Physics Notes available in Help For Entrance App.
SURFACE TENSION
Property of free surface of liquid of virtue of which it tends to contract and occupies minimum surface area.
Surface tension is measure by force per unit length on imaginary line drawn on the free surface of liquid, the
direction of force being perpendicular to line.
F
T= 𝑙
Surface tension depends only on nature of liquid and not on area of surface or length of line considered.
Surface tension decreases with rise in temperature and becomes zero at critical temperature.
For molten cadmium and copper, surface tension ↑ when temperature ↑.
If impurities are highly soluble, surface tension of liquid increases due to increase in intermolecular force.
If impurities are insoluble or sparingly soluble (like soap, camphor), surface tension of liquid decrease.
On contamination, surface tension decreases.
If ring of radius 'R' is floating on liquid surface of surface tension 'T', then force
F = T × 2(2πR)
For straight thread of length 'l' placed on liquid of surface tension T, force on thread
F = T × 2l
Work done in increasing surface area against surface tension is stored in surface as potential energy and is given
as
U = TΔA
Work done in forming drop or air bubble in a liquid will be
W = T × 4πr2
For a soap bubble in air
W = T × (2 × 4πr2)
Where 2 is for two free surface
Work done in increasing size of bubble
W = T × 4π(r22 – r12)
If large drop of radius 'R' is split into 'n' equal small drops of radius 'r', then work done is
W = T × 4π R2(n1/3 – 1)
If area↑, energy gets stored and if area↓, energy gets released.
Excess pressure: Difference of pressure between two sides of the liquid surface.
For liquid drop or air bubble inside a liquid,
2T
Pexcess = r
For soap bubble in air
4T
Pexcess = (Being two free surfaces)
r
Physics Notes available in Help For Entrance App.
For cylindrical surface,
T
P=
r
2T
For liquid film of thickness 'd' between two glass plates, Pexcess = d
Force required to separate the plates is given by F= Pexcess * Area
Angle of contact (θ): Angle between tangents drawn on liquid surface and solid surface inside liquid at point
of contact.
Angle of contact for:
ordinary water and glass = 8o approx.
glass and mercury= 135o approx.
pure water and glass = 0
pure water and silver = 90
Angle of contact↑ if highly soluble impurities is dissolved in liquid and ↓ sparingly soluble impurities is
dissolved in it.
θ↓ on increasing temperature.
Capillarity:
Rise or fall of liquid inside capillary tube.
Height raised or fallen inside capillary tube is
2T cos θ
h= r ρg
2T
For pure water in clean glass, θ = 0, h = rρg
Capillarity depends on the nature of liquid and solid.
If θ > 90o meniscus is convex i.e. liquid will descend.
If θ < 90o, meniscus is concave.
If θ = 90o , no capillary action is observed.
For given liquid and solid, ρ, T, θ are constant
1
hr = constant i.e. h ∝ r
If a vertical capillary, tube with liquid column raised to height 'h' is filted through an angle 'α' with vertical,
then length 'l' of liquid column in fitted capillary tube is given by
l = h sec(α)
Important Notes:
Physics Notes available in Help For Entrance App.
When two bubbles of different radii r1, r2 (r2> r1) come into contact, the radius of common interface is
r2 r1
R=
r2 −r1
When several bubble same liquid get coalesced in vacuum isothermally to form a big bubble, then radius of
big bubble 'R' is given by
PV= constant
PV= P1V1+ P2V2+……..+PNVN
R2 = r12 + r22 + …………. + rn2 R = N1/2 r
If r1 = r2 = ……… = rn = r1 R = N1/2 r
Due to surface tension, liquid drops assume spherical surface to have minimum surface area.
Surface tension force on disc of radius R with concentric hole of radius 'r' is = T × 2π (R + r)
If number of small drops of liquid of density ρ, specific heat C, surface tension T and each of radius 'r' coalesce
to form big drop of radius R,
Then rise in temperature is
3T 1 1
Δθ = JρC ( r − R)
J = Mechanical equivalent of heat
Surface tension of liquids is due to intermolecular force.
Hairs of brushes when dipped in water spread out, but as soon as it is taken out , its hair stick together due to
surface tension.
If a small piece of camphor floats on the surface of pure water, it doesn’t remain steady but dances on the surface
due to the surface tension.
On electrifying the surface of the liquid bubble, its surface tension decreases but its radius expands.
At critical temperature the surface tension becomes zero.
The tip of the glass tube becomes round due to the effect of the surface tension.
If a small drop of liquid is kept in between the two layers of glass plates so that a very thin layer of large area
is formed, then pressure inside the liquid layer is less than the pressure on the plates because pressure on convex
side is greater than the pressure on the concave side.
Rise of oil in wick of lamp is due to capillarity.
On tilting the capillary tube, the angle of contact remains the same.
If a capillary tube is dipped in the liquid in the state of the weightlessness, the water will rise to the other end
but doesn’t overflow.
