Thermodynamics and Statistical Physics (उष्मागतिकी तथा सांख्यिकीय भौतिकी )

Part B – Content of the Course

Total Numbers of Lectures (in Hours): 60

Unit

Topics

Number of Lectures

I

Historical Background and Laws of Thermodynamics

12

1. Historical background:

1.1. A brief historical background of thermodynamics and statistical Physics in context of India and Indian culture, Contribution of S.N. Bose in Statistical Physics.

2. Laws of Thermodynamics

2.1. Thermodynamical system and thermodynamical coordinated, Thermal equilibrium, Zeroth law of thermodynamics, The concept of path function and point function, Work done by and on the system.

2.2. First law of thermodynamics, Internal energy as a state function, Reversible and irreversible change, Heat engine and its efficiency, Carnot’s cycle, Carnot’s engine and its efficiency, Carnot’s theorem, Otto engine, Otto cycle, Diesel engine.

2.3. Second law of thermodynamics, Statement of Kelvin-Plank and Clapeyron, Absolute scale of temperature: Zero of absolute scale, Size for degree, Identity of a perfect gas scale and absolute scale.

Keywords/Tags: Thermodynamics, Internal energy, Heat engine, Absolute scale.

II

Entropy

1)       Concept of entropy, Clausius theorem, Entropy as a point function, Change in entropy in reversible and irreversible processes.

2)       Change in entropy of an ideal gas, Change in entropy when two liquids at different temperatures are mixed (or two bodies at different temperatures are kept in contact).

3)       Principle of increase of Entropy, Change in entropy of the universe in an irreversible process, Disorder and heat death of universe.

4)       Physical significance of Entropy, Temperature-Entropy (T-S) diagram, third law of thermodynamics.

Keywords/Tags: Reversible process, Entropy, Ideal gas.

12

III

Thermodynamic Potentials and Kinetic Theory of Gases

1. Thermodynamic Potential and its Application:

1.1. Thermodynamic potentials, Thermal equilibrium, internal energy, Helmholtz free energy, Enthalpy and Gibbs free energy.

1.2. Derivation of Maxwell’s relations from thermodynamic potentials, Gibbs-Helmholtz equation, Thermodynamic energy equation for ideal and van der Wall gas.

1.3. TdS equation, Derivation of expressions for C_P-C_V and their special cases for ideal and van der Waals gases, derivation of the expression E_S/E_t = C_P/C_V.

1.4. Clausius-Clapeyron latent heat equation, Temperature change in adiabatic process, Principle of refrigeration, Joule-Thomson effect, Cooling by adiabatic demagnetisation, Production and measurement of very low temperatures.

2. Kinetic Theory of Gases:

2.1. Behaviour of a real gas and its deviation from an ideal gas, Virial equation, Andrews experiment on CO₂ gas.

2.2. Critical constant, continuity of the liquid and gaseous state, Vapour and gas state, Boyle temperature, van der Waals equation for real gas, Values of critical constants, Law of the corresponding state.

Keywords/Tags: Potential, Enthalpy, Adiabatic, Real gas, Critical constant.

12

IV

Classical Statistics

1)       Probability, Distribution of N particles in two identical boxes, Probability of occurrence of either event, probability of composite events, Weightage probability.

2)       Probability distribution and its narrowing with the increase in number of particles, Expression for average properties, constraints, Accessible and non-accessible microstates.

3)       Ensemble theory (Macro-canonical, Canonical and Grand-canonical), Macro and micro states with examples, Principle of equal a prior probability, concept of phase space.

4)       Boltzmann Canonical distribution law: Application: average energy of one-dimensional harmonic oscillator.

5)       Derivation of law of equipartition of energy from statistics, Equilibrium between two system in thermal contact and b parameter, Statistical interpretation of entropy and relation S=k logW.

6)       Boltzmann partition function and derivation of expression for Internal energy, Helmholtz free energy, Enthalpy and Gibbs free energy.

Keywords/Tags: Probability, Microstate, Ensemble theory, Partition function.

12

V

Quantum Statistics

1)       Indistinguishability of particles and its consequences, Maxwell-Boltzmann statistics (Classical statistics): Maxwell-Boltzmann distribution law of velocity and speed, Maxwell-Boltzmann statistics and its distribution law.

2)       Quantum statistics: Bose-Einstein statistics and distribution law, Derivation of Planck’s radiation law from B-E statistics, Rayleigh-Jeans law, Wein’s displacement law and Stefan’s law.

3)       Fermi-Dirac statistics and its distribution law, Explanation of free electron theory, Fermi level and Fermi energy.

4)       Comparison between the Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics.

Keywords/Tags: Indistinguishability, Velocity distribution, Fermi level.

12

Hkkx c& ikB~;Øe dh fo"k;oLrq

O;k[;kuksa dh dqy la[;k ¼?kaVs esa½&60

bdkbZ

fo"k;

O;k[;kuksa dh la[;k

I

,sfrgkfld i`"BHkwfe vkSj Å"ekxfrdh ds fu;e

12

1)       ,sfrgkfld i`"BHkwfe

1.1)      Hkkjr rFkk Hkkjrh; laL—fr ds lanHkZ esa Å"ekxfrdh rFkk lkaf[;dh; HkkSfrdh dh la{ksi esa ,frgkfld i`"BHkwfe] lkaf[;dh; HkkSfrdh esa ,l-,u-cksl dk ;ksxnkuA

2)       Å"ekxfrdh ds fu;e

2.1)      Å"ekxfrdh fudk; rFkk Å"ekxfrdh funsZ’kkad] Å"eh; lkE;koLFkk] Å"ekxfrdh dk 'kwU;ok¡ fu;e] ekxZ Qyu vkSj fcUnqQyu dh /kkj.kk] fudk; }kjk rFkk fudk; ij fd;k x;k dk;ZA

2.2)      Å"ekxfrdh dk ÁFke fu;e] voLFkk Qyu ds :i  esa vkarfjd ÅtkZ] mRØe.kh; rFkk vuqRØe.kh; ifjorZu] Å"ek batu vkSj bldh n{krk] dkuksZ pØ] dkuksZ batu vkSj bldh n{krk] dkuksZ Áes;] vksVks batu] vksVks pØ] Mhtu batuA

2.3)      Å"ekxfrdh dk f}rh; fu;e] dSfYou&Iykad rFkk Dysijku ds dFku] rki dk ije ekiØe& ije ekiØe dk 'kwU;] fMxzh dk vkdkj] ,d vkn’kZ xSl ekiØe vkSj ije ekiØe dh igpkuA

Lkkj fcanq ¼dh oMZ½@VSx& Å"ekxfrdh] vkarfjd ÅtkZ] Å"ek batu] ije igpkuA

II

,UVªkWih

12

1)       ,UVªkWih dh vfHk/kkj.kk] Dykfl;u Áes;] ,UVªkWih fcUnq Qyu ds :i esa] mRØe.kh; ,oa vuqRØe.kh; ÁØeksa esa ,UVªWkih esa ifjorZuA

2)       vkn’kZ xSl dh ,UVªkWih esa ifjorZu] ,UVªkWih esa ifjorZu tcfd fofHkUu rkiksa ij nks æoksa dks feyk;k tkrk gS ¼vFkok fofHkUu rkiksa ij nks oLrqvksa dks lEidZ esa j[kk tkrk gS½A

3)       ,UVªkWih o`f) dk fu;e] vuqRØe.kh; ÁØe esa czãk.M dh ,UVªkWih esa ifjorZu] vO;oLFkk vkSj czãk.M dk Å"eh; var ¼ghV MsFk½A

4)       ,UVªkWih dk HkkSfrd egRo] rki&,UVªkWih vkjs[k ¼T-S½] Å"ekxfrdh dk r`rh; fu;eA

Lkkj fcanq ¼dh oMZ½@VSx& mRØe.kh; ÁØe] ,UVªkih] vkn’kZ xSlA

II

Å"ekxfrdh foHko rFkk xSlksa dk v.kqxfr fla)kUr

12

1)       Å"ekxfrd foHko rFkk buds vuqÁ;ksx

1.1)      Å"ekxfrd foHko] Å"eh; lkE;koLFkk] vkUrfjd ÅtkZ] gsYegksYV~t+ eqDr ÅtkZ] ,UFkSYih ,oa fxCl eqDr ÅtkZA

1.2)      Å"ekxfrd foHkoksa ls eSDlosy ds laca/kksa dh O;qRifÙk] fxCl&gsYegksYV~t+ lehdj.k] vkn’kZ xSl rFkk ok.Mj cky xSl ds fy;s Å"ekxfed ÅtkZ lehdj.kA

1.3)      TdS lehdj.k] C_P-C_v ds fy, O;atd dh O;qRifÙk ,oa vkn’kZ xSl rFkk ok.Mj oky xSl ds fy;s mudh fo’ks"k fLFkfr] O;atd E_S/E_t = C_P/C_v dh O;qRifÙkA

1.4)      Dykfl;l& DySijku xqIr Å"ek lehdj.k] j)ks"e ÁØe esa rki ifjorZu] Á’khru dk fl)kar] twy& Fkkelu ÁHkko] :)ks"e fopqacdu ls 'khryu] vfr fuEu rkiksa dk mRiknu rFkk ekiuA

2)       xSlksa dk v.kqxfr fl)kUr

2.1)     okLrfod xSl dk O;ogkj ,oa vkn’kZ xSl ls fopyu fofj;y lehdj.k] CO₂ xSl ds fy;s ,aMª;wt dk Á;ksxA

2.2)     Økafrd fu;rkad] æo rFkk xSlh; voLFkk dh fujarjrk] ok"i rFkk xSl voLFkk] ckW;y rkieku] okLrfod xSlksa ds fy, ok.Mj oky xSl lehdj.k] Økafrd fu;rkadksa ds eku] laxr voLFkk dk fu;eA

Lkkj fcanq ¼dh oMZ½@VSx& foHko] ,UFkSYih] :)ks"e] okLrfod xSl] Økafrd fu;rkadA

IV

fpjlEer lkaf[;dh

12

1)       Ákf;drk] n d.kksa dk nks ,d leku cDlksa esa forj.k] fdlh ,d ?kVuk ds ?kfVr gksus dh Ákf;drk] ,d lkFk ?kVukvksa ds ?kfVr gksus dh Ákf;drk] Hkkfjr Ákf;drkA

2)       Ákf;drk forj.k rFkk d.kksa dh la[;k esa o`f) ds lkFk bldk ladqpu] vkSlr xq.kksa ds fy, O;atd] Áfrca/k] vfHkxE; rFkk vuvfHkxE; lw{e voLFkk;saA

3)       leqnk; fl)kar ¼ekbØks] fofgr ,oa o`gn leqnk;½] mnkgj.k lfgr lw{e vkSj LFkwy voLFkk;sa] iwoZ Ákf;drk dk lekurk dk fl)kar] dyk vkdk’k dh vo/kkj.kkA

4)       cksYV~teSu dSuksfudy forj.k fu;e& vuqÁ;ksx] ,d foeh; vkorhZ nkSfy= dh vkSlr ÅtkZ] ÅtkZ ds lefoHkktu fu;e dk lkaf[;dh ls fuxeu] Å"eh; laidZ esa nks fudk;ksa dk larqyu rFkk b iSjkehVj] ,UVªkWih dk lkaf[;dh; O;k[;k rFkk lEcU/k S = K logW A

5)       cksYV~teSu dk laforj.k Qyu ,oa vkarfjd ÅtkZ] gSYegksYV~t eqDr ÅtkZ] ,UFkSYih vkSj fxCl eqDr ÅtkZ ds fy;s O;atd dk fuxeuA

lkj fcanq ¼dh oMZ½@VSx& Ákf;drk] lw{e voLFkk] leqnk; fl)kar] laforj.k QyuA

V

DokUVe lkaf[;dh

12

1)       d.kksa dh vÁsHks|rk vkSj mlds ÁfrQy] eSDlosy&cksYVt~eSu lkaf[;dh; ¼fpjlEer lkaf[;dh½] eSDosy&cksYVt~eSu dk osx forj.k ,oa pky forj.k fu;e] eSDlosy&cksYV~teSu lkaf[;dh dk forj.k fu;eA

2)       DokUVe lkaf[;dh& cksl&vkbaLVkbu lkaf[;dh vkSj forj.k fu;e] cksl&vkbaLVkbu lkaf[;dh ls Iykad fofdj.k fu;e dk fuxeu] chu dk foLFkkiu fu;e] jSys&thu dk fu;e vkSj LVhQu dk fu;eA

3)       QehZ&fMjkd lkaf[;dh rFkk forj.k fu;e] eqDr bysDVªku fl)kar dh O;k[;k] QehZ Lrj rFkk QehZ ÅtkZA

4)       eSDlosy& cksYV~teSu] cksl&vkbaLVkbu rFkk QehZ&fMjkd lkaf[;dh esa rqyukA

lkj fcanq ¼dh oMZ½@VSx& vÁHks|rk] osx forj.k] QehZ LrjA