Properties of Solids and Liquids

= Solids =

Elasticity
The property of a body, by the virtue of which material bodies regain their original dimensions (size , shape or both ) after removal of deforming forces is called elasticity.

Plasticity
Plasticity is the property of a body to undergo permanent deformation even after the removal of deforming forces.

Rigidity
Deformation α Deforming Force

Strain α Stress

Stress / Strain = Constant

Stress And Strain
1) Longitudinal Stress & Strain (along length)

Longitudinal Stress = Applied Force / Cross Section Area

Longitudinal Strain = ( l - l0 ) / l0= ∆L / L

2) Volume Stress & Strain (with Volume)

Volume Stress = Applied Force / Volume

Volume Strain = ∆V / V

3) Shearing Stress & Strain (with shape)

Shearing Stress = Tangential Applied Force / Area

Shearing Strain = θ

Elasticity Modulus (Hooke's Law)
(Young's Modulus and Hooke's Law for JEE)

Deformation α Deforming Force

Strain α Stress

Stress / Strain = M ; where M is a constant, called as Modulus of Elasticity.

Young's Modulus
(for longitudinal strain and stress)

Y = Longitudinal Stress / Longitudinal Strain

Bulk Modulus
(for Volume Strain and Strain)

K = Volume Stress / Volume Strain

Compressibility = 1 / Bulk Modulus

Modulus of Rigidity
(for Shearing Strain and Stress)

η = Shearing Stress / Shearing Strain

Poisson's Ratio
σ = lateral strain / longitudinal strain 

Elastic Energy
Strain Energy = 1/2 load x extension

Strain Energy per unit volume = 1/2 x (Strain)2

Strain Energy is defined as an elastic potential energy gained by a wire during elongation by stretching force.

Application of Elasticity
= Liquids =

Molecular Theory
Surface tension is a molecular phenomenon and it's origin lies in electromagnetic forces.

Intermolecular Forces :

1) Cohesive Force : The force of attraction between two molecules of the same substance.

2) Adhesive Force : The force of attraction between two molecules of different substances.

Range of Molecular Forces

The maximum distance between two molecules up to which intermolecular forces are effective is called range of molecular attraction.

Sphere of Influence

An imaginary sphere drawn with given molecule as centre and radius equal to the molecular range is called the sphere of influence.

Surface Energy
The Potential Energy per unit area of the liquid surface under isothermal condition is called surface energy per unit area. Surface

Energy = T(dA)

Surface Tension
The force per unit length acting at right angles to an imaginary line drawn on the free surface of liquid is called surface tension.

Surface Tension (T) = F / L

Also, T = Work Done / Change in Area (Multiplying displacement on Numerator ad Denominator)

Or, T = Surface Energy / dA

Angle of Contact
When a liquid is in contact with a solid, the angle between tangent drawn to the free surface of the liquid and the surface of solid at the point of contact measured inside the liquid is called angle of contact.

1) For a given solid-liquid pair, the angle of contact is constant.

2) The value of angle of contact depends upon nature of liquid and solid in contact.

3) It depends upon medium which exists above the free surface of liquid.

4) The angle of contact changes due to impurity.

5) The angle of contact changes with temperature.

6) If θ is acute, Adhesive Force > cohesive force , liquid rises in the capillary tube and liquid meniscus is concave.

7) If θ is obtuse, cohesive force > Adhesive Force , liquid gets depressed in the tube and the liquid meniscus is convex.

Capillarity
The phenomenon of rise or fall of a liquid inside a capillary tube when it is dipped in a liquid is called capillarity.

Surface Tension (T) = rhdg / 2cosθ

Thus, we can calculate the surface tension of a liquid , by immersing a capillary tube in it , and measuring the rise or fall in liquid. h = h + r/3

Vertical Force due to S.T. F = 2πTcosθ

Jurin's Law

h α 1/r

For convex meniscus in the capillary tube, the angle of contact should be obtuse. For Concave meniscus in the capillary tube, the angle of contact should be acute

h1/h2 = r2/r1

Soap Bubbles
1) W = 2T [4πR22- 4πR12] = 8πT[R22 - R12]

2) for a liquid drop ,

3) W = 4πT (r22 - r12)

4) Excess Pressure P = 4T / r

5) Pressure inside drop of a liquid  P = 2T / r

6) Resultant Radius of two superpositioning bubbles is given by ,

r = sqrt (r12 + r12)

7) Total PRessure = hρg + 2T/r

8) P α 1 / r

Effect on Surface Temperature
Effect of impurities

Surface Tension increases due to highly soluble impurities and decreases due to sparingly soluble impurities.

Effect of temperature

Surface tension of a liquid decreases with rise in temperature.

T = T0(1 - αθ)