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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.

Effect of density:- Density of liquid also affects its surface tension. Surface tension of a liquid is given by,

T = A (ρ - ρ')n

Here, ρ is the density of liquid, ρ' is the density of saturated vapors of liquid and A is the constant depending on the nature of liquid.

Pressure difference across a liquid surface:-

(a) Plane surface:- There is no difference of pressure on the two sides of the film.

(b) Convex surface:-Pressure below the surface film must be greater than that just above it.

(c) Concave surface:- Pressure on the upper side is greater than that just below it.

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 for an Air Bubble in Liquid Drop

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)