Surface Energy -Definition, Formula, FAQs

What is Surface Energy?

Surface Energy is the energy required to increase the surface area of a liquid by a unit amount.

In simple words, the molecules on the surface of a liquid have higher energy than those inside because they experience an unbalanced force—they are pulled inward by neighboring molecules. To create or expand the surface, extra energy is needed to overcome these forces.

Surface Energy Formula

Surface energy is defined as the energy per unit area of a surface.

$
\text { Surface Energy }=\frac{\text { Energy }}{\text { Area }}\left(J / m^2\right)
$

Now, since 1 Joule $=1$ Newton $\times 1$ meter,

$
\text { Surface Energy }=\frac{\text { Newton } \times \text { meter }}{\text { meter }^2}=\frac{\text { Newton }}{\text { meter }}
$

So, the unit of surface energy can also be written as $\mathrm{N} / \mathrm{m}$.

And since Newton is the unit of force,

$
\text { Surface Energy }=\frac{\text { Force }}{\text { Length }}
$

Hence, surface energy and surface tension have the same units $\mathrm{N} / \mathrm{m}$ or $\mathrm{J} / \mathrm{m}^2$.

Surface Energy Units and Dimensions

Surface Energy units and dimensions in SI, MKS, and CGS systems are given below -

Relation Between Surface Energy and Surface Tension

The relation between Surface Energy and Surface Tension is very close because both describe the same physical concept - the energy associated with the surface of a liquid.

$
\text { Surface Energy }=\text { Surface Tension } \times \text { Increase in Area }
$
Surface Tension (T) is the force per unit length acting along the surface of a liquid.
Surface Energy (E) is the work done (or energy required) to increase the surface area of the liquid by a unit amount.

What is Meant by Surface Tension?

Surface tension is the property of the liquid by which the free surface of the liquid at rest tends to contain a minimal area and as such, it performs like a stretched elastic membrane. Force exerted per unit length of a line drawn on the liquid surface and normal to it parallel to the surface is known as the force of surface tension.

Surface tension depends not only on forces of attraction among particles inside the specified liquid but also on the forces of attraction of liquid, solid, or gas in contact with it. The energy liable for the phenomenon of surface tension may be thought of as nearly equivalent to the energy or work necessary to remove the surface layer of particles in a unit area.

Generally, surface tension is measured in dynes/cm, the force in dynes is needed to divide a film of 1 cm length.

Factors Affecting Surface Tension

1. The surface tension of a liquid reduces with the rise in temperature and becomes zero at a critical temperature.
2. At boiling point, the surface tension of a liquid will be zero and becomes the highest at the freezing point.
3. Surface tension reduces when partially soluble impurities like detergent, soap, phenol, Dettol, etc are added to water.
4. Surface tension arises when highly soluble impurities such as salt are added to water.
5. When dust particles or oil spreads over the surface of the water, its surface tension decreases.
6. When the charge is given to a soap bubble, its size increases because the surface tension of the liquid decreases due to electrification.
7. In weightless conditions, the liquid does not rise in a capillary tube.

How can Surface Energy be Changed?

High surface energy is essential for solution wetting, particularly in processes like spin coating. The vast majority of solids with high surface energy will not maintain the high-energy surface when it is exposed to weather conditions. Hydrocarbon pollutants present inside the air will adsorb onto the surface of solid, decreasing surface energy. The most common way of tuning surface energy is by surface treatment, which is usually intended to increase energy by eliminating these pollutants or creating high surface energy functional groups. A lot of these methods generate only temporary changes to the surface energy. This is due to the adsorption of low surface energy molecules will occur over time gradually decreasing the average surface energy.

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Solved Examples Based on Surface Energy

Example 1: Extra energy associated with surfaces of liquid is due to

1) Difference in surrounding around surface.

2) Due to viscosity

3) Due to greater height of surface

4) None of the above

Solution

Surface Energy

It is defined as the amount of work done to increase the area of the liquid against surface tension.

Due to differences in surroundings, the molecules at the surface are not in equilibrium. because of this molecules at the surface of the liquid possess more energy than molecules in the bulk.

Hence, the answer is the option (1).

Example 2: Work done $W=0.5 \mathrm{~J}$ to increase surface area by $A=0.02 \mathrm{~m}^2$. Find surface energy $E \left(\mathrm{J} / \mathrm{m}^2\right)$.
Solution : $E=\frac{W}{A}$

$
E=\frac{0.5}{0.02}=\frac{0.5}{0.02} \times \frac{100}{100}=\frac{50}{2}=25
$
Answer: $E=25 \mathrm{~J} / \mathrm{m}^2$

Example 3 - Surface tension of water $T=0.072 \mathrm{~N} / \mathrm{m}$. Energy to create area $A=0.01 \mathrm{~m}^2$ ?
Solution: $E=T \times A$
$
E=0.072 \times 0.01=0.00072
$
Answer: $E=7.2 \times 10^{-4} \mathrm{~J}$

Example 4 - $T=0.072 \mathrm{~N} / \mathrm{m}$. Convert to dyne/cm.
Solution : $1 \mathrm{~N} / \mathrm{m}=10^3$ dyne $/ \mathrm{cm}$.

$
0.072 \times 10^3=72
$
Answer: $T=72$ dyne $/ \mathrm{cm}$

Example 5 - A tangential force $F=0.2 \mathrm{~N}$ acts along a line of length $l=0.05 \mathrm{~m}$ on a liquid surface. Find surface tension $T$ and surface energy per unit area.
Solution : $T=\frac{F}{l}$ and numerically $T(\mathrm{~N} / \mathrm{m})=\operatorname{surface}$ energy $\left(\mathrm{J} / \mathrm{m}^2\right)$.

$
T=\frac{0.2}{0.05}=\frac{0.2}{0.05} \times \frac{100}{100}=\frac{20}{5}=4
$

Answer: $T=4 \mathrm{~N} / \mathrm{m}$ and surface energy $=4 \mathrm{~J} / \mathrm{m}^2$.

Summary

Surface energy refers to the excess energy present at a material's surface due to unbalanced molecular forces. It is related to surface tension, which is the force per unit length acting on a liquid's surface. Surface energy is crucial in phenomena such as adhesion, wetting, and capillarity. Factors like temperature, impurities, and external forces influence both surface tension and energy, and they play significant roles in real-life applications such as coating, painting, and the behavior of liquids on surfaces.