A certain number of spherical liquid drops of | vedclass

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

Question

(C) The change in surface energy is given by $E = T(\Delta A)$,where $\Delta A$ is the change in surface area.Initial surface area $A_i = n(4\pi r^2)$

Vedclass · Accepted Answer

$E=3 V T\left[\frac{1}{r}-\frac{1}{R}\right]$ is released.

Vedclass · Answer

(C) The change in surface energy is given by $E = T(\Delta A)$,where $\Delta A$ is the change in surface area.Initial surface area $A_i = n(4\pi r^2)$ and final surface area $A_f = 4\pi R^2$.Since volume is conserved,$n(\frac{4}{3}\pi r^3) = \frac{4}{3}\pi R^3$,which implies $n = \frac{R^3}{r^3}$.The change in surface area is $\Delta A = A_i - A_f = 4\pi(nr^2 - R^2)$.Substituting $n = \frac{R^3}{r^3}$,we get $\Delta A = 4\pi(\frac{R^3}{r} - R^2) = 4\pi R^3(\frac{1}{r} - \frac{1}{R})$.Since $V = \frac{4}{3}\pi R^3$,we have $4\pi R^3 = 3V$.Thus,$\Delta A = 3V(\frac{1}{r} - \frac{1}{R})$.Since $r  0$ represents a decrease in surface area,meaning energy is released.Therefore,$E = 3VT(\frac{1}{r} - \frac{1}{R})$ is released.

$A$ certain number of spherical liquid drops of radius $r$ coalesce to form a single drop of radius $R$ and volume $V$. If $T$ is the surface tension of the liquid,which one of the following statements is true for the energy $(E)$ in the process?

Similar Questions

The radii of two soap bubbles are $r_1$ and $r_2$. In isothermal conditions,they meet together in a vacuum. Then the radius of the resultant bubble is given by

An air bubble of radius $0.1\, cm$ is in a liquid having surface tension $0.06\, N/m$ and density $10^3\, kg/m^3$. The pressure inside the bubble is $1100\, N/m^2$ greater than the atmospheric pressure. At what depth $h$ (in $m$) is the bubble below the surface of the liquid? $(g = 9.8\, m/s^2)$

The work done in breaking a drop of liquid of radius $R$ (Surface tension $T$) into $64$ equal drops is

The excess pressure due to surface tension in a spherical liquid drop of radius $r$ is directly proportional to

Vedclass Test Series

Exam Paper Generator

Online Exam Module