Iit-jee And Mh-cet Surface Tension

By Nitin Oke For Safe Hands

Surface tension

Few things you need to know •01. Cohesive force: Force of attraction / repulsion between the molecules of the same substance is called as cohesive force. •02. Adhesive force: Force of attraction between the molecules of different substances is called as adhesive force. •In general the intermolecular force is of the order of 10-11N where as gravitational force is 10-50N •Intermolecular distances are of the order of 10-10m

• Range of molecular attraction: Maximum distance up to which cohesive force exerted by molecule is effective is called as range of molecular attraction. Range of molecular attraction is generally of the order of 10 –9 m in case of solids and liquids. Sphere of influence :An imaginary sphere of radius equal to molecular range drawn with molecule as center is called as sphere of influence.

Surface Energy. Potential energy per unit surface area of liquid surface is called as surface energy. • It is clear that molecule on the surface of liquid possesses more potential energy than a molecule in the interior of a liquid. To reduce this energy liquid will try to reduce surface area • The tendency of liquid to reduce its surface area is called as Surface tension.

Surface tension

• If surface area is to be reduced then the force must act in tangential direction to surface. This force must act at ‘end” of liquid surface hence it is defined as – • Force due to Surface Tension: Tangential Force per unit length acting at right angle on either side of imaginary line drawn 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 this unit is same as that of force constant • [T] = [ML0T-2]

Surface tension

Surface tension FF T == 4824aπr

Relation between surface tension & surface energy: • Consider an open rectangular frame ABCD A P D of a wire. • Wire PQ is able to slide over the rectangular frame without friction. B Q C Length of wire PQ is equal to ‘L’. • Let rectangular frame ABCD is dipped in soap solution. Soap Film is formed in the region ABQP. Due to surface tension soap film tries to contract in area.

Relation between surface tension & surface energy: •Therefore a force “F” acts On wire PQ. Direction of A this force is towards AB. Magnitude of force ‘F’ =T (2L) Factor ‘2’ is because, soap film has two surfaces B front surface & back surface in contact with wire. •Let wire PQ is pulled away from AB in order to increase area of film. Mechanical force required to pull the wire PQ is F’ As

P

D

Q

C

F = F’ in magnitude but F = -F’ ∴F’ = T x 2l. If wire PQ is displaced through dx. Then work done 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 of potential energy. • If dA = 1m2 then T = W Thus surface tension is amount of work done in order to increase surface area through one unit area. •SI unit of surface tension is also J/m2.

• Work done •in forming a soap bubble of radius R is T. dA = T. 2.(4πR2 ) = T. 8πR2 during formation of soup bubble energy will be absorbed, due to which the temperature will fall down in adiabatic process, chemically such reactions are called as endothermic reactions. R

• Work done (ii) in breaking a big drop of radius R in n drops of equal radius ‘r’ is W = 4πR2T (n 1/ 3 – 1) = 4πr2T (n – n 2/ 3) When a big drop is broken into large number of small drops, then energy is absorbed because the surface area increases. Above result is obtained by using (4/3)π n.r3=(4/3) πR3

Energy liberated in combining n equal drops of radius r to form a big drop of radius R is obtained by using (4/3)πR3 =n.(4/3)πr3 R3 =n.r3 hence R2 =n2/3r2 E = 4πR2T (n 1/ 3 – 1) = 4πr2T (n – n 2/ 3) When a large number of drops combine to form a big drop, then the energy will be liberated because the surface area decreases, due to which the temperature will increase in adiabatic process, chemically such reactions are called as exothermic

Angle of contact When a liquid is in contact with solid, the liquid surface at the point of contact is curved. The angle between the tangent drawn to liquid surface at point of contact and solid surface measured inside the liquid is called as angle of contact. Angle of contact may have any value between 00 and 1350.

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 usual water + glass • liquids which completely wets the solid angle of contact is 0o eg. Pure Water + glass, • For liquid, which does not wet the solid, angle of contact is obtuse e.g. mercury + glass.

Explanation of angle of contact Various forces acting on molecule ‘A’ are • Negligible weight of molecule , which acts vertically down ward • Adhesive force FA by solid molecule acting at right angle to solid. • Cohesive force FC in side liquid by molecules of same liquid act at 45o to surface. • Adhesive force by air molecules which is very small and hence it is neglected. This force is negligible because very small number of air molecules are present in sphere of influence. Direction of resultant vector decides shape of liquid at the point of contact in particular the liquid surface must be normal to resultant.

Explanation of angle of contact

FA

mg

FC

Explanation of angle of contact

FA If FA is too large than FC then angle of contact is zero liquid weights the solid completely.

mg

FC

Explanation of angle of contact

FA If Fc is too large than FA then angle of contact is zero liquid weights the solid completely.

mg

FC

Explanation of angle of contact

FA If FA = FC then angle of contact is 67.50 liquid just weights the solid.

mg

FC

Explanation of angle of contact

FA If √2.FA = FC then angle of contact is 900 liquid just weights the solid. If √2.FA > FC then R will turn outward hence liquid surface will be concave If √2.FA < FC then R will turn outward hence liquid surface will be convex

mg

FC

Rise of liquid in Capillary tube Ascent formula

• The phenomeno n of rise or fall of a liquid in a capillary tube is known as capillarity.

Capillarity • Fcosθ = weight of lifted liquid column -½(4 π r /3) 2 2 3 F.cosθ = πr h +[ πr r – ½(4 πr /3)]ρ g F. sinθ +πr2r 3

πr2h

r

FT h

Capillarity • Fcosθ = weight of lifted liquid column = πr2h +[ πr2r – ½(4 πr3/3)] ρg T(2πr) cos

θ = πr2(h–r/3) ρg

T = r[h-(r/3)] ρg ≅ rhρg /2

cos

cos

θ /2

θ

h= 2 Tcos θ/ r ρ g 2πr is called wetted perimeter

r FT h

Tilt of Capillary θ

L=h/cosθ

Capillary of short length

L=h/cosθ

Capillary of short length

h1R1=h2R2

as h decreases R increases

Shape of drop T2

• Phenomenon of surface tension is θ observed along a surface separating T3 T1 any two media. Consider a liquid drop in equilibrium on flat solid mg surface. • Let T1 is surface tension for solid-liquid interface T2 is surface tension for airsolid interface T3 is surface tension for air-liquid interface. Angle of contact θ is always from liquid side.

Shape of drop T3 sinθ T2

T3 θ T3 cosθ T1

• In equilibrium the horizontal and vertical forces must be in equilibrium.Thus • T2 = T1 + T3 cosθ

• cosθ = (T2 - T1 )/ T3

T2 θ T3

T1

cosθ = (T2 - T1 )/ T3 i) When T2 > T1; cosθ is positive, θ is acute.

T2 θ

T3

T1

cosθ = (T2 - T1 )/ T3 i) When T2 < T1; cosθ is negative, θ is obtuse.

T2 θ

T3

T1

cosθ = (T2 - T1 )/ T3 i) When T2 = T1; cosθ is zero, θ is 90o.

cosθ = (T2 - T1 )/ T3 i) When T2 - T1 > T3 ;cosθ is not possible as > 1 Liquid drop can never have equilibrium and will spred over the entier surface.

Notable notes • When a bubble is formed the pressure inside the bubble is 4T/R • When a bubble is formed inside the liquid the pressure inside 2T/R the bubble is

4T/R PoP+ 4T/R o +

Po + 2T/R

Notable notes • When a liquid drop is formed the excess pressure inside 2T/R the drop is

Po + 2T/R

Notable notes

h

4T/R = hρg

Notable notes

1 1 1 = R− R R2 R1 1

R is radius of interface of two bubbles of radius R1 and R2.This is due to fact that P on interface is difference of pressure of two faces

R2 R

Bubbles coalescing notes with each other Notable isothermally in vacuum

R2

R R1

R = R +R 2

2 1

2 2

Effect of temperature

• Over a small range of temperature the surface tension decreases linearly as temperature increases. Result by Jaeger • T = T0(1-αt) where α is temperature coefficient of surface tension. • Eotvos formula is Tt= K(tc- t) where tc is critical temperature • The formula was corrected by

Effect of temperature

• Modified by Ramsay and Shields T.(M.V.x)3/2=K.(tc- t - d) Where t0is critical temperature, x is coefficient of association of liquid at t.”d” is a constant ( 6 < d < 8 for most of liquids) M is molecular weight V is volume and K is constant (2.12< K <2.22) • Ferguson’s formula is for wide range of temperature variation

Effect of impurity

• It is found that when an inorganic substance such as sodium chloride (common salt) is dissolved in water, the surface tension of water increases. • On the other hand, when an organic substance such as soap solution is added to water, the surface tension of water decreases. • Generally if highly soluble substance is added to a liquid its surface tension increases. • An impurity insoluble in a liquid

For everything listed below the reason is surface tension • Blotting paper absorbs ink • Towel can soak water due to fibrous structure • Sap rises in plants • Fields are ploughed to avoid evaporation of water inside the field • Water oozes from earthen pot used during summer days • Sponge retains water

For everything listed below the reason is surface tension • Hair of brush spreads out in water but as taken out they cling together • Liquid drops are spherical in absence of gravity. • Needle floats on liquid surface • Oil spreads on cold water • Ink pain has split nib • During soldering of wire the flux is applied before soldering.