Question

Consider the following two statements A and B and identify the correct answer.
A) The work done in blowing a bubble of volume V is W, then the work done in blowing a soap bubble of volume 2V will be 2${}^{2/3}$ W.
B) The excess pressure inside a soap bubble of diameter D and surface tension S is $\frac{8S}{D}$.

• A. A&B are false
• B. A is false but B is true
• C. A is true but B is false
• D. A & B are true.

Answer 1

Answer: (D)

A & B are true.

Excess pressure inside a soap bubble $P_{ex}=\frac{4T}{R}$
$P_{ex}=\frac{4T}{D/2}=\frac{8T}{D}$
Work done in blowing a soap bubble of radius r is
$2ST=2\times 4\pi r^2\times T=8\pi r^{2}T$
$If{V}^{{}^{\prime }}=2V$
$\Rightarrow R^{{}^{\prime }}=(2{)}^{1/3}r$
$workdone{W}^{{}^{\prime }}=8\pi (2^{1/3}r{)}^{2}T$
$=8\pi 2^{2/3}{r}^{2}T$
$=2^{2/3}W$