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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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Explanation of angle of contact
FA
mg
FC
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Explanation of angle of contact
FA
mg
FCIf FA is too large than FC then
angle of contact is zero liquidweights the solid completely.
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Explanation of angle of contact
If Fc is too large than FA
then angle of contact iszero liquid weights the solid
completely.
FA
mg
FC
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Explanation of angle of contact
FA
mg
FCIf FA = FC then angle of
contact is 67.5
0
liquid justweights the solid.
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Explanation of angle of contact
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