1. Tardigrade
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  4. A soap bubble is formed from 10- 3g of soap solution. When it is filled with hydrogen of density 0.00009g/cm3, it floats in impure argon gas of density 0.00199g/cm3. What will be the excess pressure nearly in dyne per cm2 ,If surface tension of soap solution is 12dyne/cm . (Take π - 1 = 0 . 318

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Q. A soap bubble is formed from $10^{- 3}g$ of soap solution. When it is filled with hydrogen of density $0.00009g/cm^{3},$ it floats in impure argon gas of density $0.00199g/cm^{3}.$ What will be the excess pressure nearly in dyne per $cm^{2}$ ,If surface tension of soap solution is $12dyne/cm$ . (Take $\pi ^{- 1} = 0 . 318$

NTA AbhyasNTA Abhyas 2022

Solution:

Let the volume of bubble be $V$ .
Balancing the weight, we get
$10^{- 3}+0.00009V=0.00199V\Rightarrow V=\frac{10^{- 3}}{1 . 9 \times 10^{- 3}}=0.526cm^{3}$
Since, $V=0.526=\frac{4}{3}\pi r^{3}\Rightarrow r=0.5cm$ .
Now, excess pressure, $P=\frac{4 T}{r}=\frac{4 \times 12}{0 . 5}=96dynepercm^{2}$ .