1.Chapter 1- Review of Thermedynamic Priciples

7/30/2019 1.Chapter 1- Review of Thermedynamic Priciples

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Pow er Generation1landbook


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CHAPTERlReview of

ThermodynamicPrinciples

The design, operation, and performance of electricity-generating Power plants arebased on thermodynamic pnnciples'

The First Law of ThermodYnamicsThe first law of thermodynamics is the lar^,' of consert ation of energy. It states thatenergy can be neither created nor destroyed. Howerret the energy of a system can.hut1lge by unclergoing a process, for example, heat exchange, with the surroundings. Tt.ur-r olso be converted from one form to another it'ithin that system.

Astlstenr is a specified region, not necessarily of constant volume or fixed boundaries,where transfer urld ac,r-ro'".rions of energv and mass are taking place. An open stlstem isone where energy and mass cross the boundaries of the s,vstem. A steady-state opensystent,also call# th e steadtl-stnte, steady-Jlow (SSSF) syslera, is a system where m11s a1d"r1".gy flows across its boundaries do not vary u'ith time, and the mass r'r'ithin thesystem remains cclnstant. An SSSF system is sholt'n in Fig l'1'The first-law equation for that systenr is

PE,+KE,+IE,+FEr+AQ=PEz+KE'+IEr+FEr+A{,(11)where pf = potential energY 1- ntzg, / {,,, where /n = mass of quantity of fluid enteringind leaving the s1'stem' z = elevation of station 1 or 2 above a datum'

g = gravitaiictnal acceleration, and g, = gravitational conversion factortZz.ll,, ftl(lb, s:)or 10 kg m/(N s':)]' .KE = kinetic "'-"'gy 1= ntV ''1 /2g,)' where V' = velocitv of tl.re mass'IE = internal "r-r"ig,v (= uy. rne'internal energy is a soie function of temperaturefor perfect gu'-i", ur-r.l a strong function if temperature and lveak functionof pressurc f.r nonperfect g.ises, \.itpors, and liquids. It is a measure of theinternal (molecular) activity arrtl jnteractiorL of ti-re fluid.FE = flor,rl "rl".gu e pv -Ir,[r). The flon,energy clr fior,r,work is the workdone by tnl rionuir1g fluicl to push a mass ir1 into or out of the system'

1


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Chapter 0neFrcune 1.1 Schematic of a steadY-state, steady-flow (SSSF) systemwith one inlet and one outlet.

PEIKErlErFEr awt

PEzKEzlErFEz

AQ = net heat added [= Qo - | Q,l, whererejected across system boundaries;heat that depends upon the Process king place betr,veen 1 and 2' Valuesof c, vary with the Process (refer to T 1 1)1.AWu = net steady-flow mechanical work d by the system [= Wo, - I W.^ l, where) and W,," = work done on systemWou = work done bY sYstem (Posit(negative)1.

a = heat added and Q, = heatt, = trc,, (Tr- T), where c, = sPecific

AWrt=

A relationship between P and V isgiven byPV'--

where l'tfor certa lled the

where ilcommon

The most general(1.2)

relationship is

(1.3)

between zero and infinity. Its value

(14)

ist of

n ls called tne Poiytroplc ex:ain processes is given in Tal,,s oli *r,_P,c, 28, '

= U/m (specif ic internathermodynamic symbol

POIlerlt. rr. vdrr:le 1.1. The firs70),+Lq=|2o-4''U d.

energy) ands is presented

-law equation becomes/2:L+ u. + P"u. + LW.,o-d.t = V/m (specific volume)..n Table 1.2.

Process c nConstant pressule , ",cglrslSl] t9-11p91-.!yle '. *Adiabatic reversible , O

i:cir, c.= k-nt,

oI

cc

o--Trale 1.1 Values of c, and n for Various


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Enth

Review of ermodynamic PrinciPles

c.. P.c,-.Y,.-hI!MnP

= specific heat at constant pressure, Btu/(lb. "F) lJ/(kg= specific heat at constant volume, Biu/(lb. "F) IJl(kg K= specific enthalpy, Btu/lb. (J/kB)= total enthalpy, Btu (J)= energy conversion factor = 778.t6 ft lbr,/Btu (1.0 Nm/l= molecular mass, lb./lb mol or kglkg mol= r;t,^;;fi: "-g_""".! ii'"I:F":a "= absolute pressure (gauge pressure + barometric pressul(commonlV written PSia, or Pa)

()ll__

),\b,/tI2i unit may be lb,/in2g = heat tlansferred to or from syst-eml Btu or J, or Btu/cvclR = gas constant, lbr' ft/(lb, . "R) or J/(kg 'K\ =R/M; =-;;il;;;-rc".;;;;i;"Lis+s.3!;'il; ft/ii; morR). = .p"liiil "niropv, etuZ(lb, ' "R) or J/(kg K)S = total entropy, Btu/'R or J/kg

I t = temperature, "F or 'CI I =,-temperature on absolute scale, 'R or KI , = specific internal energy, BIu/lb^or )/kgI u = total internal energy. Btu or JI " = specific volume, fI3/lb.or m'/kgt-I v = totut volume. ft" or mrI w = yorr, done bv o' ol lv-l-bT:1?r,I_"i l: ll Bt-'1illl" "-l:I " - quality of a two-phase mixture = mass of vapor dividedII 1-- gl]: "ispeciric n:-ul1:ru-', 9lT:i:i9il""I n = efficiency' as dimensionless fraction or percent

or )/cycle

, a3t434 x AO3 J/(kE mol K)

/ total mass, dimensionless

Subscripts used in vapor table1 refers to saturated liquidg refers to saturated vaporurated liquid to saturated vaporfg refers to change in property because of change from sa

TreLe 1.2 Some Common Thermodynamic SymbolsalpyEnthalpy is defined as

U+ h-LtVand the first law becomes

mzrg umVlr+H.+ AO ="'8 -ryix 28, 8, /-8,Pu

+Hr+AW,, (1 .s)


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4 Chapter 0neEnthalpies and internal energies are properties of the fluid. This means that eachwould have a single value at any given state of the fluid. The specific heat at constantrtolume is

(1.6)

The specific heat at constant Pressure ls(7.7)

where R is the gas constant.For ideal gases:dtt = c.dT (1 8)dh - cydT

where c,, and c,, are constants- They are independent of temperatr,lre for mon.rtomicgases such u, 4". They irrcrease with temperature for cliatomic gases such as air, and*or" so for triatomic gases such as CO, and so forth. Therefore, for constant specificheats or for small changes in temperature:

Ltt= c,LT (1 9),\h = c,LT

Following are some examPles:. For a steam generator, AW., = 0, PE, - PE, is negligible, KE, - KE1 is negligible'

AQ = H, - H,, and Lq =hr- hr'. For gas or steam turbir-ie, AQ is negligible, PE, - PE, is negiigible, KE, - KE, isnegligible, and AW,, = Hr- Hr.o For water (or incompressible fluid) pump, AQ is negligible, PE' - PF' is negligible,KEr-KE,isnegligibte,LIr=l),,Vr=Vr=V(incomPressiblefluid),andAW"t:FE, - FE, = V(P' Pr).

Glosed SystemIn the open system, mass crosses the boundaries' trn the closed systent, only energy crossesthe boundaries. The first law for the closed system becomes

AQ = AU + aW.' (change with time' before and after theprocess has taken Place) (1'10)

ldrr II'' -lar I\ /r,

(ar )" =lal

c -c -R


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Review of Ihermodynamic Principles

Fil..r.z Pressure-volumera ) and temPerature-entroPYioi Jiugtu.. of an ideal diesel cvcle

AW., is called the no-flow work' It(1.11)

The cycle vert enersy from heat to work :i " ::l'l:::::^11??;ilil::*,:'":5".'J:"-"cvcle' A cycle isi '"'i"' of processes t#;d;;^J ""at at the same state and can berepeated i'-'a"fi'ttJyiig"fu f Z illustrates Jn ldeul diesel cycle'Process 1 to 2' Ideal and adiabatic (no heat exchanged) compressionPtocess 2 trt 3' Heat addition at constant pressureProcess 3 to 4' Ideal and adiabatic expansion processProcess 4 to'1' Constant-r'olume heat rejection

The first law becomes (1.i2)AQ"",=Qo- lQ.i=AW.",

(b)(a)

is given bYAw* = lindv

Proper$ RelationshiPsPerfect Gases ' r- r^" '-lifferent Drocesses are given in Table 1 3'Property relationships for perfect gases

for different Processesanet?f.. p"tf"tig"t"'Aperfect (or ideat)gns is one that' at ""y ';;;' ;ys the equation of state for perfect gases:Po = RT (1'13)

Nonperfect Gasgs , ^-. ^-^ -r^"o ennrrqh to exert forces on eachA ttonperfectgas is one in which the moiecules are ciose enough to e>other, as when a pertect gas is highly:o*,-t::* ""Jlclt higf,ly'cooled with respect toits critical conditions ttr-e Uet-'avior of nonperfect gases is given byPt: = ZRT (f i4)

where Z is thecompressibility factor thatdepends on P' I and the gas itself'


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a(oC)Io.Ooo-acacoa.gcaCo]foC)E.oC'+O0)!0)o_c?F{ItIJlEl


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Review of Thermodynamic Principles

Vapor-Liquid Phase Equilibrium in a Pure SubstanceConsi.der a piston-cylinder arrangement containing 1 kg of _water

(refer to Fig l'3)'Suppose the inltial p."rr.l.u and tJmperature inside the cylinder are 0.1 MPa and 20"C,respectively. As heat is transferred to the water, the temperature increases while thep."rr.,.u remains constant. When the temperature reaches ,99'6'C, additional heattransfer resuits in a change of phase, as indicated in Fig. 1.3b. Some of the liquidbecomes vapor. Hower.etirring tnis Process, both temperature and Pressure remainconstant, but the specific volumelncreases considerably. When all the liquid has vapor-ized, additional heat transfer results in increase in both temperature and specific vol-ume of the vaPor-The satttration temperatureis the temperature at which vaporization occurs at a givenpressure. This pressure is called the saitrration Pressure for the given temperature' Fore*umple, for water at 0.1 MPa, the saturation temperature is_99.6"C.For a pure substance, there is a relationship between the saturation temperatureand the saturation pressure. Figure 1.4 iilustrates this relationship. The curve is calledthe u aP o r - P r essur e curtl e.If a substance exists as liquid at the saturation temperature and Pressure, it is calledsaturated liquid.Ifthe temperiture of the liquid is lor't'er than the saturation temperaturefor the existing pressure, it is called srhcooled liqttid (or compressed liquid, rmplying ihatthe pressure is greater than the saturation Pressure for the given temperature)'When a substance exists as part liquid and part vapor at the saturation temperatureand pressure, its quality (.r) is defined as the ratio of the vapor mass to the total mass'

(c)b)hase for a pure substance; (a) liquid

water, (b) liquid water-water vapor, (c) water vapor'

ircunE 1.4 Vapor-pressure curve ofa pure substance.ooc

Temperature


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Chaptet 0ne

a tlnEFrcune 1.5 Temperature-volume diagram for water showing liquid and vapor phases (not to scale).

If the substance exists as vapor at the saturation temperature, it is called satttrntedtnpor. When the vapor is at a temperature greater than the saturation temperature (forthe existing pressure), it is called superhettte d uaTtor. The temperature of a superheatedvapor mav increase while the pressllre remains constant.Figure 1.5 iilustrates a temperatule-voiume diagram for water showing liquicland vapor phases. Note thatl,vhen the pressure is 1 MPa, vaporization (saturationtemperature) begins at 779,9'C. Point G is the saturated-r'apor state, and line CHrepresents the constant-pressure process in which the steam is superheated. A con-stant pressure of 10 MPa is representcd by line I/KL. The saturation temperature is311.1"C. Line N/FB represents the saturated-liquid line, and line NKGC represents thesaturated-r'apor line.At a pressure 22.09 MPa, represented by iine MNo, we find, however, that there isno constant-temperature vaporization Process. Instead, there is one point, N, where thecurve has a zero siope. This point is called the critical poit'Lt. At this point, the saturated-liquid and saturated-vapor states are identicalThe temperature, pressure, and specific volume at the critical point are called thecriticnl tetnpirattre, critical pressure, and critical ttolume, respectively. The critical-pointdata for some substances are presented in Table 1.4.A constant-pressure process at a pressure greater than the critical Pressure is repre-sented by line PQ. If water at a pressure of 40 MPa and 20"C is heated in a constant-pressure process. there will never be two phases present. However, there will be acontinuous change of densitY.

aloooEoF

The Second Law of ThermodYnamicsThesecondlalt'putsaiimitationontheconversionofheattowork'Workcanalwaysbeconverted to heit; however, heat cannot always be converted to work.The portion of heat that cannot be converted to work i.s called ttnauailable (nergyIt must be rejected as iow-grade heat afier work is generated'

Volume


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Review of Thermodynamic PrinciplesP"

OR

557.I

T1KFluid

ArrAmmoniaCarbon dioxideCarbon monoxideFreon L2HeliumHydrogenMethaneN itrogenOctaneOxygenSulfur dioxideWater

238.34547 56239.24693 29e:4

59.83l 343.26, 227.16ro24 92

278.60775.26

1165.09

309.50I JZ.+r| 304.20, 732.9Li 38s.to

, 51933.24190.70

', L26 20569.40

I 1.54.78, 430 70647.27

547 .43 ' 37 .7 44]1635.67 1-1,2.A03

1,O71,.34 7 3.884s'oi ia sa.sss596.66 41-j,482a 1A 1 )41

188.07 , L2.97067.31 46.414AAa a1 "" oo1:..:362.71 24.973

: 736 86 i 50 817' 1,143.34 78.8503206.18 , 22t.LL2

':'lvluliiply valr,res of R by 5.343 tLr convert to ]/(kg K)

The

TreLe 1,4 Constants for Some FluidsIn a porver plant, application of the secclnd law meaus that the thermai efficiencl' ofconvertirrg heal to work must be less than 100 percer-Lt. The Carnot cvcle represents anideal heat engine that gives tl-Le maximum value of that efficiency between any trvo tem-perature limiis. hr a steam or gas po\,ver plant, heat is received from a high-temperature,esertoi, (a rescr\oir is a source of -heat or heat sink large enough that it does not undergo

a change in temperature when heat is added or subtracted from it), such as steam gen-erators or combustors.Heat is also rejected in a steam Or gas po\,ver plant to a low-temperature reservolr/sr-rch as condensers or the enr.irontnent. The work produced in tire steam or gas Po\ rerplant is the difference betvveen the heat received from the high-ten-rperature reserr-oirind the heat rejected to the low-temperature resen'oir'

Concept of ReversibilitySadi Carnot intrclduced the concept of reversibiiitv and laid the foundations of thesecond larv. A reuersiblc prlcess, also called an ideal procass, can IeYerSe itself exactly bvfollorn'ing the same path it took in the first place. Thr-is, it restores to the svstem or the.l.r.r.,rr-,.jir-rgs the same heat and r't'ork Previouslv erxchangecl'In realit1., tirere are no icletrl l.eu"rsible; proi"rr"r. Reil prc',cesses are irreversible'Hrtrt'e.r.er, the clegree of irreversibility Varies betrveen proceSses'Therearemanysourcesofirreversibilityinnature'Th:t:o:limportantonestlrefriction, heat transfer, throttling, and mixing. Mechar-Lical friction is one in whichmechanical work is airriput"a into a heatini effect. onr er.rmple would be a shaft


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10 Chapter 0nergtating in a bearing. 1t is not possibie to add the same heat to the bearing to cause rota-tion of the shaft.An example of fluid friction is when the fluid expands through the turbine,undergoing internal friction. This friction results in the dissipation of part of itsenergy into heatirrg itself at the expense of useful work. The fluid tl-ren does lesswork and exhausts at a higher temperature. The more irreversible ihe process, thernore the heating effect and the iess the workHeat transfer in any form cannot reverse itself. Heat transfer causes a loss of avail-ability because no work is done between the high- and low-temperature bodies.

External and lnternal lrreversibilitiesExternnl irreoersibilities are those that occur across the boundaries of the sysiem Theprimary source of external irreversibiiity in power systems is heat transfer both at thehigh- and low-temperature ends.Internal irreuersibilities are those that occur within the boundaries of the system. Theprimary source of internal irreversibilities in por,r,er systems is fluid friction in rotarymachines, sttch as turbines, compressors, and pumps.

The Concept of EntropyEntropy is a property (e.g., pressure, temperature, and enthaipy). Entropv is given bythe equation

l)\Q - J;7,/5 (rer ersible process orrly)For a reversible, adiabatic process, AO - 0.Therefore,

(ljtrt = o) - (ds = o) -+ (s = constant) (1.16)Figure 1.6 illustrates a few processes on the temperature-entropy diagram. A revers-ibL adiabatic process is shown as 1-2. in Fig. 1.6. Assume that the expanding fluid is

Frcune 1,5 Expansion (a) andcompression (b) of a gas from P, toP2 on the I-S diagram. Process 1-2.is adiabatic reversible; process 1-2is adiabatic irreversible; andprocess 1-2, is throttling.

(i.15)


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Review of Thermodynamic Principles 11a perfect gas (the same conclusion can be drawn for vapor or a mixture of liquidur-rd uupoti. Lines P, and P- in Fig. 1.6 are constant-pressure lines (PL > Pr).Process 1-2in Fig. i.6 illustrates an adiibatic but irreversible process. lrreversibility has manifesteditself in an increase in temperature of the gas at P, (T. > Tr.).More irreversible expansion results in greater self-heating of the gas, as shown inprocess 1-2. Therefore, when irreversibility increases in an adiabatic process, the entropyi,-r.r"or", as we1l. The work produced decreases with an increase in irreversibility.Process 1-2, is a constant-temPerature process (for a gas, it is a constant enthalpy :rswell). This is a throttling process, where AH is zero and all the energy is dissipated in fluidfriction. This is the most irreversible process. It creates the most increase in entropY.Tlre degree of irreversibility for an expansion in a turbine is given by the polytroytictttrbine efficiency,lr (sornetimes called the isentropit: or ddiabatic turbine efficiency).It tsequal to the ratio of actual work to ideal work.The polytropic turbine efficiency is given by

H.-H, h,-lt,nr = Hl-; - h,_ h" (1.1 7)For constant specific heats \,=P (1 18)'' lr-Tr.

lf the fluid is being compressed (Fig. i.6b), an adiabatic reversible compression follou'sthe constant entropy path l-2.. If ihe process ciranges to adiabatic irreversible compres-siorr, the gas leaves at higl-rer temperature, Tr.

The fluid in this process absorbs some work input, which is dissipated in fluid fric-tion. The greater the irreversibility, the greater the exit temperature (T ,, > T: > Tr.) anclthe greater the increase in entropy.Since dft = c,dT for gases, then,

Hz' > Hz> H',and the work absorbed in compression lW. I increases r.vith irreversibilitV.The degree of irreversibility is given by the compressor efficiency. It is called thepolytropic cotllpressor efficiency, 11 (sometimes it is called the isentropic or ntlinbaticcoffipressor e.fficiency).It is eqr-ral tcl the ratio of ideal r,r'ork to actual work (the reverseof that of the expansion) and is given by

(1.1e)

(1.20)

(t.21)For constant specific heats

H. -H, lt..-lt,'"- H.-H, ltr-lt,T -7.rt. =#!-i12-'1

We can conclude that the change clf entropy is a measure of the unavailarble energl''Therefore, entropy is a measure of irreversibility. This impiies that entropy is a measttreof disorder. Entiopy of the universe is continually increasing and available energy iscontinually decreasing.


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t2 Chapter 0ne

(a)Frcune 1.7 Expansion of a vapor from P,1-2" is adiabatic reversible, and process to P" on the (a) I-s and (b) Mollier (h-s) diagrams Process12 G adiabatic irreversible.

Figure 1.7 illustrates vapor expanding from pressure P, to pressure P,, where P, isin the"two-phase region. Even if the exit temperature of the adiabaiic reversible andadiabatic irieversible processes is the same, the exit enthalpy is greater in the case of theirreversible process (h, > h,.) and the work is iess:hr- h,


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Review of Thermodynamic Principles 13

(b)a)Frcune 1.8 Carnot cycle on the (a) P V and (b) I-S diagrams.

Thus, the thermal efficiency of the Carnot cycle, q., is given by7.. -7,r !'lr ?- (1.27)

The thermal efficiency of the Carnot cycle is dependent on the heat source and heat sinktemperatures. It is independent of the working fluid.Since the Carnot cycle is reversible, it produces the maximum amount of workbetween two given temperature limits, T" and Tr. Therefore, a reversible cycle operat-ing between given temperature limits hal the highest possible thermal efficiency of all.yil"r op".uting between these same temperature limits. The Carnot cycle efficiency isto be considered an upper efficiency limit that cannot be exceeded in reality.

BibliographyEl-Wakil, M. M., Power PlantTechnology, McGraw-Hill, New York, 1984'Van Wylen, J. G., FtLnclarnentals of Ctassical Thermodqnarn lcs, John Wiley & Sons, NewYork,7976.

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1.Chapter 1- Review of Thermedynamic Priciples