Question

The unit of surface energy per unit area may be expressed as
A. Nm$^{-2}$
B. Nm$^{-1}$
C. Nm
D. Nm$^1$

Answer 1

Use dimensional analysis to find the required unit.

Complete step by step solution:
The dimension of energy is $M{{L}^{2}}{{T}^{-}}^{2}$
The dimension of area is ${{L}^{2}}$
Therefore, the dimension of surface energy per unit area is
$\dfrac{\text{surface energy}}{\text{area}}=M{{T}^{-}}^{2}$
Now, the dimension of force is $ML{{T}^{-}}^{2}$ and unit is N. Hence, the unit of surface energy per unit area is Nm$^{-1}$

The correct answer is option B.

Additional information:
Surface energy of various substances is measured using contact angle experiments. Several liquids are used in this method to measure the contact angle of the surface. Surface energy is also calculated using the first principles like density functional theory.
Water molecules are strongly attracted to each other due to hydrogen bonding. As a result water has a higher surface tension and surface energy than most other liquids. Wetting is described as the tendency of a liquid to spread out on a surface. A surface with high energy will cause good wetting while low surface energy will cause poor wetting.

Note: Surface energy is the excess energy at the surface of a material compared to its volume and is equal to the work done per unit area to build a particular surface. The atoms in the bulk of a material are stable as the forces acting on them are balanced. In contrast, atoms at the surface experience unbalanced forces and have some extra bonding energy. Hence, this energy arises due to disruption of the intermolecular forces when surfaces are built. It is also known as interfacial free energy. Cutting solid bodies increases their surface area and hence increases the free energy.