# Surface Tension Introduction | Relation between Surface Tension and Surface Energy | Physics Grade XI

### Fluid Mechanics # Surface Tension Introduction | Relation between Surface Tension and Surface Energy

Types of Molecular forces

• Force of cohesion: The force of attraction between the molecules of the same substance is called force of cohesion or cohesive force.
• Force of adhesion: The force of attraction between the molecules of the different substances is called the force of adhesion or adhesive force.

Surface Tension
Surface Tension is the property of liquid at rest by virtue of which its surface behaves like a stretched membrane and tries to occupy minimum possible surface area is called surface tension.

Mathematically, it is the force per unit length of an imaginary line drawn in the plane of the liquid surface acting right angles to this line. If F is the force acting on the imaginary line of length l, then

Surface tension, T = F/l ...… (i)
Its unit is Nm-1 in SI system and dyne/ cm in CGS-system.
Its dimension is [MT-2]

Surface energy
The potential energy per unit area of the surface film is called surface energy. It is also defined as the amount of work done in increasing the area of a surface through unity.

Mathematically,
Surface energy, σ = Work done in increasing surface area / Increase in surface area

Relation between surface Tension and Surface Energy Consider a rectangular frame of wire ABCD as shown in the figure in which wire BC is movable. If we dip the frame in a soap solution, a thin film is formed which pulls the wire BC toward left due to surface tension. It T is surface tension of the film and l is length of wire BC, then the force F on BC due to surface tension is given by,

F = T * 2l
As the film has two surfaces in contact with air and so total length of wire, BC is 2l.

Suppose the wire is now moved through a distance x from BC to B|C| against surface tension force F so that surface area of the film increase. In order to increase the film area, work has to be done against F.
Work done in increasing area = F * distance = T * 2l * x
Where 2l * x is the increase in surface area.
.:  surface energy, σ = Work done in increasing surface area / Increase in surface area
= (T * 2l * x) / (2l * x)
.: σ = T
Thus, surface tension T is numerically equal to surface energy.

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