1. Intermolecular forces exist between molecules in solids, liquids, and gases and arise from potential energy and thermal energy of molecules. 2. The surface tension of a liquid is defined as the force per unit length acting at the surface perpendicular to the surface. It is a measure of the work required to enlarge the surface area of the liquid. 3. Capillary action in thin tubes occurs due to differences in intermolecular attractive forces between the liquid and tube material, resulting in a net force that causes liquids to rise or fall in the tube depending on the contact angle.

1. SURFACE TENSION
INTERMOLECULAR FORCE
Force which exist between the molecules of solid, liquid
and gaseous are known as intermolecular forces. These forces
arise from the two main causes (i) The potential energy of the
molecules (ii) The thermal energy of the molecules this is K.E of
the molecules and it depends on the temperature of the substance
concerned
The figure below shown a force separation graph from inter
molecular forces between two molecules.

2. 𝚛o is the (separation) Equilibrium separation of the to
molecules. The net force here is zero. When the separation of
the two molecules is less than ro the net force is repulsive
and when the separation is greater than ro the net force is
attractive.
N:B the force between two molecules changes as they
gradually brought together from the separation greater than
ro to one less than ro. At large distance the force is
negligible. As the molecules are brought closer there is a net
attractive force which increases to a maximum value before
diminishing to zero ro. Further bringing the molecules
together results cute a net repulsive force.
The figure below shows that the potential energy separation
graph for intermolecularforces betweentwo molecules.

3. From the figure above than be observed that the separation
of the molecules for the minimum potential energy is ro and
the net force on the molecules at the minimum potential
energy position is zero. The potential energy have positive
values at small separations but negative values at large
separations. Positive value means that the work has to be
done molecules.
Molecules in solids are said to be in a condensed phase or
state. They have relatively low thermal energy compared
with their R.E U and vibrating about which the minimum of
the curve
If the thermal Energy is increase by amount corresponding
to cc the molecules oscillate between the limits X AND Y the
molecules on the left of C experienced as greater force to
wards it than when on the right. Thus the molecule return
(quickly) e quicker to CI therefore the means position is on

4. the right of CI this corresponds to a mean separation of
molecules which is greater than ro . Thus the sold expands
when its. Thermal energy is in creased.
SURFACE TENSION
If the clean glass rod is dipped into the water and then
removed some water aling to the glass rod. We say that the
water wet the glass. The adhesion of molecules of water to
glass must therefore be greater than the cohesion to glass.
If you carefully place the razor blade on the surface of water
it remains in the surface even though it has more than seven
times as dense as water
The water acts as through it has a thin elastic film
These as observations shows that surface of a liquid acts like
an elastic skin covering the liquid or in state of tension. All
liquids shows surface tension.
In many liquids the surface tension is not as strong as that of
water or mercury. The cleaning action as that of water or
mercury. The cleaning action of the water or mercury. The
cleaning action of the water or mercury. The cleaning action
detergents is due to their ability to lower the surface tension
of the water making it possible for the water and detergents
more readily into the pores of the substances being cleaned.

5. Molecules at A attracted in all directions by cohesion force of
the surrounding molecules. A molecules at B attracted
equally on all side but move strongly downwards. The
molecules at c is not attracted in upward direction at all.
There is unbalanced force tendency to pull such surface
molecules towards the enter of the liquid and keep the free
surface of the liquid as small as possible.
The effect of this unbalanced contracting force i to make the
liquid behave as though it was contained in a stretched
elastic skin. The tension in the is skin is the surface tension
when the force acts on a liquid surface firm and distort it the
cohesive if the liquid molecules exerts an equal and opposite
forces to restore the horizontal surface.
Thus the weight of the supported razor blade produce a
depression in the water surface firm. The cohesion of water
molecules exert balancing upward force on the razor blade
by intending to restore the surface of the liquid to its original
condition.
Definitionof thesurface tensionits unit and dimension

6. The surface tension of a liquid in the coefficient of the
surface tension of the liquid as defined as the force per unit
length acting in the surface at right angles to one side of the
side of the line drawn in the surface. The unit of the ɤ is
newton meter (NM the dimension of surface tension is
= = = MT2
SURFACE ENERGY
Molecules on the surface of the liquid of constant by pulled
inwardly and therefore in order to bring the molecule from
within the liquids to surface of the water. Some work has to
be done. All molecules in the surface film has higher
potential energy than those deep inside the liquid. This
shows that work has to be done to create a surface is known
as surface energy.
Consider the wire frame A B C D such that AB is moving over
it. The surface tension will pull the wire inwards by a force F
given by F = 2 ɤL

7. When ɤ is the surface tension and L is the length. AB the
factor of 2 is because of the fact that the soap film has the
surface let A ‘B’ be the film by small distance x. Let A ‘B’ be
the new position of the A B Work done in enlarging surface
Energy = Force x distance
= 2 ɤ L.X
= ɤ 2LX
But the 2LX is the total increase in the surface area of the
film.

8. Work done per unit area in enlarging area ɤ. Thus the
surface tension ɤ is defined as the work done per unit are a
in increasing the surface area of the liquid under Isothermal
conditions. Surface tension is therefore also called the free
surface energy per unit area.
CAPILLARITY TUBE ɤ ANGLEOF CONTACT
When the capillary tube is immersed in water and one end is
on the surface of water the following are observations in
case of mercury level in the tube compared to outside level
there is depression. All these explain the phenomenon of
capillarity. The molecular explanation of this due to adhesive
and forces of interaction
It is assured that the meniscus of water assumes a
hemispherical shape and if the glass tube is less. But in
uncleaned tube there occurs as angle of contact from the fig
above the tangent X,y makes an angle with the table
surface.

9. The angle ÆŸ is known as angle of contact and is
measured through the liquid and its is an acute angle. In
case of mercury the angle of contact is an obtuse.
Phenomenon of soap bubbles and the tension of the thread
on the soap bubbles
When the thread is tied cross the ring and dipper the soap of
the soap film and the thread is loose.
Loose thread with soap film Tension of an thread after
breaking oneside
If the however the film on the one side of the thread is
broken it is immediately drawn foward the other side of the
tension which now exists along the boundary of the film.

10. A thread subjected to a pull by soap film in one side only.
Consider an element of the thread APB. Let the radius of
curvature of P be r and the all which subtends the angle dÆŸ
at the centre 0, the length AB = rdθ and the arc is in
equilibrium under three forces
i) Forces acting tangentially at A and B.
Force 2 ɤ r d Ɵ acting normally outward at P
Resolving in the direction of OP and at right angles to it the
component of F at right angles to OP cancel and that in the
directionof OP we have.

11. 2ƔrdƟ = F sin + F sin
29rdÆŸ = 2F sin
As dÆŸ sin
Thus 2ɤ r dƟ =2F
F = 2ɤr
As the surface tension is the same wherever P is taken and
the tension F in the string must be the same throughout its
length it follows that must be the same wherever P is taken
so that the tread sets in an arc of a circle.
Pressure difference in a bubble or curved surface.

12. Consider a bubble formed inside a liquid. The bubble is in
equilibrium under three forces.
 The forces due to external pressure P1 (FP1)
 The surface tension force Fɤ
 The force due to internal pressure P2 inside the bubble (FP2)
For equilibrium we have
Force due to external pressure + Force due to surface
tension = Force due to internal pressure P2
FP1 + Fɤ= FP2
P1πr2 + 2πrγ = P2πr2
P2 – P1 =
Now (P2 – P1) is the Excess pressure P in the bubbles over
the out side p pressure

13. Excess pressure = P1 =
Although use consider a bubble the same formula for excess
pressure holds for any curved surface or meniscus where r is
its radius it circumference and r its surface tension provided
the angle of contact is zero. If the angle of contact is ÆŸ the
formula is modified by replacing ɤ by ɤCOSƟ.
Thus excess pressure P1 =
EXCESSPRESSURE IN A SOAP BUBBLE
A soap bubble with radius r has two surface so in case of
liquid bubbles, the soap bubble is in equilibrium under three
forces namely
FP1,Fγ and FP2

14. FP1 + Fɤ =Fp2
The factor of 2 in Fɤ occur because the soap bubbles have
two surface.
P2 – P1 = , hence the excess pressure P =
MEASUREMENT OF SURFACE TENSION BY CAPILLARYTUBE.
Suppose a clean glass capillary tube is dipped into water,
water level rises and the angle of contact is zero let Ɣbe its
magnitude of surface tension. The fig below shows a section
of the meniscus M at B which is hemisphere.

15. Glass AB is tangent to the liquid at its meniscus.
The surface tension force acts along the boundaries of the
liquid and the air verticallydown wards on the glass.
According to reaction and action the glass exerts an upward
force on the liquid meniscus if r is the radius of the capillary
tube length of water in contact with glass is 2xr.
2 = Upward force on liquid (I)
This force supports the light of the liquid column of height h
above the outside level.
Volume of the liquid =

16. Mass of the liquid = where P is density
The weight of liquid =
From i) we have
2 =
=
Therefore, the angle of contact is assumed equal to zero. The
weight of small amount of liquid above the meniscus, has been
neglected.
CAPILLARY RISE AND FALL BY PRESSURE METHOD
In figure (I) below the liquid rises up the tube to a height (h), so
that the pressure P1 has a less than pressure P2 and

17. If the capillary tube is dipped into water the angle of contact is
practically zero. Fig (i) This is the atom ospheric pressure and P1
is the pressure in the liquid we have
P2 – P1 =
If H is the atmospheric pressure h is the height of the liquid the
liquid in the table and its density
P2 =H and P1 = H – h ρÉ¡
H –(H - hρÉ¡) =
hρÉ¡ =
h =

18. increases as r decrease ie the narrow the tube the greater the
height to which the water raised. Suppose tube is pulled down
until the top of height
if the height l of the tube is above the water than the calculated
value of h in the above formula the water surface at the top of
the tube now meet at an angle of contact. This angle is an acute
one. The radius R of the meniscus is greater than the capillary
tube of radius r.
From figure we have COSÆŸ =
From the excess formula for the meniscus
P2 – P1 =
H – (H - hρÉ¡) = = L
L=
Cos ÆŸ = =
Let the depression of the mercury inside the tube of radius r be h
in figure below, the pressure P2 below the curved surface of
mercury is the atmospheric pressure R
Out side the curved surface

19. P2 – P1 = 2ɤ CosÆŸ
When ÆŸ is the supplement of an obtuse angle of contact of
mercury with the glass.
ie ÆŸ is an acute angle and its cosine is positive
But P1 = H and P2 = H + hƿɡ
( H + hρÉ¡) – H =
hρÉ¡ =
h =

20. The height of depression h increased as the radius decrease.
Example
A glass U-tube is inverted with an open end of straight limbs of
diameters respectively 0.5mm and 1.00min below the surface of
water in the beaker.
The air pressure in the upper part is immersed until the
maximum in one limb is level with the water outside. Find the
level of water in the other limb.
Solution
Given
ɼₕ = 0.025, ɼ₂ = 0.05
H –(H -Æ¿É¡h) =

21. P1 – p2 =
But P2 = H - ρÉ¡h
P – H + ρÉ¡h =
+ ρhÉ¡ =
ρhÉ¡ = -
h = ( - )
ɤ = 7.5 x 10-1
Questions
1. Water rises to a height of 5cm in a certain capillary tube in
the same tube. Mercury is depressed by 1.71 cm. Compare the
surface tension of water and mercury specific gravity of mercury
is 13.6, angle of contact for water is zero and that of mercury is
135°
2. A liquid of surface tension γ is used to form a film between a
horizontal rod of length L and another shorter of rod of mass m
supported from by the two light mentensible strings of egual
length. Joining adjacent end of each rod. The film fells the
verticle place within rods and strings. What is the shape of each

22. string?
Show how that the tension in each is
Where ÆŸ is the angle which the tangent to each string make
with the upper net.
3. A soup bubbles in Vacuum has a radius of 3cm and another
soap bubbles in the vaccum has a radius of 6cm. If the two
bubble coalesce under isothermal conditions. Calculate the
radius of the bubble formed under isothermal conditions ɤ is
constant.