1. Surface tension :
It is the property by virtue of which the free surface of a liquid at rest behaves
like an elastic stretched membrane leading to contract so as to occupy minimum
surface area.
Surface tension is measured as the force acting per unit length
of an imaginary line drawn on the liquid surface.
F ∝ ℓ
F = S ℓ
S =
F
ℓ
surface tension = Force
length
0
SI Unit N/m
2. Surface energy:
Surface energy is equal to the work done in increasing the area of the
surface film by unit amount.
Surface energy = Work done
Increase in surface area
F = S x ℓ
Work done = force x distance
Work done = 2. ( S x ℓ ). x
Increase in surface area of film = 2.ℓ.x
Surface energy = Work done
Increase in surface area
Surface energy =
2Sℓx
2ℓ x
Surface energy = S
Surface energy of liquid numerically equal to it’s surface tension.
σ
ℓ
0
3. Pressure difference across curved liquid surface :
a) If the surface is plane
PL = PV
Note: whenever a liquid surface is curved, the pressure on its concave side is grater
the pressure on convex side
S S
S
S
S S
A
A
A
0
b) If the surface is concave,
PV > PL
c) If the surface is convex,
PL > PV
4. Excess of pressure inside the liquid drop :
Initial surface area = 4π R2
Final surface area = 4π (R + dR)2
= 4π(R2 + 2RdR + dR2)
Final surface area = 4π R2 + 8π R dR
Increase surface area = 4π R2 + 8π R dR - 4πR2
Increase surface area = 8π R dR
Work done in enlarging the drop = increase in surface energy
= increase in surface area x surface tension
= 8π R dR x S ……..(1)
Work done = Force x distance
Work done = Pressure x area x distance
Work done = p x 4π R2 x dR ………………………….(2)
p x 4π R2 x dR = 8 π R dR x S
p =
2S
R
Excess pressure
5. Angle of contact :
It is defined as the angle θ between the tangent to the liquid surface at point of
contact and the solid surface inside the liquid.
The value of angle of contact depends on
Nature of the solid and the liquid in contact.
Cleanliness of surface in contact.
Medium above the free surface of liquid.
Temperature of solid.
Note
a) When Adhesive force > Cohesive force: Liquid wets solid surface and has
concave meniscus. θ is acute (less than 900) Ex: Water and glass.
b) When Adhesive force < Cohesive force: Liquid does not wets solid surface and
has convex meniscus. θ is obtuse (grater than 900) Ex: Mercury & glass
c) When Adhesive force = Cohesive force: Liquid surface is plane. θ =900
Ex: Water and silver 0
6. Capillarity or Capillary Action
Capillary tube: A long tube of very narrow
width (radius << length) is called capillary tube.
Capillarity: The phenomenon of
rise or fall of a liquid inside a capillary
tube when it is dipped in the liquid is
called capillarity.
7. Capillary Action in Different Liquids
• If capillary tube is dipped inside
such liquids which wet the solid
surface (Ex- water, alcohol), the
liquid rises in the tube from the
liquid surface.
Critical angle 𝜽 < 𝟗𝟎°
(Concave Miniscus)
• If capillary tube is dipped inside
such liquids which do not wet the
solid surface (Ex- mercury), the
liquid will depress in the tube
from the liquid surface.
Critical angle 𝜽 > 𝟗𝟎°
(Convex Miniscus)
8. For a particular set of liquid and solid
surface the value of critical angle 𝜃 is
constant. At constant temperature
surface tension S and density 𝜌 remains
constant. So,
𝒉 ∝
𝟏
𝒓
9. Why do we prefere hot soup?
With an increase in temperature of the liquid, its surface
tension decreases. So that it tends to acquire a larger area.
Hence hot soup having a low value of surface tension spread
properly on our tongue & provides better taste than cold soup.
10. Why do we use hot water to wash clothes?
As we know, when temperature increases, the surface tension
of liquid decreases. Due to this reason, hot water spreads in a
large area than cold water. So it is better to wash clothes in a hot
soap solution.
