Surface tension and surface energy of liquid

Surface energy and surface tension formula

The surface tension of a liquid is its surface property and tension can be related to the intermolecular attraction present in the liquids. In other words, the amount of work or energy required to increase the surface area of the liquid by unity called surface tension.

Let us consider a molecule A in the bulk of the liquid. So the molecules uniformly surrounded by other molecules and attracted from all directions. Thus the resultant force on its become nil.

But the molecule B on the surface partiality surrounded by other molecules and experience a resultant inward pull.

As a result, the molecules on the surface try to leave and enter into the bulk of the liquid.

Thus the liquid surface under tension and tries to get the minimum area. This unbalanced force of attraction on the surface molecules of the liquid is the origin of the property surface tension.

Surface tension definition

Since γ is under tension any attempt to make a penetration along any line on the surface will require an application of force to holds the separate position of the surface together. This force is called surface tension or γ.

Higher the Inter-molecular attraction force (cohesive force) greater will be the magnitude of γ.

SI unit of surface tension

γ expressed as force per length.

\therefore Unit\, of\, surface\, tension=\frac{unit\, of\, force}{unit\, of\, length}

CGS unit of γ = dyne/cm
=dyne cm-1

SI unit of γ = newton /metre
=newton meter-1

Why raindrop is spherical in shape?

Liquids assume a shape that has a minimum surface area because that enables the maximum number of molecules to remain on the bulk rather than the surface.

For this reason, when rain droplets fall freely it takes the spherical shape. Because the surface area of the spheres is minimum.

Classification of liquids

Liquids are classified into two types depending on the ability to wet the solid surface. But the extent of wetting measured by the angle of contact on the solid surface.

  1. Wetting liquids
  2. non-wetting liquids

Properties of wetting liquids

If the forces of attraction between the molecules of the liquid and surface of the solid are greater than the attraction amongst the liquid, then the liquids have the tendency to spared on the solid surface. These types of liquids are known as wetting liquids.

Thus the properties of these types of liquids are

  1. Wetting liquids have a tendency to spared on the solid surface.
  2. The liquids in the capillary tube are concave upwards and so there rise of liquids in the tube.
  3. The intermolecular attraction between the liquid molecules re less than the attraction between solid and liquid molecules.

Non-wetting liquid definition

  • The liquids which have the tendency to detach the solid surface are known non-wetting liquids.
  • The intermolecular attraction between the liquid molecules (cohesion) is greater than between the liquid molecule and solid molecule (adhesion).
  • Thus the liquid in the capillary tube given convex upward because there is a fall of liquid in the tube.

The surface energy of a liquid

If the area of the liquid surface increases than more molecules from the balk going to its surface of the liquid.  This requires some energy to bringing molecules from the bulk aginst the inward attractive forces. Thus the amount of work done in increasing the area by unity is known as surface energy.

Hence any increases in the surface area of the liquids against its natural tendency to contract will require performance to work.

Let us consider a film of liquid stretched on the ware frame having a moveable membrane.

Surface tension and surface energy of liquid
Liquid film surface

If the liquid film stretched by an area = l × x.

Thus the opposing force against the attaching due to γ.

∴ Opposing force = γ × 2l

Since the length of the film in contact with the ware l on each side. Thus the total length = 2l.

So the work required to increase the surface area

W = opposing force × displacement
= (γ × 2l) × x = γ × 2(l × x)
= γ × ΔA
where ΔA = increase of the surface area of the film on both sides.

Thus W = surface energy associated with the area ΔA.

\therefore \gamma=\frac{W}{\Delta A }

The amount of work or energy required to increase the surface area of the liquids by unity is defined as the surface tension of the liquid.

Unit of surface energy

Surface\, tension=\frac{Surface\, energy}{Surface\, area}

Thus the energy per unit area, numerically equal to the γ of the pure liquid.

Quantity SI units CGS units
Surface energy J m-2 erg cm-2
Surface tension newton m-1 dyne cm-1

Surface\, energy=\frac{force\times distance}{area}SI\, unit\, of\, surface\, energy=\frac{N\,\times m}{m^{2}}=N\, m^{-1}These are the SI units of surface energy and tension.