 cm by blowing, if the surface te

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The work done by a boy in making a soap bubble of diameter...

The work done by a boy in making a soap bubble of diameter $1.4 \mathrm{~cm}$ by blowing, if the surface tension of soap solution is $0.03 \mathrm{~N} / \mathrm{m}$, is : (a) $3 \times 10^{-5} \mathrm{~J}$ (b) $3.696 \times 10^{-5} \mathrm{~J}$ (c) $2 \times 10^{-5} \mathrm{~J}$ (d) $4.2 \times 10^{-5} \mathrm{~J}$

The work done by a boy in making a soap bubble of diameter $1.4 \mathrm{~cm}$ by blowing, if the surface tension of soap solution is $0.03 \mathrm{~N} / \mathrm{m}$, is :
(a) $3 \times 10^{-5} \mathrm{~J}$
(b) $3.696 \times 10^{-5} \mathrm{~J}$
(c) $2 \times 10^{-5} \mathrm{~J}$
(d) $4.2 \times 10^{-5} \mathrm{~J}$

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Key Concepts

Surface Tension

Surface tension is a property of liquids that results from the cohesive forces between liquid molecules at the interface with a gas or another immiscible liquid. It is expressed as force per unit length and is crucial for phenomena like bubble formation, where it acts to minimize the surface area of the liquid.

Work Done in Creating a Surface

The work performed against surface tension to create a new surface is equivalent to the energy required to increase the liquid's surface area. In the context of a soap bubble, this energy is calculated by multiplying the surface tension with the area being created. Since a soap bubble has both an inner and an outer surface, the total work involves contributions from both surfaces.

Surface Area of a Sphere

The surface area of a sphere is a key geometric concept for calculating the area involved in the work done for bubble formation. For a sphere, the surface area is given by 4?r², and in the case of a soap bubble, this area is doubled to account for its two surfaces. This calculation is essential for determining the total energy or work required to blow a bubble.

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