If T is the surface tension of soap solution, the amount of work … - Vidyadip

MCQ

If $T$ is the surface tension of soap solution, the amount of work done in blowing a soap bubble from a diameter $D$ to a diameter $2D$ is:

A
$2\pi\text{D}^2\text{T}$
B
$4\pi\text{D}^2\text{T}$
✓
$6\pi\text{D}^2\text{T}$
D
$8\pi\text{D}^2\text{T}$

✓

Answer

Correct option: C.

$6\pi\text{D}^2\text{T}$

A soap bubble has two free surfaces.
Therefore increase in area of soap bubble
$\therefore\frac{656.5}{1425}=1.25\text{e}^{-\frac{\text{y}}{8000}}$
$\text{e}^{-\frac{\text{y}}{8000}}=\frac{656.5}{14.25\times1.25}$
$\text{e}^{-\frac{\text{y}}{8000}}=\frac{1425\times1.25}{656.5}=2.7132$
Taking $\log$ on both sides,
$\frac{\text{y}}{8000}=\log\text{e }2.7132=2.3026\log102.7132$
$=2.3026\times0.4335\approx1$
$\text{y}=8000\times1$
$=8000\text{m}$
$=8\text{km}$
$=2\Big[\frac4\pi\frac{(2\text{D})^2}{4}-\text{4}\pi\frac{\text{D}^2}{4}\Big]$
$=6\pi\text{D}^2$
Work done $=6\pi\text{D}^2\text{T}$

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