ENGR 222 Thermodynamics notes Week 2
ENGR 222 Thermodynamics notes Week 2 ENGR 222
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This 24 page Class Notes was uploaded by Peter Idenu on Monday October 5, 2015. The Class Notes belongs to ENGR 222 at Louisiana Tech University taught by Dr.Moore in Summer 2015. Since its upload, it has received 27 views. For similar materials see Thermodynamics in Applied Science at Louisiana Tech University.
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Date Created: 10/05/15
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
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