lets discuss the concept of surface energy.

. when we talk about the stretched spring it always stores. some potential energy in

it. so whenever we talk about an elastic body , if it is an undeformed state we can say

that there is no potential energy in it but when we talk about its stretched state. whenever

we stretch a spring some work is done and that is stored in form of potential energy

in it which we term as elastic potential energy. similarly when we talk about , free surface

. of a liquid . as we have discuss that due to surface tension the free surface of a liquid

also behave like a stretched membrane , so we can say in free surface of liquid also

some. potential energy stored in it. and this energy is only stored in the surface of the

liquid which is behaving like a stretched membrane. that’s why this potential energy

is termed as . surface energy. so lets analyze the surface energy mathematically and, to

understand the surface energy lets have an experiment. say we are given with a u shaped

wire frame . on which, a slider is placed. and say the length of this slider is l. and

in the enclose part of this u tube and this slider we make, a soap film, say for example

we are making a soap film here . then obviously we can say the soap film will act like a stretched

membrane due to its surface tension. and if the soap film is having surface-tension t.

then this will exert a force on the slider in leftward direction as on the right side

there is no liquid. in a left side of the slider there is a soap film. as the film is

having two surfaces one is above the film and other is below the film. so net force

on it we can simply write . force on slider. due to surface tension this force we can write

as twice of t-l. as we already discuss that t is force acting per unit length, normal

to this. or normal to any line considered in contact with liquid . so here due to the

film there are two surface in contact with a slider , so net force on the slider in inward

direction will be “ 2”-t-l. now if we wish to move slider in outward direction we

need to apply an external force. and we can say to slowly. move the slider out. this external

force must be equal to the force which is applied by the surface tension that is two-t-l.

and say if we displace the slider by distance delta x, in outward direction. so we can say

if it is pulled outward by distance delta-x, the surface area of film will also increase.

and some work is done by the external force in pulling the slider outward , so whatever

work is done by the external force will be stored in the film in form of its surface

energy . in the similar way like if we are having a spring , which is already stretched

and if we further stretch this by an external force . then whatever work is done by the

external force will be stored in the, spring in form of elastic potential energy. so here

we can calculate work done. in displacing. slider by delta-x. is. this work delta w can

be written as actually it’ll be f-external into delta-x. and if it is slowly being pulled

in that case f-external we can substitute as, two t-l delta x . and in this situation

if we talk about its increase in area we can simply write increase in . surface area of

film. this delta s it can be written as twice of l delta x, because as we have discussed

this is a film, one surface is above the film and other is below the film. so total increase

in surface area of film will be twice of l delta-x l delta-x on one side l delta-x on

other side . so here twice l delta-x can be written as increase in area so here work done

can be written as t delta s. and as we already discussed whatever work is done , in pulling

the slider by distance delta-x , by the external agent , the work will be stored in form of,

elastic potential energy of the object being stretched and here, the film is being stretched

, so the surface of film will store this much of amount of work in form of potential energy.

so we can write this work as delta u which we can write as , increase in. surface energy

of film. and in this situation if we just rearrange this expression. here we can state

t we can write as delta u by delta, s. which gives us an idea about , the numerical value

of surface tension as. surface energy per unit area because, here the increase in area

is delta-s and increase in surface energy is delta-u, that means this delta u energy

is being stored in . this much amount of area as the whole film is uniform. so we can write

the surface tension as. surface energy. per unit area, this is another way how we can

define surface-tension. and lets have some example based on the concept of surface tension

defined as surface energy per unit area this will be more clear to u.

Ohhhh… Got it! Thank you!

I love the accent, btw! xD

Thanks a lot sir.. It was extremely helpful ππ»ππ»ππ

Drunk??

Sir, How do we know that force due to surface tension is conservative force. Because we only use the concept of energy stored in case of conservative force

very nice explanation. highly grateful

ty sir..π

why will it move …coz the fnet=0?

Dude your voice is soo bad… Like u r drunked and i feel like vomiting after hearimg ur voice

sir here if we take external force as 2TL the how can we pull the film as we appyl force 2TL in opposite direction to the surface tention and the force will be neutralized and now we have to apply some force to do work in short net force will be 0 the why will it move

Sir please give answer: Apart from liquid at the boundary, surface tension everywhere in the free surface cancels out due to opposite forces acting perpendicular to the hypothetical line but at the boundary, liquid molecules are present only in one side of the hypothetical line drawn along the boundary and because of this surface is stretched inside from all the boundaries .If Iam wrong please correct me?

A soap film consists of two layers of soap molecules separated by a thin layer of fluid, which may vary in thickness from . The largest thickness wills occur immediately after the formation of the film.

Once the film is formed it will begin to thin. The surplus water will drain away from the film by various draining processes. The thickness of the film will decrease until a final equilibrium thickness is reached.

In a state of equilibrium the surface tension is the same in all points on the surface.

When the film has reached equilibrium its surface area will have a minimal value, this minimum area property of soap films can be used to solve some mathematical minimization problems.

To understand consider a soap solution film. Suppose itβs thickness is 1 micron. Now, size of molecule as building blocks of the film is of the order of 10^(-10) m. This means that when we go from one side of the surface to the other side and count the number of molecules, it comes out to be roughly10,000. Keeping this in mind imagine a wall whose thickness is 10,000 bricks. In this situation if you disturbe one side of the wall the other side is not affected. In this sense two surfaces are INDEPENDENT of each other. Exactly the same situation exists in film of soap solution or in the wall of soap solution bubble in air. Therefore, we say that a film and a bubble in air has TWO independent surfaces.

You are simply awesome. Thank you. π

Work is negative time potential energy. Why there no.negative sign

Dear sir on moving the slider will it not be more difficult to move a slider over the distance (i.e force req . is directly proportional to distance .)

So we need to integrate. Or it is not what I am thinking.π€

3:03 why we take 2l

Why Fext =2Tl

Why βs=2lβx

Thank you so much sir now only alhamdhulillah my doubt cleared

thanks a lot sir very very tq

sir if nothing is given then do we have to consider soap flim on both the side always

Sir Kya ap tuition padhate h?

Sir I have a problem in imagination that how it is 2Tl please reply?

https://youtu.be/5NCOnr3VSAY

See these to understand surface tension better..