NUCLEAR PHYSICS

Nucleus:

Nucleus is the central core of an atom. Entire mass of an atom is concentrated in the nucleus. The atomic nucleus was discovered in 1911 by Rutherford. Nucleus consists of protons and neutrons and in general protons and neutrons are called nucleons. Hydrogen nucleus does not contain neutron and has only one proton.

Proton:

The rest mass of proton is 1.007277 amu and charge of proton is +1.6 x 10^–19 coulomb. The rest mass of proton is 1836 times the rest mass of electron.

Neutron:

The rest mass of neutron is 1.008665 amu and charge of neutron is zero. Neutrons are slightly heavier than proton.

Atomic mass unit:

1 atomic mass unit (amu) is 1.66 x 10^-27 kg. The mass of a nucleon is 1.67 x 10^–27 kg.

Atomic mass unit is defined as mass of 1/12^th of carbon-12 atom and the energy equivalent of 1 amu is 931 MeV.

Representation of a nucleus:

The symbolic representation of a nucleus is _zX^A.  Z is the atomic number and the atomic number can be the number of protons or number of electrons. A is the mass number, which consist of the number of protons and neutrons.

Nuclear radius:

The nuclear radius is of the order of 10^–14 m to 10^–15 m. The equation for the atomic radius is given by R = r_o A^1/3, where r_o is a constant and has a value of 1.3 x 10^–15 m.

Nuclear mass:

The nuclear mass is the total mass of protons and neutrons and is also equal to the total mass of the nucleons. Nuclear mass = Zm_p + Nm_n = Am_N where Z is the number of protons and m_p is mass of one protons, N is the number of neutrons and m_n  is mass of one neutron, A is mass number and m_N is mass of one nucleon.

  

Nuclear density:

Nuclear density = nuclear mass / nuclear volume. Nuclear density is independent of mass number A. Nuclear density has value of 1.816 x10¹⁷ kg/m³. Nuclear density is extraordinarily very high and it very large compared to density of lead (1.134 x 10⁴ kg/m³), which is considered to be the highest dense material available.

Isotopes:

Elements having the same atomic number Z and different mass number A are called isotopes. Examples are isotopes of hydrogen, ₁ H ¹, ₁ H ², ₁ H ³ and ₉₂ U ²³⁵, ₉₂ U ²³⁸. Since the number of charge is responsible for the characteristic property of an atom, all isotopes

of an element have the same chemical properties but different physical properties

Isobars:

Elements having the same mass number A and different atomic number Z is called isobars. The nuclei ₈ O ¹⁶, ₇ N ¹⁶ are example of isobars. The isobars are atoms of different elements and have different physical and chemical properties

Isotones:

Elements having the same number of neutrons are called isotones. Examples are isotopes of hydrogen, ₆ C ¹⁴, ₇ N ¹⁵, ₈ O ¹⁶, N = 8 in each case.

Isomers:

Elements having the same atomic number Z and same mass number A but differ from one anther is their nuclear energy states and exhibit differences in their internal structure are called isomers. The elements are distinguished from their different half life time.

Mass defect:

Mass defect is defined as the mass difference between the sum of the masses of the constituents of an atom and its actual mass M. Mass defect Dm = [(Zm_p + Nm_n)– M]

Binding energy:

Binding energy B.E is the energy needed to bind the nucleons in the nucleus and is also the conversion of mass defect into energy to bind the nucleons in the nucleus. Binding energy = Dm C² = [(Zm_p + Nm_n)– M]C²

Nuclear force

Nuclear force is the strongest force that binds the protons and neutrons inside the nucleus. There are three types of nuclear forces namely (p-p) force, (p-n) force and (n-n) force.

  

Ø  Nuclear forces are short-range forces and they are effective only at short range.

Ø  Nuclear forces are charge independent.

Ø  Nuclear forces are the strongest known forces in nature.

Ø  Nuclear forces have saturation property which means nuclear forces are limited in a particular range. As a result each nucleon interacts only with a limited number of nucleons nearest to it.

The liquid drop model:

The liquid drop model was proposed by Neils Bohr. Neils Bohr has observed that there are certain marked similarities between an atomic nucleus and a liquid drop.

Ø  The nucleus is spherical in shape in the stable state just as a liquid is spherical due to symmetrical surface tension forces.

Ø  The force of surface tension sets on the surface of the liquid drop and similarly there is a potential barrier at the surface of the nucleus.

Ø  The density of the liquid drop is independent of its volume and similarly the density of the nucleus is also independent of its volume.

Ø  The intermolecular forces in a liquid are short-range forces. The molecules in a liquid drop interact only with their immediate neighbors. Similarly the nuclear forces are short-range forces. The nucleons interact only with their neighbors and this leads to the saturation in the nuclear forces and constant binding energy per nucleon.

Ø  The molecules evaporate from a liquid drop on raising its temperature. Similarly when energy is given to a nucleus by bombarding it with a nuclear projectile a compound nucleus is formed which emits nuclear radiation.

Ø  When a small drop of liquid is allowed to oscillate it breaks up into two smaller drops of equal size. Similarly when sufficient energy is given to a nucleus by bombarding with a nuclear projectile it breaks into two smaller nuclei.

Shell model:

Shell model is some times referred to as independent particle model. According to this model the protons and neutrons are grouped in shells in the nucleus similar to extra nuclear electrons are grouped in shells in the nucleus. The number of nucleons in each shell is limited by Paula exclusion principle.

Neutron:

Neutron is emitted when Beryllium is bombarded by alpha particles.Bothe and Becker identified them as highly penetrating radiations. Joliot and Curie detected that they can knock out protons from hydrogenous substances. Chadwick discovered that their mass is nearly equal to that of protons and he is the one who named it as neutron.

   

Ø  Neutrons are changeless particles.

Ø  They are fundamental constituents of all nuclei except hydrogen ₁H¹.

Ø  It has greatest stability and has high penetrating power.

Ø  It cannot be deflected by electric and magnetic field

Ø  The free neutron is unstable, its half-life is 13 minutes and it decays into a proton, electron and antineutrino.

Ø  Slow neutrons have energy range between 0 to 1000 eV and fast neutrons have energy range between 0.5 MeV to 10 MeV.

Ø  Fast neutrons are slowed down by moderators. Since the slow neutrons are in thermal equilibrium with the medium through which they pass, they are also called as thermal neutrons. Paraffin, heavy water and graphite are used as moderators. Slow neutrons are capable of producing fission reaction when sent to uranium nucleus.

Nuclear fission:

Nuclear fission is the process of breaking a heavy nucleus into two smaller nuclei with the release of large amount of energy. For example when Uranium is bombarded with neutron it splits into Barium, Krypton, neutron and energy. ₉₂U²³⁵ and ₉₄Pu²³⁹ are fissionable materials, which are used as fuels in nuclear reactors. by neutrons of all energies. The material ₉₂U²³⁸ is fissionable only with fast neutrons.

Chain reaction:

Chain reaction is a self-propagating process in which number of neutrons goes on multiplying rapidly almost in geometrical progression during fission till whole of fission material is disintegrated.

Chain reaction consists of two types namely controlled chain reaction, which lead to nuclear reactor, and uncontrolled chain reaction, which lead to an atom bomb.

Multiplication factor:

The multiplication factor k is defined as the ratio of number of neutrons in any one generation to the number of neutrons in the preceding generation. The fission reaction is critical or steady when k = 1, is building up or super critical when k >1 and it is dying down or sub critical when k < 1.

Critical size:

Critical size of a system containing fissile material is defined as the minimum size for which the number of neutrons produced in the fission process just balance those lost by leakage and non fission capture.

Atom bomb:

The principle of fission is made use in the construction of the atom bomb. An atom bomb consists essentially of two pieces of uranium each smaller than the critical size and a source of neutron. A cylindrical third mass of uranium is propelled so that it will fuse together with the other tow pieces.

Parts of nuclear reactor:

                                      

Ø  Fuel or fissionable materials are mostly uranium and rarely plutonium, which are sealed in aluminium cylinders.

Ø  Neutron source gives thermal neutrons to induce fission reactions.

Ø  Moderators, which are heavy water, graphite and paraffin, used to slow down the fast neutrons.

Ø  Control rods, which are cadmium or boron, can absorb neutrons so that the fission reaction can be controlled.

Ø  Neutron reflector, which reflects the escaping neutrons back to the reactor.

Ø  Coolant, which is heavy water or liquid sodium, can absorb the heat generated.

Ø  Shielding can be done by thick lead lining surrounded by concrete wall to prevent harmful radioactive radiation.

Nuclear fusion:

Nuclear fusion is the process of fusing two or more light nuclei combine together to form a single heavy nucleus with the release of large amount of energy.For example when four hydrogen nuclei are fused together, a helium nucleus is formed. The mass of the single helium nucleus formed is less than the sum of the masses of four hydrogen nuclei. The difference is mass is converted into energy according to Einstein’s mass energy equation.

In the sun hydrogen and helium are in plasma state i.e. highly in ionized state. Proton-Proton cycle takes place in sun.  Carbon-Nitrogen cycle takes place in stars whose temperature is greater than that of the sun. In this cycle carbon is used as a catalyst.

Thermonuclear reactions:

The main difficulty is the fusion of nuclei is the electric force of repulsion between the positively charged nuclei. Fusion is possible when the kinetic energy of each of the nucleus is large enough to overcome the repulsion. Fusion reaction can take place only at very high temperatures of the order of 10⁷ to 10⁹ K.

Hydrogen bomb:

Hydrogen bomb is a device, which makes use of the principle of nuclear fusion. The very high temperature required for an uncontrolled thermonuclear reaction is obtained by the detonation of an atom bomb. The atom bomb by fission process produces a very high temperature at which thermonuclear reactions start resulting in the fusion of hydrogen to form helium and release of very high energy.

Elementary particles

Baryons or heavy particles:

Proton and particles heavier than proton form this group. Protons and neutrons are called stable baryons and particles having masses greater than nucleons are called unstable baryons. Every baryon has an antiparticle.

Hyperons:

Hyperons are special cases of baryons called unstable baryons characterized by time decay of the order of 10^-10 second. Hyperons have mass value greater than the mass of nucleons or the mass value intermediate between those of neutron and deuteron. There are four types of hyperons namely Lambda, sigma, Xi and omega.

Leptons:

This group contains particles of mass less than the mass of p mesons or pions. electrons, positrons, neutrino, antineutrino, positive and negative muons are leptons.

Mesons:

The rest mass of these particles varies between 250m_e and 1000m_e. The mesons are agents of interaction between particles inside the nucleus. Baryons and mesons are jointly called hadrons and are the particles of strong interaction.

Radioactivity:

Natural radioactivity was discovered by Henry Becquerel in 1896. The rays emitted from uranium were called Becquerel rays.Madame curie and here husband Pierre Curie discovered the highly radioactive element radium

Natural radioactivity is the spontaneous emission of alpha, beta and gamma rays by elements whose atomic number are greater than 82. That is, all elements having atomic number greater than lead are natural radioactive elements.

Radioacivity was not affected by strongest physical and chemical treatment and excessive heating or cooling or powerful reagent.

The electrons orbiting the nucleus are not responsible for radioactivity. The source of radioactivity is the nucleus of an atom. Radioactivity is the result of the disintegration of an unstable nucleus.

The half-life period of a radioactive material is the time taken by the element for half the number of its atoms to disintegrate. The half-life period of a radioactive element is inversely proportional to the decay constant of the element. T = 0.6931/l.

The mean life of a radioactive material is the average or mean lifetime of all the atoms of a radioactive element present. The mean life t = total life time of all the atoms/total number of atoms = 1/l.

The unit of radiation is roentgen. The quantity of radiation that produces 1.6 x 10¹² ion pairs in 1 gm of air is defined as roentgen.

Alpha decay

The emission of alpha particle by a nucleus leads to a decrease of atomic number decreases by 2 and a decrease of mass number by 4.

Beta decay

The emission of beta particle by a nucleus leads to an increase in atomic number by 1 and mass number remains the same.

Gamma decay

The emission of gamma rays by a nucleus leaves the atomic number mass number remain unaltered.

Geiger Nuttal law:

The range of R of an alpha particle and the disintegration constant l of the radioactive element that emits it are related as logl  = A+B log R. According to this relation when the disintegration constant is high the range is also high. Since the range depends on the energy we conclude that the radioactive substances of large decay constant emit higher nervy alpha particles.

The neutrino theory of beta decay:

In 1934 Fermi developed a theory to explain the continuous beta ray emission. According to this theory, during beta decay a neutron disintegrates into a proton, electron and a neutrino. The proton remains inside the nucleus and the electron and antineutrino are released from the nucleus.

Artificial radioactivity:

Artificial radioactivity discovered in 1934 by Curie and Joliot. The disintegration of light elements leads to artificial radioactivity. Artificial radioactive substances emit electron, neutron and positron or gamma ray and they do not emit alpha rays.

The transmutation of one element into another by artificial means is called artificial transmutation or artificial radioactivity.

Radioisotopes can be produced by bombarding the element with accelerated particle from a cyclotron. An element can be converted into a radioisotope by continuous bombardment of neutron inside the reactor.

Applications of radioisotopes

Radio-hosphorous-30 is used to determine the rate of absorption of an element in a fertilizer.

Radio-cobalt-60 is used to treat malignant tumour-cancer.

Radio-iodine 131 is used to locate brain tumour, to find the extent of enlargement of thyroid gland.

Radio-sodium-24 is used to check the blood circulation in heart and other parts

Radio-carbon-14 is used to determine the age of fossils and relics.

Uranium 235 and Lead 206 are used to determine the age of rocks.

Radio carbon dating:

Living being takes carbon-14 with food and air. When death occurs the intake of carbon-14 stops. Thencarbon-14 deacy and get converted into nitrogen-14. By determining the percentatge of carbon-14 in dead matter the age of specimen can be estimated. This method is used to find the age of mummies and relics. Thus carbon-14 provides radioactive clock for anthropologists.

Uranium dating:

The age of earth has been determined by the amount of uranium-235 and Lead-206 present in the specimen

Geiger Muller counter:

Geiger Muller counter is a device used to detect the radiation. The neon gas is used for ionization. The principle of this counter is based on the property of alpha particles have the highest ionizing power, beta particles have lower ionizing power and gamma rays have lowest ionizing power. The Geiger Muller counter has a cylinder containing a gas and if the radioactive rays sent to the gas it gets ionized based on the type of radioactive ray. The emf developed due to ionization is amplified to activate an electronic counter.

Nuclear interaction and particle accelerators:

The rearrangement of nucleons leading to the formation of new nuclei when two or more nuclei are close together is called nuclear interaction. Nuclear reactions are produced by bombardment with energetic projectiles like protons, deuterons, alpha particles, neutrons and electrons.

Cyclotron:

The cyclotron is one of the particle accelerators, which accelerates particles to very high kinetic energy. The cyclotron is a spiral type accelerator and was developed by Lawrence in 1930. It has a hollow cylinder divided into tow sections known as Dees. The Dees are connected to high frequency oscillator. A magnetic field perpendicular to the place of the Dees is applied.

By the action of high frequency oscillator and magnetic field the ion inside the Dees describes a circular path of angular velocity w = v/r = Bq/m is a constant. The frequency of rotation in a cyclotron is equal to Bq/2pm and the time period of rotation is equal to 2pm/Bq.

The advantages of cyclotron:

Ø  Cyclotron can accelerate protons, deuterons and alpha particles.

Ø  It requires comparatively low voltages and occupies a comparatively low space.

The limitations of cyclotron:

Ø  It is difficult to arrange an intense magnetic field over a large area and the deflector plates consume a large voltage.

Ø  At very high voltages the frequency Bq/2pm is not a constant and thus lead to phase instability. The frequency of the ion can be kept constant by increasing the magnetic field. In another form of apparatus the frequency of the applied ac is varied so that it is always equal to the frequency of rotation of the ion.

Ø  Electrons cannot be accelerated by cyclotrons due to their relativistic mass variation eve at low energy level of 20 keV.

Synchrocyclotron:

Synchrocyclotron is a modified form of the Lawrance cyclotron. This consists of only one Dee placed in a vacuum chamber between the poles of an electromagnet. Instead of second Dee opposite the opening of the Dee there is a metal sheet connected to the earth. The alternate potential difference applied to the Dee is made to ruse and fall periodically instead of remaining constant.

The frequency is changed at such a rate that as the ion lags a little due to the increase in mass caused by increase in velocity the electric field frequency also automatically lags in variation. Hence the particle always enters the Dee at the correct moment when it can experience maximum acceleration.

The Betatron:

Betatron is a device used to accelerate electrons (beta particles) to very high energies. D.W.Kerst constructed it in 1941. It consists of a doughnut shaped vacuum chamber placed between the pole pieces of an electromagnet. The electromagnet is energized by an alternating current. The magnet produces a strong magnetic field in the doughnut. The electrons are produced by an electron gun and are allowed to move in a circular orbit to constant radius in the vacuum chamber. The magnetic field varies very slowly compared with the frequency of the electrons in the equilibrium orbit.

The linear accelerator:

The linear accelerator consists of a series of coaxial hollow metal cylinders or drift tubes 1,2,3,4,5, etc. They are arranged linearly in a glass vacuum chamber. The alternate cylinders are connected together, the odd numbered cylinders being joined to one terminal and the even numbered ones the second terminal of the high frequency oscillator. After half a cycle the polarities are revered ie 1 and 3 will be negative and 2 and 4 positive.

The positive ions enter along the axis of the accelerator during the half cycle, when the drift tube 1 is negative so that the positive ions pass through the first tube with a velocity. The length of the tube 1 is so adjusted that as the positive ions come out of it, the tube has a positive potential and the next tube 2 has a negative potential and thus the positive ions are accelerated with high kinetic energy.

The limitations of linear accelerator:

Ø  The length of the accelerator becomes inconveniently large and it is difficult to maintain vacuum in a large chamber.

Ø  The ion current available is in the form of short interval impulses because the ions are injected at an appropriated moment.

THERMAL PHYSICS

                       

Part C Questions

1. a).State zeroth law of thermodynamics

b). Explain the construction and working of platinum resistance thermometer

c).Explain the Callendar and Grifith bridge to measure the resistance and temperature

2. a).State the first law of thermodynamics

b). Derive an expression for internal energy (U) based on temperature and volume

c). Derive an expression for internal energy (U) based on temperature and pressure

3. a). Explain the working of an ideal carnot’s engine based on four stages

b). State second law of thermodynamics

4. a). Derive expressions for entropy of reversible and irreversible processes.

b). Derive expressions for entropy of isothermal change and adiabatic change.

c). Derive expressions for entropy of an ideal gas.

5. Derive the six Maxwell’s thermodynamics equations.

6. a). State Joule Thomson effect

b). Explain Porous plug experiment

c). Discuss the results obtained

7. Explain the experimental method of liquefaction of helium

8.. Explain the experimental method of liquefaction of air.

9. a). Explain adiabatic demagnetization by a suitable experiment.

b). State third law of thermodynamics.

10. a). Derive Maxwell distribution equation.

b). Hence deduce equations for average, mean square and most probable speeds.

11. a).Explain Lee’s disc method of determining the thermal conductivity of a bad conductor

12. a).Derive Plack’s law of radiation

b). Deduce Rayleigh Jean’s law and Wien’s law

THERMAL PHYSICS

PART B QUESTIONS

1)      Discuss the different types of thermometric scales

2)      Explain the construction and working of platinum resistance thermometer

3)      Explain the Callendar and Griffith bridge to measure the resistance and temperature

4)      Based on first law of thermodynamics, derive an expression for internal energy based on temperature and volume.

5)      Based on first law of thermodynamics, derive an expression for internal energy based on temperature and pressure.

6)      Explain the working of a Carnot’s ideal heat engine

7)      State and prove Carnot’s theorem.

8)      Explain thermodynamic scale of temperature

9)      Discuss Clausius inequality

10)  Based on the Maxwell thermodynamic relations, show that

C_p-C_v = T(dP/dT)_v(dV/dT)_p

11)  Based on the Maxwell thermodynamic relations, show that

C_p-C_v = -T(dV/dT)²_p(dP/dV)_T

12)  Explain the porous plug experiment with suitable diagram

13)  Explain the adiabatic demagnetization with a suitable experiment

14)  Write the postulates of kinetic theory of gases

15)  Explain the experimental verification of Maxwell distribution law.

16)  Explain the Lee’s disc experiment to determine the thermal conductivity of a bad conductor.

17)  Explain the energy distribution in black body radiation with suitable graph.

THERMAL PHYSICS

PART A QUESTIONS

UNIT I

Define heat

Define temperature

State zeroth law of thermodynamics

What is the principle of platinum resistance thermometer?

What are advantages and disadvantages of platinum resistance thermometer?

What is a thermodynamic system?

What are thermodynamics variables?

What is a quasistatic process?

State first law of thermodynamics

UNIT II

What is reversible process?

What is irreversisble process?

What are the parts of Carnot’s engine

What Carnot’s heat engine is an ideal heat engine

State Carnot’s theorem

Define entropy

What is thermodynamic scale of temperature?

UNIT III

What are the applications of Maxwell thermodynamics relations

State Joule Thomson effect

What are the results of porous plug experiment

What is adiabaltic demagnetization

State third law of thermodynamics

UNIT IV

What is the significance of kinetic theory of gases

Write the Maxwell distribution law equation

Write the equation for average speed of molecule.

Write the equation for root mean square speed of molecule.

Write the equation for most probable speed of molecule.

What is the ratio of three speeds namely average speed, root mean square speed and most probable speed?

UNIT V

Define coefficient of thermal conductivity

Define a black body

State Kirchoff’law

State Wien’s law

State Stefan Boltzmann law

State Planck’s law of radiation

State Rayleigh Jean’s law

THERMAL PHYSICS 

1. What is thermometry

The branch of heat that deals with the measurement of temperature with scientific precision is called thermometry and the instrument used tomeasure temperature is called thermometer.

2. What is principle used in the construction of platinum resistance thermometer?

The electrical resistance of a metal is found to increase gradually and fairly uniform with temperature over a wide range and this principle is used in the construction of electrical resistance thermometer.

3. What are the merits of platinum resistance thermometer

It is very compact. It can be used to measure temperatures over a wide range of temperature. (-200^oC to 1200^oC)

It is free from changes of zero point as pure platinum has always the same resistance at the same temperature

4. Define a thermodynamics system

A thermodynamics system refers to a region in space or a quantity of matter bounded by some closed surface. A system may be a gas contained in a cylinder having a movable piston.

5. What are thermodynamics co-ordinates?

The state of thermodynamics system can be represented by specifying its pressure P, volume V, temperature T and entropy S.These variables are known as thermodynamics co-ordinates of the system.

6. State zeroth law of thermodynamics

The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third system, then they must be in thermal equilibrium with each other.

7. State first law of thermodynamics

The amount of heat given to a system is equal to the sum of the increase in the internal energy of the system and the external work done.

That is, dQ = dU + dW, where dQ is the quantity of heat given to a system, dU the change in internal energy and dW the external work done.

8. Define a quasistatic process

A process in which the deviation from the thermodynamic equilibrium is infinitesimally small is known as quasistatic process. It is an ideal concept and the condition for such a process cannot be satisfied rigorously in practice.

9. Define an isothermal process

If a system is perfectly conducting to the surroundings and the temperature remains constant throughout the process, it is called an isothermal process. An isothermal change is represented by the equation, PV = constant at constant temperature.

10. Define an adiabatic process

A process in which neither heat is given to the system nor heat is taken from the surroundings is called an adiabatic process. An adiabatic change is represented by equation, PV^γ = constant, where γ is the ratio of specific heat capacities of a gas.

11. Define a reversible process

A reversible process from the thermodynamical point of view is the one which can be retraced in the opposite direction so that the working substance passes through exactly the same condition as it does in the direct process.

12. Define an irreversible process

Any process which is not reversible exactly is an irreversible process.The processes which cannot be retraced in opposite order by reversing the controlling factors are called irreversible processes.

13. What is an indicator diagram?

A graphical method of studying the isothermal processes and adiabatic processes and representing the behaviour of a system is known as indicator diagram. This helps to understand the performance of heat engines.

14. What are the parts of a Carnot engine?

The carnot engine consists of source of heat energy, sink of heat energy, non-conducting stand, cylinder with piston and working substance.

15. State Carnot’s theorem

Statement I: All reversible engines working between the same two temperatures have the same efficiency whatever be the working substance and quantity of heat absorbed or rejected.

Statement II: Of all the heat engines working between the same two temperatures of source and sink the reversible heat engine has the maximum efficiency possible.

16. State second law of thermodynamics

Kelvin statement based on forward Carnot cycle: It is impossible to get continuous supply of work from a body by cooling it to a temperature lower than that of surroundings

Clausius statement based on reverse Carnot cycle: It is impossible to make heat flow from a body at a lower temperature to a body at a higher temperature.

17. Define one Kelvin on the thermodynamic scale

If an engine works between the steam point and ice point of water and if the area of engine’s indicator diagram is divided into 100 equal parts, the area of each part represents a temperature of 1K on the thermodynamic scale.

18. Define absolute zero based on thermodynamic scale.

The absolute zero on the thermodynamic scale is defined as that temperature of the sink at which no heat is rejected to it and the whole of the available energy has been used up in doing useful work and the engine will have 100% efficiency.

19. Define entropy

The entropy of system is defined as dS = dQ/T, where dQ is the amount of heat taken in reversibly by the system at temperature T.

20. State third law of thermodynamics

Planck in 1911 made the hypothesis that not only does the entropy difference vanish as T tends to zero but that the entropy of every solid or liquid substance in internal equilibrium at absolute zero is itself zero.

The third law also implies that it is impossible to reduce the temperature of a system to absolute zero in any finite number of operations. This is called the unattainability statement of third law.

21. What is Joule Thomson effect?

When a gas under constant high pressure passes adiabatically through a porous plug (narrow orifice) it undergoes a large drop of pressure and its temperature changes. This effect is called Joule-Thomson effect or Joule- Kelvin effect.

22. What is temperature of inversion

It is defined as the initial temperature of the gas at which the cooling effect becomes heating effect. At temperature above the temperature of inversion the gases show heating effect. The temperature of inversion is different for different gases.

23. What is the principle of regenerative cooling?

The gas is first compressed and the compressed gas is cooled below its temperature of inversion. The gas is then made to expand through a porous plug and the gas uses its part of energy to overcome the molecular forces of attraction. The gas is thereby cooled and the cooled gas is now made to flow round the incoming gas which on expansion falls further in temperature. This progressive cooling of the gas is continued till it finally liquefies. This is known as the principle of regenerative cooling and has been used for the liquefaction of gases.

24. What is adiabatic demagnetization?

When a paramagnetic substance is magnetized, external work done on it and its temperature rises. But on the other hand when a substance is adiabatically demagnetized, work is done by the substance and its temperature falls. This effect is called magnetic caloric effect. Maximum cooling can be obtained by employing strong magnetic field and low initial temperature.

25. Define thermal conduction

Conduction is the processes of heat transmission from one point to another though the substance without the actual motion of the particle.

26. Define coefficient of thermal conductivity

The coefficient of thermal conductivity is defined as the quantity of heat flowing per second through unit area of cross section of the material when the temperature gradient is unit. The unit of thermal conductivity is Wm^-1K^-1

27. Define thermal diffusivity

The thermal diffusivity is defined as the ratio of the thermal conductivity to the thermal capacity per unit volume.

28. Define thermal radiation

Radiation is the process of heat transmission from one place to other place that does not require the presence of any material medium.

29. Define a black body.

A perfect black body is defined as one which completely absorbs radiation of all wavelengths incident on it and also emits radiation of all possible wavelengths when heated.

30. Define emissive power

The emissive power of a substance is defined as the ratio of the amount of heat radiation emitted by unit area of a surface in one second to the amount of heat radiated by a perfectly black body per unit area of one second under identical conditions.

31. Define absorptive power

The absorptive power of a substance is defined as the ratio of the amount of heat absorbed in a given time by the surface to the amount of heat incident on the surface in the same time.

32. State Kirchoff’s law

At a given temperature the ratio of the emissive power to the absorptive power for all bodies is constant and is equal to the emissive power of a perfectly black body.

33. State Stefan-Boltmann law

The total rate at which a black body emits heat radiation is proportional to the fourth power of its absolute temperature.

34. State Wien’s law

The wavelength corresponding to the maximum energy is inversely proportional to its temperature.

35. State few postulates of kinetic theory of gases

The gas is composed of small individual particles called molecules. The molecules are considered to be rigid, perfectly elastic solid spheres and identical in all respects. They are however of negligible size as compared with their distance apart.

In a gas the distance between the molecules is large as compared to that of a silid or liquid and hence the inter-molecular force of attraction is negligible. Hence in a gas the molecules are in a state of incessant random motion moving in all directions with all possible velocities.

Question bank for properties

of matter and acoustics

Part A questions

Elasticity

1. Define elasticity and plasticity
2. Define stress and strain
3. Explain stress and strain diagram
4. What is elastic limit?
5. Define the elasticity applicable only to fluids
6. Define rigidity modulus of elasticity
7. Define young’s modulus of elasticity
8. Define bulk modulus of elasticity
9. Define Poisson’s ratio
10. State Hook’s law
11. Write the expression for the Poisson’s ratio in terms of elastic constants
12. What is a cantilever?
13. What is uniform bending
14. What is non-uniform bending
15. What is the difference between uniform and non uniform bending

Surface tension, viscosity, osmosis and diffusion

1. Define  surface tension and surface energy
2. Write an expression for the excess pressure inside the spherical bubble
3. What is the effect of temperature on the surface tension of a liquid?
4. Write two applications of surface tension.
5. Define coefficient of viscosity
6. What is the effect of temperature on the viscosity of a liquid?
7. What are the practical applications of viscosity?
8. Define osmosis
9. What is osmotic pressure
10. Define the term diffusion
11. State Fick’s law of diffusion
12. State Graham’s law of diffusion of gases
13. What is meant by effusion
14. Define the term transpiration

Waves, oscillations and acoustics

1. Define longitudinal and transverse waves
2. Define the terms wavelength, frequency, period and phase.
3. Define simple harmonic motion
4. Define forced oscillations.
5. Define damped oscillations.
6. What is resonance?
7. Give two examples of forced vibrations
8. Define ultrasonic wave.
9. State two properties of ultrasonic waves
10. Give two important applications of ultrasonic waves
11. What is magnetostriction effect?
12. What is piezoelectric effect?
13. What is reverse piezoelectric effect?
14. Define absorption coefficient of a materials
15. Define reverberation and reverberation time.

Part B questions

Elasticity

1. Explain stress-strain diagram
2. Calculate the work done in twisting a wire
3. Calculate the work done in stretching a wire
4. Derive the relation between elastic constants
5. Obtain an expression for twisting couple on a cylinder
6. Obtain an expression for the time period of cantilever oscillations
7. Derive and expression for the internal bending moment of a bar

Surface tension, viscosity, osmosis and diffusion

1. Write short note on the variations of surface tension with temperature
2. Describe an experiment to determine the viscosity of a liquid
3. Write short note on the variations of viscosity with temperature
4. Derive Poiseuille’s formula for viscosity by the method of dimensions
5. State the laws of osmotic pressure.
6. Write short note on osmosis and boiling point of a solution
7. Write short note on osmosis and freezing point of a solution

Waves, oscillations and acoustics

1. Derive an expression for the displacement, velocity and acceleration of a simple harmonic motion and hence deduce the equation for simple harmonic motion.
2. What are free, damped and forced vibrations
3. Discuss the applications of ultrasonic waves as NDT and SONAR.
4. What is acoustics of a building? Explain the factors affecting acoustics of a building.
5. Enumerate the features that an auditorium should have for good acoustics.

Part C questions

Elasticity

1. Describe an experiment with torsional pendulum to determine rigidity modulus of wire and moment of inertia of disc.
2. Define cantilever. Obtain an expression for the depression produced at its free end when the weight of the beam is negligible. Discuss various special cases.
3. Describe with relevant theory an experiment to determine Young’s modulus of a bar by cantilever depression method.
4. Describe an experiment to determine the young’s modulus of a material by non-uniform bending.
5. Describe an experiment to determine the young’s modulus of a material by uniform bending.

Surface tension, viscosity, osmosis and diffusion

1. Derive an expression for excess pressure inside a curved liquid surface. Discuss the variation of surface tension with temperature.
2. Describe the Jaeger’s method of studying the variation of surface tension of water with temperature.
3. Describe an experiment to determine the coefficient of viscosity of a liquid.
4. What is the principle of reverse osmosis? Explain the working of osmotic plant. What are the advantages of reverse osmosis?

Waves, oscillations and acoustics

1. Derive an expression for displacement due to forced vibrations. Also obtain an expression for amplitude and resonance.
2. Explain the theory of damped vibrations and discuss the applications of damped oscillations.
3. Describe the principle, construction and working of piezoelectric oscillator.
4. Explain how ultrasonics are produced in a magnetostriciton oscillator
5. Describe with necessary theory a method of measuring reverberation time.
6. Derive Sabine’s formula for the reverberation time of a building.