# Surface Tension

Molecular Range: It is the maximum distance up to which a molecule can exert some appreciable force of attraction for another molecule. It is of the order of 10-9 m in solids and liquids.

Sphere of Molecular influence or sphere of molecular activity:
It is a sphere drawn around a particular molecule as centre and molecular range as radius. The central molecule is attracted by all the molecules lying in the sphere of influence.

### Surface tension of a liquid :

It is a property by virtue of which the free surface of a liquid at rest behaves like a stretched elastic membrane tending to contract to possess minimum surface area.

$\large \sigma = \frac{F}{l}$

Imaging a line AB in the free surface of a liquid at rest. The force of surface tension is measured by the force acting per unit length on either side of the imaginary line. The direction of this force is perpendicular to the line and tangential to the liquid surface. If F be the force acting and l the length of the imaginary line, then the surface tension is given by.

Units: In cgs system, it is expressed in dyen cm-1 . In SI, it is expressed in N m-1

Surface Film:
Surface film is a thin film of liquid near its surface and having thickness equal to the molecular range for that liquid. The phenomenon of surface tension is intimately linked with this film

#### Molecular Theory of Surface Tension:

AB is the free surface of a liquid at rest. ABCD is the surface film. Consider three molecules P, Q and S. These have been represented by central dots in the Fig. The sphere of influence has been drawn around each molecule.

The molecule P is attracted equally in all directions by the neighbouring molecules. So, the net force acting on this molecule is zero.

The molecule Q experiences some net downward force of attraction. This is because the number of molecules in the lower half part of the sphere of influence is more than the number in the upper half part.

The molecule S is in the surface of the liquid. The upper half of its sphere of influence lies completely outside the surface of the liquid. So, this molecule experiences maximum downward force.

From the above discussion, we conclude that all the molecules lying in the surface film experience a net force of cohesion in the downward direction. This force goes on increasing as the free surface of the liquid is approached. It becomes maximum for molecules in the top of the film. This downward force acting on the liquid surface per unit area is called the ‘ cohesion pressure ‘ or ‘ intrinsic pressure ‘.

### Surface Energy:

The free surface of a liquid at rest is always in a state of tension. The force of surface tension tends to decrease the surface area to the minimum. If the surface area of the liquid is to be increased, work shall have to be done against the force of surface tension. This work done is stored in the liquid surface film as its potential energy.

The potential energy per unit area of the surface film is called the surface energy.

Or ,  It is the amount of work done in increasing the area of a surface film through unit under *isothermal conditions.

$\large Surface \; Energy = \frac{Work \; done \; in \; increasing \; the \; surface \; Area}{increase \; in \; surface \; Area}$