Question
Define surface tension. Obtain the relation between surface tension and surface energy.
✓
Answer
Surface tension $T$ is defined as, the tangential force acting per unit length on both sides of an imaginary line drawn on the free surface of liquid.
Relation between surface tension and surface energy
Consider a rectangular frame $P ^{\prime} PSS$ ' having a movable wire QR . Let $Q R=P S=L$. If a soap film is formed on the frame PQRS, then the surface tension will try to pull the wire inward by a force $F$.
$\therefore $ Surface tension $=\frac{\text { Force }}{\text { Free surface }}$
$\therefore \ T=\frac{F}{2 L}$
$\therefore \ F=T(2 L)$
If the wire is pulled out to $Q ^{\prime} R$ ' through distance ' $d x^{\prime}$ ', then work done is given by
$d w=F . d x$
$\therefore \ d w=T .2 L . d x$
But increase in area $=d A=2 L . d x$
$\therefore \ d w=T . d A$
This work done in stretching the film is stored in the area dA of the film as its potential energy. This energy is called surface energy.
$\therefore $ Surface energy $=T . d A$
Above expression represents the relationship between surface tension and surface energy.
Relation between surface tension and surface energy
Consider a rectangular frame $P ^{\prime} PSS$ ' having a movable wire QR . Let $Q R=P S=L$. If a soap film is formed on the frame PQRS, then the surface tension will try to pull the wire inward by a force $F$.
$\therefore $ Surface tension $=\frac{\text { Force }}{\text { Free surface }}$
$\therefore \ T=\frac{F}{2 L}$
$\therefore \ F=T(2 L)$
If the wire is pulled out to $Q ^{\prime} R$ ' through distance ' $d x^{\prime}$ ', then work done is given by
$d w=F . d x$
$\therefore \ d w=T .2 L . d x$
But increase in area $=d A=2 L . d x$
$\therefore \ d w=T . d A$
This work done in stretching the film is stored in the area dA of the film as its potential energy. This energy is called surface energy.
$\therefore $ Surface energy $=T . d A$
Above expression represents the relationship between surface tension and surface energy.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Do we need a banked road for a two wheeler? Explain.
Four moles of a gas expand isothermally at $300 K$. If the final pressure of the gas is $80 \%$ of the initial pressure, find the work done by the gas on its surroundings. ( $R=8.314 J / mol . K )$
→State the postulates of Bohr’s atomic model.
A potentiometer wire of length $5\ m$ is connected to a battery. For a certain cell having negligible internal resistance, the null point is obtained at $250\ cm$. If the length of the potentiometer wire is increased by $1\ m$, where will be the new position of the null point?
→What is meant by thermal equilibrium ? What is meant by the expression "two systems are in thermal equilibrium" ?
A toroidal coil has an inductance of $47 mH$. Find the maximum self-induced emf in the coil when the current in it is reversed from $15 A$ to $-15 A$ in $0.01 s$.
→What is a toroid? With a neat diagram, describe the magnetic field produced by a toroid carrying a steady current.
Calculate De Broglie's wavelength of the bullet moving with speed $90\ m/sec$ and having a mass of $5\ gm.$
→The diameters of two pistons in a hydraulic press are $5 \mathrm{~cm}$ and $25 \mathrm{~cm}$ respectively. A force of $20 \mathrm{~N}$ is applied to the smaller piston. Find the force exerted on the larger piston.
→Describe an experiment for the study of characteristics of photoelectric effect.