NEET Physics Notes Mechanics-Properties of Matter-Surface Energy
Surface Energy
Surface Energy
Surface energy of a liquid is the potential energy of the molecules of a surface film of the liquid by virtue of its position.When the surface area of a liquid is increased, work is done against the cohesive force of molecules and this work is stored in the form of additional surface energy.
Increase in surface potential energy
- Work done in Blowing a Liquid Drop
If a liquid drop is blown up from a radius ra to r2, then work done in the process,
- Work done in Blowing a Soap Bubble
As a soap bubble has two free surfaces, hence, work done in blowing a soap bubble so as to increase its radius from TX to r2, is given by 
- Work done in Splitting a Bigger Drop into n Smaller Droplets
If a liquid drop of radius R is split up into n smaller droplets, all of the same size, then radius of each droplet
- Coalescence of Drops
If n small liquid drops of radius r each, combine together so as to form a single bigger drop of radius R = n1/3r, then in the process, energy is released. Release of energy is given by
Angle of Contact
Angle of contact for a given liquid-solid combination is defined as the angle subtended between the tangents to the liquid surface and the solid surface, inside the liquid, the tangents are drawn at the point of contact.
Value of the angle of contact depends on the nature of liquid and solid both. For a liquid having concave meniscus, angle of contact θ is acute θ < 90° but for a convex meniscus, the angle of contact is obtuse θ > 90°
Value of angle of contact θ decreases with an increase in temperature.
Excess Pressure Over a Liquid Film
If a free liquid surface film is plane, then pressure on the liquid and the vapour sides of the film are the same, otherwise there is always some pressure difference. Following cases arise.
For a spherical liquid drop of radius r, the excess pressure inside the drop \(p=\frac{2 S}{r}\)
S = surface tension of the liquid.
For an air bubble in a liquid, excess pressure \(p=\frac{2 S}{r}\)
For a soap bubble in air, excess pressure \(p=\frac{4 S}{r}\)
Capillary Rise or Capillarity
Capillarity is the phenomenon of rise or fall of a liquid in a capillary tube as compared to that in a surrounding liquid.
The height h up to which a liquid will rise in a capillary tube is given by 
Where r is the radius of the capillary tube
the rise in capillary tube
\(h \propto \frac{1}{r}\)
If a capillary tube, dipped in a liquid is tilted at an angle a from the vertical, the vertical height h of the liquid column remains the same. However, the length of the liquid column (l) in the capillary
tube increases to
\(l=\frac{h}{\cos \alpha}\)
If the capillary tube is of insufficient length, the liquid rises up to the upper end of the tube and then the radius of its meniscus changes from R to’R’ such that hR = h’ R’, where, h’ = insufficient length of the tube.
After connection due to the weight of liquid contained in the meniscus, the formula for the height is given by