Question

how much work is required to form a bubble of 2cm radius from soap solution having surface tention 0.07N/m​

Answer 1

$\color{darkblue}\underline{\underline{\sf Given-}}$

• Radius of soap bubble (R) = 2cm
• Surface Tension (S) = 0.07 N/m

$\color{darkblue}\underline{\underline{\sf To \: Find-}}$

• Work Done (W)

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$\color{green}\underline{\sf Formula\:Used-}$

$\color{violet}\bullet\underline{\boxed{\sf Surface\: Tension=\dfrac{Work\:Done}{Area}}}$

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R = 2cm

Convert it in "metre"

$\implies{\sf R= \dfrac{2}{100}}$

$\implies{\sf R=2×10^{-2}m }$

Bubble have two surface .

⛬

$\color{violet}\implies{\sf Area \; of \: bubble =2(4πR^2)}$

$\implies{\sf 2(4×3.14×(2×10^{-2})^2}$

$\implies{\sf 2(50.2×10^{-4}) }$

$\implies{\sf 2×50.2×10^{-4}}$

$\implies{\sf 100×10^{-4}}$

$\color{red}\implies{\sf Area=10^{-2}m^2}$

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Now putting value in the formula.

$\implies{\sf 0.07=\dfrac{W}{10^{-2}}}$

$\color{red}\implies{\sf W=7×10^{-4}J}$

$\color{darkblue}\underline{\underline{\sf Answer-}}$

Work is required to form a bubble of 2cm radius from soap solution having surface tention 0.07N/m is $\color{red}{\sf 7×10^{-4}J}$

Answer 2

$\mathtt{ \huge{ \fbox{Solution :)}}}$

Given ,

• Radius of the bubble = 2 cm or 0.02 m
• Surface tension = 0.07 n/m

We know that , surface tension is numerically equal to surface energy and surface energy is given by

$\large \mathtt{\fbox{Surface \: energy = \frac{work \: done \: in \: increasing \: surface \: area}{increase \: in \: surface \: area} }}$

Thus ,

$\sf \hookrightarrow Work \: done = 0.07 \times (2 \times 4\times \frac{22}{7} \times {(0.02)}^{2} ) \\ \\\sf \hookrightarrow Work \: done = \frac{ \cancel7 \times 176 \times 4}{100 \times \cancel7 \times10000 } \\ \\\sf \hookrightarrow Work \: done = 704 \times {(10)}^{ - 6} \: \: joule$

Hence , the work done is 704 × (10)^-6 J

Remmember :

Area of the bubble = 2 × 4π(r)² , Because bubble has two surfaces

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