side of an imaginary line drawn over the liquid surface.
(b) For a rectangular block:- F = T×2(l+d) (Here l is the length and d is the thickness of the rectangular block)
• Surface energy:-
Potential energy per unit area of the surface is called surface energy.
(a) Expansion under isothermal condition:-
To do work against forces of surface tension:-
W= T×A (Here A is the total increase in surface area)
To supply energy for maintaining the temperature of the film:-
E = T+H
(b) Expansion under adiabatic conditions:-
E = T
Force of surface tension is numerically equal to the surface energy under adiabatic conditions.
• Drops and Bubbles:-
(a) Drop:- Area of surface film of a spherical drop of radius R is given by, A = 4πR2
(b) Bubble:- The surface area of the surface films of a bubble of radius R is, A = 2×4πR2
• Combination of n drops into one big drop:-
(a) R = n1/3r
(b) Ei = n (4πr2T), Ef =4πR2T
(c) Ef/ Ei = n -1/3
(d) ΔE/Ei = [1-(1/n1/3)]
(e) ΔE = 4πR2T (n1/3-1) = 4πR3T (1/r – 1/R)
• Angle of contact:- Angle of contact, for a pair of solid and liquid, is defined as the angle between tangent to the liquid surface drawn at the point of contact and the solid surface inside the liquid.
(a) When θ < 90º (acute):-
Fa >Fc/√2
(i) Force of cohesion between two molecules of liquid is less than the force of adhesion between molecules of solid and liquid.
(ii) Liquid molecules will stick with the solid, thus making solid wet.
(iii) Such liquid is put in the solid tube; it will have meniscus concave upwards
• Capillarity:-
Capillarity is the phenomenon, by virtue of which the level of liquid in a capillary tube is different from that outside it, is called capillarity.
Weight of liquid, W = Vρg = πr2[h+(r/3)]ρg (Here r is the radius meniscus)
If weight of meniscus is taken into account, the force of surface tension will be,
T = [r(h+(r/3)) ρg]/2 cosθ
For fine capillary, force of surface tension, T = rhρg/2 cosθ
So height, h = 2T cosθ/ rρg
This signifies, height of liquid risen (or depressed) in a capillary tube varies inversely as the radius of tube. Smaller the diameter of capillary tube, greater is the rise of liquid in it.
• Tube of insufficient length:
Rh = 2T/ρg
As, T, ρ and g are all constant, Rh = Constant
Smaller the value of h, greater will be the value of R. But liquid will never flow.
• Effect of temperature affecting surface tension of liquids:-
Surface tension of a liquid decreases with an increase in its temperature.
Tθ = K (θc-θ)
Here Tθ is the surface tension at a particular temperature θ while θc is the critical temperature of the liquid and K is constant.
• General formula for excess pressure:-
Pexcess =T[1/R1 + 1/R2]
• Excess pressure in liquid drop:-
Pexcess = 2T/R, Here R is the radius of liquid drop.
• Excess pressure for an air bubble in liquid drop:-
Pexcess = 2T/R
• Excess pressure in soap bubble:-
Pexcess = 4T/R, Here R is the radius of soap bubble.
• Pressure inside an air bubble at a depth h in a liquid:- Pin = Patm+ hdg + (2T/R)
• Forces between two plates with thin water film separating them:-
(a) ΔP = T (1/r – 1/R)
(b) F = AT (1/r – 1/R)
(c) If separation between plate is d, then ΔP = 2T/d and F = 2AT/d
• Radius of curvature of common film:- Rcomon = rR/R-r
• Capillary depression, h = 2T cos (π-θ)/rdg
•Shape of liquid surface:-
(a) Plane surface (as for water – silver) if Fadhesive > Fcohesive/√2
(b) Concave surface (as for water – glass) if Fadhesive > Fcohesive/√2
(c) Convex surface (as for mercury-glass) if Fadhesive < Fcohesive/√2
• Increase in temperature:-
Δθ = 3T/ρs (1/r – 1/R) or Δθ = 3T/ρsJ (1/r – 1/R)
