A certain number of spherical drops of a liqu | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $n$ droplets each of radius $r$ coalesce to form a big drop of radius $R$.Volume of $n$ droplets = Volume of big drop$n 	imes \frac{4}{3}\pi

Vedclass · Accepted Answer

energy $= 3VT \left( \frac{1}{r} - \frac{1}{R} \right)$ is released.

Vedclass · Answer

(C) Let $n$ droplets each of radius $r$ coalesce to form a big drop of radius $R$.Volume of $n$ droplets = Volume of big drop$n 	imes \frac{4}{3}\pi r^3 = \frac{4}{3}\pi R^3 \Rightarrow n = \frac{R^3}{r^3}$ $(i)$Volume of big drop,$V = \frac{4}{3}\pi R^3$ $(ii)$Initial surface area of $n$ droplets,$A_i = n 	imes 4\pi r^2 = \frac{R^3}{r^3} 	imes 4\pi r^2 = \frac{4\pi R^3}{r} = \left( \frac{4}{3}\pi R^3 ight) \frac{3}{r} = \frac{3V}{r}$ $(Using (i) 	ext{ and } (ii))$Final surface area of big drop,$A_f = 4\pi R^2 = \left( \frac{4}{3}\pi R^3 ight) \frac{3}{R} = \frac{3V}{R}$ $(Using (ii))$Decrease in surface area,$\Delta A = A_i - A_f = \frac{3V}{r} - \frac{3V}{R} = 3V \left( \frac{1}{r} - \frac{1}{R} ight)$Energy released = Surface tension $	imes$ Decrease in surface areaEnergy released $= T 	imes \Delta A = 3VT \left( \frac{1}{r} - \frac{1}{R} ight)$.

$A$ certain number of spherical drops of a liquid of radius $r$ coalesce to form a single drop of radius $R$ and volume $V.$ If $T$ is the surface tension of the liquid,then

Similar Questions

The surface tension of a liquid is $5 \,N/m$. If a film is held on a ring of area $0.02 \,m^2$,its surface energy is about ........... $J$.

$8000$ identical water drops are combined to form a big drop. Then the ratio of the final surface energy to the initial surface energy of all the drops together is

$A$ mercury drop of radius $1 \ cm$ is divided into $10^6$ droplets of equal size. If the surface tension of mercury is $35 \times 10^{-3} \ N/m$,then the change in surface energy in the process is:

The potential energy of a molecule on the surface of a liquid compared to one inside the liquid is

Energy needed in the breaking of a drop of radius $R$ into $n$ drops of radius $r$ is given by : (With $S$ surface tension and $P$ atmospheric pressure)

Vedclass Test Series

Exam Paper Generator

Online Exam Module