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Nonlinear Insights
Understanding Physical Chemistry [Vol- 1]
  • ISBN: 9788196097813
  • Year: 2023
  • Edition: 1

Overview :

The author, Prof. Hrishikesh Chatterjee has used almost four decades of his rich and valuable teaching experience in undergraduate honours and postgraduate classes at Ramakrishna Mission Residential College, Narendrapur while writing this book. The book will enable readers to understand physical chemistry and enhance their depth of knowledge on the subject. The book is appraised both by the students and the faculty members across the country. The following key features will help the students enjoy going through the book: Specifically designed for the four-year honours courses according to the latest syllabus framed by UGC; Very lucid presentation in a student-friendly manner; Not a single step of theoretical discussion and derivation remains unexplained; A large number of MCQs, short and thought-provoking explanatory questions are included along with answers at the end of each chapter; A large number of worked-out examples at the end of each chapter have been included for students’ evaluation.

  • Chapter 1: KINETIC THEORY OF GASES 1 - 56
    • 1.1 Assumptions (Postulates) of Kinetic theory 2
    • 1.2 Consequences of the assumptions 2
    • 1.3 Justification of the fact that collisions are perfectly elastic 3
    • 1.4 Concept of Pressure and temperature 3
    • 1.5 Velocity of molecules 3
    • 1.6 Derivation of pressure from kinetic theory 5
    • 1.7 Concept of temperature from kinetic theory 6
    • 1.8 More about pressure of a gas from kinetic equation 7
    • 1.9 Gas laws from kinetic theory 7
    • 1.10 Definite pattern of distribution of molecular speed is a necessity 8
    • 1.11 Assumptions for Maxwell’s law of distribution of molecular speed 8
    • 1.12 Maxwell’s law of distribution of molecular speed 9
    • 1.13 Characteristic features of speed distribution law for three dimension 14
    • 1.14 Calculation of the magnitude of average properties 16
    • 1.15 Frequency of collision of molecules with unit area of the wall 20
    • 1.16 Application of wall collisions frequency 21
    • 1.17 Frequency of binary collision between similar molecules 22
    • 1.18 Frequency of binary collision between molecules of different gases 24
    • 1.19 Mean free path 25
    • 1.20 Effect of Pressure on mean free path 25
    • 1.21 Effect of Temperature on mean free path 26
    • 1.22 Distribution of kinetic energy 26
    • 1.23 Fraction of molecules possessing Kinetic energy 28
    • 1.24 Average kinetic energy for three dimension 29
    • 1.25 Energy distribution function in two dimension 29
    • 1.26 Fraction of molecules possessing kinetic energy ≥ ε' in two dimension 29
    • 1.27 Degrees of freedom 30
    • 1.28 Equipartition Principle 31
    • 1.29 Heat Capacity from equipartition principle 32
    • 1.30 Boltzmann distribution law 33
    • 1.31 Characteristics of barometric formula 34
    • 1.32 Flow of gas and transport phenomena (i.e. Transport Properties of Gas) 35
    • 1.33 Viscosity of gas 37
      • 1.33.1 Assumptions in the Derivation of η from kinetic theory 37
      • 1.33.2 Derivation of the expression 37
    • 1.34 Dependence of η on Temperature 39
      • 1.34.1 The Equation is not valid at very low pressure or very high pressure 39
      • 1.34.2 Short review of the chapter 40
      • 1.34.3 Worked Out Problems 43
      • 1.34.4 Exercise, MCQ and Questions 47
  • Chapter 2: REAL GAS 57 - 88
    • 2.1 Deviation from ideal behaviour 57
    • 2.2 Causes of deviation 60
    • 2.3 Van der Waals equation of state 61
    • 2.4 Origin of intermolecular interactions 63
    • 2.5 Validity of Van der Waals’ equation 66
      • 2.5.1 Experimental P-V Isotherm of a Real Gas 66
      • 2.5.2 Continuity of states 66
      • 2.5.3 PV-Isotherm from Van der Waals Equation 67
    • 2.6 Critical State in the light of Van der Waals equation 68
      • 2.6.1 Explanation of PV-P curve, (i.e. Amagat’s curve) by Van der Waals equation 69
    • 2.7 Amagat curve of a gas at various temperatures 70
      • 2.7.1 Boyle temperature from Van der Waals equation 71
    • 2.8 Compressibility factor 72
    • 2.9 Reduced equation of state 74
    • 2.10 Dieterici equation of state 76
      • 2.10.1 Dieterici equation at low pressure 76
      • 2.10.2 Verification of Dieterici’s equation 77
    • 2.11 Berthelot equation 78
      • 2.11.1 Calculation of ‘b’ from density temperature 78
      • 2.11.2 Values of the critical parameters in terms of ‘a’ and ‘b’ 78
      • 2.11.3 Modified Berthelot equation 79
      • 2.11.4 Relation between TB and TC 79
      • 2.11.5 Reduced equation of state 79
    • 2.12 Virial equation state 80
      • Short review of the chapter 82
      • Worked Out Problems 82
      • Exercise, MCQs and Questions 84
  • Chapter 3: Thermodynamics - I (Pages 89 - 124)
    • 3.1 Introduction (89)
    • 3.2 Fundamental terms used in thermodynamics (90)
      • 3.2.1 System (91)
      • 3.2.2 Surroundings (90)
      • 3.2.3 Universe (91)
      • 3.2.4 Classification of system (91)
      • 3.2.5 Process (92)
      • 3.2.6 Properties (92)
    • 3.3 Thermodynamic equilibrium (93)
    • 3.4 State function (93)
    • 3.5 Mathematical aspects of a state function (94)
      • 3.5.1 Mathematical relations regarding state function (95)
    • 3.6 Work (96)
    • 3.7 Heat (97)
    • 3.8 Internal energy (98)
    • 3.9 dq and dw are not exact differentials (99)
    • 3.10 Zeroth law of thermodynamics (99)
    • 3.11 1st Law of thermodynamics - its development (99)
      • 3.11.1 Basic consequence of 1st law (100)
    • 3.12 Importance of consideration of frictionless, weightless piston and thermostat (101)
    • 3.13 Ways of transformation of state (102)
    • 3.14 Show that during expansion |Wrev| > |Wirr| (106)
    • 3.15 Joule’s Experiment (107)
    • 3.16 Enthalpy (H) (108)
      • 3.16.1 Enthalpy for an ideal gas (109)
    • 3.17 A better criterion for ideality of a gas (109)
    • 3.18 Heat Capacity (C) (110)
      • 3.18.1 Relation between CP and CV (111)
      • 3.18.2 CP–CV for different cases (112)
    • 3.19 Adiabatic change (114)
      • 3.19.1 Reversible adiabatic expansion of an ideal gas (115)
      • 3.19.2 PVγ = constant is not an equation of state (116)
      • 3.19.3 P-V relationship for a gas obeying the equation P(V – b) = RT (116)
      • 3.19.4 P–V relationship for a Van der Waals gas (116)
      • 3.19.5 Comparison of slopes of P–V adiabat and P–V isotherm in case of an ideal gas (117)
      • 3.19.6 Reversible adiabatic work during expansion (117)
      • 3.19.7 Irreversible adiabatic change (118)
      • 3.19.8 Enthalpy change (119)
    • Short review of the chapter (119)
    • MCQs and Questions (122)
  • Chapter 4: Thermochemistry (Pages 125 - 153)
    • 4.1 Introduction (125)
    • 4.2 Laws of thermochemistry (126)
    • 4.3 Both the laws can be established from the 1st law of thermodynamics (128)
    • 4.4 Heat of formation (128)
    • 4.5 Dependence of heat of reaction on temperature (129)
    • 4.6 Heat of combustion (130)
    • 4.7 Heat of solution (130)
    • 4.8 Heat of neutralisation (132)
    • 4.9 Heat of formation of aqueous solution (133)
    • 4.10 Bond enthalpy and bond energy (134)
    • 4.11 Resonance energy (136)
    • 4.12 Adiabatic flame temperature (137)
    • Short review of the chapter (138)
    • Worked out problems (Chapters - 3 and 4) (139)
    • Exercise - (Chapters - 3 and 4), MCQs and Questions (147)
  • Chapter 5: Thermodynamics - II (Pages 154 - 234)
    • 5.1 Need for second law (154)
    • 5.2 Conversion of heat into work (155)
    • 5.3 Carnot cycle or Carnot engine (157)
    • 5.4 Conclusion derived from Carnot cycle (159)
      • 5.4.1 The reversed Carnot cycle - a refrigerator or a heat-pump (160)
    • 5.5 Kelvin-Planck statement and Clausius statement are equivalent (160)
    • 5.6 Carnot theorem (162)
    • 5.7 Clausius inequality from Carnot cycle (163)
    • 5.8 Thermodynamic scale of temperature (164)
    • 5.9 Entropy a new concept to understand spontaneity (164)
    • 5.10 Entropy change for irreversible processes (175)
    • 5.11 Free Energy (187)
    • 5.12 Criteria of Spontaneity and equilibrium (188)
    • 5.13 Lowering of Gibbs free-energy at constant P, T means increase of entropy of the universe (190)
    • 5.14 Properties of G (190)
    • 5.15 Variation of G with Pressure (191)
    • 5.16 Gibbs-Helmholtz equation (192)
    • 5.17 Characteristics of transformation depending upon ΔH and ΔS (194)
    • 5.18 Maxwell’s relations (195)
    • 5.19 TdS equations (197)
    • 5.20 Thermodynamic equation of state (199)
    • 5.21 Heat capacity relations (201)
    • 5.22 Joule-Thomson expansion (204)
    • Short review of the chapter (214)
    • Worked Out Problems (216)
    • Exercise, MCQs and Questions (226)
  • Chapter 6: Chemical Kinetics (Pages 235 - 313)
    • 6.1 Introduction (235)
    • 6.2 Rate of a reaction (236)
    • 6.3 Rate law and Rate constant (237)
    • 6.4 Order and Molecularity (238)
    • 6.5 Integrated rate laws for isolated reactions (239)
    • 6.6 Determination of order of reaction (250)
    • 6.7 Fast reactions (252)
    • 6.8 Opposing reaction (255)
    • 6.9 Consecutive reaction (257)
      • 6.9.1 Application of Steady-State approximation (260)
    • 6.10 Concept of Pre-equilibrium Step (261)
    • 6.11 Parallel reaction (262)
    • Thermodynamically controlled and kinetically controlled reactions (263)
    • 6.12 Temperature dependence of reaction rate (264)
    • 6.13 Chain Reactions (268)
      • 6.13.1 Branching chain reaction (271)
    • 6.14 Theories of reaction rates (273)
      • 6.14.1 Collision Theory (274)
      • 6.14.2 Unimolecular reaction (Lindemann Mechanism) (278)
      • 6.14.3 Potential Energy Surface, Activation Energy and Reaction Coordinate (282)
      • 6.14.4 Transition state theory (284)
      • 6.14.5 Transition state theory using partition function (287)
    • 6.15 Kinetics of catalytic reactions (290)
      • 6.15.1 Introduction (290)
      • 6.15.2 Catalyst increases the rates of forward and backward reactions equally (290)
      • 6.15.3 Classification of catalytic reactions (291)
      • 6.15.4 Mechanism of homogeneous catalysis (292)
      • 6.15.5 Pre-equilibrium treatment (292)
      • 6.15.6 Mechanism of acid-base catalysis (293)
      • 6.15.7 Acid catalysed reaction (294)
      • 6.15.8 Protolytic mechanism (294)
      • 6.15.9 Prototropic mechanism (295)
      • 6.15.10 Enzyme catalysis (296)
      • 6.15.11 Effect of pH (298)
      • 6.15.12 Effect of temperature (299)
    • 6.16 Effect of ionic strength on rate of reaction in solution (Primary kinetic salt effect) (299)
    • 6.17 Secondary Kinetic Salt Effect (300)
    • Short review of the chapter (301)
    • Worked Out Problems (304)
    • Exercise, MCQs and Questions (307)
  • Chapter 7: Viscosity (Pages 314 - 334)
    • 7.1 Introduction (314)
    • 7.2 Stream line flow (314)
    • 7.3 Turbulent flow (315)
    • 7.4 Viscosity (316)
    • 7.5 Viscosity coefficient (η) (317)
    • 7.6 Newtonian liquid and non-Newtonian fluid (318)
    • 7.7 Critical velocity (318)
    • 7.8 Derivation of Poiseuille’s equation (319)
    • 7.9 Error in the determination of η largely depends upon the error of ‘r’ (321)
    • 7.10 Temperature dependence of viscosity coefficient of liquid (322)
    • 7.11 Effect of pressure on viscosity coefficient (322)
    • 7.12 Determination of viscosity coefficient (323)
    • 7.13 Application of Poiseuille’s formula for gas (325)
    • 7.14 Rankine’s Method (326)
    • 7.15 Viscosity of solution containing macromolecule (326)
    • Short review of the chapter (328)
    • Worked Out Problems (329)
    • Exercise, MCQs and Questions (332)
  • Chapter 8: Thermodynamics of System of Variable Composition (Pages 335 - 358)
    • 8.1 Systems with variable composition (335)
    • 8.2 Concept of partial molar free energy and partial molar properties (336)
    • 8.3 Lowering of μi determines the direction of mass transfer (339)
    • 8.4 μi is also called chemical potential (340)
    • 8.5 Gibbs Duhem equations (341)
    • 8.6 Condition of spontaneity and equilibrium from Gibbs-Duhem equation (342)
    • 8.8 Variation of chemical potential with pressure (342)
    • 8.9 Free energy change during mixing (344)
    • 8.10 Thermodynamic criteria of ideal solution (346)
    • 8.11 Fugacity, the measure of escaping tendency (346)
    • 8.12 Standard state of a real gas (347)
    • 8.13 Activity and activity coefficient (in gas mixture) (348)
    • 8.14 Real solution and activity (349)
    • 8.15 Standard state for solvent (350)
    • Short review of the chapter (351)
    • Worked Out Problems (352)
    • Exercise, MCQs and Questions (354)
  • Chapter 9 - Chemical Equilibrium (Pages 359 - 396)
    • 9.1 Introduction - Page 359
    • 9.2 Variation of free energy of the reaction mixture with the advancement of the reaction - Page 359
    • 9.3 Concept of equilibrium constant from free energy change - Page 361
    • 9.4 Some aspects of equilibrium constant when expressed in terms of pressure, concentration and mole reaction - Page 363
    • 9.5 Equilibrium constant and free energy change: The reaction isotherm - Page 366
    • 9.6 Variation of Kp with temperature (Van’t Hoff equation) - Page 369
    • 9.7 Effect of pressure on equilibrium composition - Page 370
    • 9.8 Le Chatelier’s principle of mobile equilibrium - Page 371
    • 9.9 Effect of addition of a constituent on equilibrium composition - Page 372
    • 9.10 Effect of addition of inert gas on the equilibrium condition - Page 373
    • 9.11 Dimerisation of Benzoic Acid - Page 378
      • 9.11.1 Distribution Law - Page 377
      • 9.11.2 Solvent extraction - Page 379
    • Short review of the Chapter - Page 381
    • Worked Out Problems - Page 382
    • Exercise, MCQs and Questions - Page 386
  • Chapter 10 - Ionic Equilibrium (Pages 397 - 441)
    • 10.1 Ionic equilibrium - Page 397
    • 10.2 Ionic product of water - Page 399
    • 10.3 True dissociation constant of weak acid - Page 400
    • 10.4 pH – a way of expressing aH+ in dilute solution - Page 401
    • 10.5 Ionisation of monoprotic acid - Page 402
    • 10.6 Dissociation of diprotic acid (weak dibasic acid) - Page 403
    • 10.7 Dissociation of triprotic acid (H3A) - Page 404
    • 10.8 Hydrolysis of salt - Page 405
    • 10.9 Buffer solution - Page 409
    • 10.10 Mechanism of buffer action - Page 409
    • 10.11 Expression of pH of buffer solution - Page 409
    • 10.12 Buffer capacity - Page 410
    • 10.13 Buffer used in chemistry - Page 412
      • 10.13.1 Buffer used in physiological process in human body - Page 412
    • 10.14 Calculation of pH at different stages of titration - Page 414
    • 10.15 Acid-base indicator - Page 419
    • 10.16 Solubility product and activity product - Page 421
    • 10.17 Effect of added electrolyte on solubility of the salt - Page 422
    • 10.18 Common ion effect - Page 424
    • 10.19 Application of solubility product in group analysis of basic radicals - Page 426
    • 10.20 Dependence of solubility product on temperature - Page 426
    • 10.21 Determination of solubility product - Page 427
    • Short review of the Chapter - Page 427
    • Worked Out Problems - Page 428
    • Exercise, MCQs and Questions - Page 435
  • Chapter 11 - Ideal Solution and Colligative Property (Pages 442 - 470)
    • 11.1 Solution - Page 442
    • 11.2 Ideal solution - Page 442
    • 11.3 Raoult’s law-(an important thermodynamic criterion of ideal solution) - Page 444
    • 11.4 Raoult’s law in binary liquid mixture - Page 445
    • 11.5 Properties of ideal solutions (colligative property) - Page 446
    • 11.6 Raoult’s law of relative lowering of vapour pressure - Page 446
    • 11.7 Raoult’s law verification (Ostwald-Walker method) - Page 447
    • 11.8 Chemical potential, elevation of boiling point and depression of freezing point - Page 448
    • 11.9 Elevation of boiling point - Page 450
    • 11.10 Depression of freezing point - Page 452
    • 11.11 Osmosis and osmotic pressure - Page 454
    • 11.12 Relation between different colligative properties - Page 456
    • 11.13 Deviation from ideal behaviour - Page 457
    • 11.14 Dissociation of solute and Van’t Hoff’s factor - Page 458
    • 11.15 Ideal dilute solution - Page 458
    • 11.16 Measurement of molecular weight from colligative properties - Page 459
    • Short review of the Chapter - Page 461
    • Worked Out Examples - Page 462
    • Exercise, MCQs and Questions - Page 464
  • Chapter 12 - The Liquid State (Pages 471 - 517)
    • 12.1 Introduction (471)
    • 12.2 Structure of Liquid (472)
    • 12.3 Eyring Hole Theory of Liquid (474)
    • 12.4 Surface Tension: A Property of the Liquid Surface (476)
      • 12.4.1 Phase, Interphase, and Surface (Gibbs Dividing Surface) (476)
      • 12.4.2 Surface Free Energy (477)
      • 12.4.3 Surface Tension (479)
      • 12.4.4 Contact Angle (480)
      • 12.4.5 Work of Cohesion and Work of Adhesion (481)
      • 12.4.6 Spreading of Liquid (482)
      • 12.4.7 Shape of Liquid Meniscus within a Capillary (484)
      • 12.4.8 Excess Pressure Inside a Curved Membrane (486)
      • 12.4.9 Consequences of Excess Pressure - Capillary Rise or Capillary Depression (488)
      • 12.4.10 Application of Capillary Rise Phenomenon (491)
      • 12.4.11 Temperature Dependence of Surface Tension (491)
      • 12.4.12 Variation of Surface Tension with Concentration (492)
    • 12.5 Methods of Determination of Surface Tension (494)
    • 12.6 Vapour Pressure (496)
      • 12.6.1 Vapour Pressure and Its Dependence on Temperature (497)
      • 12.6.2 Vapour Pressure and Boiling Point (500)
      • 12.6.3 Variation of Vapour Pressure with Change in Pressure on the Liquid Phase Only (500)
    • 12.7 Measurement of Vapour (504)
    • Short Review of the Chapter (505)
    • Worked Out Problems (507)
    • Exercise, MCQs, and Questions (510)
  • Chapter 13 - Conductance (Pages 518 - 569)
    • Introduction (518)
    • 13.1 Conduction of Electricity by an Electrolyte in Solution (519)
    • 13.2 Hittorf’s Rule (522)
      • 13.2.1 Derivation of Hittorf’s Rule (Page 522)
    • 13.3 Methods of Determination of Transport Number (523)
    • 13.4 Conductance (527)
    • 13.5 Equivalent Conductance (530)
    • 13.6 Measurement of Conductivity (532)
    • 13.7 Debye-Huckel Onsager Theory of Interionic Attraction (533)
    • 13.8 Temperature Dependence of Ionic Conductance (536)
    • 13.9 Variation of Specific Conductance with Dilution (536)
    • 13.10 Variation of Equivalent Conductance with Dilution (537)
    • 13.11 Kohlrausch’s Law of Independent Migration of Ions (538)
    • 13.12 Ostwald Dilution Law (539)
    • 13.13 Hydration and Ionic Conductance (539)
    • 13.14 Abnormal High Ionic Mobilities and Ionic Conductances of H+ and OH Ions (540)
    • 13.15 Application of Conductance Measurement (541)
    • 13.16 Ionic Strength (548)
    • 13.17 Debye Huckel Limited Law (548)
    • 13.18 Effect of Dielectric Constant on Activity Coefficient (554)
    • Short Review of the Chapter (554)
    • Worked Out Problems (557)
    • Exercise, MCQs, and Questions (562)
    • Index (571)
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Preface

Elementary Physical Chemistry (For Minor and Generic courses) is published in one volume for all the semesters of Three-year B.Sc. (Minor) and B.Sc. (Generic) courses. The book is a result of my long teaching experience of forty years at the undergraduate (Honors) and post-graduate levels at RAMAKRISHNA MISSION RESIDENTIAL COLLEGE, NARENDRAPUR, WEST BENGAL. My interaction with the students and their reciprocal Understanding Physical Chemistry (Vol. -1) is published for the students of undergraduate honours course. Some major changes in the structure of the syllabus, as well as in the pattern of examination have been introduced from time to time during the recent period. Understanding Physical Chemistry (Vol. -1) is written with a completely different outlook and thought from the previous books of mine. This volume and Vol. - 2 will cover the coming syllabus of proposed four years degree course throughout the country.

In present days, students are not only engaged with their university curricula and syllabus but also take preparations for national level examinations such as N.E.T, G.A.T.E, J.A.M. for admission to post graduate courses to pursue for higher studies and research work after graduation. Therefore, it becomes difficult for them to concentrate for a longer period of time on any particular topic. Considering this, each chapter is presented in a lucid and methodical way so that a student can easily grasp the subject matter and the discussion is tailored to the needs of the undergraduate students. The book is dedicated to the legendary professor of physical chemistry, Late P.C. Rakshit whose constant inspiration led me to write this book. This is a tribute to him. The students following this book will face no difficulty in appearing for any examination.

Pedagogy

A brief summary is given point wise at the end of each chapter to facilitate revision of key concepts...

A large number of numerical problems are given in three phases but the problems are not alike and not monotonous, being of same type. In the first phase, early one- third of the problems have been fully solved mentioning the use of units at each step which most of the students usually do not follow. As a result, they are totally unaware of whether they are proceeding in the right direction. Unit balance of both sides of the equation at each step will determine the correct pathway of solving the problems. In the next phase, another one-third of the problems are given with hints or full solutions, depending on the merit of the problem with a trust that the students have learnt the utility of doing the problems with units. In the last phase, problems are given to the students for self-solving and thereby developing selfconfidence.

Theoretical questions are given in four stages:

  • Stage-1: Multiple choice questions
  • Stage-2:Very short type answer type questions where for answering the question only a word is sufficient.
  • Stage-3:Short answer type questions where for answering the question only a sentence is enough and finally,
  • Stage-4:Long answer type questions which should be thought provoking for the students.

As a teacher, I feel that when a chapter is presented in this structure, students will never get scared to appear for any examination. I am sure that this book will develop an affinity within the students for physical chemistry and many of them will pursue for higher studies in physical chemistry, out of love for the subject. Finally, if any teacher or student or any reader can guide us with suggestions for improving the material from the students’ perspective, I shall be delighted to consider the same.

-Hrishikesh Chatterjee

ABOUT THE BOOK

Understanding Physical Chemistry through Theories and Problems (Vol.1) is written for undergraduate students of Chemistry honours, following the latest syllabus as approved by UGC and the syllabus followed by neighboring countries. In the present system, a student gets nearly four months' time to cover the entire syllabus. Considering this aspect, the book is presented rationally so that a student can grasp the subject matter thoroughly within the scheduled period of time. The subject matter has been developed stepwise lucidly so that any student, while going through any chapter, will find the answers to all the queries without any difficulty. Thus the student will develop a great love towards the subject and a sense of satisfaction in understanding the topics. A large number of worked out examples are given at the end of each chapter, covering all aspects and topics. In each problem, a student will learn how to insert the magnitude of each parameter with proper unit in the problem and this will lead him or her to solve the problem correctly.

Key Features :

  • Each article is developed very systematically and logically with complete explanation of the relevant matter so that any critical question on that topic can be answered.
  • Sufficient number of numerical problems on the application of all the working formulae is given at the end of each chapter as worked out examples.
  • Each example is included showing the application of proper unit of each term. This will help the students to understand at every step, whether the problem is done correctly or any mistake has crept in.
  • At the end of each chapter theoretical questions are given in four stages and in each stage ten questions are set. Stage (A) - Multiple choice questions (MCQ) where only tick mark is needed for the correct answer; Stage (B) - Very short answer type questions are set for one word answer, Stage (C) Short answer type questions where answer requires a sentence or a few words and Stage (D) -.Containing descriptive and explanatory questions where the student has to answer the questions according to the ability of expression and understanding.
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