MHT-CET : Physics Entrance Exam

MHT - CET : Physics - Properties of Fluids Page 1

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1.

Behaviour of Liquid Surfaces

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

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

Sphere of Influence: Molecular forces are of short range and are effective only when the distance between molecules is of the order of 10-9 m. The maximum distance up to which the molecular force is effective is called the molecular range. If a sphere is drawn with a molecule as the centre and the molecular range as radius, all molecules lying within this sphere will exert forces of attraction on each other. Such a sphere is called a sphere of influence.

Consider four molecules, P,Q, R and S.

Molecule P: The sphere of influence is fully within the liquid. It is attracted equally on all sides and hence experiences no resultant force in any direction.

Molecule Q: A part of the sphere of influence is outside the liquid surface. Hence, the downward cohesive force exerted on it is more. There is a resultant downward force on it.

Molecule R: Half the sphere of influence is outside the liquid surface. Hence, it experiences maximum cohesive force downwards.

Molecule S: Only a small part of the sphere of influence is within the liquid surface. It experiences a slight net downward force.

Explanation: At every point on the liquid surface, there is a net downward cohesive force as seen from the above examples. This net force per unit area is called the cohesive pressure. If a molecule has to be brought to the surface from the interior of the liquid, work has to be done against the downward cohesive force. This amount of work is stored as potential energy of the molecule. Thus, molecules on the surface have more potential energy than molecules in the interior. Since every system tries to minimise its potential energy, liquid surfaces tend to have the least possible area.

Surface Energy: The potential energy per unit area of the surface is called surface energy.

2.

Shape of a Liquid Surface in Contact with a Solid Surface

Consider a fluid in a container. Molecules which are near the walls of the container are under the adhesive attractive force due to the molecules of the solid container. Thus, they experience a resultant force different from liquid molecules which are far from the walls of the container.

Consider a molecule near the walls of the container. The forces acting on it are:

• Its weight (W) acting vertically downwards.
• Adhesive force (fa) directed into the solid.
• Cohesive force (fc) directed into the liquid.

Case I: If fa > fc
The resultant force
fR is directed into the solid. Since Fr has to be perpendicular to the liquid surface, the liquid molecules pile up against the wall, wetting the surface and forming a concave meniscus. For example, water and glass.

Case II : If fc > fa
Here
Fr is directed into the liquid. Since Fr has to be perpendicular to the liquid surface (for stability) the surface of the liquid becomes convex. For example, mercury and glass.

3.

Surface Energy and Surface Tension

Experiment:

ABCD is a rectangular frame. PQ is a thin movable wire placed across as a slider.

Dip the frame in soap solution, to form a soap film. The film pulls PQ towards BC since it has a tendency to contract. To keep PQ in equilibrium, a force F has to be applied. F depends on the length PQ. Since the film has two surfaces, the force F is proportional to
2 × PQ.

 \ F µ 2 l , where PQ = l F = T. 2l , where the constant proportionality T is called the surface tension of the liquid.

Definition of Surface Tension

Surface tension is defined as the force acting normally per unit length on either side of an imaginary line drawn on the free surface of the liquid. This force is perpendicular to the line and tangential to the surface of the liquid.

Units of Surface Tension

Newton/metre (N/m) in the SI system and dyne/centimetre (dyne/cm) in the CGS system

Dimensions of Surface Tension: [ML°T -2]

Surface Energy: If the wire PQ is displaced through an infinitesimal distance dx, the work done (dw) against the force of contraction is given by,

dw =
F.dx = 2T l dx = T.dA, where dA is the increase in the free surface area of the film. (Since the film has 2 surfaces, increase in free surface area = 2 × ldx)

 \ dw = T.dA or T = dw dA

Thus, surface tension is the work done per unit area in increasing the area of the film. The work done is stored as potential energy of the molecules on the surface.

Definition of Surface Energy: The work done to increase the free surface area of a liquid by unit area under isothermal conditions is called the free surface energy of the liquid and it is numerically equal to the surface tension.

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