MHT-CET : Physics Entrance Exam

### MHT - CET : Physics - Properties of Fluids Know More

• Intermolecular Forces

i.            The molecular forces between two molecules are called intermolecular forces. They are also called Van der Waals' forces or Van der Waals' interaction.

ii.            These forces are electrical in origin. When the distance between two molecules is greater than 35 nm (35 ´ 10-9 m), the distribution of charges is such that the average distance between the opposite charges in the molecules is slightly less than that between their like charges. As a result, a force of attraction develops. When the intermolecular distance is less than 35 NM (35 ´ 10-9 m), there is overlapping of the electron clouds of the molecules. This results in a strong force of repulsion.

iii.            Intermolecular forces are of two types:

i.            Cohesive Forces: The mutual force of attraction between molecules of the same substance is called cohesive force.

ii.            Adhesive Forces: The mutual force of attraction between molecules of different substances is called adhesive force.

iv.            The distance of separation between two molecules where the intermolecular forces of attraction becomes zero is called normal distance.

v.            The intermolecular forces do not obey the inverse square law. Since they are effective only over very short distances, they are also called short-range forces.

• Intermolecular Binding Energy: The minimum energy required to separate two molecules from each other's influence is called intermolecular binding energy.
• Surface Film: A thin film of a liquid near its surface that has a thickness equal to the molecular range for that liquid is called surface film. The phenomenon of surface tension exhibited by a liquid is due to its surface film.
In the figure, the layer of the liquid between AB and CD is called the surface film.

 Surface Film
•
• Angle of Contact
(i) Factors on which Angle of Contact of a Liquid Depends:

i.            The nature of the solid-liquid pair in contact: The angle of contact depends only on the nature of the solid or liquid. It is independent of the manner in which the two are brought in contact with each other.

ii.            The medium above the free liquid surface.

iii.            The cleanliness of the surfaces in contact.

(ii) Angle of Contact for Some Common Solid-Liquid Pairs:

 Pair of Surfaces Angle of Contact Pure water and clean glass 0° Ordinary water and glass Between 8° and 18° Pure water and pure silver 90° Mercury (exposed to air) and glass 140° Ordinary water and chromium 160°

• Surface Tension
Factors on which Surface Tension of a Liquid Depends:

i.            Nature of the Solid-liquid Surfaces: Surface tension of a liquid depends on the nature of the solid-liquid pair in contact.

ii.            Temperature of the Liquid: Surface tension in most of the liquids decreases with increase in temperature. For a small temperature difference, it decreases almost linearly with increase in temperature. However, in case of molten copper and cadmium, it increases with increase in temperature. The surface tension of water is about 0.0757 N/m at 0°C but it reduces to 0.072 N/m at 20°C. The temperature at which the surface tension of a liquid becomes zero is called critical temperature.

iii.            Contamination of the Liquid: The surface tension of a liquid increases when inorganic substances are dissolved in it. For example, common salt in water. But surface tension of a liquid decreases when organic substances are dissolved in it. For example, detergent or soap mixed in water.

iv.            Concentration of the Liquid Solution: The surface tension of a liquid depends on the concentration of the liquid solution.

• Shape of Liquid Drops

Let us consider a liquid drop to be in equilibrium on a plane solid surface. We notice that there are three interfaces namely, liquid-air, solid-air and solid-liquid. The drop will be under the action of the following forces due to surface tension:

i.            Surface tension TLA between liquid and air.

ii.            Surface tension TSA between solid and air.

iii.            Surface tension TSL between solid and liquid.

Let q be the angle of contact of the liquid with the solid surface at its point of contact O. For the molecule at O to be in equilibrium, the horizontal components of the surface tensions at O must balance each other. The component TLA sinq balances the weight mg of the molecule at O.

\
TSL + TLA cosq = TSA

 \ cosq = TSA - TSL TLA

Cases:

iv.            When TSA > TSL, cosq is positive, i.e. q lies between 0° and 90°. So the angle of contact is acute. Such liquids 'wet' the solid surface in contact by spreading on it. For example, water on glass surface.

v.            When TSA < TSL, cosq is negative, i.e. q lies between 90° and 180°. So the angle of contact is obtuse. Such liquids do not 'wet' the solid surface in contact and take the shape of a drop. For example, mercury on a glass surface.

• Capillarity: Ascent Formula (Derivation)

Consider a glass capillary with uniform and fine bore of radius r, which is open at both the ends and dipped vertically in a liquid that wets glass. As soon as the capillary tube is dipped in water, the water creeps up along the glass wall due to force of adhesion between water and glass molecules. The adhesion of liquid to the walls of a capillary causes an upward force on the liquid at the edges and results in a meniscus, which turns upward. The surface tension acts to hold the surface intact, so instead of just the edges moving upward, the whole liquid surface is dragged upward. The vertical force due to surface tension pulls the liquid upwards.
Let
q be the angle of contact, r be the density and T be the surface tension of the liquid.
The liquid surface is in contact with the walls of the tube all along a horizontal circle called as circle of contact. If
r is the radius of the capillary tube, then the circumference of the circle of contact is 2pr.
Since the liquid surface has a tendency to contract, it pulls the tube inward all along the circumference of the circle with a force T acting per unit length. According to
Newton's third law of motion, the tube will give an equal and opposite reaction force to the meniscus of the liquid. The reaction N (which equals T) at each point along the circle of contact can be resolved into two rectangular components:

i.            Horizontal component N sinq acting radially outwards. The horizontal component at any point along the circle of contact is cancelled by an equal and opposite component at other end of the diameter. These components cancel out each other. Moreover, horizontal components cannot be responsible for the vertical rise of the liquid

ii.            Vertical component N cosq acting vertically upwards.

Since all the vertical components N cosq act in the same direction along the circle of contact,

 the total upward force on the liquid, F = 2pr´ N cosq = 2pr´ T cosq     (... N = T) …(1)

As the liquid rises, its weight increases and at a particular height say '
h', the force due to surface tension in the upward direction becomes equal to the weight of the liquid in the downward direction. The liquid then ceases to rise.
The weight of the liquid in the capillary, W = (Volume of cylindrical liquid column of height
h + Volume of the liquid in meniscus) ´ r ´ g,
where
g is the acceleration due to gravity.
Now, volume of cylindrical liquid column =
pr2h
For convenience, we consider the meniscus as to be hemispherical in shape.
\ Volume of the liquid in the meniscus = Volume of cylinder of height h and radius r - Volume of hemisphere

 = pr2 ´ r - 1 4 pr3 = pr3 - 2 pr3 2 3 3

 = 1 pr3 3

 \ Weight of the liquid in the capillary W = pr2h + 1 pr3 ´ r ´ g 3
 Liquid Meniscus
 \ W = pr2 h + r ´ r ´ g…(2) 3

In the equilibrium position, F = W
Equating equations (1) and (2), we get

 2pr´ T cosq = pr2 h + r ´ r ´ g 3

\T =

 r h + r ´ r ´ g 3

…(3)

2cosq

 When the tube is of very fine bore, r << h. 3
 Capillary rise

 Neglecting r as compared to h in equation (3), we get, 3

 T = hrgr 2cosq

 \ h = 2Tcosq rrg

This expression is called the ascent formula.

Jurin's Law:
It states that the smaller the radius of a tube, greater is the rise or fall of a liquid in it

 h µ 1 . r

• Rise of Liquid in a Tube of Insufficient Length: Consider a ca pillary tube of radius r open at both ends and dipped in a liquid, which wets the walls of the tube. Let the liquid be of density r and surface tension T. The height h to which the liquid will rise in the tube is given by
 \ h = 2Tcosq …(1) rrg

• where
gis the acceleration due to gravity.
Let O be the centre of curvature and R be the radius of curvature of the meniscus.
In the right-angled triangle, ACO, we have,
 cosq = AC = r AO R
 \ r = R cosq …(2)

• Substituting equation (2) in equation (1), we get,
 h = 2Tcosq = 2T Rcosq rg Rrg
 \ Rh = 2T rg

• Since T,
r and g are constants, we have,
 Rh = 2T = constant …(3) rg
 Rise of Liquid in a Tube of Insufficient Length

• In a tube of insufficient length, the liquid rises up to the top of the tube and starts spreading till the liquid is in equilibrium.
Let '
h' be the insufficient length of the capillary tube and R' be the new radius of curvature of the meniscus.
According to equation (3), we have,
R
h = R'h'
 \ h' = R h R'

• Since
h'< h, we have
R' > R

\
The radius of curvature of the meniscus increases from R to R'.
The liquid will not overflow from the tube as it will violate the law of conservation of energy.
• Expression for Excess Pressure
(i) For a Liquid Drop in Air (No Derivation):
Consider a spherical liquid drop of radius R. If T is the surface tension of the liquid, then the excess pressure inside the liquid drop in air is given by
 p = 2T R

• (ii) For a Soap Bubble in Air (No Derivation):
Consider a spherical soap bubble of radius R. If T is the surface tension of the soap solution, then the excess pressure inside the soap bubble in air is given by
 p = 4T R

• (iii) For an Air Bubble in Liquid (No Derivation):
Consider a spherical air bubble of radius R. If T is the surface tension of the liquid, then the excess pressure inside the air bubble in the liquid is given by
 p = 2T R

• (iv) For a Liquid-Air Interface:
The pressure on the concave side of liquid-air interface is greater than the convex side by
 p = 2T , where T is the surface tension and R is the radius of curvature of the surface. R

• Note:
A liquid drop in air or an air bubble in liquid has only one free surface area. Hence they have the same expression for excess pressure.
A soap bubble in air has two free surface areas. Hence the expression for its excess pressure is twice that for a liquid drop in air or an air bubble in liquid.

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