Engineering Thermodynamics (3rd Edition) by R. K. Rajput - PDF

ENGINEERING THERMODYNAMICS THIRD EDITION SI Units Ve r s io n R. K. Rajput E N G I N E E R I N G S E R I E S ENGINEERING THERMODYNAMICS  Also available : ST...

ENGINEERING THERMODYNAMICS THIRD EDITION SI Units Ve r s io n R. K. Rajput E N G I N E E R I N G S E R I E S ENGINEERING THERMODYNAMICS  Also available : STEAM TABLES and MOLLIER DIAGRAM (S.I. UNITS) Edited by R.K. RAJPUT Patiala DHARM M-therm\TITLE.PM5 i i  ENGINEERING THERMODYNAMICS [For Engineering Students of All Indian Universities and Competitive Examinations] S.I. UNITS By R.K. RAJPUT M.E. (Heat Power Engg.) Hons.–Gold Medallist ; Grad. (Mech. Engg. & Elect. Engg.) ; M.I.E. (India) ; M.S.E.S.I. ; M.I.S.T.E. ; C.E. (India) Principal (Formerly) Punjab College of Information Technology PATIALA, Punjab LAXMI PUBLICATIONS (P) LTD BANGALORE l CHENNAI l COCHIN l GUWAHATI l HYDERABAD JALANDHAR l KOLKATA l LUCKNOW l MUMBAI l RANCHI NEW DELHI l BOSTON, USA  Published by : LAXMI PUBLICATIONS (P) LTD 113, Golden House, Daryaganj, New Delhi-110002 Phone : 011-43 53 25 00 Fax : 011-43 53 25 28 www.laxmipublications.com [email protected] © All rights reserved with the Publishers. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher. ISBN: 978-0-7637-8272-6 3678 Price : Rs. 350.00 Only. First Edition : 1996 Second Edition : 2003 Third Edition : 2007 Offices : India USA Bangalore (Phone : 080-26 61 15 61) Boston Chennai (Phone : 044-24 34 47 26) 11, Leavitt Street, Hingham, Cochin (Phone : 0484-239 70 04) MA 02043, USA Guwahati (Phones : 0361-254 36 69, 251 38 81) Phone : 781-740-4487 Hyderabad (Phone : 040-24 75 02 47) Jalandhar (Phone : 0181-222 12 72) Kolkata (Phones : 033-22 27 37 73, 22 27 52 47) Lucknow (Phone : 0522-220 95 78) Mumbai (Phones : 022-24 91 54 15, 24 92 78 69) Ranchi (Phone : 0651-230 77 64) EET-0556-350-ENGG THERMODYNAMICS C—12751/06/07 Typeset at : Goswami Printers, Delhi Printed at : Ajit Printers, Delhi  Preface to The Third Edition I am pleased to present the third edition of this book. The warm reception which the previous editions and reprints of this book have enjoyed all over India and abroad has been a matter of great satisfaction to me. The entire book has been thoroughly revised ; a large number of solved examples (questions having been selected from various universities and competitive examinations) and ample additional text have been added. Any suggestions for the improvement of the book will be thankfully acknowledged and incorporated in the next edition. —Author Preface to The First Edition Several books are available in the market on the subject of “Engineering Thermo- dynamics” but either they are too bulky or are miserly written and as such do not cover the syllabii of various Indian Universities effectively. Hence a book is needed which should assimilate subject matter that should primarily satisfy the requirements of the students from syllabus/examination point of view ; these requirements are completely met by this book. The book entails the following features : — The presentation of the subject matter is very systematic and language of the text is quite lucid and simple to understand. — A number of figures have been added in each chapter to make the subject matter self speaking to a great extent. — A large number of properly graded examples have been added in various chapters to enable the students to attempt different types of questions in the examination without any difficulty. — Highlights, objective type questions, theoretical questions, and unsolved examples have been added at the end of each chapter to make the book a complete unit in all respects. The author’s thanks are due to his wife Ramesh Rajput for rendering all assistance during preparation and proof reading of the book. The author is thankful to Mr. R.K. Syal for drawing beautiful and well proportioned figures for the book. The author is grateful to M/s Laxmi Publications for taking lot of pains in bringing out the book in time and pricing it moderately inspite of heavy cost of the printing. Constructive criticism is most welcome from the readers. —Author DHARM M-therm\TITLE.PM5 v  Contents Chapter Pages Introduction to S.I. Units and Conversion Factors (xvi)—(xx) Nomenclature (xxi)—(xxii) 1. INTRODUCTION—OUTLINE OF SOME DESCRIPTIVE SYSTEMS... 1—13 1.1. Steam Power Plant... 1 1.1.1. Layout... 1 1.1.2. Components of a modern steam power plant... 2 1.2. Nuclear Power Plant... 3 1.3. Internal Combustion Engines... 4 1.3.1. Heat engines... 4 1.3.2. Development of I.C. engines... 4 1.3.3. Different parts of I.C. engines... 4 1.3.4. Spark ignition (S.I.) engines... 5 1.3.5. Compression ignition (C.I.) engines... 7 1.4. Gas Turbines... 7 1.4.1. General aspects... 7 1.4.2. Classification of gas turbines... 8 1.4.3. Merits and demerits of gas turbines... 8 1.4.4. A simple gas turbine plant... 9 1.4.5. Energy cycle for a simple-cycle gas turbine... 10 1.5. Refrigeration Systems... 10 Highlights... 12 Theoretical Questions... 13 2. BASIC CONCEPTS OF THERMODYNAMICS... 14—62 2.1. Introduction to Kinetic Theory of Gases... 14 2.2. Definition of Thermodynamics... 18 2.3. Thermodynamic Systems... 18 2.3.1. System, boundary and surroundings... 18 2.3.2. Closed system... 18 2.3.3. Open system... 19 2.3.4. Isolated system... 19 2.3.5. Adiabatic system... 19 2.3.6. Homogeneous system... 19 2.3.7. Heterogeneous system... 19 2.4. Macroscopic and Microscopic Points of View... 19 2.5. Pure Substance... 20 2.6. Thermodynamic Equilibrium... 20 2.7. Properties of Systems... 21 2.8. State... 21  ( vii ) Chapter Pages 2.9. Process... 21 2.10. Cycle... 22 2.11. Point Function... 22 2.12. Path Function... 22 2.13. Temperature... 23 2.14. Zeroth Law of Thermodynamics... 23 2.15. The Thermometer and Thermometric Property... 24 2.15.1. Introduction... 24 2.15.2. Measurement of temperature... 24 2.15.3. The international practical temperature scale... 31 2.15.4. Ideal gas... 33 2.16. Pressure... 33 2.16.1. Definition of pressure... 33 2.16.2. Unit for pressure... 34 2.16.3. Types of pressure measurement devices... 34 2.16.4. Mechanical type instruments... 34 2.17. Specific Volume... 45 2.18. Reversible and Irreversible Processes... 46 2.19. Energy, Work and Heat... 46 2.19.1. Energy... 46 2.19.2. Work and heat... 46 2.20. Reversible Work... 48 Highlights... 58 Objective Type Questions... 59 Theoretical Questions... 61 Unsolved Examples... 61 3. PROPERTIES OF PURE SUBSTANCES... 63—100 3.1. Definition of the Pure Substance... 63 3.2. Phase Change of a Pure Substance... 64 3.3. p-T (Pressure-temperature) Diagram for a Pure Substance... 66 3.4. p-V-T (Pressure-Volume-Temperature) Surface... 67 3.5. Phase Change Terminology and Definitions... 67 3.6. Property Diagrams in Common Use... 68 3.7. Formation of Steam... 68 3.8. Important Terms Relating to Steam Formation... 70 3.9. Thermodynamic Properties of Steam and Steam Tables... 72 3.10. External Work Done During Evaporation... 73 3.11. Internal Latent Heat... 73 3.12. Internal Energy of Steam... 73 3.13. Entropy of Water... 73 3.14. Entropy of Evaporation... 73 3.15. Entropy of Wet Steam... 74 3.16. Entropy of Superheated Steam... 74 3.17. Enthalpy-Entropy (h-s) Chart or Mollier Diagram... 75 DHARM M-therm\TITLE.PM5 v i i  ( viii ) Chapter Pages 3.18. Determination of Dryness Fraction of Steam... 89 3.18.1. Tank or bucket calorimeter... 89 3.18.2. Throttling calorimeter... 92 3.18.3. Separating and throttling calorimeter... 93 Highlights... 96 Objective Type Questions... 97 Theoretical Questions... 99 Unsolved Examples... 99 4. FIRST LAW OF THERMODYNAMICS... 101—226 4.1. Internal Energy... 101 4.2. Law of Conservation of Energy... 101 4.3. First Law of Thermodynamics... 101 4.4. Application of First Law to a Process... 103 4.5. Energy—A Property of System... 103 4.6. Perpetual Motion Machine of the First Kind-PMM1... 104 4.7. Energy of an Isolated System... 105 4.8. The Perfect Gas... 105 4.8.1. The characteristic equation of state... 105 4.8.2. Specific heats... 106 4.8.3. Joule’s law... 107 4.8.4. Relationship between two specific heats... 107 4.8.5. Enthalpy... 108 4.8.6. Ratio of specific heats... 109 4.9. Application of First Law of Thermodynamics to Non-flow or Closed System... 109 4.10. Application of First Law to Steady Flow Process... 150 4.11. Energy Relations for Flow Process... 152 4.12. Engineering Applications of Steady Flow Energy Equation (S.F.E.E.)... 155 4.12.1. Water turbine... 155 4.12.2. Steam or gas turbine... 156 4.12.3. Centrifugal water pump... 157 4.12.4. Centrifugal compressor... 157 4.12.5. Reciprocating compressor... 158 4.12.6. Boiler... 159 4.12.7. Condenser... 159 4.12.8. Evaporator... 160 4.12.9. Steam nozzle... 161 4.13. Throttling Process and Joule-Thompson Porous Plug Experiment... 162 4.14. Heating-Cooling and Expansion of Vapours... 183 4.15. Unsteady Flow Processes... 210 Highlights... 215 Objective Type Questions... 216 Theoretical Questions... 219 Unsolved Examples... 219 DHARM M-therm\TITLE.PM5 viii  ( ix ) Chapter Pages 5. SECOND LAW OF THERMODYNAMICS AND ENTROPY... 227—305 5.1. Limitations of First Law of Thermodynamics and Introduction to Second Law... 227 5.2. Performance of Heat Engines and Reversed Heat Engines... 227 5.3. Reversible Processes... 228 5.4. Statements of Second Law of Thermodynamics... 229 5.4.1. Clausius statement... 229 5.4.2. Kelvin-Planck statement... 229 5.4.3. Equivalence of Clausius statement to the Kelvin-Planck statement... 229 5.5. Perpetual Motion Machine of the Second Kind... 230 5.6. Thermodynamic Temperature... 231 5.7. Clausius Inequality... 231 5.8. Carnot Cycle... 233 5.9. Carnot’s Theorem... 235 5.10. Corollary of Carnot’s Theorem... 237 5.11. Efficiency of the Reversible Heat Engine... 237 5.12. Entropy... 252 5.12.1. Introduction... 252 5.12.2. Entropy—a property of a system... 252 5.12.3. Change of entropy in a reversible process... 253 5.13. Entropy and Irreversibility... 254 5.14. Change in Entropy of the Universe... 255 5.15. Temperature Entropy Diagram... 257 5.16. Characteristics of Entropy... 257 5.17. Entropy Changes for a Closed System... 258 5.17.1. General case for change of entropy of a gas... 258 5.17.2. Heating a gas at constant volume... 259 5.17.3. Heating a gas at constant pressure... 260 5.17.4. Isothermal process... 260 5.17.5. Adiabatic process (reversible)... 261 5.17.6. Polytropic process... 262 5.17.7. Approximation for heat absorbed... 263 5.18. Entropy Changes for an Open System... 264 5.19. The Third Law of Thermodynamics... 265 Highlights... 298 Objective Type Questions... 299 Theoretical Questions... 302 Unsolved Examples... 302 6. AVAILABILITY AND IRREVERSIBILITY... 306—340 6.1. Available and Unavailable Energy... 306 6.2. Available Energy Referred to a Cycle... 306 6.3. Decrease in Available Energy When Heat is Transferred Through a Finite Temperature Difference... 308 6.4. Availability in Non-flow Systems... 310 DHARM M-therm\TITLE.PM5 i x  (x) Chapter Pages 6.5. Availability in Steady-flow Systems... 311 6.6. Helmholtz and Gibb’s Functions... 311 6.7. Irreversibility... 312 6.8. Effectiveness... 313 Highlights... 336 Objective Type Questions... 337 Theoretical Questions... 338 Unsolved Examples... 338 7. THERMODYNAMIC RELATIONS... 341—375 7.1. General Aspects... 341 7.2. Fundamentals of Partial Differentiation... 341 7.3. Some General Thermodynamic Relations... 343 7.4. Entropy Equations (Tds Equations)... 344 7.5. Equations for Internal Energy and Enthalpy... 345 7.6. Measurable Quantities... 346 7.6.1. Equation of state... 346 7.6.2. Co-efficient of expansion and compressibility... 347 7.6.3. Specific heats... 348 7.6.4. Joule-Thomson co-efficient... 351 7.7. Clausius-Claperyon Equation... 353 Highlights... 373 Objective Type Questions... 374 Exercises... 375 8. IDEAL AND REAL GASES... 376—410 8.1. Introduction... 376 8.2. The Equation of State for a Perfect Gas... 376 8.3. p-V-T Surface of an Ideal Gas... 379 8.4. Internal Energy and Enthalpy of a Perfect Gas... 379 8.5. Specific Heat Capacities of an Ideal Gas... 380 8.6. Real Gases... 381 8.7. Van der Waal’s Equation... 381 8.8. Virial Equation of State... 390 8.9. Beattie-Bridgeman Equation... 390 8.10. Reduced Properties... 391 8.11. Law of Corresponding States... 392 8.12. Compressibility Chart... 392 Highlights... 407 Objective Type Questions... 408 Theoretical Questions... 408 Unsolved Examples... 409 9. GASES AND VAPOUR MIXTURES... 411—448 9.1. Introduction... 411 DHARM M-therm\TITLE.PM5 x  ( xi ) Chapter Pages 9.2. Dalton’s Law and Gibbs-Dalton Law... 411 9.3. Volumetric Analysis of a Gas Mixture... 413 9.4. The Apparent Molecular Weight and Gas Constant... 414 9.5. Specific Heats of a Gas Mixture... 417 9.6. Adiabatic Mixing of Perfect Gases... 418 9.7. Gas and Vapour Mixtures... 419 Highlights... 444 Objective Type Questions... 444 Theoretical Questions... 445 Unsolved Examples... 445 10. PSYCHROMETRICS... 449—486 10.1. Concept of Psychrometry and Psychrometrics... 449 10.2. Definitions... 449 10.3. Psychrometric Relations... 450 10.4. Psychrometers... 455 10.5. Psychrometric Charts... 456 10.6. Psychrometric Processes... 458 10.6.1. Mixing of air streams... 458 10.6.2. Sensible heating... 459 10.6.3. Sensible cooling... 460 10.6.4. Cooling and dehumidification... 461 10.6.5. Cooling and humidification... 462 10.6.6. Heating and dehumidification... 463 10.6.7. Heating and humidification... 463 Highlights... 483 Objective Type Questions... 483 Theoretical Questions... 484 Unsolved Examples... 485 11. CHEMICAL THERMODYNAMICS... 487—592 11.1. Introduction... 487 11.2. Classification of Fuels... 487 11.3. Solid Fuels... 488 11.4. Liquid Fuels... 489 11.5. Gaseous Fuels... 489 11.6. Basic Chemistry... 490 11.7. Combustion Equations... 491 11.8. Theoretical Air and Excess Air... 493 11.9. Stoichiometric Air Fuel (A/F) Ratio... 493 11.10. Air-Fuel Ratio from Analysis of Products... 494 11.11. How to Convert Volumetric Analysis to Weight Analysis... 494 11.12. How to Convert Weight Analysis to Volumetric Analysis... 494 11.13. Weight of Carbon in Flue Gases... 494 11.14. Weight of Flue Gases per kg of Fuel Burnt... 495 11.15. Analysis of Exhaust and Flue Gas... 495 DHARM M-therm\TITLE.PM5 x i  ( xii ) Chapter Pages 11.16. Internal Energy and Enthalpy of Reaction... 497 11.17. Enthalpy of Formation (∆Hf)... 500 11.18. Calorific or Heating Values of Fuels... 501 11.19. Determination of Calorific or Heating Values... 501 11.19.1. Solid and Liquid Fuels... 502 11.19.2. Gaseous Fuels... 504 11.20. Adiabatic Flame Temperature... 506 11.21. Chemical Equilibrium... 506 11.22. Actual Combustion Analysis... 507 Highlights... 537 Objective Type Questions... 538 Theoretical Questions... 539 Unsolved Examples... 540 12. VAPOUR POWER CYCLES... 543—603 12.1. Carnot Cycle... 543 12.2. Rankine Cycle... 544 12.3. Modified Rankine Cycle... 557 12.4. Regenerative Cycle... 562 12.5. Reheat Cycle... 576 12.6. Binary Vapour Cycle... 584 Highlights... 601 Objective Type Questions... 601 Theoretical Questions... 602 Unsolved Examples... 603 13. GAS POWER CYCLES... 604—712 13.1. Definition of a Cycle... 604 13.2. Air Standard Efficiency... 604 13.3. The Carnot Cycle... 605 13.4. Constant Volume or Otto Cycle... 613 13.5. Constant Pressure or Diesel Cycle... 629 13.6. Dual Combustion Cycle... 639 13.7. Comparison of Otto, Diesel and Dual Combustion Cycles... 655 13.7.1. Efficiency versus compression ratio... 655 13.7.2. For the same compression ratio and the same heat input... 655 13.7.3. For constant maximum pressure and heat supplied... 656 13.8. Atkinson Cycle... 657 13.9. Ericsson Cycle... 660 13.10. Gas Turbine Cycle-Brayton Cycle... 661 13.10.1. Ideal Brayton cycle... 661 13.10.2. Pressure ratio for maximum work... 663 13.10.3. Work ratio... 664 13.10.4. Open cycle gas turbine-actual brayton cycle... 665 13.10.5. Methods for improvement of thermal efficiency of open cycle gas turbine plant... 667 DHARM M-therm\TITLE.PM5 x i i  ( xiii ) Chapter Pages 13.10.6. Effect of operating variables on thermal efficiency... 671 13.10.7. Closed cycle gas turbine... 674 13.10.8. Gas turbine fuels... 679 Highlights... 706 Theoretical Questions... 707 Objective Type Questions... 707 Unsolved Examples... 709 14. REFRIGERATION CYCLES... 713—777 14.1. Fundamentals of Refrigeration... 713 14.1.1. Introduction... 713 14.1.2. Elements of refrigeration systems... 714 14.1.3. Refrigeration systems... 714 14.1.4. Co-efficient of performance (C.O.P.)... 714 14.1.5. Standard rating of a refrigeration machine... 715 14.2. Air Refrigeration System... 715 14.2.1. Introduction... 715 14.2.2. Reversed Carnot cycle... 716 14.2.3. Reversed Brayton cycle... 722 14.2.4. Merits and demerits of air refrigeration system... 724 14.3. Simple Vapour Compression System... 730 14.3.1. Introduction... 730 14.3.2. Simple vapour compression cycle... 730 14.3.3. Functions of parts of a simple vapour compression system... 731 14.3.4. Vapour compression cycle on temperature-entropy (T-s) diagram... 732 14.3.5. Pressure-enthalpy (p-h) chart... 734 14.3.6. Simple vapour compression cycle on p-h chart... 735 14.3.7. Factors affecting the performance of a vapour compression system... 736 14.3.8. Actual vapour compression cycle... 737 14.3.9. Volumetric efficiency... 739 14.3.10. Mathematical analysis of vapour compression refrigeration... 740 14.4. Vapour Absorption System... 741 14.4.1. Introduction... 741 14.4.2. Simple vapour absorption system... 742 14.4.3. Practical vapour absorption system... 743 14.4.4. Comparison between vapour compression and vapour absorption systems... 744 14.5. Refrigerants... 764 14.5.1. Classification of refrigerants... 764 14.5.2. Desirable properties of an ideal refrigerant... 766 14.5.3. Properties and uses of commonly used refrigerants... 768 Highlights... 771 Objective Type Questions... 772 Theoretical Questions... 773 Unsolved Examples... 774 DHARM M-therm\TITLE.PM5 xiii  ( xiv ) Chapter Pages 15. HEAT TRANSFER... 778—856 15.1. Modes of Heat Transfer... 778 15.2. Heat Transmission by Conduction... 778 15.2.1. Fourier’s law of conduction... 778 15.2.2. Thermal conductivity of materials... 780 15.2.3. Thermal resistance (Rth)... 782 15.2.4. General heat conduction equation in cartesian coordinates... 783 15.2.5. Heat conduction through plane and composite walls... 787 15.2.6. The overall heat transfer coefficient... 790 15.2.7. Heat conduction through hollow and composite cylinders... 799 15.2.8. Heat conduction through hollow and composite spheres... 805 15.2.9. Critical thickness of insulation... 808 15.3. Heat Transfer by Convection... 812 15.4. Heat Exchangers... 815 15.4.1. Introduction... 815 15.4.2. Types of heat exchangers... 815 15.4.3. Heat exchanger analysis... 820 15.4.4. Logarithmic temperature difference (LMTD)... 821 15.5. Heat Transfer by Radiation... 832 15.5.1. Introduction... 832 15.5.2. Surface emission properties... 833 15.5.3. Absorptivity, reflectivity and transmittivity... 834 15.5.4. Concept of a black body... 836 15.5.5. The Stefan-Boltzmann law... 836 15.5.6. Kirchhoff ’s law... 837 15.5.7. Planck’s law... 837 15.5.8. Wien’s displacement law... 839 15.5.9. Intensity of radiation and Lambert’s cosine law... 840 15.5.10. Radiation exchange between black bodies separated by a non-absorbing medium... 843 Highlights... 851 Objective Type Questions... 852 Theoretical Questions... 854 Unsolved Examples... 854 16. COMPRESSIBLE FLOW... 857—903 16.1. Introduction... 857 16.2. Basic Equations of Compressible Fluid Flow... 857 16.2.1. Continuity equation... 857 16.2.2. Momentum equation... 858 16.2.3. Bernoulli’s or energy equation... 858 16.3. Propagation of Disturbances in Fluid and Velocity of Sound... 862 16.3.1. Derivation of sonic velocity (velocity of sound)... 862 16.3.2. Sonic velocity in terms of bulk modulus... 864 16.3.3. Sonic velocity for isothermal process... 864 16.3.4. Sonic velocity for adiabatic process... 865 DHARM M-therm\TITLE.PM5 x i v  ( xv ) Chapter Pages 16.4. Mach Number... 865 16.5. Propagation of Disturbance in Compressible Fluid... 866 16.6. Stagnation Properties... 869 16.6.1. Expression for stagnation pressure (ps) in compressible flow... 869 16.6.2. Expression for stagnation density (ρs)... 872 16.6.3. Expression for stagnation temperature (Ts)... 872 16.7. Area—Velocity Relationship and Effect of Variation of Area for Subsonic, Sonic and Supersonic Flows... 876 16.8. Flow of Compressible Fluid Through a Convergent Nozzle... 878 16.9. Variables of Flow in Terms of Mach Number... 883 16.10. Flow Through Laval Nozzle (Convergent-divergent Nozzle)... 886 16.11. Shock Waves... 892 16.11.1. Normal shock wave... 892 16.11.2. Oblique shock wave... 895 16.11.3. Shock Strength... 895 Highlights... 896 Objective Type Questions... 899 Theoretical Questions... 901 Unsolved Examples... 902 l Competitive Examinations Questions with Answers... 904—919 Index... 920—922 l Steam Tables and Mollier Diagram... (i)—(xx) DHARM M-therm\TITLE.PM5 x v  Introduction to SI Units and Conversion Factors A. INTRODUCTION TO SI UNITS SI, the international system of units are divided into three classes : 1. Base units 2. Derived units 3. Supplementary units. From the scientific point of view division of SI units into these classes is to a certain extent arbitrary, because it is not essential to the physics of the subject. Nevertheless the General Confer- ence, considering the advantages of a single, practical, world-wide system for international rela- tions, for teaching and for scientific work, decided to base the international system on a choice of six well-defined units given in Table 1 below : Table 1. SI Base Units Quantity Name Symbol length metre m mass kilogram kg time second s electric current ampere A thermodynamic temperature kelvin K luminous intensity candela cd amount of substance mole mol The second class of SI units contains derived units, i.e., units which can be formed by com- bining base units according to the algebraic relations linking the corresponding quantities. Several of these algebraic expressions in terms of base units can be replaced by special names and symbols can themselves be used to form other derived units. Derived units may, therefore, be classified under three headings. Some of them are given in Tables 2, 3 and 4. (xvi) INTRODUCTION TO SI UNITS AND CONVERSION FACTORS (xvii) Table 2. Examples of SI Derived Units Expressed in terms of Base Units SI Units Quantity Name Symbol area square metre m2 volume cubic metre m3 speed, velocity metre per second m/s acceleration metre per second squared m/s2 wave number 1 per metre m–1 density, mass density kilogram per cubic metre kg/m3 concentration (of amount of substance) mole per cubic metre mol/m3 activity (radioactive) 1 per second s–1 specific volume cubic metre per kilogram m3/kg luminance candela per square metre cd/m2 Table 3. SI Derived Units with Special Names SI Units Quantity Name Symbol Expression Expression in terms of in terms of other SI base units units frequency hertz Hz — s–1 force newton N — m.kg.s–2 pressure pascal Pa N/m2 m–1.kg.s–2 energy, work, quantity of heat power joule J N.m m2.kg.s–2 radiant flux quantity of electricity watt W J/S m2.kg.s–3 electric charge coloumb C A.s s.A electric tension, electric potential volt V W/A m2.kg.s–3.A–1 capacitance farad F C/V m–2.kg–1.s4 electric resistance ohm Ω V/A m2.kg.s–3.A–2 conductance siemens S A/V m–2.kg–1.s3.A2 magnetic flux weber Wb V.S. m2.kg.s–2.A–1 magnetic flux density tesla T Wb/m2 kg.s–2.A–1 inductance henry H Wb/A m2.kg.s–2.A–2 luminous flux lumen lm — cd.sr illuminance lux lx — m–2.cd.sr dharm \M-therm\th0-1 (xviii) ENGINEERING THERMODYNAMICS Table 4. Examples of SI Derived Units Expressed by means of Special Names SI Units Quantity Name Symbol Expression in terms of SI base units dynamic viscosity pascal second Pa-s m–1.kg.s–1 moment of force metre newton N.m m2.kg.s–2 surface tension newton per metre N/m kg.s–2 heat flux density, irradiance watt per square metre W/m2 kg.s–2 heat capacity, entropy joule per kelvin J/K m2.kg.s–2.K–1 specific heat capacity, specific joule per kilogram kelvin J/(kg.K) m2.s–2.K–1 entropy specific energy joule per kilogram J/kg m2.s–2 thermal conductivity watt per metre kelvin W/(m.K) m.kg.s–3.K–1 energy density joule per cubic metre J/m 3 m–1.kg.s–2 electric field strength volt per metre V/m m.kg.s–3.A–1 electric charge density coloumb per cubic metre C/m 3 m–3.s.A electric flux density coloumb per square metre C/m 2 m–2.s.A permitivity farad per metre F/m m–3.kg–1.s4.A4 current density ampere per square metre A/m 2 — magnetic field strength ampere per metre A/m — permeability henry per metre H/m m.kg.s–2.A–2 molar energy joule per mole J/mol m2.kg.s–2mol–1 molar heat capacity joule per mole kelvin J/(mol.K) m2.kg.s–2.K–1.mol–1 The SI units assigned to third class called “Supplementary units” may be regarded either as base units or as derived units. Refer Table 5 and Table 6. Table 5. SI Supplementary Units SI Units Quantity Name Symbol plane angle radian rad solid angle steradian sr dharm \M-therm\th0-1 INTRODUCTION TO SI UNITS AND CONVERSION FACTORS (xix) Table 6. Examples of SI Derived Units Formed by Using Supplementary Units SI Units Quantity Name Symbol angular velocity radian per second rad/s angular acceleration radian per second squared rad/s2 radiant intensity watt per steradian W/sr radiance watt per square metre steradian W-m–2.sr–1 Table 7. SI Prefixes Factor Prefix Symbol Factor Prefix Symbol 1012 tera T 10–1 deci d 109 giga G 10–2 centi c 106 mega M 10–3 milli m 103 kilo k 10–6 micro µ 102 hecto h 10–9 nano n 101 deca da 10–12 pico p 10–15 fasnto f 10–18 atto a B. CONVERSION FACTORS 1. Force : 1 newton = kg-m/sec2 = 0.012 kgf 1 kgf = 9.81 N 2. Pressure : 1 bar = 750.06 mm Hg = 0.9869 atm = 105 N/m2 = 103 kg/m-sec2 1 N/m2 = 1 pascal = 10–5 bar = 10–2 kg/m-sec2 1 atm = 760 mm Hg = 1.03 kgf/cm2 = 1.01325 bar = 1.01325 × 105 N/m2 3. Work, Energy or Heat : 1 joule = 1 newton metre = 1 watt-sec = 2.7778 × 10–7 kWh = 0.239 cal = 0.239 × 10–3 kcal 1 cal = 4.184 joule = 1.1622 × 10–6 kWh 1 kcal = 4.184 × 103 joule = 427 kgf-m = 1.1622 × 10–3 kWh 1 kWh = 8.6042 × 105 cal = 860 kcal = 3.6 × 106 joule FG 1 IJ kcal = 9.81 joules 1 kgf-m = H 427 K dharm \M-therm\th0-1 (xx) ENGINEERING THERMODYNAMICS 4. Power : 1 watt = 1 joule/sec = 0.860 kcal/h 1 h.p. = 75 m kgf/sec = 0.1757 kcal/sec = 735.3 watt 1 kW = 1000 watts = 860 kcal/h 5. Specific heat : 1 kcal/kg-°K = 0.4184 joules/kg-K 6. Thermal conductivity : 1 watt/m-K = 0.8598 kcal/h-m-°C 1 kcal/h-m-°C = 1.16123 watt/m-K = 1.16123 joules/s-m-K. 7. Heat transfer co-efficient : 1 watt/m2-K = 0.86 kcal/m2-h-°C 1 kcal/m2-h-°C = 1.163 watt/m2-K. C. IMPORTANT ENGINEERING CONSTANTS AND EXPRESSIONS Engineering constants M.K.S. system SI Units and expressions 1. Value of g0 9.81 kg-m/kgf-sec2 1 kg-m/N-sec2 2. Universal gas constant 848 kgf-m/kg mole-°K 848 × 9.81 = 8314 J/kg-mole-°K (3 1 kgf-m = 9.81 joules) 8314 3. Gas constant (R) 29.27 kgf-m/kg-°K = 287 joules/kg-K 29 for air for air 4. Specific heats (for air) cv = 0.17 kcal/kg-°K cv = 0.17 × 4.184 = 0.71128 kJ/kg-K cp = 0.24 kcal/kg-°K cp = 0.24 × 4.184 = 1 kJ/kg-K 5. Flow through nozzle-Exit 91.5 U , where U is in kcal 44.7 U , where U is in kJ velocity (C2) 6. Refrigeration 1 ton = 50 kcal/min = 210 kJ/min 7. Heat transfer The Stefan Boltzman Q = σT4 kcal/m2-h Q = σT4 watts/m2-h Law is given by : when σ = 4.9 × 10–8 when σ = 5.67 × 10–8 kcal/h-m2 -°K4 W/m2 K4 dharm \M-therm\th0-1 INTRODUCTION TO SI UNITS AND CONVERSION FACTORS (xxi) Nomenclature A area b steady-flow availability function C velocity °C temperature on the celsius (or centigrade) scale c specific heat cp specific heat at constant pressure cv specific heat at constant volume Cp molar heat at constant pressure Cv molar heat at constant volume D, d bore ; diameter E emissive power ; total energy e base of natural logarithms g gravitational acceleration H enthalpy h specific enthalpy ; heat transfer co-efficient hf specific enthalpy of saturated liquid (fluid) hfg latent heat hg specific enthalpy of saturated vapour ; gases K temperature on kelvin scale (i.e., celsius absolute, compressibility) k thermal conductivity, blade velocity co-efficient L stroke M molecular weight m mass  m rate of mass flow N rotational speed n polytropic index, number of moles ; number of cylinders P power p absolute pressure pm mean effective pressure pi indicated mean effective pressure pb brake mean effective pressure, back pressure dharm \M-therm\th0-1 (xxii) ENGINEERING THERMODYNAMICS Q heat, rate of heat transfer q rate of heat transfer per unit area R gas constant ; thermal resistance ; radius ; total expansion ratio in compound steam engines R0 universal gas constant r radius, expansion ratio, compression ratio S entropy s specific entropy T absolute temperature ; torque t temperature U internal energy ; overall heat transfer co-efficient u specific internal energy V volume v specific volume W work ; rate of work transfer ; brake load ; weight w specific weight ; velocity of whirl x dryness fraction ; length Greek Symbols α absorptivity γ ratio of specific heats, cp/cv ∈ emissivity ; effectiveness η efficiency θ temperature difference, angle ρ density σ Stefan-Boltzmann constant φ relative humidity, angle. dharm \M-therm\th0-1  1 Introduction—Outline of Some Descriptive Systems 1.1. Steam power plant : Layout—components of a modern steam power plant. 1.2. Nuclear power plant. 1.3. Internal combustion engines : Heat engines—development of I.C. engines— different parts of I.C. engines—spark ignition engines—compression ignition engines. 1.4. Gas turbines : General aspects—classification of gas turbines—merits and demerits of gas turbines—a simple gas turbine plant—energy cycle for a simple-cycle gas turbine. 1.5. Refrigeration systems—Highlights—Theoretical questions. 1.1. STEAM POWER PLANT 1.1.1. Layout Refer to Fig. 1.1. The layout of a modern steam power plant comprises of the following four circuits : 1. Coal and ash circuit. 2. Air and gas circuit. 3. Feed water and steam flow circuit. 4. Cooling water circuit. Coal and Ash Circuit. Coal arrives at the storage yard and after necessary handling, passes on to the furnaces through the fuel feeding device. Ash resulting from combustion of coal collects at the back of the boiler and is removed to the ash storage yard through ash handling equipment. Air and Gas Circuit. Air is taken in from atmosphere through the action of a forced or induced draught fan and passes on to the furnace through the air preheater, where it has been heated by the heat of flue gases which pass to the chimney via the preheater. The flue gases after passing around boiler tubes and superheater tubes in the furnace pass through a dust catching device or precipitator, then through the economiser, and finally through the air preheater before being exhausted to the atmosphere. Feed Water and Steam Flow Circuit. In the water and steam circuit condensate leav- ing the condenser is first heated in a closed feed water heater through extracted steam from the lowest pressure extraction point of the turbine. It then passes through the deaerator and a few more water heaters before going into the boiler through economiser. In the boiler drum and tubes, water circulates due to the difference between the density of water in the lower temperature and the higher temperature sections of the boiler. Wet steam from the drum is further heated up in the superheater for being supplied to the primemover. After expanding in high pressure turbine steam is taken to the reheat boiler and brought to its original dryness or superheat before being passed on to the low pressure turbine. From there it is exhausted through the condenser into the hot well. The condensate is heated in the feed heaters using the steam trapped (blow steam) from different points of turbine. 1 2 ENGINEERING THERMODYNAMICS To atmosphere Chimney Air from boiler Air preheater Flue Steam Generator gases turbine Coal/Oil Boiler Econo- with miser Superheater Condenser Cooling tower Feed water pump Pump Fig. 1.1. Layout of a steam power plant. A part of steam and water is lost while passing through different components and this is compensated by supplying additional feed water. This feed water should be purified before hand, to avoid the scaling of the tubes of the boiler. Cooling Water Circuit. The cooling water supply to the condenser helps in maintaining a low pressure in it. The water may be taken from a natural source such as river, lake or sea or the same water may be cooled and circulated over again. In the latter case the cooling arrangement is made through spray pond or cooling tower. 1.1.2. Components of a Modern Steam Power Plant A modern steam power plant comprises of the following components : 1. Boiler (i) Superheater (ii) Reheater (iii) Economiser (iv) Air-heater. 2. Steam turbine 3. Generator 4. Condenser 5. Cooling towers 6. Circulating water pump 7. Boiler feed pump 8. Wagon tippler 9. Crusher house 10. Coal mill 11. Induced draught fans 12. Ash precipitators 13. Boiler chimney 14. Forced draught fans 15. Water treatment plant 16. Control room 17. Switch yard. Functions of some important parts of a steam power plant : 1. Boiler. Water is converted into wet steam. 2. Superheater. It converts wet steam into superheated steam. 3. Turbine. Steam at high pressure expands in the turbine and drives the generator. dharm \M-therm\Th1-1.pm5 INTRODUCTION—OUTLINE OF SOME DESCRIPTIVE SYSTEMS 3 4. Condenser. It condenses steam used by the steam turbine. The condensed steam (known as condensate) is used as a feed water. 5. Cooling tower. It cools the condenser circulating water. Condenser cooling water ab- sorbs heat from steam. This heat is discharged to atmosphere in cooling water. 6. Condenser circulating water pump. It circulates water through the condenser and the cooling tower. 7. Feed water pump. It pumps water in the water tubes of boiler against boiler steam pressure. 8. Economiser. In economiser heat in flue gases is partially used to heat incoming feed water. 9. Air preheater. In air preheater heat in flue gases (the products of combustion) is par- tially used to heat incoming air. 1.2. NUCLEAR POWER PLANT Fig. 1.2 shows schematically a nuclear power plant. Hot coolant Steam Steam turbine Generator Reactor core Steam Steam Cooling generator water Reactor Water Coolant Water Feed pump Coolant pump Fig. 1.2. Nuclear power plant. The main components of a nuclear power plant are : 1. Nuclear reactor 2. Heat exchanger (steam generator) 3. Steam turbine 4. Condenser 5. Electric generator. In a nuclear power plant the reactor performs the same function as that of the furnace of steam power plant (i.e., produces heat). The heat liberated in the reactor as a result of the nuclear fission of the fuel is taken up by the coolants circulating through the reactor core. Hot coolant leaves the reactor at the top and then flows through the tubes of steam generator and passes on its heat to the feed water. The steam so produced expands in the steam turbine, producing work, and thereafter is condensed in the condenser. The steam turbine in turn runs an electric generator thereby producing electrical energy. In order to maintain the flow of coolant, condensate and feed water pumps are provided as shown in Fig. 1.2. dharm \M-therm\Th1-1.pm5 4 ENGINEERING THERMODYNAMICS 1.3. INTERNAL COMBUSTION ENGINES 1.3.1. Heat Engines Any type of engine or machine which derives heat energy from the combustion of fuel or any other source and converts this energy into mechanical work is termed as a heat engine. Heat engines may be classified into two main classes as follows : 1. External Combustion Engine. 2. Internal Combustion Engine. 1. External Combustion Engines (E.C. Engines) In this case, combustion of fuel takes place outside the cylinder as in case of steam engines where the heat of combustion is employed to generate steam which is used to move a piston in a cylinder. Other examples of external combustion engines are hot air engines, steam turbine and closed cycle gas turbine. These engines are generally needed for driving locomotives, ships, gen- eration of electric power etc. 2. Internal Combustion Engines (I.C. Engines) In this case combustion of the fuel with oxygen of the air occurs within the cylinder of the engine. The internal combustion engines group includes engines employing mixtures of combusti- ble gases and air, known as gas engines, those using lighter liquid fuel or spirit known as petrol engines and those using heavier liquid fuels, known as oil compression ignition or diesel engines. 1.3.2. Development of I.C. Engines Many experimental engines were constructed around 1878. The first really successful engine did not appear, however until 1879, when a German engineer Dr. Otto built his famous Otto gas engine. The operating cycle of this engine was based upon principles first laid down in 1860 by a French engineer named Bea de Rochas. The majority of modern I.C. engines operate according to these principles. The development of the well known Diesel engine began about 1883 by Rudoff Diesel. Al- though this differs in many important respects from the otto engine, the operating cycle of modern high speed Diesel engines is thermodynamically very similar to the Otto cycle. 1.3.3. Different parts of I.C. Engines A cross-section of an air-cooled I.C. engines with principal parts is shown in Fig. 1.3. A. Parts common to both petrol and diesel engines 1. Cylinder 2. Cylinder head 3. Piston 4. Piston rings 5. Gudgeon pin 6. Connecting rod 7. Crankshaft 8. Crank 9. Engine bearing 10. Crank case 11. Flywheel 12. Governor 13. Valves and valve operating mechanism. B. Parts for petrol engines only 1. Spark plugs 2. Carburettor 3. Fuel pump. C. Parts for Diesel engine only 1. Fuel pump. 2. Injector. dharm \M-therm\Th1-1.pm5 INTRODUCTION—OUTLINE OF SOME DESCRIPTIVE SYSTEMS 5 Rocker arm Petrol tank Exhaust valve Push rod Silencer Inlet manifold Inlet valve Engine throttle Spark plug Cooling Jet fins Exhaust Petrol Air inlet Piston ring supply pipe High tension Carburettor cable Piston Magnet Connecting rod Crank Roller Intercam Crankshaft Gear exhaust Crankcase cam Oil pump Fig. 1.3. An air-cooled four-stroke petrol engine. 1.3.4. Spark Ignition (S.I.) Engines These engines may work on either four stroke cycle or two stroke cycle, majority of them, of course, operate on four stroke cycle. Four stroke petrol engine : Fig. 1.4 illustrates the various strokes/series of operations which take place in a four stroke petrol (Otto cycle) engine. Suction stroke. During suction stroke a mixture of air and fuel (petrol) is sucked through the inlet valve (I.V.). The exhaust valve remains closed during this operation. Compression stroke. During compression stroke, both the valves remain closed, and the pressure and temperature of the mixture increase. Near the end of compression stroke, the fuel is ignited by means of an electric spark in the spark plug, causing combustion of fuel at the instant of ignition. Working stroke. Next is the working (also called power or expansion) stroke. During this stroke, both the valves remain closed. Near the end of the expansion stroke, only the exhaust valve opens and the pressure in the cylinder at this stage forces most of the gases to leave the cylinder. Exhaust stroke. Next follows the exhaust stroke, when all the remaining gases are driven away from the cylinder, while the inlet valve remains closed and the piston returns to the top dead centre. The cycle is then repeated. dharm \M-therm\Th1-1.pm5 6 ENGINEERING THERMODYNAMICS Air-fuel S.P. S.P. S.P. S.P. Exhaust mixture gases I.V. E.V. I.V. E.V. Gases E.C. C.R. C Suction Compression Working Exhaust stroke stroke stroke stroke I.V = Intel valve, E.V. = Exhaust valve, E.C. = Engine cylinder, C.R. = Connecting rod, C = Crank, S.P. = Spark plug. Fig. 1.4. Four stroke otto cycle engine. Two stroke petrol engine : In 1878, Dugald-clerk, a British engineer introduced a cycle which could be completed in two strokes of piston rather than four strokes as is the case with the four stroke cycle engines. The engines using this cycle were called two stroke cycle engines. In this engine suction and exhaust strokes are eliminated. Here instead of valves, ports are used. The exhaust gases are driven out from engine cylinder by the fresh change of fuel entering the cylinder nearly at the end of the working stroke. Fig. 1.5 shows a two stroke petrol engine (used in scooters, motor cycles etc.). The cylinder L is connected to a closed crank chamber C.C. During the upward stroke of the piston M, the gases in L are compressed and at the same time fresh air and fuel (petrol) mixture enters the crank chamber through the valve V. When the piston moves downwards, V closes and the mixture in the crank chamber is compressed. Refer Fig. 1.5 (i) the piston is moving upwards and is compressing an explosive change which has previously been supplied to L. Ignition takes place at the end of the stroke. The piston then travels downwards due to expansion of the gases [Fig. 1.5 (ii)] and near the end of this stroke the piston uncovers the exhaust port (E.P.) and the burnt exhaust gases escape through this port [Fig. 1.5 (iii)]. The transfer port (T.P.) then is uncovered immediately, and the compressed charge from the crank chamber flows into the cylinder and is deflected upwards by the hump provided on the head of the piston. It may be noted that the incoming air petrol mixture helps the removal of gases from the engine-cylinder ; if, in case these exhaust gases do not leave the cylinder, the fresh charge gets diluted and efficiency of the engine will decrease. The piston then again starts moving from bottom dead centre (B.D.C.) to top dead centre (T.D.C.) and dharm \M-therm\Th1-1.pm5 INTRODUCTION—OUTLINE OF SOME DESCRIPTIVE SYSTEMS 7 the charge gets compressed when E.P. (exhaust port) and T.P. are covered by the piston ; thus the cycle is repeated. Spark plug L L L M E.P. M T.P. E.P. T.P. T.P. E.P. M V V V C.C. C.C. C.C. (i) (ii) (iii) L = Cylinder ; E.P. = Exhaust port ; T.P. = Transfer port ; V = Valve ; C.C. = Crank chamber (i) (ii) (iii) Fig. 1.5. Two-stroke petrol engine. The power obtained from a two-stroke cycle engine is theoretically twice the power obtain- able from a four-stroke cycle engine. 1.3.5. Compression Ignition (C.I.) Engines The operation of C.I. engines (or diesel engines) is practically the same as those of S.I. engines. The cycle in both the types, consists of suction, compression, ignition, expansion and exhaust. However, the combustion process in a C.I. engine is different from that of a S.I. engine as given below : In C.I. engine, only air is sucked during the stroke and the fuel is injected in the cylinder near the end of the compression stroke. Since the compression ratio is very high (between 14 : 1 to 22 : 1), the temperature of the air after compression is quite high. So when fuel is injected in the form of a spray at this stage, it ignites and burns almost as soon as it is introduced. The burnt gases are expanded and exhausted in the same way as is done in a S.I. engine. 1.4. GAS TURBINES 1.4.1. General Aspects Probably a wind-mill was the first turbine to produce useful work, wherein there is no precompression and no combustion. The characteristic features of a gas turbine as we think of the name today include a compression process and an heat addition (or combustion) process. The gas dharm \M-therm\Th1-1.pm5 8 ENGINEERING THERMODYNAMICS turbine represents perhaps the most satisfactory way of producing very large quantities of power in a self-contained and compact unit. The gas turbine may have a future use in conjunction with the oil engine. For smaller gas turbine units, the inefficiencies in compression and expansion processes become greater and to improve the thermal efficiency it is necessary to use a heat exchanger. In order that a small gas turbine may compete for economy with the small oil engine or petrol engine it is necessary that a compact effective heat exchanger be used in the gas turbine cycle. The thermal efficiency of the gas turbine alone is still quite modest 20 to 30% compared with that of a modern steam turbine plant 38 to 40%. It is possible to construct combined plants whose efficiencies are of order of 45% or more. Higher efficiencies might be attained in future. The following are the major fields of application of gas turbines : 1. Aviation 2. Power generation 3. Oil and gas industry 4. Marine propulsion. The efficiency of a gas turbine is not the criteria for the choice of this plant. A gas turbine is used in aviation and marine fields because it is self-contained, light weight, not requiring cooling water and generally fits into the overall shape of the structure. It is selected for power generation because of its simplicity, lack of cooling water, needs quick installation and quick starting. It is used in oil and gas industry because of cheaper supply of fuel and low installation cost. The gas turbines have the following limitations : (i) They are not self-starting ; (ii) Low efficiencies at part loads ; (iii) Non-reversibility ; (iv) Higher rotor speeds ; and (v) Overall effi- ciency of the plant is low. 1.4.2. Classification of Gas Turbines The gas turbines are mainly divided into two groups : 1. Constant pressure combustion gas turbine : (a) Open cycle constant pressure gas turbine (b) Closed cycle constant pressure gas turbine. 2. Constant volume combustion gas turbine. In almost all the fields open cycle gas turbine plants are used. Closed cycle plants were introduced at one stage because of their ability to burn cheap fuel. In between their progress remained slow because of availability of cheap oil and natural gas. Because of rising oil prices, now again, the attention is being paid to closed cycle plants. 1.4.3. Merits and Demerits of Gas Turbines Merits over I.C. engines : 1. The mechanical efficiency of a gas turbine (95%) is quite high as compared with I.C. engine (85%) since the I.C. engine has a large many sliding parts. 2. A gas turbine does not require a flywheel as the torque on the shaft is continuous and uniform. Whereas a flywheel is a must in case of an I.C. engine. 3. The weight of gas turbine per H.P. developed is less than that of an I.C. engine. 4. The gas turbine can be driven at a very high speeds (40,000 r.p.m.) whereas this is not possible with I.C. engines. 5. The work developed by a gas turbine per kg of air is more as compared to an I.C. engine. This is due to the fact that gases can be expanded upto atmospheric pressure in case of a gas turbine whereas in an I.C. engine expansion upto atmospheric pressure is not possible. dharm \M-therm\Th1-1.pm5 INTRODUCTION—OUTLINE OF SOME DESCRIPTIVE SYSTEMS 9 6. The components of the gas turbine can be made lighter since the pressures used in it are very low, say 5 bar compared with I.C. engine, say 60 bar. 7. In the gas turbine the ignition and lubrication systems are much simpler as compared with I.C. engines. 8. Cheaper fuels such as paraffine type, residue oils or powdered coal can be used whereas special grade fuels are employed in petrol engine to check knocking or pinking. 9. The exhaust from gas turbine is less polluting comparatively since excess air is used for combustion. 10. Because of low specific weight the gas turbines are particularly suitable for use in aircrafts. Demerits of gas turbines 1. The thermal efficiency of a simple turbine cycle is low (15 to 20%) as compared with I.C. engines (25 to 30%). 2. With wide operating speeds the fuel control is comparatively difficult. 3. Due to higher operating speeds of the turbine, it is imperative to have a speed reduction device. 4. It is difficult to start a gas turbine as compared to an I.C. engine. 5. The gas turbine blades need a special cooling system. 1.4.4. A Simple Gas Turbine Plant A gas turbine plant may be defined as one “in which the principal prime-mover is of the turbine type and the working medium is a permanent gas”. Refer to Fig. 1.6. A simple gas turbine plant consists of the following : 1. Turbine. 2. A compressor mounted on the same shaft or coupled to the turbine. 3. The combustor. 4. Auxiliaries such as starting device, auxiliary lubrication pump, fuel system, oil system and the duct system etc. Fuel Condenser C T Generator C = Compressure T = Turbine Air in Exhaust Fig. 1.6. Simple gas turbine plant. A modified plant may have in addition to above an intercooler, regenerator, a reheater etc. The working fluid is compressed in a compressor which is generally rotary, multistage type. Heat energy is added to the compressed fluid in the combustion chamber. This high energy fluid, at high temperature and pressure, then expands in the turbine unit thereby generating power. Part of the power generated is consumed in driving the generating compressor and accessories dharm \M-therm\Th1-1.pm5 10 ENGINEERING THERMODYNAMICS and the rest is utilised in electrical energy. The gas turbines work on open cycle, semiclosed cycle or closed cycle. In order to improve efficiency, compression and expansion of working fluid is carried out in multistages. 1.4.5. Energy Cycle for a Simple-Cycle Gas Turbine Fig. 1.7 shows an energy-flow diagram for a simple-cycle gas turbine, the description of which is given below : Combustor Fuel in Power gas Compressed air Compressor Turbine Air in Exhaust Fig. 1.7. Energy flow diagram for gas-turbine unit. — The air brings in minute amount of energy (measured above 0°C). — Compressor adds considerable amount of energy. — Fuel carries major input to cycle. — Sum of fuel and compressed-air energy leaves combustor to enter turbine. — In turbine smallest part of entering energy goes to useful output, largest part leaves in exhaust. Shaft energy to drive compressor is about twice as much as the useful shaft output. Actually the shaft energy keeps circulating in the cycle as long as the turbine runs. The important comparison is the size of the output with the fuel input. For the simple-cycle gas tur- bine the output may run about 20% of the fuel input for certain pressure and temperature condi- tions at turbine inlet. This means 80% of the fuel energy is wasted. While the 20% thermal efficiency is not too bad, it can be improved by including additional heat recovery apparatus. 1.5. REFRIGERATION SYSTEMS Refrigeration means the cooling of or removal of heat from a system. Refrigerators work mainly on two processes : 1. Vapour compression, and 2. Vapour absorption. Simple Vapour Compression System : In a simple vapour compression system the following fundamental processes are completed in one cycle : 1. Expansion 2. Vapourisation 3. Compression 4. Condensation. dharm \M-therm\Th1-1.pm5 INTRODUCTION—OUTLINE OF SOME DESCRIPTIVE SYSTEMS 11 The flow diagram of such a cycle is shown in Fig. 1.8. S Condenser N Compressor Receiver Expansion M valve Evaporator L Fig. 1.8. Simple vapour compression cycle. The vapour at low temperature and pressure (state ‘M’) enters the compressor where it is compressed isoentroprically and subsequently its temperature and pressure increase considerably (state ‘N’). This vapour after leaving the compressor enters the condenser where it is condensed into high pressure liquid (state ‘S’) and is collected in a receiver. From receiver it passes through the expansion valve, here it is throttled down to a lower pressure and has a low temperature (state ‘L’). After finding its way through expansion valve it finally passes on to evaporator where it extracts heat from the surroundings and vapourises to low pressure vapour (state ‘M’). Domestic Refrigerator : Refrigerators, these days, are becoming the common item for house hold use, vendor’s shop, hotels, motels, offices, laboratories, hospitals, chemists and druggists shops, studios etc. They are manufactured in different size to meet the needs of various groups of people. They are usually rated with internal gross volume and the freezer volume. The freezer space is meant to preserve perishable products at a temperature much below 0°C such as fish, meat, chicken etc. and to produce ice and icecream as well. The refrigerators in India are available in different sizes of various makes, i.e., 90, 100, 140, 160, 200, 250, 380 litres of gross volume. The freezers are usually provided at top portion of the refrigerator space occupying around one-tenth to one-third of the refrigerator volume. In some refrigerators, freezers are provided at the bottom. A domestic refrigerator consists of the following two main parts : 1. The refrigeration system. 2. The insulated cabinet. Fig. 1.9 shows a flow diagram of a typical refrigeration system used in a domestic refrigera- tor. A simple domestic refrigerator consists of a hermetic compressor placed in the cabinet base. The condenser is installed at the back and the evaporator is placed inside the cabinet at the top. The working of the refrigerator is as follows : — The low pressure and low temperature refrigerant vapour (usually R12) is drawn through the suction line to the compressor. The accumulator provided between the suction line and the evaporator collects liquid refrigerant coming out of the evaporator due to incom- plete evaporation, if any, prevents it from entering the compressor. The compressor then compresses the refrigerant vapour to a high pressure and high temperature. The compressed vapour flows through the discharge line into condenser (vertical natural draft, wire-tube type). — In the condenser the vapour refrigerant at high pressure and at high temperature is condensed to the liquid refrigerant at high pressure and low temperature. dharm \M-therm\Th1-1.pm5 12 ENGINEERING THERMODYNAMICS Low pressure gas Condenser (wire-tube type) Accumulator High pressure Evaporator liquid High pressure gas Low pressure liquid Sound deadner Expansion device (Capillary tube) Filter Compre- ssor Discharge line Suction line Fig. 1.9. Domestic refrigerator. — The high pressure liquid refrigerant then flows through the filter and then enters the capillary tube (expansion device). The capillary tube is attached to the suction line as shown in Fig. 1.9. The warm refrigerant passing through the capillary tube gives some of its heat to cold suction line vapour. This increases the heat absorbing quality of the liquid refrigerant slightly and increases the superheat of vapour entering the compressor. The capillary tube expands the liquid refrigerant at high pressure to the liquid refrigerant at low pressure so that a measured quantity of liquid refrigerant is passed into the evaporator. — In the evaporator the liquid refrigerant gets evaporated by absorbing heat from the container/articles placed in the evaporative chamber and is sucked back into the com- pressor and the cycle is repeated. HIGHLIGHTS 1. The layout of a modern steam power plant comprises of the following four circuits : (i) Coal and ash circuit (ii) Air and gas circuit (iii) Feed water and steam flow circuit (iv) Cooling water circuit. 2. Any type of engine or machine which derives heat energy from the combustion of fuel or any other source and converts this energy into mechanical work is termed as a heat engine. 3. The major fields of application of gas turbines are : (i) Aviation (ii) Power generation (iii) Oil and gas industry and (iv) Marine propulsion. 4. A simple gas turbine plant consists of the following : — Turbine — Compressor dharm \M-therm\Th1-1.pm5 INTRODUCTION—OUTLINE OF SOME DESCRIPTIVE SYSTEMS 13 — Combustor — Auxiliaries such as starting device, auxiliary lubrication pump, fuel system, oil system and the duct system etc. 5. Refrigeration means the cooling or removal of heat from a system. Refrigerators work mainly on two processes (i) Vapour compression and (ii) Vapour absorption. THEORETICAL QUESTIONS 1. Give the layout of a modern steam power plant and explain its various circuits. 2. List the components of a nuclear power plant. 3. Draw the cross-section of an air cooled I.C. engine and label its various parts. 4. Explain with neat sketches the working of a four stroke petrol engine. 5. How are gas turbines classified ? 6. What are the major fields of application of gas turbines ? 7. With the help of a neat diagram explain the working of a simple gas turbine plant. 8. Draw the energy cycle for a simple-cycle gas turbine. 9. Explain with a neat sketch the working of a simple vapour compression system. 10. Draw the neat diagram of a domestic refrigerator, showing its various parts. Explain its working also. dharm \M-therm\Th1-1.pm5  2 Basic Concepts of Thermodynamics 2.1. Introduction to kinetic theory of gases. 2.2. Definition of thermodynamics. 2.3. Thermodynamic systems—system, boundary and surroundings—closed system—open system—isolated system—adiabatic system—homogeneous system—heterogeneous system. 2.4. Macroscopic and microscopic points of view. 2.5. Pure substance. 2.6. Thermodynamic equilibrium. 2.7. Properties of systems. 2.8 State. 2.9. Process. 2.10. Cycle. 2.11. Point function. 2.12. Path function. 2.13. Temperature. 2.14. Zeroth law of thermodynamics. 2.15. The thermometer and thermometric property—introduction— measurement of temperature—the international practical temperature scale—ideal gas. 2.16. Pressure—definition of pressure—unit for pressure—types of pressure measurement devices—mechanical-type instruments—liquid manometers—important types of pressure gauges. 2.17. Specific volume. 2.18. Reversible and irreversible processes. 2.19. Energy, work and heat—energy—work and heat. 2.20. Reversible work—Highlights—Objective Type Questions—Theoretical Questions— Unsolved Examples. 2.1. INTRODUCTION TO KINETIC THEORY OF GASES The kinetic theory of gases deals with the behaviour of molecules constituting the gas. According to this theory, the molecules of all gases are in continuous motion. As a result of this they possess kinetic energy which is transferred from molecule to molecule during their collision. The energy so transferred produces a change in the velocity of individual molecules. The complete phenomenon of molecular behaviour is quite complex. The assumptions are therefore made to simplify the application of theory of an ideal gas. Assumptions : 1. The molecules of gases are assumed to be rigid, perfectly elastic solid spheres, identical in all respects such as mass, form etc. 2. The mean distance between molecules is very large compared to their own dimensions. 3. The molecules are in state of random motion moving in all directions with all possible velocities and gas is said to be in state of molecular chaos. 4. The collisions between the molecules are perfectly elastic and there are no intermolecu- lar forces of attraction or repulsion. This means that energy of gas is all kinetic. 5. The number of molecules in a small volume is very large. 6. The time spent in collision is negligible, compared to the time during which the mol- ecules are moving independently. 7. Between collisions, the molecules move in a straight line with uniform velocity because of frictionless motion between molecules. The distance between two collisions is called ‘free path’ of the molecule, the average distance travelled by a molecule between succes- sive collision is known as ‘mean free path’. 8. The volume of molecule is so small that it is negligible compared to total volume of the gas. 14 BASIC CONCEPTS OF THERMODYNAMICS 15 Pressure exerted by an Ideal Gas : Let us consider a quantity of gas to be contained in a cubical vessel of side l with perfectly elastic wall and N represent the very large number of molecules in the vessel. Now let us consider a molecule which may be assumed to have a velocity C1 in a certain direction. The velocity can be resolved into three components u1, v1, w1 parallel to three co-ordinate axes X, Y and Z which are again assumed parallel to the sides of the cube as shown in Fig. 2.1. Fig. 2.1 Thus, C12 = u12 + v12 + w12. Let this molecule having mass m strike wall surface ABCD of the cube with velocity u1. Since the collision is perfectly elastic, the molecule will rebound from this surface with the same velocity u1. Therefore, The momentum of the molecule before it strikes the face ABCD = mu1 The momentum of the molecule after impact = – mu1. Hence change of momentum at each impact in direction normal to the surface ABCD = mu1 – (– mu1) = 2mu1 After striking the surface ABCD, the molecule rebounds and travels back to the face EFGH, collides with it and travels back again to the face ABCD covering 2l distance. This means molecule covers 2l distance to hit the same face again. Hence the time taken by the same molecule to strike 2l the same face ABCD again is. u1 Therefore, the rate of change of momentum for one molecule of the gas 2 mu1 mu12 = = 2l l u1 dharm M-therm/th2-1.pm5 16 ENGINEERING THERMODYNAMICS According to Newton’s second law of motion the rate of change of ‘momentum is the force’. If F1 is the force due to one molecule, then mu12 F1 = l Similarly, then force F2 due to the impact of another molecule having velocity C2 whose components are u2, v2, w2 is given by mu22 F2 = l Hence total force Fx on the face ABCD due to impact of N molecules is given by m Fx = (u12 + u22 +...... uN 2) l Since the pressure (p) is the force per unit area, hence pressure exerted on the wall ABCD is given by F m px = 2x = 3 (u12 + u22 +...... uN 2 ) l l Similarly, if py and pz represent the pressures on other faces which are perpendicular to the Y and Z axis respectively, we have m py = 3 (v12 + v22 +...... vN 2 ) l m and pz = 3 (w12 + w22 +...... wN 2 ) l Since pressure exerted by the gas is the same in all directions, i.e., px = py = pz the average pressure p of the gas is given by px + py + pz p= 3 m or p = 3 [(u12 + v12 + w12 ) + (u22 + v22 + w22 ) +......(uN 2 + vN 2 + wN 2 )] l But C12 = (u12 + v12 + w12) C22 = (u22 + v22 + w22 ) and so on l3 = V = volume of gas (m3) 1 m ∴ p= (C12 + C22 + C32 +...... CN 2 ) 3 v 1 m or p= NC 2...(2.1) 3 v FC2 + C22 + C32 +......CN 2 I where C2 = GH 1 N JK known as mean square velocity C12 + C22 + C32 +......CN 2 or C = N where C is called the root mean square velocity of the molecules and equal to the square root of the mean of square of velocities of individual molecules which is evidently not the same as mean of velocities of different molecules LMi. e., C C1 + C2 + C3 +...... CN OP N mean = N Q dharm M-therm/th2-1.pm5 BASIC CONCEPTS OF THERMODYNAMICS 17 1 or m NC 2 pV =...(2.2) 3 This equation is the fundamental equation of kinetic theory of gases and is often referred to as kinetic equation of gases. Equation (2.2) may be written as pV = 2/3 × 1/2 m NC 2 where 1 mN C 2 is the average transmission or linear kinetic energy of the system of particles. 2 Equation (2.1) can be written as p = 1/3 ρ C 2...(2.3) where ρ is the density. LM3 mN , i.e., ρ= Total mass OP NV Total volume Q This equation expresses the pressure which any volume of gas exerts in terms of its density under the prevailing conditions and its mean square molecular speed. From equations (2.2) and (2.3), 3p 3 pV C = = ρ mN Kinetic interpretation of Temperature : If Vmol is the volume occupied by a gram molecule of a gas and N0 is the number of moles in one gram molecule of gas, M = molecular weight = mN0....(i) Since p Vmol = R0T......Molar gas equation...(ii) From equations (2.2) and (ii), 1/3 m N0 C = R0T R0 = Universal gas constant 1 or 2/3 × 2 m N0 C 2 = R0T N0 = Avogadro’s number 1 R0 or 2 m C 2 = 3/2 KT...(2.4) N0 = K (Boltzman’s constant) (i.e., K.E. per molecule = 3/2 KT) 3KT or C = m 3R0T K R0 R or C = 3 = = 0 M m N0 m M R or C = 3RT...(2.5) 3 R= 0 M where R is characteristic gas constant. From equation (2.4) it is seen that temperature is a measure of the average kinetic energy of translation possessed by molecule. It is known as the kinetic interpretation of temperature. Hence, the absolute temperature of a gas is proportional to the mean translational kinetic energy of the molecules it consists. If the temperature is fixed, then the average K.E. of the molecules remains constant despite encounters. dharm M-therm/th2-1.pm5 18 ENGINEERING THERMODYNAMICS 2.2. DEFINITION OF THERMODYNAMICS Thermodynamics may be defined as follows : l Thermodynamics is an axiomatic science which deals with the relations among heat, work and properties of system which are in equilibrium. It describes state and changes in state of physical systems. Or Thermodynamics is the science of the regularities governing processes of energy conversion. Or Thermodynamics is the science that deals with the interaction between energy and material systems. Thermodynamics, basically entails four laws or axioms known as Zeroth, First, Second and Third law