ENGR 222 Thermodynamics Notes
ENGR 222 Thermodynamics Notes ENGR 222
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Energy Transfer Heat Transfer amp Work ENGR 222 Thermodynamics Louisiana Tech University Fall 2015 Unauthorized reproduction is prohibited Forms of Energy Energy can eXist in many forms Thermal Mechanical Kinetic Potential Electric Magna c Specialized Chemical gt rarely discussed Nuclaar in this course The sum total of the above forms of energy represents the total energy E of a system On a per mass basis eEm kJkg Thermodynamics is mostly concerned With changes in energy AE rather than an absolute value Total Energy of a System Sum of all forms of energy ie thermal mechanical kinetic potential electrical magnetic chemical and nuclear that can eXist in a system 0 For systems we typically deal within this course sum of internal kinetic and potential energies EUKEPE E Total energy of system U internal energy KE kinetic energy mV22 PE potential energy mgz Microscopic vs Macroscopic Forms of Energy Iquot Microscopic farms 0f energy are related to the systemh molecular structure an degree of rueleeulaar activity Mieroseepie energy farms ere independent efutside reference frumee 39 The sum of all the systemi s micmsmpie turns it ehergy is its internal energy U it e per mess basis HIE m kl 39 By centresL maeruscopie forms if energy are those that are dEpeedee on err outside reference frame Kinetic energy reeleeity relative tr tether 1 r2 KE m kl kequot Peterrtiel energy elere tieh reletirre to whetquot k1 p6 e klkg Total Energy for Closed and Open Systems TotalEnergy E UKEPEUmImgz A M2 Change in Total Energy AE QU l AK E PE QU l mg z Total Energy Per Unit Mass 8 in k6 p6 u 92 M2 Change in Total Energy Per Unit Mass 36 u 168 3198 All T g z For most Closed systems Changes in kinetic and potential energy are negligible For open systems mass terms become mass ow rate pACV kgs A AC 7TD24 Vavg 70 pAcVavu and energy becomes energy ow rate 1 gt Steam E n ze E me R 39s v Mechanical Energy Mechanical energy The form of energy that can be converted to mechanical work completely and directly by an ideal mechanical device such as an ideal turbine Kinetic and potential energies The familiar forms of mechanical energy 6 V f Mechanical energy of a new 39 5quot owing uid per unit mass 39 P V2 Rate of mechanical energy of Ell39l lj39l Inel39ll l l m 7 a owing uid Change in mechanical energy of a uid during incompressible ow per unit mass 39 P2P1 Vii v I I Aemech p 8Z2 Z1 M kg Rate of mechanical energy change of a uid during incompressible ow VVP2P1 i39nech l mech l9 Internal Energy Molecular translation C i spin of microscopic Molecular rotation lilcctron Molecular translation vibration o3 g3 quot Electron Nuclear spin The various forms energies that make up sensible energy Sensible and latent energy c Chemical energy Nuclear energy The internal energy of a system is the sum of all forms of the microscopic energies Sensible energy The portion of the internal energy of a system associated with the kinetic energies of the molecules Latent energy The internal energy associated with the phase of a system Chemical energy The internal energy associated with the atomic bonds in a molecule Nuclear energy The tremendous amount of energy associated with the strong bonds within the nucleus of the atom itself Heat and Heat Transfer Heat The form of energy that is transferred between two systems or a system and its surroundings by Virtue of a temperature difference The only two forms of energy interactions associated with a closed system are heat transfer and work The difference between heat transfer and work An energy interaction is heat transfer if its driVing force is a temperature difference Otherwise it is work System boundary Room ah 250C J No heal Heat Heat transfer 8 13 1618 gt Heat I i Win eld I z I l l CLOSED l SYSTEM 1F WOI k I i I I l Eraal O 25 C m constant L 4 Temperature difference is the driVing force Energy can cross the boundaries for heat transfer The larger the temperature of a closed system in the form of difference the higher is the rate of heat heat and work transfer Energy Transfer by Work Work The energy transfer associated with a force acting through a distance A rising piston a rotating shaft and an electric wire crossing the system boundaries are all associated with work interactions Traditional Sign convention Heat transfer to a system and work done by a system are positive heat transfer from a system and work done on a system are negative Alternative to sign convention is to use the subscripts in and out to indicate direction This is the primary approach in this class and in the textbook Sun39oundings W Z J Work done per unit mass Qin Qoul l Power is the 30 work done per work unit time kW System I l I l Wi n I Wout L l Specifying the directions of heat and work Heat vs Work 2 i div V2 V1 2 1 Both are recognized at the boundaries of a system as they cross the boundaries That is both heat and work are boundary phenomena Systems possess energy but not heat or work Both are associated with a process not a state Unlike properties heat or work has no meaning at a state Both are path functions ie their magnitudes depend on the path followed during a process as well as the end states Properties are point functions have exact differentials d Path functions have inexact differentials 5 AVA 3 m3 WA 8 k Z 3 I1131WB 2 m3 5 m3 V Properties are point functions but heat and work are path functions their magnitudes depend on the path followed 2 l Electrical Work Electrical power When potential difference and current change with time 2 J wax Id 1 When potential difference and current remain constant VI 1 E I Vl R lt lt gt V2R Electrical power in terms of resistance R current I and potential difference V Mechanical Forms of Work There are two requirements for a work interaction between a system and its surroundings to eXist there must be a force acting on the boundary the boundary must move 39 4 S gtl If there is no movement no work is done The work done 1s proportlonal to the force applied F and the distance traveled s 12 Energy Balances amp The First Law of Thermodynamics ENGR 222 Thermodynamics Louisiana Tech University Fall 2015 Unauthorized reproduction is prohibited The Three Maj or Principles of Thermodynamics Conservation of Mass Thermodynamics Conservation of Energy Entropy First Law Second Law Review Total Energy for Closed and Open Systems TotalEnergy E UKEPE Ummgz A M2 Change in Total Energy AE QU ERIE EPE EU mg z Total Energy Per Unit Mass 6 ta k9 138 ta g M2 Change in Total Energy Per Unit Mass 36 u 168 3198 u T g z For most Closed systems Changes in kinetic and potential energy are negligible For open systems mass terms become mass ow rate z QAV 165quot A 2 p p C AC7TD Van quotO7 pAcVavu and energy becomes energy ow rate 1 gt 9 Steam E rite E me R s V The First Law of Thermodynamics The first law of thermodynamics is essentially the conservation of energy principle Energy can be neither created nor destroyed during a process it can only change forms 39quot PE 10 U Q quot 5 k M KE 0 Energy being converted A 2 I from PE to gil it KE total energy PE2 7 k remains v m KE 3 k unchanged The change 1n total energy for a potato in an oven is equal to the amount of heat transferred to it The First Law in Action Simple Examples Q 3 Id Adiabatic The work electrical done on an adiabatic system is equal to the increase in the energy of the Battery SyStem Qin 15 kJ Adiabatic In the absence of any work interactions the energy change of a system is equal to the net heat transfer The work shaft done on an adiabatic system is equal to the increase in the energy of the system Wsmin8k1 Putting the First Law to Work Energy Balances The net change increase 0r decrease in the t0tal energy 0f the system during a pr0cess is equal to the difference between the t0tal energy entering and the t0tal energy leaving the system during that pr0cess Total energy gt Total energy gt Change in the total entering the system I leaving the system energy of the system quotnut Esystel n Qoul 3 The energy Change of a system during a process is equal to the I I l AE15 36 I I net work and heat I I I I I 18kJ transfer between the system and its surroundings lab in Z 6 Id Energy Change of a System Components Energy Change Energy at final state Energy at initial state AEsystem Efinai Z 1 AE APE Manifested as Change in temperature Internal kinetic and potential energy Changes AU mwg Ln Stationary Systems A E Adiabatic Z Z2 APE 0 VI 3 gt AKE O mgz2 Z1 AE AU AE8kJ 8kJ sh in Means of Energy Transfer Heat transfer Work transfer Mass ow open systems only Using in out sign convention in nut nut r nnt n1assjn massgnut system E k E DUI ELSE in V Net energy transfer Change in internal kinetics by heat work and mass potential etet energies Rate of net energy transfer Rate of change in internal by 113 W fkt and mass kinetiet potentiah etetr energies dEdt r Closed Systems vs Open Systems Cycles For a closed system cycle Where the end state and mm ELI E11 cycle initial state are identical the sum of the energy P A For a cycle AE 0 changes around the cycle must be zero thus Q W Changes in energy for a closed system involves only heat transfer and work Transfer of mass in open systems may also cause a change in energy as the mass carries energy With it Example increasing mass flow rate or increasing temperature of a constituent stream Qnet Wnct ltv m 2 kgS 1723 3 kgs I I I I I I I I I CV I I I I I I I m3 ml 1713 5 kgs Energy Efficiency aSY 00110619 Desued output Performance Required input but BE AWARE OF THE APPLICATIONSPECIFIC DEFINITION Example Hot water heaters efficiency 2 energy delivered to houseenergy being supplied to the water heater pp7879 in CampG for details For electric water heaters 100 of electrical power transferred to water small losses through container walls For gas water heaters definition of heating value for gas fuel drives the efficiency lower AND there is significant cost difference between supplying gas fuel vs electricity Type Ef ciency Gas conventional 55 Gas highefficiency 62 Electric conventional 90 Electric highef ciency 94 Examples Generator A device that converts mechanical energy to electrical energy 0 Generator efficiency The ratio of the electrical power output to the mechanical power input 0 Thermal efficiency of a power plant The ratio of the net electrical power output to the rate of fuel energy input norera 7cornlmration ntl39l l39l39l l l ngenerator OVCfall Cf ClCIle Of a pOWCI plant Overall efficiency is the product of the individual component efficiencies Lighting efficacy The amount of light output in lumens per W of electricity consumed A lSW compact uorescent lamp provides as much light as a 60W incandescent lamp ISW 60W Efficiencies of Electrical and Mechanical Devices Fan Mechanical Efficiency Mechanical energy eutth Enmmm ll E mm gg 5quot W Ii 050 kgs mm 1 HPUE Emccl i in Emechdn The effectiveness of the conversion process between the mechanical work supplied or extracted and the mechanical v0a12ms energy of the u1d 1s expressed by the pump effic1ency and 1 2 turblne effic1ency pI 2 p2 Pump Efficiency Energy Consuming Devices 77 Ali39mmm mvgZ V mcch fun 39 39 Mechanical energy increase of the uid mmmi Wpuml m Wmm m Wquot 39 Tinmm w 050 kgs 12 ms 2 Mechanical energy input iiiSham WWW 50 W r r r 072 mech uid mechgut I IlEGl Li The mechamcal Turbine Efficiency Energy Producing Device effiCiGIle Of a fan iS the Mechanical energy routpnt WWW Wurmm rat Of the klnetlc nergy Tilurh39inc Mechanical energy decre ge Ohm uid EWMUM Wurhim of an at the fan eX1t to the mechanical power input AEmech uid Ememi El e h ut Efficiencies of Electrical and Mechanical Devices Mechanical pwer utput ngmfmn n Pump tinctor V 1dr H H Electric power input Wigwam Eff1c1ency Electric utput Wmmim Generator 7133961 1xfif ilt tquot l 1 Mechanical input Wall m EfflClenCY Wpu 1391in iquotlquot1EElL lJ id Pump Motor npump 139139Ictcr 7 1311391391p7 meter 2 Weiech Weiectiin overall EfflCICnCy Weiectiout Welectiout Turbine Generator ntul39hine gen ntul39hinengenerator O 39 39 verallEff1c1enc Wu 1quot inc it I mech fl 1 id I y nturbinc 03975 ngencrator 097 f Turbine MGeneramr The overall efficiency of a turbine generator is the product of the efficiency of the turbine and the efficiency of the generator and nlurbine gen nturbinen generator represents the fraction Of the 075 X 097 mechanical energy of the uid 2 073 converted to electric energy l3 Pure Substances and Phases ENGR 222 Thermodynamics Louisiana Tech University Fall 2015 All images are used here strictly for academic purposes Most are from Thermodynamics An Engineering Approach and copyright McGrawHill Unauthorized reproduction is prohibited Processes amp Paths Process when a system changes from one equilibrium state to another one some special processes isobaric process constant pressure isothermal process constant temperature isochoric process constant volume isentropic process constant entropy Path series of states which a system passes through during a process Final state Proo ng path Initial state The Brayton Cycle The Ideal Cycle for Gas Turbine Engines Fuel gt A i Combustion chamber An opencycle gasturbine engine Compressor CD Fresh air 1 2 Isentropic compression in a compressor 23 Constantpressure heat addition 34 Isentropic expansion in a turbine 4 1 Constantpressure heat rejection w Cl Turbine gt qin Exhaust Heat gases I exchanger p Wnct Compressor Turbine il Heat exchanger qOUl A closedcycle gasturbine engine Rankine Cycle The Ideal Vapor Power Cycle The Rankine cycle is the ideal cycle for vapor power plants 1 2 Isentropie compression in a pump 2 3 Constant pressure heat addition in a boiler I 3 4 Isentropie expansion in a turbine Ema 4 1 Constant pressure heat rejection in a condenser iii in Lil Yb 5 G H Turine H pr rip5 in P n In p Condenaer The simple ideal Rankine cycle The Ideal VaporCompression Cycle The vaporcompression refrigeration cycle is the ideal model for refrigeration systems WARM environment Qll Condenser lt 3 22 X Expansion We Compressor 4quot l gt Evaporator QL COLD refrigerated space W m Isentropic compression in a compressor Constant pressure heat rejection in a condenser Throttling in an expansion device Constant pressure heat absorption in an evaporator This is the most Widely used cycle for refrigerators AC systems and heat pumps Pure Substances Pure substance A substance that has a fixed chemical composition throughout Air is a mixture of several gases but it is considered to be a pure substance VAPOR N2 LIQUID a H 2 0 Pure Pure Pure Substance Substance Substance Approx Composition of Air by Volume N2 78 O2 21 Ar C02 other 1 VAPOR LIQUID 7 AIR NOT a pure substance due to differences in composition When liquified Intermolecular Forces CK fl bits 3 J gtJ mtg s 35gt E5 3333 I forces fquot g a 39 83 r 39 4 gtJ gt3 gtJ 33 at t 3 In a solid the attractive ngclgswe and repulsive forces between the molecules tend to maintain them at relatively constant Attractive distances from each other Force f The molecules in a sis 3 solid are kept at 82 their pos1tions by the intermolecular Equilibrium position Weak interactions a Interatomic Distance Phases of a Pure Substance I Increasing Separation gt lt1 Increasing Strength of Interaction Phases of 21 Pure Substance Boron Nitride want 1 5131 2512 Fr ssurre Fa h jr Eiii r i39JELFF F H39 F a TIEEl I i NJ I i W 1i 7777777777777 WI quotIr H mm i Temp ratum Iii iii Phases of Pure Substances Carbon 100000 10000 1000 100 Pressure in GPa 001 0 1 2 3 4 5 6 397 8 9 10 r I I J I lI I I I 1 II I I I I I I I I I I I I I I I I I I I I I I I IE 2 Q6 dlamond gt 39 E E E K9 39 E a a diamond qqI 5 metastable graphite 39 39 a E I 0 14970 E graphite vq 39 metastable diamond 39 39 39 E E Z 11qu1d 39 I I I I M 39 metagt A 1 lq 3 39 graphite vapor I 0 E E 3939 3 7 III I I I l I l I I I I I I I I I I I I l l I I I I I I I l I I I I I I I l I I I l I I I I l I 0 1 2 3 4 5 6 397 8 9 10 Temperature in 103 K H 0 U1 I A C 3945 p s C CO H O N 101 Jeq 111 aJneseld 10 Phase Change Processes of Pure Substances Consider a Closed system of water Within a cylinder with a movable piston to Which we begin adding heat Compressed liquid subcooled liquid A substance that it is not about to vaporize Saturated liquid A liquid that is about to vaporize STATE 1 At 1 atm and 200C water eXists in the liquid phase compressed liquid STATE 2 P 1 atm T 100 C 2 Heat At 1 atm pressure and 1000C water exists as a liquid that is ready to vaporize saturated liquid Phase Change Processes of Pure Substances Saturated liquid vapor mixture The state at Which the liquid and vapor phases coexist in equilibrium Saturated vapor A vapor that is about to condense Superheated vapor A vapor that is not about to condense ie not a saturated vapor STATE 3 STATE 4 S t t d avggif P 1 atm P 1 atm T 1000C T 1000C Saturated liquid 4 Heat As more heat is transferred part of the saturated liquid vaporizes saturated liquid vapor mixture 3 Heat At 1 atm pressure the temperature remains constant at 1000C until the last drop of liquid is vaporized saturated vapor STATE 5 P 1 atm T 300 C 2 Heat As more heat is transferred the temperature of the vapor starts to rise superheated vapor Phase Change Processes of Pure Substances T OCA Entire curve for process 1s at constant pressure Q 300 2 Saturated 3 mixture Constant temperature during phase change 100 20 ltV Saturation Temperature and Pressure The temperature at which water starts boiling depends on the pressure therefore if the pressure is fixed so is the boiling temperature Water boils at 100 C at 1 atm pressure Saturation temperature T salt The temperature at which a pure substance changes phase at a given pressure Saturation pressure Psat The pressure at Which a pure substance changes phase at a given temperature mm 34 P kPa Saturation boiling pressure of sat water at various temperatures Saturation wzs m N Temperature pressure mpmmmm m g 253E r Pm kPa 600 1 1 525 39quot 5 55 551 H 400 5 552 1553333339 1 125 5222 wow 15 m WM 200 2 254 d 4 2 5 iiii l l a c ui to I I I I thesuriaceoilhe O i iii 0 so 100 150 200 lg 155 15 5252 255 1555 25s 5525 so 5555 M Effects of Phase Changes and Energy Latent heat The amount of energy absorbed T LE 3 2 or released during a phasechange process Variatian at tha standard Latent heat of fusion The amount of energy atmaapzharia praaaura and the absorbed during melting It is equivalent to b iling Emmiin 133m DEFEJEUFE 0f the amount of energy released during freezing Water With alti de atmaapharia ailing E lavatian praaau Fa tm para r39n IaF a tura Latent heat of vaporization The amount of energy absorbed during vaporization and it is equivalent to the energy released during condensation The magnitudes of the latent heats depend on the temperature or pressure at which the phase change occurs At 1 atm pressure the latent heat of fusion of water is 3337 kJkg and the latent heat of vaporization is 22565 kJkg The atmospheric pressure and thus the boiling temperature of water decreases with elevation t5 Phase Diagrams of Pure Substances T 0C1 37395 A T v diagram is shown While Pv and T P diagrams also used to illustrate phase change processes of pure substances Constant temperature during phase change but increasing volume Each curve is for a given pressu7 I l N Saturated vapor Saturated liquid l l Region of phase change substance is a mixture of liquid and vapor lb 0003106 v m3kg Landmarks of the Phase Diagram T A 0 saturated liquid line c 39t39 1 a 4 1 saturated vapor 11ne quot compressed 11qu1d reglon x Q37 0537 superheated vapor reglon COMPRESSED 39 LIQUID QN 39 saturated 11qu1d vapor mlxture REGION SUPERHEATED reglon wet reglon VAPOR REGION T It U SATURATED 9 LIQUID VAPOR REGION P 7 0 O l l f l T amp Cr Critical 13 point Q Tv dIagram of a pure substance gt Phase change At supercritical pressures P gt Per there is no distinct phase change boiling process CI Pv Diagrams pI l Critical point I SUPERHEATED VAPOR REGION COMPRESSEDX LIQUID x REGION 79 t SATURATED 1 fonsr gt T LIQUID VAPOR REGION I V lt What about solid phases 100000 10000 1000 100 Pressure in GPa 001 O 1 2 3 4 5 6 397 8 9 10 I I I J I lI I I I I II I I I I I I I I I I I I I I I I I I I I I I I IE 2 Q6 dlamond gt 39 E E k 39 E a diamondihr wu 5 metastable graphite 39 39 a E I 0 H970 E graphite vq 39 metastable diamond 39 39 39 i E Z 11qu1d 39 I I I I M f metagt A 1 lq 3 39 graphite vapor z I a E E 139 7 I39I I I I I I I I I I l I I I I I I I I I I I I I I I l I I I I I I I I I I I I I I I I l I I I 0 1 2 3 4 5 6 397 8 9 10 Temperature in 103 K L C U I A C 3945 p s C CO p a O N 101 19q 11 SJHSSQJECI IQ Expanding the Diagram Pll Critical point Critical point VAPOR LIQUID VAPOR SOLID SOLID LIQUID LIQUID VAPOR LIQUID VAPOR Triple line l Triple line L r SOLID VAPOR SOLID VAPOR Pv diagram of a substance that contracts on freezing V Pv diagram of a substance that expands on freezing such as water 03053 quot avgljk 39 39 quotZrquot VAPOR g Tr1p1e p01nt for water 0 quotE 3 9339 0303 2 Ttp 001 0 At the triplepoint pressure and temperature a substance eXists in three phases in equilibrium Ptp 06117 kPa LIQUID 20 l Is it always solid liquid vapor for phase changes Sublimation Passing from the P Substances Substances sol1d phase d1rectly 1nto the that expand that contract vapor phase on freezmg on freezmg Critical pomt 6 20 3 z a 39 a i 3 39 A o J o o a r quot 0 0 I ta 0 n0 v I b ag e quoton 20 a quot0 539 039 39 quot l v 0 0 5 3 3quot a g 3 v Trlple pomt 39 39r Jig Java 33 B u a u to 39 3 gt VAPOR 00 39c lton 9 5 x 0 SOLID 9 PT diagram of pure substances At low pressures below the triple point value solids evaporate Without melting first sublimation Consolidating T v Pv and P T Diagrams The PvT surfaces contain a wealth of information but it is typically more convenient to work with twodimensional projections of the 3D space such as the Pv and T v diagrams Solid Liquid Critical Pressure Pressure PvT surface of a substance that contracts PvT surface of a substance that on freezing expands on freezing like water Review Mechanical Energy Mechanical energy The form of energy that can be converted to mechanical work completely and directly by an ideal mechanical device such as an ideal turbine Kinetic and potential energies The familiar forms of mechanical energy 6 Z 5 L Mechanical energy of a m h p g owing uid per unit mass 39 P V2 Rate of mechanical energy of Emech Inernech m 7 a owing uid Change in mechanical energy of a uid during incompressible ow per unit mass Aemh V g Z2 Zl Idkg p 2 Rate of mechanical energy change of a uid during incompressible ow a v a v i39nech l mech 31 Enthalpy and the Property Tables Enthal A Combination Pro ert py p y The combination or Pv is frequently h 2 u PU Idkg encountered in the analysis of control 39 volumes Fundamentally enthalpy is the combination of internal energy u and ow work Pv HUPV kJ H I I i A 7 P1 V1 I I AC 2 77D 4 I I I Control I I 1 I Vavg m quot pAcvavg i L19 Steam E the I I gt L Jl P2 V2 v For most substances the relationships among thermodynamic properties are too complex to be expressed by simple equations Therefore certain properties are frequently presented in the form of tables Some thermodynamic properties can be measured easily but others cannot and are calculated by using the relations between them and measurable properties The results of these measurements and calculations are presented in tables in a convenient format Saturated Liquid and Saturated Vapor States Table A 4 Saturation properties of water for various temperatures Table A 5 Saturation properties of water for various pressures A partial list of Table A 4 Uf specific volume of saturated liquid Specific volume 3 U specific volume of saturated vapor Sat m kg g Tgmp Egess Isad Sat 39Lfg difference between Ug and 39tf that is tfg Ug O a 1 UI va or Cf p Enthalpy of vaporlzatlon h Latent heat of T P sat V8 fg f I vaporlzatlon The amount of energy needed to 85 57868 0001032 2398261 aporize a unit mass of saturated liquid at a 90 70183 0001036 593 95 84 609 0 001040 1 9 8 temperature or pressure i i 1 Stir Specific Specific temperature volume of saturated Q7 1i uid SUPS EEEQTE q REGION Corresponding Specific Us gllgjgiggli x saturation volume of REGION pressure saturated vapor Working With Saturated Mixtures Quality x The ratio of the mass of vapor to the total mass of the mixture Quality is between 0 and 1 Where 0 corresponds to sat liquid and l to sat vapor The properties of the saturated liquid are the same whether it exists alone or in a mixture with saturated vapor vapor lintoral r Saturated VEIPUIquot Vat g S aturated V liquid vapor f Q mixture Saturated llqu1d A twophase system can be treated as a homogeneous mixture for convenience Int0t a inliquid Ignie39 POI ling PorT l L Quality is related to the horizontal distances on Pv and Tv diagrams Working With the Properties of Mixtures 1 Ill g Mayg l havg P or T P if T A Sat liquid Quahty 1s related Vg to the horizontal Sat liquid distances on Pv Vf and Tv diagrams The v value of a saturated liquid vapor mixture lies between I the vf and vg values at i gt the specified T or P lt Cu lt 0 S lt lt lt 0 lt N N ltV Superheated Vapor In the region to the right of the Compared to saturated vapor superheated vapor saturated vapor line and at is ChafaCtefiZCd by temperatures above the critical Lower pressures lt W at a given point temperature a substance eXists as superheated vapor In this region temperature and pressure are independent Higher internal energies Li 3 Mg at a given or properties Higher enthalpies 5 E IE at a given or Tit Higher tempreatures T gt 550 at a given P Higher specific vlumes U E Mg at a given 01 U at h TFC m3kg kJkg kJkg P 01 MP5 996150 Sat 16941 2505 6 2675 0 100 16959 25062 2675 150 1 25 27766 1560 72605 46872 54155 P 05 MP5 15153 gt Sat 037483 25607 2748 I 200 042503 26433 250 047443 2723 29610 Compressed Liquid The compressed liquid properties depend on temperature much more Higher pressures P PSat at a given T strongly than they do on pressure A E yfo T A more accurate relation for h E hf r l39 e r or Given P and T VEWT u A compressed liquid may be approximated as a saturated liquid at the given temperature yvuorh Lower ternpreatures T Sat at a given P Lower specific volumes U Uf at given P or T Lower internal energies at of at given P or T Lower enthalpies h hf at given P or T At a given P and T a pure substance Will 15183 eX1st as a 75 compressed liquid if T Tsar e P l J V L E f 750C u The Use of Reference States The values of a h and s cannot be measured directly and they are calculated from measurable properties using the relations between properties However those relations give the changes in properties not the values of properties at specified states Therefore we need to choose a convenient reference state and assign a value of zero for a convenient property or properties at that state The referance state for water is 0010C and for Rl34a is 400C in tables Some properties may have negative values as a result of the reference state chosen Sometimes different tables list different values for some properties at the same state as a result of using a different reference state However in thermodynamics we are concerned with the changes in properties and the reference state chosen is of no consequence in calculations Saturated water Ternperatu re table Speeifie uelume internal emerge E fllalp Errt39rqey m3ka ltJfltg ltJfltg ltJi ltg H Sat Sat Sat Set Set Sat Sat Sat Sat Terrie preea liquid uapr liquid Euap uapqr liquid Euap uapr liquid Euaq uapr T 3390 P5 kPa u 15 u ufg ug h mg a a 59 5g 01 01 1 00010 20000 0000 23000 231 00 0 1 2 50 2 5 0 0000 01550 1 550 5 8 25 000100 10103 21 23000 23818 21020 251001 2511 00103 8 011 00200 Saturated refrigerantBela Temperature table Specific irdlume internal energ Entrianlpy Entrdp m3lkg kJrkg liJlltg kJi kg Sat Sat Sat Sat Sat Sat Sat Sat Sat Temp preee liquid reaper liquid Errata vapor liquid Eileen trapdr liquid Evan vapor T 30 P3 We u 0 u Mfg ug ii mg g 3 354 3 ril0 5125 quot00quot05il quot36001 quotquot36 20140 2013 00quotquot 22506 22516 096060 quot06066 iyEi l l liil Property Tables Equations of State ENGR 222 Thermodynamics Louisiana Tech University Fall 2015 All images are used here strictly for academic purposes Most are from Thermodynamics An Engineering Approach and copyright McGrawHill Unauthorized reproduction is prohibited Landmarks of the Phase Diagram Tl At supercritical pressures P gt C1 there is no distinct phase change boiling process P Critical point 4Q a c9Q w QW O o COMPRESSED f LIQUID quot Q REGION SUPERHEATED VAPOR REGION U SATURATED 8 LIQUID VAPOR REGION Tv diagram of a pure substance 7 saturated liquid line saturated vapor line compressed liquid region superheated vapor region saturated liquid vapor mixture region wet region Tl CI Critical point Phase change CI Saturated Liquid and Saturated Vapor States Table A 4 Saturation properties of water for various temperatures Table A 5 Saturation properties of water for various pressures A partial list Of Table A4 luff specific volume of saturated liquid Specific volume q m3kg 39tg specific volume of saturated vapor Sat Tgmp Egess lsatd Sat 39Lfg difference between Ug and 39tf that is tfg Ug tf O 1 u1 va or T P a q p Enthalpy of vaporlzatlon hfg Latent heat of V VI Sat 8 vaporlzatlon The amount of energy needed to 85 57868 0001032 28261 aporize a unit mass of saturated liquid at a 90 70183 0001036 593 95 84609 0001040 19 8 temperature or pressure T Critical q point 7 Specific Specific g temperature volume of saturated q SUPERHEATED lquId VAPOR REGION Corresponding Specific SATURATED x r s LIQUID VAPOR saturatlon volume of REGION pressure saturated vapor Working With Saturated Mixtures Quality x The ratio of the mass of vapor to the total mass of the mixture Quality is between 0 and 1 Where 0 corresponds to sat liquid and l to sat vapor The properties of the saturated liquid are the same whether it exists alone or in a mixture with saturated vapor vapor lintoral r Saturated VEIPUIquot Var g S aturated V liquid vapor f Q mixture Saturated llqu1d A twophase system can be treated as a homogeneous mixture for convenience Intoi a inliquid Inverter ling PorT l L Quality is related to the horizontal distances on Pv and Tv diagrams Working With the Properties of Mixtures 1 Ill g Mayg l 1an P or T P if T A Sat liquid Quahty 1s related Vg to the horizontal Sat liquid distances on Pv Vf and Tv diagrams The v value of a saturated liquid vapor 9 mixture lies between T I I l I the vf and vg values at i l i i i I gt the specified T or P i i Vf Vavg Vg V vf uf lt v lt vg vg V Superheated Vapor In the region to the right of the Compared to saturated vapor superheated vapor saturated vapor line and at is ChafaCtefiZCd by temperatures above the critical Lower pressures lt W at a given point temperature a substance eXists as superheated vapor In this region temperature and pressure are independent Higher internal energies Li 3 Mg at a given or properties Higher enthalpies 1 E frag at a given r Tit Higher tempreatures T E eat at a given Higher specific vlumes U E Mg at a given 01 U at h TFC m3kg kJkg kJkg P 01 MP3 996150 Sat 16941 2505 6 2675 0 100 16959 25062 2675 150 1 25 27766 1360 72605 46822 541313 F 05 MPa 1518350 gt Sat 037483 25607 2748 I 200 042503 26433 250 047443 2723 29610 Compressed Liquid The compressed liquid properties depend on temperature much more Higher pressures P PSat at a given T strongly than they do on pressure A E yfo T A more accurate relation for h E hf T T T Given P and T VEWT u A compressed liquid may be approximated as a saturated liquid at the given temperature yvuorh Lower ternpreatures T Sat at a given P Lower specific volumes U Uf at given P or T Lower internal energies at of at given P or T Lower enthalpies h hf at given P or T At a given P and T a pure substance Will 15183 eX1st as a 75 compressed liquid if Tsar e P l J V Ll E Ll Consolidating T v Pv and P T Diagrams The PvT surfaces contain a wealth of information but it is typically more convenient to work with twodimensional projections of the 3D space such as the Pv and T v diagrams Solid Liquid Critical Pressure Pressure PvT surface of a substance that contracts PvT surface of a substance that on freezing expands on freezing like water Understanding the PVT behavior of substances Phase diagrams Property tables Equation of state The Ideal Gas Equation of State Equation of state Any equation that relates the pressure temperature and specific volume of a substance The simplest and bestknown equation of state for substances in the gas phase is the idealgas equation of state This equation predicts the PvT behavior of a gas quite accurately for speci c sets of conditions gttNOTA LAWgt lt P R V Ideal gas equation of state R R substancespecific gas constant M molar mass of the substance kgkmol Ru universal gas constant t s3l447 kJkmm K s3l447 kPa ifkm 003 M47 bar mEkmm K i mss tulbmol R 11073931J16 psia ft il39bmol R 54537 R lbflbmol R 39I The Ideal Gas Equation of State Mass Molar mass x Mole number m kg Various expressions of ideal gas equation mt PV mRT U NU PU RHT gt ltP1quotoperties per unit mole are denoted with a bar on the top quotd Ideal gas equation at two states for a fixed mass Real gases behave as an ideal gas at low densities ie low pressure high temperature The idealgas relation often is not applicable to real gases thus care should be exercised when using it Is Water Vapor an Ideal Gas 7quot O C At pressures below 10 kPa water vapor can be treated as an ideal gas regardless of its temperature with negligible error less than 01 percent 108 50 24 05 00 00 00 7 3 r 600 500 At higher pressures however the ideal gas assumption yields unacceptable errors particularly in the vicinity of the critical point and the saturated vapor line 40039 39 39 00 300 In air conditioning applications the water vapor in the air can be treated as an ideal gas 100 kPa 100 In steam power plant applications however the pressures involved are usually very high therefore ideal gas relations should not be used 10 kPa 08 kPa I 0 I 00 00m 001 01 l l0 100 v m3kg Percentage of error vtable videallvtabe x100 involved in assuming steam to be an ideal gas and the region where steam can be treated as an ideal gas with less than 1 percent error Z A Measure of Deviation from Ideal Gas Compressibility factor Z A The farther away Z is from unity 10 the more correction factor that the gas deviates from ideal gas behavior accounts for the deViation 0f Gases behave as an ideal gas at low densities real gases from ideal39gas i e low pressure high temperature behavior at a given The pressure or temperature of a gas is high or temperature and Pressure low relative to its critical temperature or pressure PIV IVE Tr Pu ZRT Z Z Z m Videal IDEAL REAL as E GAS GASES REAL P O IDEAL gt1 GAS GAS Z 1 Z 1 lt 1 At very low pressures all gases approach ideal The 0011le CSSibility faCtOIquot is unity gas behavior regardless of their temperature for ideal gases Working With the Compressibility Factor 10 0 Ethylene A Ethane O Propan C D n Butanc Average curve based on data on hydrocarbons I l 9 nHcptane A Nitrogen 0 Carbon dioxide Water l P i t Uar2tua1 PR 2 P b 39 Per 2 a UR l Flgr A455 RCduced RCdUCCd Pseudoreduced quot RTcrPcr J P1quot 633111 6 temperature specific volume Z can also be determined from a knowledge of PR and vR Comparlson of Z factors for various gases Th w a A A 7200 4 Ideal gas i334 O Nonidealgas behawor K km on T CJ39SO 39LEAJ39A LA 2 behaViOr x 7 x lt V KNXL T 13930 gaff03 A O X W 3 x 0312 Idealgas 39 gtlt X P behavior My 0 Legend gt X Methane I lsopentane V Gases deviate from the ideal gas behavior the most in the neighborhood of the M 30 35 40 45 Reduced pressure PR 50 55 60 70 critical point Other Equations of State Several equations have been proposed to represent the Pv T behavior of substances accurately over a larger region with no limitations Van der Waals Equation of State P U l 2 RT M 271227 R7 a 39 SP 64F Xi H Critical isotherm of a pure substance has an in ection point at the critical state This model includes two effects not considered in the ideal gas model the intermolecular attraction forces and the volume occupied by the molecules themselves The accuracy of the van der Waals equation of state is often inadequate van der Waals Bertvelet RedlichKwang BeattieBridgetttan BenedictWebbRubin S trob ridge Vi rial ltV Other Equations of State BeattieBridgeman Equation of State The constants are given in Table 3 4 for various substances It is known to be reasonably accurate for densities up to about 08 per BenedictWebbRubin Equation of State P B R T A Cu 1 bRHT a m 5 I a III q J The constants are given in Table 3 4 This equation can handle substances at densities up to about 25 per Virial Equation of State RT I U U 2 U U4 U 51 The coefficients 617 9T 67 and so on that are functions of temperature alone are called Virial coe iciems Relative Accuracy of the Various EoS T K1 W T r A 1 CL E E S E 5 0 j V l N C O 19 10 05 01 00 lt Vun der Waals top 300 01 01 00 00 00 Beattic Bridgcnmn middle 01 01 00 00 00 Bencdict chbRubin bottom 23 11 05 01 00 01 01 01 00 00 00 00 00 00 00 28 12 05 01 00 200 01 01 00 00 00 01 01 00 00 00 207 32 04 01 00 00 141 01 01 00 00 00 21 10 04 02 00 00 q S 57 152 09 04 X 3900 593 745 79 01 01 gt100 187 510 07 52 01 01 gt100 52 06 33 gt100 37 04 25 16 70 08 04 0 0 1 13 8 01 39 03 0 1 1111111 1111111 11111 11111111 11 gt l 7 Tiklnol Percentage of error involved in various equations of state for nitrogen error 112table vequationl vtable x100 van der Waals 2 constants Accurate over a limited range BeattieBridgeman 5 constants Accurate for p s 08pCI BenedictWebbRubin 8 constants Accurate for p 3 25pm Strobridge l6 constants More suitable for computer calculations Virial may vary Accuracy depends on the number of terms used Complex equations of state represent the PvT behavior of gases more accurately over a Wider range First Law Analysis of Closed Systems ENGR 222 Thermodynamics Louisiana Tech University Fall 2015 All images are used here strictly for academic purposes Most are from Thermodynamics An Engineering Approach and copyright McGrawHill Unauthorized reproduction is prohibited Work Done by a Moving Boundary Moving boundary work P dV work Quasiequilibrium process A process The expansion and compression work in a during which the system remains nearly pistoncylinder device in equilibrium at all times 5ij F ds PA is P d39l Wb is positive gt for expansion Wb is negative gt for compression Z J I P The work associated The mov1ng 1 w1th a mov1ng boundtuy boundary is called c I T A gas does a boundary work I J differential A 3 amount of work L 6WD as it forces I ll Hill I thepistonmm I I I I I P by a differential GAS i GAS amount ds Work Done by a Moving Boundary PA I I Process path I I I A PdV I 4 lt I I IV l i l The area under the process curve on a PV diagram represents the boundary work 2 2 Area A J M J Pdl v1 PA The boundary work done during a process depends on the path followed as well as the end states The net work done during a cycle is the difference between the work done by the system and the work done on the system 2 A I I I I I l 39 I l I l I I I gt I2 v v PI WB 8 I I I I I l 2 I I I I v V II Isothermal Isobaric and Polytropic Processes P VIZ n1 Ul nl l 2 J CU av C 39 l P2 V2 P1 UK1 Polytropic process 2 W5 J Paw l mRE T1 nl l n Polytropic process for an ideal gas b l n 2 2 W5 J P iv J C U1 iv Flt1112 When n l isothermal process 1 1 39 P P P Constant pressure process 1 1 PM What 1s the boundary II I work for a constant P 1 1 1 VI P 2V2 volume process a I I PV const p2 2 Schemat1c and PV d1agran1 39 for a polytrop1c process I I V1 V2 Energy Balance for Closed Systems V j Energy balance for any system Net energy transfer Change in internaL kinetics by heat werk and mass netentiah etei energies undergolng any process E in en 2 agitaterri Energy balance Rate of net energy transfer Rate of change in internaL by heat WEEK and mass kinetier petentiaL eters energies 1n the rate form The total quantities are related to the quantities per unit time is W a dEdr r kJ em em AeaEmm Energy balance per unit mass basis Energy balance in in out Sjr39atern 0r 560m 2 d w mn differential fOfm ham 2 Qnet m 01 Qn t m Energy balance for a cycle V netrent Energy Balance for Closed Systems mat Q quot 1130th system nenout quotyour Energy balance when s1gn conventlon 1s used 1e heat input and work output are positive heat output and work input are negative PA General Q W AE Stationary systems Q W AU Per unit mass q w Ae Differential form Sq SW de l gt V Various forms of the firstlaw relation for For a Cycle A5 0 thus Q W closed systems when sign convention is I used The first law cannot be proven mathematically but no process in nature is known to have violated the first law and this should be taken as sufficient proof Energy Balance for a Constant Pressure Expansion or Compression Process E in out system n n a Net energyr transfer Change in internal kinetie For a Constant pressure expanSIOn or by been work and nines potentinL ere energies compression process An example of constantpressure process HUPU P kPa 300 V lt Specific Heat Internal Energy amp Enthalpy ENGR 222 Thermodynamics Louisiana Tech University Fall 2015 All images are used here strictly for academic purposes Most are from ThermodynamicsAn Engineering Approach and copyright McGrawHill Unauthorized reproduction is prohibited Review Energy Balance for a Constant Pressure Expansion or Compression Process E in nut system a a a Net energyr transfer Change in internal kinetie For a Constant pressure expanSIOn or by been work and ITLEISS petentinL ere energies C ompres Sion prOC es S PUV2 VI U2 U1 An example of constantpressure process U2 U1 Plv39l t Wain en t H PU tilether l P kPa i I l l 2 H20 300 m 25 g PIP23OOkPa Sat vapor quot 5 min Q C E II 5 l w a lt Specific Heats Speci c heat at constant volume cv The energy required to raise the temperature of the unit mass of a substance by one degree as the volume is maintained constant Speci c heat at constant pressure 01 The energy required to raise the temperature of the unit mass of a substance by one degree as the pressure is maintained constant Table A2 amp A2E for various ideal gases m 1 kg AT10C Specific heat 2 5 kJkg C 1 5k Specific heat is the energy required to raise the temperature of a unit mass of a substance by one degree in a specified way Vzconstant m 1 kg AT 1 C kJ cv312 kgoc 3l2 kl 59 k Constantvolume and constant pressure specific heats CV and cp values are for helium gas Specific Heats CV and cp are properties Formal definitions Of CV and cp CV is related to the changes in internal energy and cp t0 the changes in enthalpy A common unit for specific heats is kJkg 0C or kJkg K the change in internal energy with temperature Vinnie mlkg m1kg i 300 gt 301 K 1000 gt 1001 K 1 I 0718 k 0855 kJ change in enthalpy with The specific heat of a substance changes temperature at e gtwam Preeeure with temperature 9 AIR AIR 7 True or False cp is always greater than cv Internal Energy Enthalpy and Specific Heats of Ideal Gases AIR Evacuated high pressure Joule showed using this experimental apparatus that mum For ideal gases u h CV and cp vary with temperature only Thermometer u V PU RT hLrlRT u 2 MT du TAT dT Li Hg H1 J CUT l r EMT dT 1 Internal energy and enthalpy Change of an ideal gas Internal Energy Enthalpy and Specific Heats of Ideal Gases 0 At low pressures all real gases approach idealgas behavior and therefore their specific heats depend on temperature only 0 The specific heats of real gases at low pressures are called idealgas speci c heats or zero pressure specific heats and are often denoted CPO and CV0 Ideal gas constantpressure specific heats for some gases see Table A ZC for Cp equations r kJkm l 0 50 10 30 n 20 r Ar Hc Ne Kr Xc Rn 39lbmpcralurc K M and h data for a number of gases have been tabulated These tables are obtained by choosing an arbitrary reference point and performing the integrations by treating state 1 as the reference state Table A17 amp A17E for air AlR T M kJikg it kakg 0 0 0 21407 30019 310 22125 31024 In the preparation of ideal gas tables 0 K is chosen as the reference temperature Temperature Dependence of Specific Heat Internal energy and enthalpy change When specific heat is taken constant at an average value H2 Li CuavgTZ CpavgB The relation A u 2 CV ATis valid for any kind of process constantvolume or not AIR TI 2 200C Ql T2 300c 9 V constant AuchAT 718 kJkg lekg AIR P constant Tl 200C T2 We Au 2 CV AT 718 kJkg l pl Approximation Actual IQ IkilV39g I T Tj T Tl tug For small temperature intervals the specific heats may be assumed to vary linearly with temperature Strategies for Calculating Au and Ah 1 Property table values for u and h This is the easiest and most accurate way when tables are readily available 2 By using the 0 or Cl relations Table A2c as a function of temperature and performing the integrations This is very inconvenient for hand calculations but quite desirable for computerized calculations The results obtained are very accurate 3 Average specific heats This is very simple and certainly very convenient when property tables are not available The results obtained are reasonably accurate if the temperature interval is not very large Au 112 M1 table 2 Au J cu T 631quot 1 Au E 6 AT avg Specific Heat Relations of Ideal Gases Li RT it R dT db cpdT and du chT AIR at 300 K CV 0718 kJkg K 01 2080 kJkmol K 8314 kJkmol K CV RH 29114 kJkmol K The cp of an ideal gas can be determined from a knowledge of CV and R l The relationship between 6 CV and R On a molar basis Z M a k 2 Specific heat CU ratio 0 The specific heat ratio varies with temperature but this variation is very mild 0 For monatomic gases helium argon etc its value is essentially constant at 1667 0 Many diatomic gases including air have a specific heat ratio of about 14 at room temperature Solids and Liquids Incompressible substance A substance Whose specific volume or density is constant Solids and liquids are incompressible substances LIQUID V constant IRON 250C 6 2 CV c 045 kJkg C SOLID L VS constan39 The specific volumes of The CV and cp values of incompressible incompressible substances substances are identical and are remain constant during a denoted by c pI39OCCSS Changes in Internal Energy do CV 07 allquot 2 a H2 a J CTdT klkg 1139 H E Cavgf2 h n PV 0 M as d at 2 da d P For solids the term U m9 is insignificant and thus A as E rmgampT For Ziqaids two special cases are commonly encountered 1 FISHERfpi ESS Iti processes as in heaters AP 0 Alt ms E c wAT onstatarrempammre processes as in pumps AT 0 Ah U AP m h jpj f T TCP Sat The enthalpy of a compressed liquid A more accurate relation than h a or E fliers T First Law of Open Systems ENGR 222 Thermodynamics Louisiana Tech University Fall 2015 All images are used here strictly for academic purposes Most are from Thermodynamics An Engineering Approach and copyright McGrawHill Unauthorized reproduction is prohibited Conservation of Mass Conservation of mass Mass like energy is a conserved property and it cannot be created or destroyed during a process Closed systems The mass of the system remain constant during a process Control volumes Mass can cross the boundaries and so we must keep track of the amount of mass entering and leaving the control volume pm M V 11 J 1 ME Definition of A H average velocity m m p K lA Volume flow rate V iL39l pVaig kg 390 J V 1A VA 11133 quotAc U Mass flow i m 39 39I p U rate ch vuvg gt 7 I 39 The average velocity V Valve 6 E 39 Vng is defined as the average speed l C t39 through a cross 1085 sec Ion section The volume ow rate 1s the volume of u1d owing through a cross section per unit time Conservation of Mass for a Control Volume The conservation of mass principle for a control volume The net mass transfer to or from a control volume during a time interval At is equal to the net change increase or decrease in the total mass Within the control volume during At Total masa entering Total masa leaving Net ehange in mass during during J during min intuit Z M 0 General conservation of mass General conservation of mass in rate form Mass Balance for SteadyFlow Processes During a steady ow process the total amount of mass contained within a control volume does not change with time mCV constant Then the conservation of mass principle requires that the total amount of mass entering a control volume equal the total amount of mass leaving it I I I I I I I I I CV I I I I I I I I m3 m 1113 2 5 kgs 1123 3 kgs For steady ow processes we are interested in the amount of mass owing per unit time that is the mass flow rate 2 Z kg Multiple inlets in Out and eXits S39 l ll1A pgngg Inge i 99quot m1 m2 stream Many engineering devices such as nozzles diffusers turbines compressors and pumps involve a single stream only one inlet and one outlet Conservation of mass principle for a two inlet oneoutlet steady ow system Incompressible Flow The conservation of mass relations can be simplified even further when the uid is incompressible which is usually the case for liquids 139 Z 2 Z Steady V quot 08 m3s quotin wt N I Steady l L V1 2 V A Vb incompressible ow incompressible single stream A i r I I There 1s no such thlng as a conservatlon of volume compressor I I I principle However for steady ow of liquids the volume ow rates as well as the mass ow rates remain constant I since liquids are essentially 1ncompress1ble substances During a steady ow process volume ow 7 kOS rates are not necessarily conserved although m s 39 mass ow rates are VI 14 m3s Flow Work Flow work or flow energy The work or energy required to push the mass into or out of the control volume This work is necessary for maintaining a continuous ow through a control volume FL PAL I 1d w w kJ Wllmv I I I I CV I I I I a Before entering I P Wilmv V CV b After entering T v w my The ow energy is h if Hi5 m 1 m a 1739 Mn quot4 Wm W a aver r i T J F iii quot 39 Z w a I W Z w LL 1 a gs 1 R J by MW My We him me a M WM n A J N L P1 1 4 ix 3 ll gt J 391 r TLI LL quot ha f 4275 j quote care of by enthalpy e Pv e PU u ke pe hnPv lm this is the quot main reasen fer de ning the pmperly ff enthalpy V 39 Flowing 39A 2 Non awmg a a 9 PU u uid 1 quot uid v 2 Z The total energy consists of three parts for a non owing uid and four parts for a owing uid Energy Transported by Mass V2 Amount ofe39nergy transom WES mh gt V2 Rafe ofenergy transom WEE gt Ir 39 quot When the kinetic and potential energies of a CV uid stream are negligible E mh E ma sis ma as I l l l When the properties of the mass at each inlet or eXit Change with time as well as over the cross section Einmass J J Steady ow Processes II I 39 x Control I Under steady ow condltlons the mass and In I volume energy contents of a control volume remain I constant I mCV constant I I ECV constant I Mass I I out Under steady ow conditionS l I I quot12 the uid properties at an inlet or ml I gt I exit remain constant do not II l 7392 change with time Control I I volume I I l I m I I 3 I h Mass and Energy Balances for Steady Flow Processes Mass balance I p2V2A2 1 2 g 2 39 1th in Energy balance Rate of net energy transfer by heat work and magg J V Rate ctquot net energy transfer In by heat werk and masa 1212 m I lt I out P 39 quot win I Hot I water 0 steay Heat Electric 39 heatingy 1055 Qoul U I element CV Hotwater tank I l I I 39 m I l lt Jl Cold water in 0 J Rate of change in internal kinetic pctential etc energies EUUTL a V V Rate at net energy transfer cut by heat wcrk and maaa in For each inlet 2 0 L1 i Q 0th 2 Fit 1 it g tier each exit till Energy Balance With Sign Convention for each exit mp3 it q whE hl Hit wzmm when kinetic and potential energy Changes are negligible 191312 h Steady ow Engineering Devices Nozzles C b V wage Diffusers 23133 A modem landbased g i s Compressors Egmgffsfg e IllStage ManifOIdS Hig11 iDIcssuIc m me turbme used for electr1c Turbines LPC Tu b m power product1on Th1s 1s a Pumps 32136121121106 t 1132er General Electrlc LM5000 Fans 39 39 7 M quot turbme It has a length of 62 m it weighs 125 tons and produces 552 MW at V m 3600 rpm With steam 39 injection Throttling valves Heat Exchangers Mixing Tanks Piping systems z WE a 53 SEEE a 5 E g 3 B E 2 3 397 i 155 gm t g g E Rocket engines hke those used on the space shuttle employ Egg M convergingdiverging nozzles to accelerate gases to supersonic speeds Nozzles and Diffusers 7 Nozzle 3 V Vl 1 gt Diffuser gt V3 ltlt VI L Nozzles and diffusers are shaped so that they cause large changes in uid velocities and thus kinetic energies A common energy balance for a nozzle or diffuser Since E 0 Nozzles and diffusers are commonly utilized in jet engines rockets spacecraft and even garden hoses A nozzle is a device that increases the velacily of a fluid at the expense of pressure A diffuser is a device that increases the pressure ofafluid by slowing it down The crosssectional area of a nozzle decreases in the ow direction for subsonic ows and increases for supersonic ows The reverse is true for diffusers rislt Isl l EDUI 2 v2 I l m 12 2 Ein 2 V1 z 2 0 Turbines and Compressors 0th F 1 P3 600 kPa NJLfAmK AIR m 002 kgs I I m Energy balance for the compressor in this figure E111 out since Aka Ape E A turbine converts a pressure difference into mechanical work As the uid passes through the turbine work is done against the blades which are attached to the shaft As a result the shaft rotates and the turbine produces work A turbine drives the electric generator in steam gas or hydroelectric power plants Compressors as well as pumps and fans are devices used to increase the pressure of a uid Work is supplied to these devices from an external source through a rotating shaft A fan increases the pressure of a gas slightly and is mainly used to mobilize a gas A compressor is capable of compressing gases to very high pressures Pumps work very much like compressors except that they handle liquids instead of gases Throttling Valves ltXgt a An adjustable valve 099900 9990 3323 b A porous plug Throttling valves are any kind Of owrestricting devices that cause a significant pressure drop in the uid The pressure drop in the uid is often accompanied by a large drop in temperature and for that reason throttling devices are commonly used in refrigeration and air conditioning applications Energy 1 12 quot it balance MI I IV Liz l 2 C A capillary tUbe Internal energy I Flow energy Constant Throttling valve Throttllng valve T IDEAL T1 T3 T u 9479 kJkg L12 8879 kJkg h 12 7 P V 11 9547 kJkg h2 9547 kJkg The temperature of an ideal gas does not change during a throttling h constant process since h 2 MD During a throttling process the enthalpy of a uid remains constant But internal and ow energies may be converted to each other l Mixing Chambers In engineering applications the section T1 60 C Where the mixing process takes place is In commonly referred to as a mixing chamber I 1 7 l I I I I MIX 1 n g l I c h am be r l I T2 171 II J A o O 0 39J H h 00 O 0 c 3 Energy balance for the adiabatic water mixing chamber in the figure is Hot T elbow i171 011 Water K k K The T elbow of an ordinary shower serves WW l39 m3h3 as the mixing chamber for the hot and the coldwater streams since E U i 0 E E Heat Exchangers Heat exchangers are devices Flu B CV boundary Flu B CV boundary Where two moving uid quotI I streams exchange heat Without l mixing Heat exchangers are lt F FluidA lt E IIeat 3 FluidA Widely used in various E Heat industries and they come in R various designs a System Entire heat 1 System Fluid A QCV 7t 0 Fluid B Chang ch 0 70C The heat transfer associated with a heat exchanger may I be zero or nonzero depending on how the control volume is selected Heat Water S00C F1Uid A Midi 20 C Mass and energy balances 0 Heat for the adiabatic heat R4341 UL exchanger in the figure is Q I 350C m1 2 mw Aheat exchanger can 2 m4 mR Q be as simple as two I I I 350C concentric pipes E111 Out 7A Pipe and Duct Flow The transport of liquids or gases in pipes and ducts is of great importance in many engineering applications Flow through a pipe or a duct usually satisfies the steady ow conditions QOLll Surroundings 200C Q Energy balance for the pipe ow shown in the figure is Heat losses from a hot uid owing through an uninsulated pipe or duct to the cooler environment may be very significant E 39 lth E III Kim 11 39l H111 out out 13 13 Ws h Pipe or duct ow may involve more than one form of work at the same time out 39 2 M W e in 15 kW V 00W 39quotn quotHi 39 A I 39 39 I I I 39 I 39 I 39 I I TI7OC I P1 100 kPa 39 I I VI 150 m3min Conservation of Mass for a Control Volume The conservation of mass principle for a control volume The net mass transfer to or from a control volume during a time interval At is equal to the net change increase or decrease in the total mass Within the control volume during At Total masa entering Total masa leaving Net ehange in mass l during during J WMth during General conservation of mass J p J M 0 General conservation of mass in rate form Energy Analysis of Unsteady Systems I gt Supply line gt Many processes of 1nterest however involve changes within the control volume with time Such processes Charging of a rigid tank from a supply line is an unsteady are called unsteadyflow or I I ow process s1nce 1t I I transzemflow processes I I 1nvolves changes I Control I Most unsteady ow processes can Within the control volume I be represented reasonably well by volume I A the uniformflow process CV boundary Uniform ow process The uid ow at any inlet or eXit is uniform and steady and thus the uid CV boundary unsteady ow process properties do not change with time The Shape and or position over the cross section of Size Of a I39 L quotI an 1nlet or eX1t If they do they are control volume I I averaged and treated as constants for may Change the entire process during an Control I volume I l u Conservations of Mass and Energy for Unsteady Processes Conservation of Mass min minim ineyetetn ieyetern im nal 39m quotinitial mi mg mg mljw i inletg exit 1 initial startlea and final state Conservation of Energy First Law Ein Enut Eeyetern Net energy transfer Eihange in internaL kinetic by been werkg and mass petentiaL etc energiee 6 Li 39 e e gin Mfin quot ma QM Went ma ii 265 Hilfigeyetent in nut fquot J Y Y Heat work and Masses and internal enthalpies of mass energies at beginning ir mass out on left and end states on right hand side hand side