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Properties of Solids and Liquids
Force of cohesion:- It is the force between two molecules of similar nature.
Force of adhesion:- It is
the force between two molecules of different nature.
Molecular range:- The
maximum distance between two molecules so that the force of attraction between
them remains effective is called molecular range.
Sphere of influence:-
Sphere of influence of any molecule is the sphere with molecule as its center
and having a radius equal to molecular range (=10-7 cm).
Surface film:- Surface film of a liquid
is defined as the portion of liquid lying on the surface and caught between two
parallel planes situated molecular range apart.
Surface Tension Surface tension is the property of a liquid
by virtue of which its free surface behaves like a stretched membrane and
supports, comparatively heavier objects placed over it. It is measured in terms
of the force of surface tension.
Force of surface tension:- It is
defined as the amount of force acting per unit length on either side of an
imaginary line drawn over the liquid surface.
(a) T = Force/length = F/l
(b) T = Surface energy/Surface area = W/A
Units:- S.I – Nm-1
C.G.S- dyn cm-1
Additional force:-
(a) For a cylindrical rod:- F = T×2πr (Here r is the radius
of cylindrical rod)
(b) For a rectangular block:- F = T×2(l+d) (Here l is the
length and d is the thickness of the rectangular block)
(c) For a ring:- F = T×2×2πr (Here r is the radius of cylindrical
rod)
Surface energy:-
Potential energy per unit area of the surface is called surface energy.
(a) Expansion under the 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 the 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)
The angle of contact:- Angle
of contact, for a pair of solid and liquid, is defined as the angle between the 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 the solid wet.
(iii)
Such liquid is put in the solid tube; it will
have a meniscus concave upwards.
(b) When θ > 90º (obtuse):-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) In this case, liquids do not wet the solids.
(iii) Such liquids when put in the solid tube will have a
meniscus convex upwards.
(c) When θ = 90º:-? Fa=Fc/√2
The surface of the liquid at the point of contact is plane. In
this case force of cohesion and adhesion are comparable to each other.
(d) cosθc = Tsa – Tsl/Tla Here, Tsa,Tsl and Tla represent
solid-air, solid-liquid and liquid-air surface tension respectively). Here θc
is acute if Tsl < Tsa while θc is obtuse if Tsl >Tsa.
Capillarity:-
Rise of Liquid in a Capillary Tube
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, a force of surface tension, T = rhρg/2 cosθ
So height, h = 2T cosθ/ rρg
