2022-08-26 16:31:56
Properties of Solids and Liquids - Revision Notes on Liquids at Rest:
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 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)
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