Thermodynamic Thermodynamic PropertiesProperties Property TableProperty Table -- from direct measurementEquation of StateEquation of State -- any equations that relates P,v, and T of a substanceIdeal -Gas Equation of StateAny relation among the pressure, temperature, and specific volume of a substance is called an equation of state. The simplest and best-knon equation of state is the ideal-gas equation of state, given ashere R is the gas constant. !aution should be e"ercised in using this relation since an ideal gas is a fictitious substance. #eal gases e"hibit ideal-gas behavior at relatively lo pressures and high temperatures.Universal Gas ConstantUniversal Gas Constant$niversal gas constant is given on #u % &.'()') k*+kmol-,% &.'()') kPa-m'+kmol-k% -.-&'()') bar-m'+kmol-,% &..-/ 0-atm+kmol-,% (.1&/& 2tu+lbmol-#% (/)/.'/ ft-lbf+lbmol-#% (-.3' psia-ft'+lbmol-#EampleEampleDetermine the particular gas constant for air and hydrogen. , kgk*-..&3kmolkg.&.13, kmolk*&.()(34##uair , kgk*).(.)kmolkg..-(5, kmolk*&.()(3#hydrogen!! !"" "uuT# PT# P#$% v T& R v PT %R P#RT PvmRT P#Ideal Gas '(a)* is a simple Ideal Gas '(a)* is a simple Equation of StateEquation of StatePercent error for applying ideal gas Percent error for applying ideal gas equation of state to steamequation of state to steam +uestion ,---+uestion ,---$nder hat conditions is it appropriate to apply the ideal gas equation of state6Ideal Gas (a)Ideal Gas (a)7ood appro"imation for P-v-T behaviors of real gases at lo densities 8lo pressure and high temperature9.Air, nitrogen, o"ygen, hydrogen, helium, argon, neon, carbon dio"ide, :. 8 ; (< error9.Compressi.ility /actorCompressi.ility /actorThe deviation from ideal-gas behavior can be properly accounted for by using the compressi.ility factor 0, defined as= represents the volume ratio or compressibility.Ideal GasZ=1Real Gases= > ( or = ; (Real GasesReal GasesPv % =#T orPv % =#uT, here v is volume per unit mole.= is knon as the compressibility factor.#eal gases, = ; ( or = > (.Compressi.ility factorCompressi.ility factor?hat is it really doing6@t accounts mainly for to thingsMolecular structureMolecular structureIntermolecular attractive forcesIntermolecular attractive forcesPrinciple of Principle of corresponding statescorresponding statesThe compressibility factor = is appro"imately the same for all gases at the same reduced temperature and reduced pressure- = % =8P#,T#9 for all gasesReduced Pressure Reduced Pressure and Temperatureand Temperaturecr#cr#TTT APPPhereB P# and T# are reduced values.Pcr and Tcr are critical properties.Compressi.ility factor for ten su.stances Compressi.ility factor for ten su.stances 1applica.le for all gases Ta.le 2-341applica.le for all gases Ta.le 2-345here do you find critical-point properties6 5here do you find critical-point properties6 Ta.le 2-7Ta.le 2-74ol8kg-4ol9#8*+kg.,9Tcrit 8,9Pcrit 84Pa9Ar .&,13 .&3,- 8---9 8---9C.'.,-- ./1,& (/),& /,-&D..,-(5 )(.),. '',' (,'-D.C(&,-(5 )5(,/ 5)3,( ..,-1!C.)),-( (&&,1 '-),. 3,'1Reduced PropertiesReduced PropertiesThis orks great if you are given a gas, a P and a T and asked to find the v.Doever, if you are given P and v and asked to find T 8or T and v and asked to find P9, trouble lies ahead.$se pseudo-reduced specific volume.Pseudo-Reduced Pseudo-Reduced Specific #olumeSpecific #olume?hen either P or T is unknon, 0 can be determined from the compressibility chart ith the help of the pseudo-reduced specific volume, defined asnot vcr 8Ideal-Gas 2pproimationIdeal-Gas 2pproimationThe compressibility chart shos the conditions for hich = % ( and the gas behaves as an ideal gasB8a9 P# ; -.(andT# > (Eercise3-!" Eercise3-!" Steam at 5-- o! E ( 4Pa. Evaluate the specific volume using the steam table and ideal gas laTsat % (&-o! therefore is superheated steam 8Table A-'9Folume % -,)-(( m'+kgT To o! !(4Pa (4Pav v'3) '3)5-- 5--(&- (&-Tcr TcrSolution -page " Solution -page " Part 8b9 ideal gas la#vapor % )5( *+kg,v % #T+P , v % )5("&3'+(-5 % -.)-' m'+kgSteam is clearly an ideal gas at this state. Error is less than -./ Cp1T4a function of temperatureThree 5ays to Calculate Three 5ays to Calculate Hu and HhHu and HhHu > u! - u" 8table9Hu >Hu > Cv&av HT1T4 dT C!"vHh > h! - h" 8table9Hh >Hh > Cp&av HT1T4 dT C!"p@sothermal Process@sothermal ProcessIdeal gas) PV = mRTGor ideal gas, PF % m#T Gor ideal gas, PF % m#T ?e substitute into the ?e substitute into the integralintegral

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.*1*1!ollecting terms and integrating yieldsBPolytropic ProcessPolytropic Process PFn % !Ideal Gas 2dia.atic Process and Reversi.le 5or@?hat is the path for process ith e"pand or contract ithout heat flu"6 Do P,v and T behavior hen I % -6To developan e"pression to the adiabatic process is necessary employB(. #eversible ork modeB d? % PdF.. Adiabatic hypothesisB dI %-'. @deal 7as 0aB Pv%#T). Specific Deat #elationships/. Girst 0a ThermodynamicsB dI-d?%d$Ideal Gas 2dia.atic Process and Reversi.le 5or@ 1cont4Girst 0aB$sing P % 4#T+F@ntegrating from8(9 to 8.9 dTv4! PdF-d$ d? dI ( )

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((.(.PPTTIdeal Gas 2dia.atic Process and Reversi.le 5or@ 1cont4An e"pression for ork is developed using PF % constant.i and f represent the initial and final states( )( ) ( )( ) ( )( ) (PF PF F F(PF?FdFPF PdF ?i f(i(fii Ideal Gas 2dia.atic Process and Reversi.le 5or@ 1cont4The path representation are lines here Pv % constant.Gor most of the gases, (.)The adiabatic lines are alays at the righ of the isothermal lines. The former is Pv % constant 8the e"ponent is unity9P Pv vI % -I % -T%const.T%const.i if ff fPolytropic ProcessPolytropic ProcessA frequently encountered process for gases is the polytropic processB PFn % c % constantSince this e"pression relates P E F, e can calculate the ork for this path.*1##.Pd# 5Polytropic ProcessPolytropic Process!onstant pressure -!onstant volume @sothermal E ideal gas(Adiabatic E ideal gas k%!p+!v

ProcessE"ponent n2oundary ork for a gas hich 2oundary ork for a gas hich obeys the polytropic equationobeys the polytropic equation11 1111*1*1*1*1 nn# #-n#vvc #d# c Pd#5n n -nn. ?e can simplify it ?e can simplify it furtherfurtherThe constant c % P(F(n % P.F.n1111 1 * *11 1 11** * &nn# P # P-n# # P4 1## P5n nnn.Polytropic ProcessPolytropic Process1111*1 1 * **1*1& n##n P#& nn# P # Pd##cPd# 5

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.E"ercise '-((E"ercise '-((A bucket containing . liters of ater at (--o! is heated by an electric resistance.a9 @dentify the energy interactions if the system boundary is i9 the ater, ii9 the electric coilb9@f heat is supplied at ( ,?, then ho much time is needed to boil off all the ater to steam6 8latent heat of vap at ( atm is ../& k*+kg9c9@f the ater is at ./o!, ho long ill take to boil off all the ater 8!p % ).(& *+kgJ!9Solution - page (Solution - page (Part a9 @f the ater is the system then I > - and ? % -. There is a temperature difference beteen the electric coil and the ater.@f the electric coil is the system then I ; - and ? ; -. @t converts (--< of the electric ork to heatKSolution - page .Solution - page .The mass of ater is of ! @g. @t comes from.liters times the specific volume of -.--( m'+kgTo boil off all the ater is necessary to supply all the vaporiLation energyBEvap > !!IGJ!>KG7B EFThe poer is the energy rate. The time necessary to supply )/3- ,* at (,*+sec is thereforeBTime > KG7B$" > KG7B seconds or "-!7 hourPart b9Solution - page 'Solution - page 'The heat to boil off all the ater initially at ./o! is the sum of B 8(9 the sensible heat to increase the temperature from ./o! to (--o!, 8.9 the vap. heat of part 8b9The sensible heat to increase from ./o! to (--o! is determined using the specific heat 8!P % ).(& k*+kgo!9 =eat > K-"IJ!J1"BB-!G4>L!7 EFThe time necessary to supply 8)/3-M5.39,* at (,*+sec is BTime > G"M7$" > G"M7 seconds or "-KK hourPart c9E"ercise '-(.E"ercise '-(.A bucket containing . liters of #-(. is left outside in the atmosphere 8-.( 4Pa9a9 ?hat is the #-(. temperature assuming it is in the saturated state.b9the surrounding transfer heat at the rate of (,? to the liquid. Do long ill take for all #-(. vaporiLe6Solution - page (Solution - page (Part a9 Grom table A-., at the saturation pressure of -.( 4Pa one findsBTsaturation % - '-o! Fliq % -.---53. m'+kg vvap % -.(/1'3/ m'+kg hlv % (5/,*+kg 8vaporiLation heat9Solution - page .Solution - page .Part b9 The mass of #-(. is m % Folume+v0, m%-.--.+-.---53. % !-MI @gThe vaporiLation energyBEvap % vap energy N mass % (5/N..1& % KM! EFTime % Deat+Poer % KM! sec or I-! minE"ercise '-(3E"ercise '-(3 A rigid tank contains saturated steam 8" % (9 at -.( 4Pa. Deat is added to the steam to increase the pressure to -.' 4Pa. ?hat is the final temperature6Solution - page (Solution - page (P P-.(4Pa -.(4Pav v11.5' 11.5'o o! !Tcr % '3) Tcr % '3)o o! !-.'4Pa -.'4Pa(''.// (''.//o o! !superheated superheated Process at constant volume, search at the superheated steam table for a temperature corresponding to the -.' 4Pa and v % (.51- m'+kg -> nearly I!BoC-E"ercise '-'-E"ercise '-'- Air is compressed reversibly and adiabatically from a pressure of -.( 4Pa and a temperature of .-o! to a pressure of (.- 4Pa.a9 Gind the air temperature after the compressionb9 ?hat is the density ratio 8after to before compression9c9 Do much ork is done in compressing . kg of air6d9 Do much poer is required to compress .kg per second of air6@n a reversible and adiabatic processP, T and v follosBP Pv vI % -I % -T%const.T%const.i if ff fSolution - page (Solution - page (

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Solution - page 'Solution - page 'Part c9 The reversible orkBPart d9 The poer isB( )( ),? '1((T T # 4dtd?P( . ( ) ( )( )( )( )( ),* '1() . -.1' /55 .&3 . (T T # 4(PF PF?( . ( .#EF EercNcios O CapNtulo 3Propriedades das Su.stPncias PurasE"ercOcios PropostosB '.5 + '.1 + '.(. + '.(5 + '..( + '... + '..5 + '.'- + '.'. + '.')Team PlayB '.( + '.. + '.)E- 3-"4 UtiliQando a Ta.ela 2-"-" ou 2-"-!& determine se os estados da Rgua sSo de lNquido comprimido& lNquido-vapor& vapor superaquecido ou se estSo nas linhas de lNquido saturado ou vapor saturado-a9 P%(,- 4PaA T%.-3 J!b9 P%(,- 4PaA T%(-3,/ J!c9 P%(,- 4PaA T%(31,1( J!A "%-,-d9 P%(,- 4PaA T%(31,1( J!A "%-,)/e9 T%')- J!A P%.(,- 4Paf9 T%')- J!A P%.,( 4Pag9 T%')- J!A P%(),/&5 4PaA "%(,-h9 T%/-- J!A P%./ 4Pai9 P%/- 4PaA T%./ J! a9 Fapor superaquecido b9 0Oquido comprimido c9 0Oquido saturado d9 0Oquido-Fapor e9 0Oquido comprimido f9 Fapor superaquecido g9 Fapor saturado h9 Fapor superaquecido - Gluido i9 0Oquido comprimido - GluidoE". '..9 Encontre o volume especOfico dos estados PbQ, PdQ e PhQ do e"ercOcio anterior.b9 P%(,- 4PaA T%(-3,/ J! vvl%-,--(-/-8utiliLar referRncia T%(-3,/J!9d9 P%(,- 4PaA T%(31,1( J!A "%-,)/ v%-,-&&(.Sv%8(-"9vlM"8vv9Th9 T%/-- J!A P%./ 4Pa v%-,-(((.' m'+kg8Tabela A-(.' Fapor Superaquecido9E". '.)9 AmUnia a P%(/- kPa, T%- J! se encontra na regiVo de vapor superaquecido e tem um volume especOfico e entalpia de -,&513 m'+kg e ()51,& k*+kg, respectivamente. Wetermine sua energia interna especOfica neste estado.u %(''1,')/ k*+kg8u % h - P v9