Black body and its Radiation

A perfectly black body is the one which absorbs all the radiations of all wavelengths incident on it. Since it neither reflects not transmits any radiation it appears black in color what may be the color of incident radiation.

According to Kirchoffs law, a body which is capable of absorbing radiation must also be capable of emitting all possible wavelengths. So a perfectly black body is a good absorber as well as good radiator. When it is heated to a suitable high temperature, it emits radiations of all wavelengths (continuous spectrum). As the radiations emitted by black body is rich in maximum possible wavelengths and hence such Radiations are known as full Radiation or Total Radiation.     

The wavelength of emitted Radiation by a black body depends only on its temperature and is independent of the material of the body.

There is no body acting as perfect black body. The nearest approach is lamp black or platinum black. These are capable of absorbing the visible and a part near infrared but far infrared (heat Radiation) are reflected. So perfectly black body is just an ideal concept. For all practical purposes a lamp blacked surface can be considered as perfectly black body.

Energy Distribution in Black body Radiation

The distribution of energy in black body radiation for different wavelengths and at various temperatures was determined experimentally by Lummer and Pringsheim in 1899. They used the black body as an electrically heated chamber with narrow aperture.

The temperature of heated enclosure is measured by thermocouple.

The parallel beam of Radiation is allowed to incident on a "fluorspar prism" instead of a glass prism. The reason behind not using glass prism is that it absorbs some heat radaition.

The radiation is detected by means of Bolometer. Bolometer is an instrument to detect Thermal Radiation. The Bolometer is a linear type due to Lummer and Kurlabaum and is fitted with galvanometer 'G'. The deflection produced in the Galvanometer gives the intensity of Radiation, Eƛ. This is defined such that quantity Eƛ.dEƛ is the energy, for wavelengths lying between ƛ and ƛ+dƛ emitted per second per unit surface area of black body.   

The wavelengths at different parts of the spectrum was calculated by "Prism Dispersion Formula".

The experiment results are as follows:

1) The emission from a Black body at any temperature is composed of Radiation from all wavelengths.

2) At a given temperature, the energy is not uniformly distributed. As the temperature of the black body increases, the intensity of radiation for each wavelength increases. This shows that the total amount of energy is radiated per unit area per unit time increases with rise of temperature.

i.e., T 𝛼 Eƛ

3) The total energy of radiation at any temperature is given by the area between the curve corresponding to that temperature and horizontal axis. The increase in area found in accordance with Stefans law.

4) The amount of radiant energy emitted is small at very short and very long wavelengths. At a particular temperature, the spectral radiance Eƛ is maximum at particular wavelength ƛm. Most of the energy is emitted at wavelengths not very  different from ƛm.

5) The wavelength corresponding to the maximum energy represented by the peak of the curve shifts towards shorter wavelengths as the temperature increases. This is called Wiens Displacement. According to this law ƛm x T = constant.

This shows that as the temperature is increased, the black body emits the radiation of shorter wavelengths such that the product of temperature 'T' and maximum wavelength ƛm is a constant. 

The constant is called Wiens Displacement constant and has value 0.2896 x 10⁻² mK. 

There is change in wavelength due to Doppler effect.

Laws Related to Black Body:

a) Kirchoffs Law
b) Stefan-Boltzmann law
c) Wiens Law
d) Rayleigh-Jeans Law
e) Plancks Law

Important points to be noted:

i)  Wiens formula agrees in short wavelength region.
ii)  Rayleigh-Jeans formula agrees for long wavelength region.
iii) Plancks formula covers the entire region.
iv) When radiation is passed through a black body is passed through a prism, acontinuous spectrum is obtained. The energy is distributed in various wavelengths varying from 0 to infinity.
v) The law that connects the intensity with the wavelength is known as law of distribution of intensity of black body radiation.
vi) According to Stefans law, u=𝝈T⁴ where 𝝈 is Stefans constant and 'u' is energy density.

Spectral Energy Density, Total Energy Density, Emmisive Power & Absorptive Power

Spectral Energy Density: 

Spectral Energy Density for a particular wave length is the energy per unit volume per unit range of wavelength.

Total Energy Density:

Total Energy Density of Thermal Radiation at any point is the total radiant energy per unit volume around that point due to all wavelengths.

Emmisive Power:

The emmisive power of a body at a given temperature and for a given wavelength, is defined as the ratio of the radiant energy absorbed for second by unit surface area of the body per unit wavelength range.

Absorptive Power

The absorptive power of a body at a given temperature and wavelength is defined as the ratio of radiant energy absorbed per second by unit surface area of the body to the total energy falling per second on the same area.   

Concept of Thermodynamics - Zeroeth Law of Thermodynamics

For a system to be in thermodynamic equilibrium the following conditions must be full filled:-

i) Mechanical equilibrium

ii) Thermal equilibrium

iii) Chemical equilibrium

Mechanical equilibrium:

When there is no unbalanced force between system and its surroundings, the system is said to be in mechanical equilibrium.

Thermal equilibrium:

When the temperature in all parts of system is same as that of surroundings, the system is said to be in thermal equilibrium.

Chemical equilibrium:

If the chemical composition is same throughout the system and surroundings it is said to be in chemical equilibrium.

Zeroeth Law of Thermodynamics:

This law was first enunciated by RH Flower in 1831. According to this law when two systems ‘A’ and ‘B’ are in thermal equilibrium with another system ‘C’ then ‘A’ and ‘B’ will also be in thermal equilibrium.

What does First Law of Thermodynamics infer us?

• It is impossible to derive any work without expenditure of an equivalent amount of energy in some other forms. 

• Heat absorbed by the system should be taken positive. Heat rejected by the system should be taken negative. 

• For an ideal gas the total kinetic energy (KE) of all its molecules is called internal energy(U). For such a gas the internal energy depends only on Temperature.

What is ENTROPY - Very important Points to be noted

1) The thermal property which remains constant during an adiabatic process is called as entropy.
     i.e. dQ/T= constant

2) It is a measure of randomness or disorderliness of molecules.

3) It is independent of the path of thermal cycle.

4) The increase in entropy implies transition from ordered state to disorder state.

5) It is an index of unavailable energy of a system.

6) Entropy could also be termed as thermal inertia since more entropy results in less amount of heat energy being converted into work.

7) The increase in Entropy of a system implies transition of thermal energy from more available energy to less available form for conversion into work.

8) The net change in entropy is zero for any reversible cycle. This statement is called as clausius theorem.

9) Clausius Theorem: - The sum of quantities of heat transfer during the isothermal change divided     by absolute temperature of the isothermal in a reversible cycle is zero. Entropy changes linearly in isothermal expansion and remains constant in adiabatic expansion or compression but decreases in isothermal compression.

The shape of Temperature (T) - Entropy (S) diagram (Tephigram) is rectangle.

10) Entropy increases in irreversible process.

11) Definition of second law of thermodynamics in terms of entropy

”Every chemical or physical or natural process in nature takes place in such a manner that total entropy increases or remains constant".

12) The principle of "degradation of energy" states that the available energy tending towards zero.

Specific Heat of Gases

Units and Designation

PRINCIPLE OF ELECTRON SPIN RESONANCE (ESR)

Electron Spin Resonance (ESR) is a branch of absorption spectra in which radiation having frequency in microwave region is absorbed by paramagnetic substances to induce transitions between magnetic energy levels of electrons with unpaired spins.

ESR also called Electronic Paramagnetic Resonance is a spectroscopic technique confined to study of those species having one or more unpaired electrons.

Phenomenon of ESR was invented by Zaveiskii in 1904.


PRINCIPLE OF ESR

When we consider an unpaired electron it is associated with spin. When a magnetic field is applied, the magnetic moment of electron interacts with field and results in splitting of otherwise degenerate field. Now the energy difference between the levels falls in microwave region.So when radiation in microwave range equal to this energy difference is made to incident on substance, transitions occur between these levels absorbing quanta of energy leading to a absorption peak.

Only spin moment contributes towards the magnetic behaviour of electrons.

Consider that system has only spin magnetic moment

μ= -gμBS ....................................(1)

'μ' & 's' are in opposite directions.

For an electron of spin S=1/2, the spin angular momentum quantum number will have values
ms = ±1/2 ..................................(2)

In absence of magnetic field, the two values of 'ms' i.e. +1/2 and -1/2 will give rise to a doubly degenerate spin energy state.

When magnetic field is applied this degeneracy is removed and thus leads to two non degenerate energy levels.

Now the interaction energy is given by

Polar Dielectric in uniform electric field

There are permanent dipoles present in polar dielectric which are randomly aligned in such a way that there is permanent dipole moment Pp. [see fig a]

 
When a dipole is present in an uniform electric field the dipole tries to align itself in the direction of electric field.

Because of this all dipoles in a polar dielectric are partially aligned in the direction of field. This partial alignment is responsible for the induced dipole moment Pi.[see fig b].                 
Therefore, the electric dipole moment is increasing.   

P =  Pp + Pi

The electric dipole moment of a polar dielectric increases
a) by increasing the applied E.
b) by decreasing the temperature
 

Dielectrics - Polar, Non Polar, uses

A dielectric is a non conducting substance introduced between the plates of a capacitor.

What is Non Polar Dielectric?

This is a substance in which the net electric dipole moment is zero because of its symmetrical structure. In this the center of gravity of positive charges and  center of gravity of negative charges
will coincide.

What is Polar Dielectric?

Because of their non symmetrical structure these dielectrics have permanent dipole moment. In this there are permanent electric dipoles present. On this if an external electric field is applied, torque acts on these dipoles rotating them in direction of applied electric field. When an external electric field is applied on non polar dielectric this dielectric gets polarized forming induced charges on the surfaces.      

Uses of Dielectric

1. It maintains mechanical separation between the plates.

2. It decreases the field as well as potential but increases the capacity

3.  Increases capacitance between metal plates
When a non polar dielectric is introduced between the plates it is leading to the displacement of negative charges in the dielectric. Because of the displacement of negative charges, the center of gravity of negative charges is not coinciding the center of gravity of positive charges, thus forming dipoles. This phenomenon of formation of electric dipoles when an external electric field is applied on a non-polar dielectric is known as Polarisation. 

Therefore, induced charges are appearing on the surfaces of dielectric forming their own electric field  Eᵢ. This Eᵢ opposes original electric field Eₒ, thus net electric field E is decreasing.

E=Eₒ-Eᵢ

Therefore, potential between the plates is also decreasing resulting in increase in capacitance.

4. Used for withstanding high potentials
 Any dielectric can withstand a maximum electric field before becoming a partial conductor. This maximum electric field, a dielectric can withstand before reaching breakdown condition is known as dielectric strength of dielectric.
Therefore, heavy capacitors use dielectrics using highest dielectric strengths to withstand large potentials. 
 

Quantities from Kinetic Theory of Gases

Electric Current in Atoms - Bohr Magneton ; magnetic moment of electron in orbit

The revolution of electron in its orbit around nucleus resembles a magnetic dipole and the magnetic moment due to this orbital motion of electron is

𝜇ₑ₁ = - (e/2m) x angular momentum

angular momentum = mr²w

The minus sign indicates that dipole moment points in direction opposite to vector representing angular momentum.

The ratio of magnetic dipole moment of the electron due to its orbital motion and angular momentum of orbital motion is called "orbital gyro magnetic ratio" represented by '𝛾'.

𝛾 = (magnetic moment/angular momentum) = e/2m

The strength of magnetic dipole is given by

 𝜇ₑ₁ = -𝜇B.l;  

𝜇B - Bohr Magneton = (eh/4πm) = 9.27 x 10⁻²⁴ Amp.m²

Therefore, '𝜇B'  represents magnetic moment of an elementary permanent magnetic dipole.

As we know that for a 'l' value there exists a quantum number 'ml' such that it takes +l to -l values hence for a d-electron for eg:

corresponding possible magnetic moment along direction of field are 2𝜇B, 𝜇B, 0, -𝜇B, -2𝜇B

 Therefore  𝜇ₑ₁ = -𝜇B.ml

Characteristics of electrical conduction in Metals

The general characteristics of electrical conduction in metals are summarized as follows:

1) The electrical current density in the steady state is proportional to electric field strength
     (Ohm's law).

2)  For pure specimens, the electric conductivity (σ) and the thermal conductivity (σ') vary with temperature as follows:

      σ∝T⁻¹ and σ' =const (for T > θD); θD is characteristic Debye temperature.

       so that  σ' / σT is independent of temperature (Weidmann-Franz law)

For T < θD;

      σ∝T⁻⁵ and σ' = T⁻² where 'θD' is characteristic Debye Temperature. 

      The relation  ρ∝T⁵ is known as Bloch-Gruneisen T⁵ law.

 3) For metals that exhibit the phenomenon of superconductivity, their resistivity disappears at temperature above 0Kand below critical temperature for superconducting phase transition (critical temp=4.15K) for mercury.

4) For metals containing small amounts of impurities, the electrical resistivity(ρ) may be written as 

                                                          ρ = ρ₀ + ρᴘ(T)

where 'ρ₀' is a constant that increases with increasing impurity content and ρ(T) is temperature dependent part of resistivity. This is known as Mattheissen's rule.

5) For most metals, the electrical resistivity decreases with increasing pressure.

6) The resistivity of alloys that exhibit order-disorder transitions shows pronounced minima corresponding to ordered phases.

  

Discovery of Artificial Disintegration

The artificial transmutation of one element into another is first accomplished by Rutherford in 1919.

The chamber 'c' was filled with a gas such as Nitrogen and Alpha particles from a radioactive source at 'A' were absorbed in the gas. A sheet of silver foil 'F', itself thick enough to absorb the alpha particles was placed over an opening in the side of chamber. A zinc sulphide screen 'S' was placed outside this opening and a microscope 'M' was used for observing any scintillatons - occuring on the screen 'S'. Scintillations were observed when the chamber was filled with Nitrogen, but when the Nitrogen was replaced by Oxygen or Carbondioxide no scintillations were observed.

Rutherford concluded that the scintillations were produced by high energy particles which were ejected from Nitrogen nuclei as a result of bombardment of these nuclei by alpha particles.

Magnetic deflection experiments indicated that these particles were Hydrogen nuclei or Protons.

Later experiments by Rutherford and Chadwick showed that these ejected Protons had Ranges upto 40cm in air.

Other light elements in the Range from Boron to Potassium were also disintegrated by bombardment with alpha particles.

The disintegration of Nuclei has also been studied with  Wilson cloud chamber. One of the first of these investigations was that of Blackett, who photographed the tracks of alpha particles in a Wilson cloud chamber containing 90% Nitrogen and 10% Oxygen. The majority of tracks photographed were straight tracks typical of alpha particle tracks.

Many of the tracks were observed to be forked tracks, indicating that an inelastic collision had taken place between an alpha particle and a Nitrogen Nucleus.

Measurement of the tracks showed that momentum of system was conserved but that the sum of kinetic energies of particles after impact was less than kinetic energy of alpha particle before impact.

On the basis of theory of nucleus advanced by Bohr, the disintegration of Nitrogen by bombardment with alpha particles may be thought as consisting of two separate parts.

The first is the capture of the alpha particle by Nitrogen nucleus which resulted in the formation of a new compound nucleus.

The second is the breaking up of compound nucleus into two particles, one of which is a Proton.

These two processes can be represented by means of a nuclear reaction equation analogous  to one representing a chemical reaction.

The nuclear reaction equation for this process is

₂He⁴ + ₇N¹⁴ --------->  (₉F¹⁸✷) ------->  ₈O¹⁷ ⁺ ₁H¹ + Q

Q is energy evolved or absorbed during nuclear reaction

Q --->  -Ve --->  energy has been absorbed (endothermic)
Q --->  +Ve ---> energy has been evolved (exothermic)
Q ---> nuclear reaction energy or disintegration energy

If sum of masses of the final particles exceeds that of initial particles, 'Q' must be negative; the energy absorbed in such a nuclear reaction must have been obtained from kinetic energies of the particle.

If 'E1' is kinetic energy of alpha particle just before capture, 'E2' the kinetic energy of Proton, 'E3' the kinetic energy of product nucleus,

Q = E2+E3-E1

In those cases in which Q is positive the sum of kinetic energies of final particles will be greater than kinetic energy of incident alpha particle.

Discovery of Meson

Yukawa predicted that it is due to the exchange of a massive particle between the nucleons leading to a short range force.

A result of much calculation is that the Range of a force is of same order of magnitude as compton wave length of exchanged particle. By analogy the nuclear force has a Range of about 1.4 x 10⁻¹³ cm.

A particle for which ℏ/mc = 1.4 x 10⁻¹³ cm will have its rest mass energy equal to 150 MeV or about 275 times the mass of electron.

The name Mesotron was given to this exchanged particle whose mass is intermediate between that   of electron and Proton. The modern name is Meson.

In 1937, a particle believed to be of the type was discovered by "S H Neddermeyer" and "C D Anderson" and independently by "J C Street" and "E C Stevenson" in cloud chamber studies of cosmic rays.

Estimates of the mass of this Meson were made from measurements of curvature of its track in a magnetic field which yielded values for mass of Meson in neighbourhood of 200 electron masses. Both positive and negative particles were observed.

WB Fretter (1946) made some very careful measurements of masses of mu particles, using two cloud chambers, one above the other. They were expanded simultaneously when ever a penetrating particle passed through them. This was accomplished by placing the Geiger Counters above each chamber, the two sets of actuating the expansion mechanism whenever an ionizing particle passed through  them as shown in below Fig.

The upper cloud chamber was placed in a magnetic induction of 5300 Gauss so that momentum of particle could be measured. The lower cloud chamber had a set of lead plates 0.5 inch thick and placed 1.5 inch apart so that Range in lead of particles could be measured. Out of 2100 tracks observed, 26 were suitable for measurement, their mass determination is yielded a value of 202Me.

The present accepted value is 207mₑ.

Later Occhialini and Powell and D M Perkins using a special nuclear emulsion photographic plates exposed at high altitudes, observed that some of Mesons stopped in photographic emulsions and produced so called stars - that is, nuclear disintegration with the emission of slow protons or alpha particles.

The photographs showed the curved track of heavy Meson which is named '𝚷' Meson; when captured by a nucleus in the emulsion, the resulting nuclear disintegration produces a star in which 3 charged particles are emitted.

The kinetic energy of muon emitted in the decay of a Pi Meson is always same and is equal to about 4 MeV.

𝚷⁺  ------------>  𝛍⁺ + 𝝂
𝚷⁻  ------------>  𝛍⁻ + 𝝂'    ;   𝝂' is anti neutrino     

Properties of Stationary Waves

When two simple harmonic waves of same amplitude, frequency and time period travel in opposite directions in a straight line, the resultant wave obtained is called a stationary or a standing wave.

Properties of stationary waves:

1) In these waves, nodes and anti nodes are formed alternately.
   Nodes are positions where particles are at their mean positions having maximum strain.
   Anti nodes are positions where the particles vibrate with maximum amplitude having minimum strain.

2) The medium is split into segments and all particles of same segment vibrate in phase. The particles in one segment have a phase difference of '𝜫 ' with the particles in neighboring segment.

3) Condensations and rarefractions do not travel forward as in progressive wave but they appear and disappear alternately at same place.

4) As condensations and rarefractions do not travel forward there is no transfer of energy.

5) The distance between two adjacent nodes is 'ƛ/2' and also the distance between two adjacent antinodes is 'ƛ/4'. Between the two nodes there is anti node and vice versa.

6) The general appearance of wave can be represented by a sine curve but it reduces to straight line twice in each time period.

REFLECTION, REFRACTION AT PLANE SURFACES

LAWS OF REFLECTION

 The angle of incidence is equal to angle of reflection.

 The incident ray, Normal and Reflected ray ray all lie in one plane. 

PROPERTIES OF IMAGE FORMED BY PLANE MIRROR

1.  The image formed by a plane mirror is "virtual", "erect" and laterally reversed.
2.  The size of image is equal to size of object.
3.  The image is as far behind the mirror as the source is in front of it.
4.  When the plane mirror is rotated through certain angle, the reflected ray turns through double the angle.
5.  When two plane mirrors are kept facing each other at an angle '𝛳 ' and an object is placed between them, multiple images of the object are formed as a result of multiple successive reflections.

            a) If (360/𝛳) is "even", then no. of images is given by n = (360/𝛳)-1

            b)  If (360/𝛳) is "odd", then following two situations arise 

     

                   i) If object lies symmetrically, then n = (360/𝛳)-1

                  ii)  If object lies unsymmetrically, then n = 360/𝛳

            c) When two plane mirrors are placed parallel to each other, then  

                 n = (360/0) = ∞ (infinite no. of images)

Note:- 

I) The point object for a mirror is a point from which the rays incident on mirror actually diverge or towards which the incident rays appear to converge.

II) An optical image is a point where rays of light either intersect or appear to do so.

REFRACTION OF LIGHT

The Refracted ray bends towards the Normal when the second medium is denser than first medium and vice versa.

The deviation 'D' suffered by refracted ray is given by D =  i-r

LAWS OF REFRACTION

1. The Incident ray, the Refracted ray and the Normal to surface separating two media lie in one plane.

2. Snells Law: For any media, the ratio of sine of angle of incidence to sine of angle of refraction is a constant for a light beam of particular wavelength.

sini/sinr = 𝜇2/𝜇1 = constant

Refractive index 𝜇 = velocity of light in vacuum / velocity of light in medium

Nature of orbits of satellites for different speeds

Let

'V' be velocity with which a body is projected from Earth.
Vs be minimum velocity of object to orbit around earth
Ve be escape velocity from surface of earth

then if,

i)  V < Vs ---  body falls to ground
ii) V = Vs --- body rotates round earth in circular orbit closer to surface of Earth
iii) Vs < V < Ve --- body revolves in elliptical orbit
iv)  V = Ve ----------body just  escapes from gravitational field
v)  V > Ve  --------- body moves in interstellar space with velocity equal to √V² -Ve²
vi)  V<Ve  ---------- Total energy of body is negative
vii)  V =Ve ---------- Total energy of body is zero

Satellites - Important points to be noted

1.  Orbital velocity of satellite is independent of mass of the satellite but depends on mass of planet and radius of orbit.

2. A satellite orbiting around a planet will have both Potential energy and Kinetic energy. Here Potential energy is negative and Kinetic energy is positive.

3. Total energy of satellite is negative.

4. With the increase of height of orbit from surface of planet, for a satellite

              a) Potential energy increases (from more negative to less negative)

              b) Kinetic energy decreases

              c) Orbital velocity decreases

              d) Total energy increases

              e) Period of revolution increases

5. A satellite orbiting very close to surface of Earth is known as its surface satellite. Orbital velocity for such a satellite is V = √gR = 8 Km.S⁻¹.

6. Relative velocity of parking satellite with respective to Earth is zero.

7. Orbital linear velocity is about 3 Km.Sec⁻¹.

8. A satellite cannot be coast in a stable orbit in a plane not passing through the Earth's center.

9. If two satellite move around the Earth in its equitorial plane such that one moves from West to East and other from East to West and other from East to West, the time period of revolution of first satellite will be more compared to other.

10. If a rocket launched in equitorial plane from West to East, advantage is up to 0.47 Km.Sec⁻¹  in the launching speed.  

11. If the Kinetic energy of an orbiting satellite is E, its Potential Energy will be -2E and total energy will be -E.

12. If a body is in a satellite which does not produce its own gravity, its true weight in that satellite W' is given by

W'/W =mg'/mg  ; W' = W/(1+[h/R])²

W - Weight of body on Earth
 h  - Height of orbit of satellite
 R - Radius of Earth

so true weight is lesser than its weight on Earth.  

13.  Apparent weight of a body in a satellite is zero and is independent of radius of orbit .

  

FRICTION - Important Points to be remembered

1.  The force which opposes the relative motion of two surfaces of bodies in contact, is called as "frictional force".

2. Friction is tangential force between the contact surfaces of two bodies.

3. Friction is due to Electromagnetic Forces between the surfaces in contact.

4. Friction is due to molecular interaction at the surfaces in contact.Friction is due to adhesive forces between molecules of two surfaces in contact.

5. Friction depends on nature of surfaces in contact and on the impurities present on these surfaces.

6. Normal Force: When two bodies are in contact or when one body is placed over another body, the contact force which either body exerts on other normal to contact surface is called Normal Force or Normal Reaction.

7. Friction is proportional to Normal Force.

8. Limiting Friction is least force necessary to set a body into motion.

9. Sliding Friction is the friction which comes into play when the surface of an object moves relative to the surface of another object.

10. Static friction is the friction which comes into play when surfaces of the objects are at rest relative to each other even there is an external force acted upon. 

11. Static friction is a self adjusting force.

12. Kinetic Friction is not a self adjusting friction.

13. The substances which reduce friction are called as lubricants.

14. Generally coefficient of static friction is less than 1 but in some cases it may exceed 1.

15. Frictional force is a "Non-Conservative" force.

16. If a body of mass 'm' is on the floor of a lift which is moving with uniform acceleration 'a', Normal force on body or its apparent weight is

N = mg ±ma = m(g±a)

a) If the lift moves up, then N = m(g+a)
b) If the lift moves down, then N = m(g-a)
c) If the lift falls freely, then N=0
d) If the lift moves with uniform velocity, then  a =0, and N=mg

17. When a person falls on a rough road, the frictional force exerted by road on him is along his direction of motion.

18. The angle made by resultant of Normal force and Limiting friction with Normal force is called angle of friction. The tangent of this angle gives coefficient of static friction.

19. The substances which reduce friction are called Lubricants. 

20. A good lubricant must be highly viscous and low volatile in nature.

21. The frictional force exerted by fluids is also called as "drag".

22. Frictional force on an object in a fluid depend on its speed with respect to fluid, on the shape of the object and on the nature of fluid.

23. Friction can produce heat.

Crystal Growth Methods - Brief Explanation

Various types of crystal growth methods are

Growth from Water Solution
Growth from Flux
Hydro Thermal Growth
Electrode Deposition
Gel Growth

Growth from Water Solution

This technique is used for soluble crystals like sugar, salt crystals for example NaCl, KCl, KBr are used. Their growth rates are very small. They have 5 mole percent solubility.

Nucleation is one such process. Liquid containing crystal solution solution having low viscosity is taken into a beaker. Crystal which has to be grown is taken in very small size which is called as seed crystal. We have to hang this crystal in the liquid in beaker. The molecules join crystal to form the crystal big in size.

Growth from Flux

This method is used for crystals which are not dissoluble. This technique uses oxide crystals/metal crystals. Crystals like quartz having high melting point of 1400 oC which is attained at higher energy are grown using this technique. For this they are combined with other crystals called as flux whose benefit is to reduce the melting point of crystals to form.

Advantages of this technique

a) Growth is at temperature well below the melting point
b) High quality crystals can be obtained
c) Doping with suitable materials could be done
d) Solid solution can be grown easily

Hydro thermal growth

This method is used for crystals whose melting point is very high. For instance, Al2O3 cannot be soluble in water. Normally Al2O3 dissolves in water at critical temperature of 353 ⁰C.

So when pressure is exerted on crystal then melting point of material decreases (of about 50000 pounds per sq. inch). So special devices such as autoclaves are used for this purpose.

conditions of growth in hydro thermal process:

i) The Temperature
ii) The Pressure
iii) The temperature difference between top and bottom ends of autoclave