Electrical Conductivity of Liquids

1) Electrical Conductivity is an intrinsic property of any given material. 

2) Volta made first electric cell in 1800 using Zinc and Copper plates dipped in Sulphuric acid. The cell he made is called a Volta cell in his honour. The word "voltage" is also derived from his name.

3) Process of coating one metal onto other by the process of electrolysis is called as "electroplating".

4) Uses of electroplating:

    a) To protect metals from corrosion by atmospheric air/moisture air/chemical environment.

    b) To increase conductivity.

    c) Ornaments & decoration items.

 

Kirchoff's Law for black body

This law states that at a given temperature, the ratio of emission power to the absorption power for a given wavelength is same for all bodies and is equal to the emissive power of a black body at the same temperature.

Energy emitted per square meter is eƛdƛ.

Energy absorbed per unit area is QƛdQ.

eƛ/aƛ = ∂Qƛ /∂ƛ = constant

where eƛ is emission power ; aƛ is absorptive power

∂Qƛ is energy falling on unit area per second within same wavelength range & temperature.

 

(∂Qƛ /∂ƛ) depends only on temperature and for a given temperature it is constant.

For a perfectly black body, aƛ = 1

Note: Kirchoffs law is true only for temperature radiation.

Pyrometers - important points for exams

1. They are instruments used for measuring high temperatures.

2. The Pyrometers based on the principles of radiation are termed as Radiation Pyrometers.

3. The fact that the radiation emitted by a black body depends only upon its temperature provides radiation methods for measuring high temperatures. 

4. There are two types of Radiation Pyrometers

i) Total Radiation Pyrometers
The instruments that measure total radiation emitted by the body under test are called as total Radiation Pyrometers.
The temperature is determined by making use of Stefans law.

ii) Optical or Spectral Pyrometers
The optical pyrometers compare the intensity of radiation of a certain wave length emitted by the body with that of radiation of same wavelength emitted by a standard body at known temperature. The temperature of the body obtained by applying Weins displacement law or Planck's law. 

5. Advantages
a) They can be used to measure any high temperatures even when the hot bodies inaccessible.
b)They need not be put in contact with the hot body not raised to the temperature of the body.
c) There is no difficulty in extrapolation because radiation laws are valid at all temperatures.  

6. Disadvantages
a) Their range roughly begins at 600 degC and so temperatures below this limit cannot be measured.
b) The temperature obtained by these Pyrometers is always less than the actual temperature of source because they use radiation laws which are only true for black bodies. So the measures are accurate for black bodies only.

7. Ferry's total Radiation Pyrometer

The distance of pyrometer from hot body should be such that image formed by concave mirror is larger than opening of mirrors.

Calculation of temperatures

Let T & T0 be the absolute temperatures of the hot body and that of pyrometer case.

Now, according to Stefans Boltzmans law, the millivolt meter deflection 𝛳 will be proportional to T⁴-T0⁴.

As T0 is very small compared to T, 𝛳 ∝ T⁴.

Note: In practice it is found that power lies between 3.8 and 4.2 due to stray reflections from the walls etc.

𝛳 ∝ T^K 

Log𝛳 = K log T

The graph drawn between log𝛳 & logT comes out to be a straight line calibration graph.
To measure a high temperature a rotating sector is used which allows only radiation equal to 𝛳/360 to enter pyrometer.

If a pyrometer measure a temperature T1, then the actual temperature T2 of the body is given by

 T1⁴/T2⁴ = 𝛳/360;   T2 = T1 (360/𝛳)

8. Disappearing filament Optical Pyrometer

First Morse made this device later Holborn and Kurlbaum improved it.

The current through filament is adjusted in such a way that filament just disappears against background. Current in filament is recorded with help of ammeter. Since both filament & image are equally bright, they must be emitting equal amounts of energy per unit area per second and hence, they must be at same temperature.

The temperature of filament 'T' (or unknown temperature of hot body) can be calculated from the formula 

I = a+bT+CT2, where I is strength of current flowing through the circuit and a,b,c are constants

The value of these constants can be determined by calibrating the instrument against known temperatures.

Note: The instrument is suitable for measuring temperatures from 600 to 1500 degC. The range can be raised to 2700 degC by using a rotating sector.

Schrodingers Time Independent Wave Equation

 

Debroglie hypothesis

As the Newtonian classical approach to deal with problems involving particles at atomic level failed, the concept of wave mechanics was introduced by Louis Debroglie in 1924 and has been successfully applied to atomic and molecular structures.

Louis Debroglie, a French scientist extended the idea of dual nature of radiation to matter. 

According to Debroglie, a materialistic particle posessess both wave and particle characteristics.  

It is to be known that dual nature of light was explained by combining Planck's expression for energy of photon 

E = h𝜈  --------------------(1)

Einsteins Mass energy relation 

E = mc² ------------------(2)

h𝜈 = mc²------------------(3)

as we know,

𝜈 = C/ƛ  -------------------(4)

From (3) & (4)

ƛ = h/P   --------------------(5)

Just in analogy with equation 5, Debroglie proposed concept of matter waves according to which a material particles of mass M moving with a velocity 'v' should have an associated wave length  ƛ called Debroglie's wavelength given by 

ƛ = h/mv = h/P ----------(6)

'm' - according to theory of relativity is not an invariable quantity as in classical physics.

m = m₀/√ 1-(v²/c²) ------ (7)

If particles like electrons are accelerated to various velocities, we can produce waves of various wavelengths. The higher the velocity of electron, the smaller the debroglie's wavelength.

If electron is accelerated by applying potential V, then work done on electron is eV.

mv²/2 = eV ----------------(8)

mv = P = √ 2meV --------(9)

substituting (9) in (6), we have

ƛ = h/√ 2meV  ------------(10)

 

Kinetic Theory of Gases - Important Points

1. The cohesive force (which binds molecules together) between particles of matter which constitutes a gas is extremely small.

2. Mathematical basis of Kinetic Theory of gases was established by Maxwell and Clausius.

3. Kinetic theory of gases relates macroscopic properties with microscopic properties of its molecules. 

 According to this theory,

4.  Molecules are rigid, perfectly elastic and identical in all respects.

5. The average distance traveled by a molecule between two collisions is known as Mean free path.

6.  On the basis of kinetic theory of gases, the pressure exerted by a gas is given by 

                                              P = (1/3)*(m*n*c²/)/V

where, 'n' is no. of moles, 'm' is mass of each molecule and 'M' is total mass of gas, V is volume of gas, c is average speed of molecules, c² is Mean square speed of molecules

c² = (c₁² + c₂² + .......+ cn²)/n

7.  Pressure exerted by a gas 'P'  is 2/3rd of total translational Kinetic energy of molecules per unit volume. 

8. Mean kinetic energy of a molecule is 

(1/2)mc² = (3/2)KT

where 'K' is Boltzmann Constant, K=R/NA  ; R is universal gas constant & NA  is Avagadro's number. 

9. Kinetic energy of a gram molecule of a gas = (3/2)RT

10. Avogadro's Number  

The number of atoms or molecules in a mole of substance is called Avogadro's number. 

Its value is 6.023 x 10²³ mol⁻¹ .

11. Kinetic energy of a molecule depends upon absolute temperature 'T' and it is quite independent of its mass. This fact is known as Kinetic interpretation of temperature.

12. According to kinetic theory of gases, at absolute zero of temperature, the Kinetic Energy of gas becomes zero i.e. molecular motion ceases.

13. Above point is strictly not true because at T=0, the molecules do have some energy known as Zero Point energy.

14. Deduction of gas laws from kinetic theory:

i) Boyles law

  P = (1/3)*Mc² ; PV=constant; 

At constant temperature, pressure of a gas is inversely proportional to volume of a gas.

ii) Charles Law

PV ∝T ; The volume of gas at constant pressure is directly proportional to the temperature (or) pressure of a gas at consatnt volume is directly proportional to temperature.

iii) Avogadro's law

N1=N2; Equal volume of ideal gases existing under same conditions of temperature and pressure contain equal number of molecules. This is called as Avogadro's law.

iv) Dalton's law or partial pressure

P=P1+P2+ ....

the total pressure exerted by gaseous mixture is sum of individual pressures that would be exerted if several gases occupied space in turn, alone.

v) Grahams law of diffusion

The rate of diffusion of a gas through a porous portion is inversely proportional to square root of its density.

Root mean square velocity (crms) = √c² = √(3KT)/m = √(3P)/ρ

15. Law of equipartition of energy (deduced by James Clark Maxwell)

i) Average value of the components of velocity 'C' (i.e. u,v & w) along 3 directions should be equal or for a molecule all 3 directions are equivalent i.e. u=v=w

ii) Total mean kinetic energy of molecule is E = (3/2)KT; 

     K is Boltzman constant and T is absolute temperature.

iii) A molecule has "three translational" degrees of freedom.

iv) Total Kinetic Energy of a dynamical system is equally divided among all its degree of freedom and it is equal or (1/2)KT per degree of freedom.This is called Law of eqipartition of energy. 

v) For a "monoatomic molecule", we have only translational motion because they are not capable of rotation. Thus for one molecule of a monoatomic gas total energy E=(3/2)KT. 

vi) For a "diatomic molecule" we can suppose it to be two sphere joined by a rigid rod. Such a molecule can rotate about any one of 3 mutually perpendicular axes. The rotational inertia about an axis along rigid rod is negligible compared to that about an axis perpendicular to rod, so rotational energy consists of to terms such as (1/2)I𝓌y² & (1/2)I𝓌z².

vii) For special description of center of mass of a diatomic gas molecule, 3 coordinates will be required. Thus, for a diatomic gas molecule having both rotational & translational motion; 

E = (3/2)KT + 2(1/2)KT = (5/2) KT

viii) For "tri-atomic gases", each molecule contains 3 spheres joined together by rods so that molecule is capable of rotating energetically 3 mutually perpendicular axes. Hence, for triatomic molecule having both translational & rotational motion energy 'E' will be 

 E = 3(1/2)KT + 3(1/2)KT = 3KT

ix) If a molecule in all has 'f' degrees of freedom, its average total energy would be (1/2)fKT. 

About Plastics

What is Plastic?

Plastic is a polymer in which monomers are arranged in linear or cross linked chains.

Alexander Parkes is the creator of first plastic known as “Parkesine”.

Types of Plastics:

a) Thermoplastic 

This is the plastic which gets deformed easily by heating. Some of the thermoplastics are polythene and PVC. This is a plastic which will soften when heated and harden when cooled. Thermoplastic is a polymer that turns into a liquid when heated and freezes to a glassy state when cooled sufficiently.

b) Thermosetting Plastics 

These are the plastics which moulded once cannot be softened/deformed by heating. Bakelite and Melamine are such plastics.

 Properties of Plastics

1.  Plastics are easily mouldable into different shapes.
2. Plastics could be recycled.
3. Plastics could be melted.
4. Plastics could be rolled into sheets.
5. Plastic could be drawn into wires
6. Plastics are nonreactive to chemicals and atmosphere.
7. Plastics are light in weight
8. Plastics are cheaper than metals.
9. Plastics are poor electric conductors and could be used as insulators.
10. Plastics are poor thermal(heat) conductors and hence could be used for cooking utensils etc.

Biodegradable and non-biodegradable Plastics

Plastics, which are decomposed by natural process through bacteria in the presence of water, sunlight and oxygen are called bio-degradable plastics.   Plastics which cannot be decomposed by natural processes are called non-biodegradable plastics.

Plastics take long time for decomposition which causes pollution of environment. Burning of plastics causes poisonous fumes into air.

SOUND - Important Notes

1. A vibrating body produces sound.
2. Sound has energy
3. Sounds are produced by vibrating bodies and the air that passes through orifices of the instruments.
4. Sound needs a medium to propagate.
5. The to and fro motion of a body from its mean position is known as one vibration.
6. The maximum displacement of vibrating body from its mean position is called as amplitude.
7. The number of vibrations per second is called as frequency.
8. The shrillness of a sound is known as pitch.
9. The pitch of the sound depends upon its frequency.
10. Normal sound consists of mixed frequencies.
11. The sounds which are pleasant to hear are called as music. Music is a combination of sounds that are produced in an order and pleasant to hear.
12. The sounds which are unpleasant to hear are called as noise.
13. The sounds that a normal human being can hear are called as audible sounds.
14. The sounds that a normal human being cannot hear are called inaudible sounds.
15. Frequency of the audible sounds ranges from 20 Hertz (20 vibrations/sec) to 20000 Hertz(20000 vibrations/sec). 

 

All about Force?

Force definition

The push or pull of a body by an object is called force on the body.

or

Force is an external influence acting on a body to change its state of motion.

Types of Forces

Contact Force 

Force which results when there is a direct physical contact between two interacting objects is known as contact force. 

Types of Contact Forces

Muscular Force

The force which we exert by using our muscles is called as muscular force.

Friction Force

The force which resists the motion of an object over the surface of other.  The direction of friction force is always opposite to the direction of the motion relative to the surface.

Normal Force

The friction force, on an object, which acts perpendicular to the surface of  its plane is called as Normal Force. 

Tension

Tension is a pulling force acting on a object by means of a string against the gravitational force.  

Field Force

The force which occurs without any physical contact is known as force at a distance or field force.

Field is region of imaginary lines around an object. When an other body is placed in this region, it will experience the force. The greater the density of these imaginary lines, the stronger the forces in that region.

Types of Field Forces

Magnetic Force

Magnetic force is a field force responsible for attraction of like poles and repulsion of unlike poles.

Electrostatic Force

Force exerted by a charged body on another charged body is known electrostatic force. This force is due to electric field from the charge.

Gravitational Force

The force of attraction that exists between any two masses n the universe is known as Gravitational force. This force is due to electric field from the charge. Gravitational force is also non contact force and hence it is also a field force.

Net Force

Multiple forces can act on an object simultaneously at a time. When the forces act in same direction then net force will be addition of all forces. When the forces are in opposite direction, then net force will be difference of the forces. When the Net force is zero, there is no change in state of object. 

The direction of motion of the object will be in the direction of Net Force. If the Net Force acts in direction of motion, the speed of the an object moving with constant speed also increase. If the Net Force acts in a direction opposite to the motion, then it either slows down the object or brings it to rest or it may change the direct of motion. 

The unit of force in SI system is Newton(N). 

Pressure

The force acting perpendicularly on unit area of a surface is called as pressure.

Pressure = Force/Area

The unit of pressure in SI system is Newton/Meter² or N/m². 

  

What is accelerated Thermal Ageing Test?

 What is Thermal Ageing?

Ageing of the materials with temperature could happen and differs for various materials. Important safety systems/equipments need to be evaluated for the effect of temperature on the materials used in the system. Even storage for long years shall also be considered for some materials like polymers to estimate the ageing effect. 

Ageing effect couldn’t be estimated practically for operating conditions or storage conditions as the duration is very high (tens of years) and the qualification of product couldn’t happen. Hence, Ageing effect due to temperature could be evaluated by exposing the unit to higher temperature for accelerated time. This is called as Accelerated Thermal ageing test.

 

How to calculate time required for Thermal Ageing of an instrument at accelerated temperature?

There are different methodologies to do Thermal Ageing test. Most commonly used methodology is application of Arhenius equation. Usually, this methodology is applicable for Polymer/Organic materials for which temperature effect is more.    

Thermal Ageing is due to the chemical process induced by the temperature, which could lead to change the bulk properties of the material over a time.  

The Arhenius methodology has been developed to simulate the accelerated ageing mechanism. As per this methodology, deterioration of materials in service is due to chemical reaction. These occur internally, sometimes between components of the material, and sometimes with compounds in the environment such as oxygen or water vapor. Chemical reactions occur more rapidly at higher temperatures.

 

Arrhenius showed that temperature dependence of chemical reactions follows an exponential equation. He postulated a consistent correlation between the amount of physical change and chemical reaction so that the time to reach a selected amount of physical change will vary according to an equation. The rate of thermal aging is the slope of the graph using the Arrhenius equation.

 

Accelerated Time calculation for Thermal Ageing Test

As per Arhenius equation,

where,

‘E’ is activation energy for the material under consideration; in eV

‘K’ is Boltzman Constant i.e. 8.617 x 10^-5 eV.K^-1 

‘t1’ is ageing time required at accelerated temperature ‘T1’.

‘t2’ is service life time operating temperature ‘T2’.

‘T1’ is accelerated temperature

‘T2’ is Operating temperature

For instance, let us consider the cross linked polyolefin cables (XLPO cables) being used for an application where the normal operating temperature is 50 oC and the expected service life is 40 years. Let us calculate the accelerated time required for thermal ageing test at accelerated temperature of 135 oC.

i) Activation energy (E) for XLPO cable is considered as 0.78 eV

[Ref: An Experimental Study on Dielectric Response of the Cross linked Polyolefin (XLPO) Insulation of the Unshielded Cable Under Electric Field and Heat Flux; Publisher: IEEE]

ii) t2 = 40 years

iii) T1 = 135 degC

Time required for accelerated Thermal Ageing test for accelerated temperature of 135 oC is ~43 days.

Picture size and Resolution explained

Pixel dimensions

The number of pixels along the height and width of an image.

The display size of an image on screen is determined by the pixel dimensions of the image plus the size and setting of the monitor.

For example, a 15 inch monitor typically displays 800 pixels horizontally and 600 vertically. An image with dimensions of 800 pixels x 600 pixels would fill this small screen. On a larger monitor with an 800 x 600 setting  the same image would still fill the screen but each pixel would appear larger. Changing the setting of this larger monitor to 1024 x 768, pixels would display the image at a smaller size, occupying only a part of the screen.

Image Resolution

The number of pixels displayed per unit of printed length in an image, usually measured in pixels per inch(ppi).In photoshop, you can change the resolution of an image; in image ready, the resolution of an image is always 72ppi.

When printed, an image of high resolution contains more and therefore smaller pixels than an image with a low resolution. For instance, a 1x1 inch image with a resolution of 72ppi contains a total of 5184 pixels (72 pixels wide x 72 pixels high = 5184). The same 1 x 1 inch image with a resolution of 300 ppi contains a total of 90,000 pixels.

Using too high a resolution increases the file size and slows the printing of an image.; further more, the device will be unable to reproduce extra detail provided by high resolution.

Monitor Resolution

The number of pixels or dots displayed per unit length on the monitor, usually measured in dots per inch (dpi). Monitor resolution depends on the size of monitor plus its pixel setting. 

understanding monitor resolution helps explain why display size of an image on screen often differs from its printed size. Image pixels are translated directly into monitor pixels. This means that when image resolution higher than monitor resolution the image appears larger on screen than its specified print dimensions. For example, when you display a 1 x 1 inch 144ppi image on a 72dpi monitor it appears in a 2 x 2 inch area on screen. Because the monitor can display only 72 pixels per inch. It needs 2 inches to display the 144pixels that make up one edge of the image.  

Modern Physics - Graduate level important notes for competitive exams - PART2

•  4n series is called as "Thorium" series.

• 4n+1 series is called as "Neptunium" series.

• 4n+2 series is called as "Uranium" series

• 4n+3 series is called as "Actinium" series

• X-rays & 𝛾-rays of same energies are distinguished by their frequencies

• Spin of a Deuteron  is 1.

• Spin of Muons is 1/2.

• Spin of Pions (π-mesons) is zero.

• Spin of Photon is 1.

• Spin of Graviton is 2.

• Mass of a Proton is 1.0072766 amu

• Mass of a Neutron is 1.0086654 amu

• The total quantum number 'n' specified "Energy" quantization.

• The azimuthal quantum number specified "Angular Momentum".

• The magnetic moment of proton is given by 2.8eħ/2mp

• The magnetic moment of Neutron is given by 1.9eħ/2mp.

• In Davisson-Germer experiment , the angle between incident beam and diffracted beam is called "co-lattitude".

• In heavy atoms the spin-orbit interaction is almost equal to "electrostatic interaction".

• L-S coupling is due to "electrostatic interaction".

• L-S coupling scheme breaks down in strong magnetic field and applies to light atoms.

• In light atoms, "orbit interaction" is less than "electrostatic interaction".

• According to shell model nucleons interact primarily with a general force field rather than directly with one another.

• Magic numbers: 2,8,20,28,50,82,126

• Debroglie wavelength associated with electron accelerated to a potential V is ƛ=12.26/√V A⁰

REFRIGERATION - IMPORTANT NOTES

Refrigerating machines are of two types 1) Vapour compression machine (Frigidaire)" and 2) "Vapour absorption machine". 

Refrigerant: 

The liquid which on evaporation produces cooling is called refrigerant. Some examples are Ammonia(NH₃), Sulphur dioxide, Freon.

Properties of Refrigerant:

1. It should have low boiling point & melting point
2. It should be vapor at normal temperature and pressure.
3. It should have high thermal conductivity
4. "Latent heat of vaporization" of the refrigerant must be large.  
5.  The specific volume should be small in order to reduce the size of compressors. 

The evaporation of liquid under reduced pressure is a cooling process. The reason is that when a substance changes from liquid to vapor phase, it is associated with absorption of heat. If this heat is not taken from any external source, the necessary heat for phase exchange is taken from itself which therefore cools.

Vapor Compression Machine

Production of temperature by making a liquid evaporate rapidly under reduced pressure and circulating evaporating liquid around enclosure.

Debye's theory of Atomic Heat Capacity of Solids - Important Notes

 The failure in Einsteins theory of specific heat at low temperature is due to assumption that the vibrations of all atoms are simple harmonic and have one and same frequency.

"Debye" improved the Einsteins theory by considering the atomic oscillators as a system of coupled oscillators having a continuous range of frequencies.

Essential difference between Debye & Einstein model:

Debye has considered the vibrational modes of a crystal as a whole, where as Einstein has considered the vibration of a single atom with the assumption that atomic vibrations are independent of each other.   

Debye has made following assumptions:

1. The solid is capable of vibrating elastically in many different modes.
2. The frequency of vibration is different for different modes.
3. The number of modes of vibration of waves solids are limited in number.
4. The maximum frequency is the fundamental frequency of solid. The maximum frequency is frequency of shorter waves which the solid can transmit. 

According to Debye, a solid can be treated as an elastic body in which vibrations of atoms generate "stationary waves" of both longitudinal & transverse types with velocities Vl & Vt respectively.

The velocities can be determined by elastic constants & densities of solids.

The frequencies range from zero to a definite upper limit.

The number of modes of longitudinal waves per unit volume with frequencies between '𝝂' & '𝝂+d𝝂 ' is represented by 4Π𝝂²d𝝂/(Vl)³.

The number of modes of transverse vibrations per unit volume with frequencies between '𝝂' & '𝝂+d𝝂 ' is represented by 8Π𝝂²d𝝂/(Vt)³. Here 8Π is taken in place of 4Π. Because transverse vibrations have two independent directions of vibration i.e. they are equivalent to two waves at right angles to each other.

So total number of modes of vibrations per unit volume with frequencies '𝝂' & '𝝂+d𝝂 ' is given by  

4Π[(1/Vl³)+(2/Vt³)]𝝂²d𝝂

The total number of independent modes of vibrations is given by  

4ΠV[(1/Vl³)+(2/Vt³)] ∫𝝂²d𝝂 ; V is volume of gm-mole of solid

Why U-235, as isotope of Uranium with only 0.7% abundance will undergo fission if it captures a thermal Neutron where as U-238 will not?

 From 'B/A' against A curve, we know that Binding Energy per Nucleon in Uranium region is about 7MeV, which is almost equal to height of potential barrier opposing fission. 

Now,U-238.in  when a Neutron is added to Nucleus of ₉₂U²³⁵, we get ₉₂U²³⁶ i.e. an Even-Even nuclide. The pairing term in mass formula for Uranium is about 0.6MeV. Thus, we see that Thermal Neutron capture in U-235 results in total energy release of 7.6 MeV and since to cross potential barrier, only about 7 MeV is required. So U-235 can undergo fission by Thermal Neutron capture.

On the other hand, U-238 nucleus, after Neutron capture becomes a U-239 nucleus which is an Even-Odd Nuclide. Due to absence of pairing term for U-239, the fission barrier cannot be crossed. So Thermal Neutrons will not induce fission.        

Useful Range of Materials for Vacuum Vessels and Pipes

 

Critical Energy required for fission of some target nucleus