iit-jee and mh-cet surface tension

8/14/2019 IIT-JEE and MH-CET Surface Tension

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Surface tensionSurface tension

ByNitin Oke

ForSafe Hands


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Few things you need to know

01. Cohesive force: Force of attraction/ repulsion between the molecules ofthe same substance is called ascohesive force.

02. Adhesive force: Force ofattraction between the molecules ofdifferent substances is called asadhesive force.

In general the intermolecular force isof the order of 10-11N where asgravitational force is 10-50N

Intermolecular distances are of the

order of 10-10m


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Range of molecular attraction: Maximumdistance up to which cohesive forceexerted by molecule is effective is called

as range of molecular attraction. Rangeof molecular attraction is generally of theorder of 10 9 m in case of solids andliquids.

Sphere ofinfluence :Animaginary sphere ofradius equal to

molecular rangedrawn with moleculeas center is calledas sphere ofinfluence.


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Surface Energy.Potential energy perunit surface area of liquid surface is calledas surface energy.

It is clear that molecule on the surface ofliquid possesses more potential energy thana molecule in the interior of a liquid. Toreduce this energy liquid will try to reducesurface area

The tendency of liquid to reduce itssurface area is called as Surface tension.


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Surface tension If surface area is to be reduced then the

force must act in tangential direction tosurface. This force must act at end ofliquid surface hence it is defined as

Force due to Surface Tension:Tangential Force per unit length acting atright angle on either side of imaginary linedrawn on the free surface of liquid is called

as surface tension of liquid.T = F/L SI unit of surface tension is N/m.CGS unit of surface tension is dyne/cm thisunit is same as that of force constant

[T] = [ML0T-2]


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Surface tension


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Surface tension

r2

FT

=

r4

FT

=

a4

FT =

a8

FT =


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Relation between surface tension & surfaceenergy:

Consider an open

rectangular frame ABCDof a wire.

Wire PQ is able to slideover the rectangular

frame without friction.Length of wire PQ is equalto L.

Let rectangular frame

ABCD is dipped in soapsolution. Soap Film isformed in the regionABQP. Due to surface

tension soap film tries tocontract in area.

A D

B C

P

Q


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Relation between surface tension & surfaceenergy:

Therefore a force F actsOn wire PQ. Direction ofthis force is towards AB.Magnitude of force F =T(2L) Factor 2 is because,

soap film has two surfacesfront surface & backsurface in contact withwire.

Let wire PQ is pulled awayfrom AB in order toincrease area of film.Mechanical force required

to pull the wire PQ is F As

A D

B C

P

Q


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F = F in magnitude but F = -F

F = T x 2l.If wire PQ is displaced through dx. Then workdone during this displacement:dW = F. dx = - T 2 L dx = T.dA

(Where dA = 2L.dx) dW = T.dA.This work done is stored in the form ofpotential energy. If dA = 1m2 then T = W Thus surface

tension is amount of work done in order toincrease surface area through one unit area.SI unit of surface tension is also J/m2.


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Work donein forming a soap bubble of radius R

is T. dA = T. 2.(4R2

)

= T. 8R2

during formation of soup bubbleenergy will be absorbed, due towhich the temperature will fall

down in adiabatic process,chemically such reactions arecalled as endothermic reactions.

R


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Work donein(ii) breaking a big drop of radius R in n drops

of equal radius r is

W = 4R2T (n 1/ 3 1)

= 4r2T (n n 2/ 3)

When a big drop is broken into large number

of small drops, then energy is absorbedbecause the surface area increases.

Above result is obtained by using (4/3)

n.r3

=(4/3) R3


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Energy liberated in combining nequal drops of radius r to form abig drop of radius R is obtained by

using(4/3)R3 =n.(4/3)r3

R3 =n.r3 hence R2 =n2/3r2

E = 4R2T (n 1/ 3 1)

= 4r2T (n n 2/ 3)

When a large number of dropscombine to form a big drop, then

the energy will be liberatedbecause the surface areadecreases, due to which thetemperature will increase inadiabatic process, chemically suchreactions are called as exothermic


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Angle of contactWhen a liquid is in contact with solid, the liquid

surface at the point of contact is curved. Theangle between the tangent drawn to liquidsurface at point of contact and solid surfacemeasured inside the liquid is called as angle ofcontact. Angle of contact may have any value

between 00 and 1350.


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Angle of contact Angle of contact is constant for given solid liquid

pair. For liquid, which merely wets the solid,

angle of contact is 90o e.g. water + silver. liquid, which partially wets the solid, angle of

contact is acute Kerosene + glass or usualwater + glass

liquids which completely wets the solid angle ofcontact is 0o eg. Pure Water + glass,

For liquid, which does not wet the solid, angle ofcontact is obtuse e.g. mercury + glass.


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Explanation of angle of contact

Various forces acting on molecule A are

Negligible weight of molecule , which actsvertically down ward

Adhesive force FA by solid molecule acting at

right angle to solid.

Cohesive force FC in side liquid by molecules ofsame liquid act at 45o to surface.

Adhesive force by air molecules which is verysmall and hence it is neglected. This force is

negligible because very small number of airmolecules are present in sphere of influence.Direction of resultant vector decides shape ofliquid at the point of contact in particular the

liquid surface must be normal to resultant.


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FA

mg

FC


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FA

mg

FCIf FA is too large than FC then

angle of contact is zero liquidweights the solid completely.


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If Fc is too large than FA

then angle of contact iszero liquid weights the solid

completely.

FA

mg

FC


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FA

mg

FCIf FA = FC then angle of

contact is 67.5

0

liquid justweights the solid.


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FA

mg

FCIf2.FA = FC then angle of contactis 900 liquid just weights the solid.

If2.FA

> FC

then R will turn

outward hence liquid surface will

be concave

If2.FA < FC then R will turnoutward hence liquid surface will

be convex


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Rise of liquid in Capillary tubeAscent formula

Thephenomenon of rise or

fall of aliquid in acapillary

tube isknown ascapillarity.


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Capillarity Fcos = weight of lifted liquid

column

= r2h +[ r2r (4 r3/3)]g

FT

F.cos

F. sin

h

r

r2

h

+r2r

-(4 r3/3)


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Capillarity

FT

h

r

T(2r) cos = r2(hr/3) g

T = r[h-(r/3)] g cos /2

rhg /2 cos

h= 2 Tcos / r g

Fcos = weight of lifted liquid column

= r2h +[ r2r (4 r3/3)] g

2r is called

wetted perimeter


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Tilt of Capillary

L=h/cos


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Capillary of short length

L=h/cos


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Capillary of short length

h1R

1=h

2R

2as

h

decreases Rincreases


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Shape of drop

Phenomenon of surface tension isobserved along a surface separating

any two media. Consider a liquid drop inequilibrium on flat solid surface.

Let T1 is surface tension for solid-liquid

interface T2

is surface tension for air-

solid interface T3

is surface tension for

air-liquid interface. Angle of contact isalways from liquid side.

T2

T1T3

mg


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Shape of dropT3

T1T2

In equilibrium the horizontal and verticalforces must be in equilibrium.Thus

T2 = T1 + T3 cos

cos = (T2 - T1 )/ T3

T3

cos

T3

sin


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cos = (T2

- T1

)/ T3

i) When T2

> T1; cos is positive, is acute.

T2

T1

T3


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cos = (T2

- T1

)/ T3

i) When T2

< T1; cos is negative, is

obtuse.

T2

T1

T3


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cos = (T2

- T1

)/ T3

i) When T2

= T1; cos is zero, is 90o.

T2

T1

T3


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cos = (T2

- T1

)/ T3

i) When T2 - T1 > T3 ;cos is not possible as >1 Liquid drop can never have equilibriumand will spred over the entier surface.


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Notable notes

When a bubbleis formed the

pressure insidethe bubble is4T/R

When a bubble

is formed insidethe liquid thepressure insidethe bubble is2T/R

Po + 4T/R

Po + 2T/R

Po + 4T/R


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Notable notes

When a liquiddrop is formed

the excesspressure insidethe drop is

2T/R

Po + 2T/R


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4T/R = hg

h

Notable notes


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R1 R2R12 R

1

R

1

R

1=

Notable notes

R is radius of interface of two bubblesof radius R1 and R2.This is due to fact

that P on interface is difference of

pressure of two faces


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R1

R2

2

2

2

1

2RRR +=

R

Bubbles coalescing with each otherisothermally in vacuum

Notable notes

Eff t f t t


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Effect of temperatureOver a small range of

temperature the surface tensiondecreases linearly astemperature increases. Result by

JaegerT = T0(1-t) where is

temperature coefficient ofsurface tension.

Eotvos formula is Tt= K(tc- t)where tc is critical temperature

The formula was corrected by Eff t f t t


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Effect of temperatureModified by Ramsay and Shields

T.(M.V.x)3/2

=K.(tc- t - d)Where t0is critical temperature, xis coefficient of association of

liquid at t.d is a constant ( 6

iit-jee and mh-cet surface tension

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