Engineering thermodynamics

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 t

O N THE CD (Software and Simulations)

■ QUICKFIELD™ STUDENTS’ VERSION (v 5.6)

QuickField is a Finite Element Analysis package for tromagnetic, thermal, and stress design simulation with

elec-coupled multi-fi eld analysis Also includes tutorials.

Intended as an introductory textbook for “applied” or engineering thermodynamics, or for use

as an up-to-date reference for practicing engineers, this book provides extensive in-text, solved examples to cover the basic properties of thermodynamics Pure substances, the fi rst and second laws, gases, psychrometrics, the vapor, gas, and refrigeration cycles, heat transfer, compressible

fl ow, chemical reactions, fuels, and more are presented in detail and enhanced with practical applications This version presents the material using SI Units and has ample material on SI conversion, steam tables, and a Mollier diagram The accompanying CD includes a fully func-

tional student version of QuickField software

(widely used in industry) with simulations, tutorials, etc.

tables, and a Mollier diagram

■ Includes a CD-ROM with QuickField ware, MATLAB simulations, and fi gures

soft-ABOUT THE AUTHOR

R K Rajput has over 35 years of experience teaching mechanical and electrical engineering and has authored

several books and journal articles in these areas He has won many distinguished awards for both teaching and research

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ENGINEERING THERMODYNAMICS

STEAM TABLES

and MOLLIER DIAGRAM (S.I UNITS)

Edited  by

R.K RAJPUT Patiala

[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

113, Golden House, Daryaganj,New Delhi-110002

Phone : 011-43 53 25 00 Fax : 011-43 53 25 28

www.laxmipublications.cominfo@laxmipublications.com

© 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

Second Edition : 2003 Third Edition : 2007

Offices :

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 (questionshaving been selected from various universities and competitive examinations) and ampleadditional text have been added

Any suggestions for the improvement of the book will be thankfully acknowledged andincorporated in the next edition

—Author

Preface to The First Edition

Several books are available in the market on the subject of “Engineering dynamics” but either they are too bulky or are miserly written and as such do not cover thesyllabii of various Indian Universities effectively Hence a book is needed which shouldassimilate subject matter that should primarily satisfy the requirements of the students fromsyllabus/examination point of view ; these requirements are completely met by this book

Thermo-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 matterself 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 examinationwithout any difficulty

— Highlights, objective type questions, theoretical questions, and unsolved exampleshave been added at the end of each chapter to make the book a complete unit inall respects

The author’s thanks are due to his wife Ramesh Rajput for rendering all assistanceduring preparation and proof reading of the book The author is thankful to Mr R.K Syalfor 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 outthe book in time and pricing it moderately inspite of heavy cost of the printing

Constructive criticism is most welcome from the readers

—Author

1 INTRODUCTION—OUTLINE OF SOME DESCRIPTIVE SYSTEMS 1—13

1.1.2 Components of a modern steam power plant 2

1.4.5 Energy cycle for a simple-cycle gas turbine 10

2 BASIC CONCEPTS OF THERMODYNAMICS 14—62

2.15 The Thermometer and Thermometric Property 24

2.16.3 Types of pressure measurement devices 34

3 PROPERTIES OF PURE SUBSTANCES 63—100

3.3 p-T (Pressure-temperature) Diagram for a Pure Substance 663.4 p-V-T (Pressure-Volume-Temperature) Surface 67

3.8 Important Terms Relating to Steam Formation 703.9 Thermodynamic Properties of Steam and Steam Tables 72

3.17 Enthalpy-Entropy (h-s) Chart or Mollier Diagram 75

Chapter Pages

3.18 Determination of Dryness Fraction of Steam 89

4.6 Perpetual Motion Machine of the First Kind-PMM1 104

4.8.1 The characteristic equation of state 105

4.8.4 Relationship between two specific heats 107

4.9 Application of First Law of Thermodynamics to Non-flow or Closed

4.10 Application of First Law to Steady Flow Process 150

4.12 Engineering Applications of Steady Flow Energy Equation (S.F.E.E.) 155

Chapter Pages

5 SECOND LAW OF THERMODYNAMICS AND ENTROPY 227—305

5.1 Limitations of First Law of Thermodynamics and Introduction to

5.11 Efficiency of the Reversible Heat Engine 237

5.12.3 Change of entropy in a reversible process 253

5.17.1 General case for change of entropy of a gas 258

5.17.3 Heating a gas at constant pressure 260

6 AVAILABILITY AND IRREVERSIBILITY 306—340

6.3 Decrease in Available Energy When Heat is Transferred Through

Chapter Pages

7.5 Equations for Internal Energy and Enthalpy 345

8.4 Internal Energy and Enthalpy of a Perfect Gas 3798.5 Specific Heat Capacities of an Ideal Gas 380

Chapter Pages

9.4 The Apparent Molecular Weight and Gas Constant 414

11.10 Air-Fuel Ratio from Analysis of Products 49411.11 How to Convert Volumetric Analysis to Weight Analysis 49411.12 How to Convert Weight Analysis to Volumetric Analysis 494

11.14 Weight of Flue Gases per kg of Fuel Burnt 495

Chapter Pages

11.16 Internal Energy and Enthalpy of Reaction 497

11.19 Determination of Calorific or Heating Values 501

13.7 Comparison of Otto, Diesel and Dual Combustion Cycles 65513.7.1 Efficiency versus compression ratio 65513.7.2 For the same compression ratio and the same heat input 65513.7.3 For constant maximum pressure and heat supplied 656

Chapter Pages

13.10.6 Effect of operating variables on thermal efficiency 671

14.2.4 Merits and demerits of air refrigeration system 724

14.3.3 Functions of parts of a simple vapour compression system 73114.3.4 Vapour compression cycle on temperature-entropy (T-s) diagram 732

14.3.10 Mathematical analysis of vapour compression refrigeration 740

14.4.3 Practical vapour absorption system 74314.4.4 Comparison between vapour compression and vapour

Chapter Pages

15 HEAT TRANSFER 778—856

15.2.2 Thermal conductivity of materials 780

15.2.4 General heat conduction equation in cartesian coordinates 78315.2.5 Heat conduction through plane and composite walls 78715.2.6 The overall heat transfer coefficient 79015.2.7 Heat conduction through hollow and composite cylinders 79915.2.8 Heat conduction through hollow and composite spheres 805

15.4.4 Logarithmic temperature difference (LMTD) 821

15.5.3 Absorptivity, reflectivity and transmittivity 834

15.5.9 Intensity of radiation and Lambert’s cosine law 84015.5.10 Radiation exchange between black bodies separated by a

16.3 Propagation of Disturbances in Fluid and Velocity of Sound 86216.3.1 Derivation of sonic velocity (velocity of sound) 86216.3.2 Sonic velocity in terms of bulk modulus 86416.3.3 Sonic velocity for isothermal process 86416.3.4 Sonic velocity for adiabatic process 865

16.4 Mach Number 86516.5 Propagation of Disturbance in Compressible Fluid 866

16.6.1 Expression for stagnation pressure (p s) in compressible flow 86916.6.2 Expression for stagnation density (ρs) 87216.6.3 Expression for stagnation temperature (Ts) 87216.7 Area—Velocity Relationship and Effect of Variation of Area for

16.8 Flow of Compressible Fluid Through a Convergent Nozzle 87816.9 Variables of Flow in Terms of Mach Number 88316.10 Flow Through Laval Nozzle (Convergent-divergent Nozzle) 886

Introduction to SI Units and Conversion Factors

Table 1 SI Base Units

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 symbolscan themselves be used to form other derived units

Derived units may, therefore, be classified under three headings Some of them are given inTables 2, 3 and 4

Table 2 Examples of SI Derived Units Expressed in terms of Base Units

SI Units Quantity

Table 3 SI Derived Units with Special Names

Table 4 Examples of SI Derived Units Expressed by means of Special Names

SI Units

in terms of

SI base units

entropy

The SI units assigned to third class called “Supplementary units” may be regarded either asbase units or as derived units Refer Table 5 and Table 6

Table 5 SI Supplementary Units

SI Units Quantity

Table 6 Examples of SI Derived Units Formed by Using Supplementary Units

SI Units Quantity

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

1 kgf-m = 1

427FHG IKJ kcal = 9.81 joules

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 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

and expressions

(3 1 kgf-m = 9.81 joules)

h f specific enthalpy of saturated liquid (fluid)

K temperature on kelvin scale (i.e., celsius absolute, compressibility)

Q heat, rate of heat transfer

steam engines

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 fourcircuits :

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 beforebeing 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 ofwater in the lower temperature and the higher temperature sections of the boiler Wet steam fromthe drum is further heated up in the superheater for being supplied to the primemover Afterexpanding in high pressure turbine steam is taken to the reheat boiler and brought to its originaldryness or superheat before being passed on to the low pressure turbine From there it is exhaustedthrough the condenser into the hot well The condensate is heated in the feed heaters using thesteam trapped (blow steam) from different points of turbine

1

Introduction—Outline of Some Descriptive Systems

1.1 Steam power plant : Layout—components of a modern steam power plant 1.2 Nuclearpower 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 ofgas turbines—a simple gas turbine plant—energy cycle for a simple-cycle gas turbine.1.5 Refrigeration systems—Highlights—Theoretical questions

miser

Econo-Flue gases

Steam turbine Generator

Cooling tower

Pump

Feed water pump

Boiler with Superheater Coal/Oil

Air from boiler

Air preheater

Chimney

To atmosphere

Condenser

Fig 1.1 Layout of a steam power plant.

A part of steam and water is lost while passing through different components and this iscompensated by supplying additional feed water This feed water should be purified before hand, toavoid 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 thesame water may be cooled and circulated over again In the latter case the cooling arrangement ismade 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

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.

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.

Steamturbine Generator

Steam

Coolingwater

Steamgenerator

Water

Water

Feed pumpSteam

Coolant pumpCoolant

Hot coolant

Reactor

core

Reactor

Fig 1.2 Nuclear power plant.

The main components of a nuclear power plant are :

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 coolantleaves the reactor at the top and then flows through the tubes of steam generator and passes on itsheat to the feed water The steam so produced expands in the steam turbine, producing work, andthereafter is condensed in the condenser The steam turbine in turn runs an electric generatorthereby producing electrical energy In order to maintain the flow of coolant, condensate and feedwater pumps are provided as shown in Fig 1.2

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 engineswhere 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 theengine 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 enginedid not appear, however until 1879, when a German engineer Dr Otto built his famous Otto gasengine The operating cycle of this engine was based upon principles first laid down in 1860 by aFrench engineer named Bea de Rochas The majority of modern I.C engines operate according tothese principles

The development of the well known Diesel engine began about 1883 by Rudoff Diesel though this differs in many important respects from the otto engine, the operating cycle of modernhigh speed Diesel engines is thermodynamically very similar to the Otto cycle

Al-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

13 Valves and valve operating mechanism

B Parts for petrol engines only

C Parts for Diesel engine only

Exhaust valve

Rocker arm Petrol

tank

Engine throttle

Petrol supply pipe

Piston Carburettor

Connecting rod Crank Roller Intercam

Crankshaft Crankcase Gear exhaust

cam

Magnet

High tension cable Piston ring Exhaust

Cooling fins

Spark plug Silencer

Air inlet Jet

Push rod Inlet manifold Inlet valve

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 strokepetrol (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 isignited 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 valveopens 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.

stroke

Compressionstroke

Workingstroke

ExhauststrokeI.V = Intel valve, E.V = Exhaust valve, E.C = Engine cylinder,C.R = Connecting rod, C = Crank, S.P = Spark plug

Gases

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 intwo strokes of piston rather than four strokes as is the case with the four stroke cycle engines Theengines 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 petrolmixture helps the removal of gases from the engine-cylinder ; if, in case these exhaust gases do notleave the cylinder, the fresh charge gets diluted and efficiency of the engine will decrease Thepiston then again starts moving from bottom dead centre (B.D.C.) to top dead centre (T.D.C.) and

the charge gets compressed when E.P (exhaust port) and T.P are covered by the piston ; thus thecycle is repeated.

L = Cylinder ; E.P = Exhaust port ; T.P = Transfer port ; V = Valve ; C.C = Crank chamber

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 theform of a spray at this stage, it ignites and burns almost as soon as it is introduced The burntgases are expanded and exhausted in the same way as is done in a S.I engine

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 withthe 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 orpetrol engine it is necessary that a compact effective heat exchanger be used in the gas turbinecycle The thermal efficiency of the gas turbine alone is still quite modest 20 to 30% compared withthat of a modern steam turbine plant 38 to 40% It is possible to construct combined plants whoseefficiencies 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 ciency of the plant is low.

effi-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, nowagain, 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 anduniform 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 notpossible 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 notpossible

6 The components of the gas turbine can be made lighter since the pressures used in it arevery 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 comparedwith I.C engines

8 Cheaper fuels such as paraffine type, residue oils or powdered coal can be used whereasspecial 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 forcombustion

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 reductiondevice

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

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, multistagetype Heat energy is added to the compressed fluid in the combustion chamber This high energyfluid, at high temperature and pressure, then expands in the turbine unit thereby generatingpower Part of the power generated is consumed in driving the generating compressor and accessories

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 iscarried 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 ofwhich is given below :

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 inexhaust

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 tions at turbine inlet This means 80% of the fuel energy is wasted While the 20% thermal

condi-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 :

The flow diagram of such a cycle is shown in Fig 1.8.

Expansion valve

Receiver

Condenser S

N

M Compressor

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 ofthe 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

Condenser (wire-tube type)

ssor Discharge line Suction line

Compre-Filter

Expansion device (Capillary tube)

Sound deadner

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 theliquid 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 pressor and the cycle is repeated

com-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 :

4 A simple gas turbine plant consists of the following :

— Turbine

— Compressor

(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.

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—opensystem—isolated system—adiabatic system—homogeneous system—heterogeneoussystem 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 ofthermodynamics 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 measurementdevices—mechanical-type instruments—liquid manometers—important types of pressuregauges 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 TypeQuestions—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 thisthey 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 possiblevelocities and gas is said to be in state of molecular chaos

4 The collisions between the molecules are perfectly elastic and there are no lar forces of attraction or repulsion This means that energy of gas is all kinetic

intermolecu-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 ecules are moving independently

mol-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 sive collision is known as ‘mean free path’.

succes-8 The volume of molecule is so small that it is negligible compared to total volume of the gas

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

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) = 2mu1After 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 the same face ABCD again is 2

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

F1=mu l12

Similarly, then force F2 due to the impact of another molecule having velocity C2 whose

components are u2, v2, w2 is given by

Similarly, if p y and p z represent the pressures on other faces which are perpendicular to the

Y and Z axis respectively, we have

Since pressure exerted by the gas is the same in all directions, i.e., p x = p y = p z the average

pressure p of the gas is given by

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 ofvelocities of different molecules

or pV=31m NC2 (2.2)

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 NC2

where 1

2mN C2 is the average transmission or linear kinetic energy of the system of particles.

Equation (2.1) can be written as

Total massTotal volume

This equation expresses the pressure which any volume of gas exerts in terms of its densityunder the prevailing conditions and its mean square molecular speed

From equations (2.2) and (2.3),

C = 3ρp = 3mN pV

Kinetic interpretation of Temperature :

If V mol is the volume occupied by a gram molecule of a gas and N0 is the number of moles inone gram molecule of gas,

From equations (2.2) and (ii),

0 = K (Boltzman’s constant) (i.e., K.E per molecule = 3/2 KT)

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 moleculesremains constant despite encounters