Let ' $W_1$ ' be the work done in blowing a soap bubble of radius ' $r$ ' from soap solution at room…

Let ' $W_1$ ' be the work done in blowing a soap bubble of radius ' $r$ ' from soap solution at room temperature. The soap solution is now heated and second soap bubble of radius ' $2 \mathrm{r}$ ' is blown from the heated soap solution. If ' $\mathrm{W}_2$ ' is the work done in forming this bubble then
  1. $\mathrm{W}_2=2 \mathrm{~W}_1$
  2. $\mathrm{W}_2=4 \mathrm{~W}_1$
  3. $\mathrm{W}_2>4 \mathrm{~W}_1$
  4. $\mathrm{W}_2 < 4 \mathrm{~W}_1$

Solution

$\mathrm{W}_1=8 \pi \mathrm{r}^2 \mathrm{~T}$ Where, $\mathrm{T}=$ surface tension $\mathrm{W}_2=8 \pi(2 \mathrm{r})^2 \mathrm{~T}^{\prime}=32 \pi \mathrm{r}^2 \mathrm{~T}^{\prime}$ Since soap solution is heated, its surface tension decrease. $\begin{aligned} & \therefore \mathrm{T}^{\prime} < \mathrm{T} \\ & \therefore \mathrm{W}_2 < 4 \mathrm{~W}_1 \end{aligned}$

Asked in: MHT CET 2021 (22 Sep Shift 1)

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