The surface tension of a soap solution is ' $\mathrm{T}$ '. Work done in blowing a soap bubble of diameter…

The surface tension of a soap solution is ' $\mathrm{T}$ '. Work done in blowing a soap bubble of diameter $2 \mathrm{~d}$ is
  1. $8 \pi d^2 T$
  2. $2 \pi d^2 T$
  3. $4 \pi d^2 T$
  4. $6 \pi d^2 T$

Solution

In this case, work done = increase in surface energy, i.e. $\mathrm{W}=\mathrm{T} \Delta \mathrm{A}$ Key point: In calculation, area of sphere have been multiplied with 2, since there are two surfaces in soap bubble. $\begin{aligned} & \therefore \mathrm{W}=\mathrm{T} \times\left[2\left(4 \pi \mathrm{d}^2\right)\right] \\ & \Rightarrow \mathrm{W}=8 \pi \mathrm{d}^2 \mathrm{~T}\end{aligned}$

Asked in: MHT CET 2022 (05 Aug Shift 2)

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