The lower end of a capillary tube of diameter $2.00 \; mm$ is dipped $8.00 \; cm$ below the surface of water in a beaker. What is the pressure required in the tube in order to blow a hemispherical bubble at its end in water? The surface tension of water at the temperature of the experiment is $7.30 \times 10^{-2} \; N m^{-1}$. Atmospheric pressure $= 1.01 \times 10^{5} \; Pa$,density of water $= 1000 \; kg m^{-3}$,$g = 9.80 \; m s^{-2}$. Also,calculate the excess pressure.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The excess pressure in a bubble of gas in a liquid is given by $P_{ex} = 2S/r$,where $S$ is the surface tension of the liquid-gas interface.
Here,the diameter of the capillary tube is $d = 2.00 \; mm = 2.00 \times 10^{-3} \; m$,so the radius of the hemispherical bubble is $r = d/2 = 1.00 \times 10^{-3} \; m$.
The excess pressure is $P_{ex} = 2S/r = (2 \times 7.30 \times 10^{-2} \; N m^{-1}) / (1.00 \times 10^{-3} \; m) = 146 \; Pa$.
The pressure outside the bubble at a depth $h = 8.00 \; cm = 0.08 \; m$ is $P_o = P_{atm} + h \rho g$.
$P_o = 1.01 \times 10^5 \; Pa + (0.08 \; m \times 1000 \; kg m^{-3} \times 9.80 \; m s^{-2}) = 1.01 \times 10^5 \; Pa + 784 \; Pa = 101784 \; Pa$.
The total pressure required inside the tube is $P_i = P_o + P_{ex} = 101784 \; Pa + 146 \; Pa = 101930 \; Pa = 1.0193 \times 10^5 \; Pa$.

Explore More

Similar Questions

When a mercury drop of radius $R$ breaks into $n$ droplets of equal size,the radius $r$ of each droplet is

Due to surface tension, the excess pressure inside a smaller drop is $9 \text{ units}$. If $27$ smaller drops combine, then the excess pressure inside the bigger drop is: (in $\text{ units}$)

$A$ large number of liquid drops each of radius $r$ coalesce to form a single drop of radius $R$. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given,surface tension of liquid $T$,density $\rho$):

Difficult
View Solution

Two mercury droplets of radii $0.1 \ cm$ and $0.2 \ cm$ coalesce into one single drop. What amount of energy is released? The surface tension of mercury is $T = 435.5 \times 10^{-3} \ N \ m^{-1}$.

Difficult
View Solution

The excess pressure inside the first soap bubble of radius $R_1$ is three times that inside the second soap bubble of radius $R_2$. The ratio of volumes of the first to second bubble is

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo