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Chemical Engineering - Thermodynamic Properties

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SECTION 24

Thermodynamic Thermodynam ic Properties Thiss sect Thi section ion con contains tains ther thermody modynami namicc charts, charts, corr correlat elations, ions, and calculation procedures.

quicker, app quicker, approximate roximate method for enthalpy determ determinations inations by the use of total enthalpy charts.

The enthalp enthalpy y correlatio correlation n pre presents sents a rigorous method for calculation of enthalpy, enthalpy, followed by an example calculation illustratin trating g th the e u use se of th the e as asso socia ciate ted d char charts. ts. Als Also o incl include uded d is is a

 An entropy correl correlation ation a and nd an ex example ample calculation showing  its use are also pres presented. ented.

FIG. 24-1 Nomenclature H = en entha thalpy lpy at d desi esired red con condit dition ions, s, Btu/lb Btu/lb m mole ole,, or B Btu tu/lb /lb 0 H = idea deal gas gas stat state e enth nthal alp py 0 H0 = enth enthal alpy py da datu tum m at zero zero p pre ress ssur ure e an and d zero zero temperature H0T = idea ideall gas gas state state en enth thalp alpy y at temp temper eratu ature re T HPT MW P Pc Pr Pk

= = = = = =

T Tc Tr R °R S S0

= = = = = = =

enthalpy enthalpy at desired desired pres pressure sure an and d temp temperatu erature re molec olecu ula larr weight ight absol bsolut ute e pres pressu sure re,, p psi sia a critical or pseudoc pseudocritical ritical pressure pressure,, psia psia re redu duce ced d pres pressu sure re = P/P P/P c converg convergenc ence e pres pressur sure e for mult multi-co i-compon mponent ent systems syst ems,, psia abso absolu lute te te temp mper eratu ature re,, °R °R critical or pseudoc pseudocritical ritical temper temperature, ature, °R reduce reduced d te temper mperature ature = T/Tc gas constant, Fig.1-4 degr egrees ees Ran anki kin ne = °F + 459. 59.7 entr tro opy, Btu/(l tu/(lb b mole  •  °R), or Bt Btu/(lb u/(lb  •  °R) idea deal gas gas stat state e entr ntropy opy

spec specif ific ic grav gravit ity y, dime dimens nsio ionl nles esss specific volume, cu ft/l b enth enthalp alpy y of liq liqui uid, d, Bt Btu/lb u/lb (S (Ste team am Tabl ables es)) enth enthal alpy py o off gas, gas, B Btu tu/lb /lb enth enthal alpy py of vapo vapori riza zati tion on (hg  – hf ) entr entrop opy y of liqui liquid, d, Bt Btu/(l u/(lb b  •  °R)(Steam Tables) ent ntrropy of gas gas, Btu/(lb u/(lb  •  °R)

an anoth other er pre press ssure ure an and/ d/or or tem tempe pera ratur ture e an and d retur returned ned to its original conditio condition. n. Mole(s): A mass mass of su subst bstanc ance e corre correspo spond nding ing to to its m mol olec ecula ularr weight, weig ht, exp express ressed ed usuall usually y eith either er as lb-m lb-moles oles or gmgm-mole moles. s. boundar undaries ies of a an n are area a on th the e P-T d diaiaPhase E nvelope Phase nvelope: The bo gram for for the m material aterial which e encloses ncloses the regi region on whe where re both vapor and liquid co coexist. exist. Quality: The The we weig ight ht fracti fraction on of vap vapor or in a va vapor por-li -liquid quid mix mix-ture. R educe duced d Pre Pr ess ssure ure: The ratio of the absolute pressure to the critical pressur pressure. e. R educe duced d Tempe Temperature rature: The ra ratio tio of th the e absolute absolute tem temperaperature to the critical critical tempera temperature. ture. Saturated Satur ated Wa Water ter: Water ater at its its boi boili ling ng te temp mper erat atur ure e for for th the e pressure exerted on it. Saturated Steam: St Stea eam m at th the e boil boilin ing g temperat eratur ure e of  water for the pr pressure essure ex exerted erted on it but contain containing ing no li liquid quid water. Specific Volume: The vo volum lume e of of a su subst bstanc ance e per per unit unit m mass ass.. (Inverse (Inv erse of den density sity.) Thermodynamics: Th The e scienc science e wh which ich d dea eals ls wit with h the ene energ rgy y of syste systems ms and its ch chan ange gess an and d effec effects. ts.

pone onents nts an and d mix ixtu ture ress hav ave e the sam ame e rela relati tive ve th ther ermo mody dy-namic proper properties ties whe when n at the same relative thermod thermodynamic ynamic state. Critical Pressure: The vapo vaporr pre pressur ssure e at the criti critical cal temperature. This website stores data such as Criti Crenable itical cal Tempe Te mperature rature emperature ure above which a comcookies to essential site: The ttemperat ponent pon ent cann cannot ot be lique liquefied. fied. For mixture mixtures, s, the tem temper peratur ature e functionality, as well as marketing, above which all of the m mixture ixture canno cannott be liquid. personalization, analytics. You. Datum:and A referen ref erence ce p point oint. may change your: settings any time Density Ma Mass ss per peratun unit it vo volu lume me of a subs substa tanc nce. e. Enthalpy : Heat con content, tent, H, compo co mposed sed of inte internal rnal e ener nergy gy,, E, or accept the default settings. and flow energy, PV. PV. Usually express expressed ed as H = E + P PV V. Entropy: A ther thermody modynam namic ic quan quantity tity, S, d define efined d by the equa equa-tio tion n – dS = dQ/T wh wher ere e Q is the amoun amountt o off he heat at e ente nterin ring g or or Privacy Policy leaving leav ing the syste system m at abso absolute lute temp temperat erature, ure, T. I de deal al Gas: A gas whi which ch fo follows llows the equa equation tion PV = nRT wher where e n = number number o off moles. Marketing Irreversibility: The The deg degre ree e of hea heatt o orr work work th that at is lo lost st whe when n a syst system em is ta take ken n from from on one e press ressur ure e an and d te temp mper erat atur ure e to Personalization

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= = = = = = =

sfg  = entr entrop opy y chan change ge on vapo vapori riza zati tion on (sg  –  – sf ) vf  = sp speci ecific fic v volu olume me o off liq liqui uid, d, ccu u ft/lb (St (Stea eam m Tabl ables es)) vg  = spec specif ific ic v vol olum ume e of g gas as,, cu fft/lb t/lb vfg  = sp speci ecific fic vo volum lume e chang change e on va vapo poriz rizat atio ion n (v g  – vf ) xi = mo mole le fract fraction ion of co comp mpone onent nt i in liqui liquid d pha phase se yi = mo mole le fract fraction ion of co comp mpone onent nt i in vapor vapor p pha hase se Greek  Σi = summat summation ion for for all all com compo ponen nents ts ω  = acen acentr tric ic fa fact ctor or Subscripts m = mixt ixture pr prop ope erty rty i = an any y on one e co compo mpone nent nt in a m mul ultic ticom ompo ponen nentt mix mixtur ture e

Acentric Factor: A fact factor or fr freq eque uent ntly ly us use ed in cor corre rela lati ting  ng  thermodynamic therm odynamic propert properties ies — defined by ω  = log Pvr – 1.00 .00 where Pvr = reduced vapor pr pressure essure at Tr = 0.7. C orr orrespo espondi nding ng State States s: The theo theory ry tha thatt propo proposes ses pu pure re co comm-

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Sp gr  V hf  hg  hfg  sf  sg 

24-1

 

the e change change of en enth thalp alpy y wit with h pre pressu ssure, re, given given (H0T − HPT) th

ENTHALPY ENTHALP Y BEHA BE HAVIOR VIOR

by the enthal enthalphy phy d diffe ifferenc rence e betw between een th the e ideall gas state ent idea enthalpy halpy and the enth enthalpy alpy at the desired desired pr pressu essure, re, bo both th qua quantiti ntities es at th the e specified temperatu temperature, re, Btu/lb mole.

The chang change e of enth enthalpy alpy with te tempe mperatur rature e and pre pressur ssure e is complex. Predicting Predicting the enthalpy for a pure component or mixtu ture re is mu mult lti-st i-step ep pr proc oced edure ure th that at requir requires es in infor format mation ion that can only be obtained obtained by e experim xperimental ental measurem measurement. ent. For pure co comp mpon onen ents ts,, use of a P-H P-H di diag agra ram m li like ke thos those e sh show own n in Fi Figs gs.. 24-35 is  is recommended. 24-22 to 24-35

Since H00 is zero at the chosen datum, zero absolute temperature, Equation Equation 24-1 can be writte written: n: HPT = HT0 − (HT0 − HPT)

The enthal enthalpy py beha behavior vior of mixt mixtures ures can be pre predict dicted ed thro through ugh thermod ther modynam ynamic ic correla correlation tions. s. Use of a g good ood cont contempo emporary rary equation equa tion of state is recomm recommend ended ed for mixt mixture ure enthapy enthapy predicpredictions. Fig. 24-2 sho shows ws grap graphica hically lly the the chan change ge in enth enthalpy alpy of  th three ree ga gass str stream eamss and two liqu liquid id st strea reams ms as p pres ressur sure e is changed chan ged at const constant ant tempera temperatur ture. e. Value aluess fo forr th the e p plot lot were were calculated by the Soave10 version of the RedlichRedlich-Kwong Kwong equation of of stat state e11. The The cur curves ves in Fig. 24-2 24-2 are  are for no p pha hase se chan change ge and show show typ typical ical behav behavior ior o off gas phase enthalpy decrea decreasing  sing  and liqui liquid d phase phase enth enthalpy alpy incre increasin asing g with incr increasi easing ng pr presessure. Enthalpies Entha lpies for mixtures of re real al gases and liquids can b be e pre pre-dicted by hand calc dicted calculat ulation ion met method hods. s. The o ones nes reco recommen mmended ded for use are are based on an ext extensi ension on of the princip principle le of correcorresponding spondin g states and are shown gr graphically aphically in F Fig. ig. 24-6 24-6 a  and nd 24-7.. 24-7

Which can be simplified to: H   =  H0 − (H0 − H)

E q 24-3

 Values  Values for the change of enthalpy with pressure for a real gas or liquid are obtained fro from m a correlation based based on the principle of corresponding corresponding states.2 The original correlat correlation ion was ex ex-tended to to low reduced tempera temperatures tures3 to cover low temperat temperature ure gas proces processing sing applicatio applications. ns. The corre correlation lation shown in Figs Figs.. 24-6 and 24-7 consi consists sts of tw two o pa parts rts.. One par partt gives gives th the e chan change ge of enthalpy enthalpy with pre pressur ssure e for a sim simple ple fluid (flu (fluid id with zer zero o acentr ace ntric ic fac factor tor). ). The se seco cond nd par partt is a corre correcti ction on for de devia viatio tion n of a real real fluid fluid fr from om th the e id ideal eal fluid fluid chang change e of e enth nthalp alpy y wit with h pressure.. The value of (H0 –H) in Eq. 24-3 is calculated by: pressure

(H − H) = 0

Ideal Gas State Enthalpies

E q 24-2

  (H0− H) RTc    RT c 

(′)

(0)

  

 (H − H)  + ω     RTc  0

  24-4   E q 24-4  

where:

Enthalpies for pure ure component nte gas gases are asEnthalpi a pow owe eres se seri rie esp of tecompone mpe perrat atur ure fores aw id ide ereadily rang ange correlated of com ompo po-nents including including all of those tthat hat occur in natural ga gass streams. Ty Typica picall values fo forr natu natural ral gas comp componen onents ts are plott plotted ed in Figs Figs.. 24-3 and 24-4 for temperatures from -200 to 900°F 900°F.. Enthalpies for gas mi mixt xture uress can can b be e obta obtaine ined d as the mo mole le fra fracti ction on av avera erage ge if mola molarr entha enthalpie lpiess are used used,, or the weight weight fract fraction ion ave average rage if  mass enthalpies enthalpies are us used. ed. Many Man y natu natural ral gas str streams eams cont contain ain und undefine efined, d, or or pseu pseudo, do, components. compone nts. Idea Ideall gas ent enthalp halpies ies for pseudo comp compone onents nts are 24-5 -5.. To use Fig. 24-5 the 24-5 the spe specific cific gravi gravity ty,, moshown in Fig. Fig. 24 lecular weight and temperature (relative den density sity,, molecular 24-5 is  is for parafparafmass and temperature) must be known. Fig. known. Fig. 24-5 finic mixtur mixtures es and sshould hould not be used for p pseudo seudo compone components nts derived form form aromatic cr crude ude oils.

chan nge o off en enth tha alp lpy y of a sim simple ple [(H0 −H) / RTc](0) the cha fluid with pressur pressure e fro from m Fi Fig. g. 24 24-6 -6.. devia viatio tion n from from the cha change nge for a sim sim-[(H0 −H) / RTc]( ′) de ple fluid from from Fig. 24-7 Figs. 24-6 24-6 and  and 24-7 can 24-7 can be used for gas an and d liquid mixtures mixtures.. If the the mix mixtur ture e is a gas gas,, use the lower lower chart chart iin n eac each h fig figur ure. e. Fo Forr liquids read read the value from the isot isotherms herms at the top of the chart chart.. The uni units ts of (H0  –H) –H) wil willl dep depen end d o on n tthe he units units of th the e universal univ ersal gas co const nstant, ant, R, and and T Tc. c. For (H0 –H) in Btu/lb mole, R=1.986 Btu/(lb mole•  °R) and Tc is in °R. The reduced reduced tem tempera perature ture and pre pressu ssure re are def defined ined as Tr = T/Tc and Pr = P/Pc, where absolute temper temperature ature and pressur pressure e must be used. Values Values for pure compon component ent critical tempera temperature, ture, pressure and acent acentric ric factor are in Se Section ction 23 Ph Physical ysical Pr Propoperties. ertie s. Sec Section tion 2 23 3 also con contains tains grap graphs hs rela relating ting A ASTM STM distildistillattio la ion n tem empe pera ratture ure, mo mole leccular ular weigh ight, specif ecific ic grav gravit ity y (relative (rela tive dens density), ity), critical critical te tempe mperatu rature, re, and critical critical pres pressur sure e for undefined fractions. fractions. The fraction acentr acentric ic factor can be estimated from Fig. 23-28. 23-28.

The enthalpy datum chosen is zero e enthalpy nthalpy at zero pressure and zero absolute ttemperatur emperature, e, the sam same e datum as used in API Project 44. 1 The choice of datum is arbitrar arbitrary y and a matter con conven venienc ience. e. Ent Enthalpy di differe fference nces, s, the valu values es of interest,of are no not t affe affected cted by halpy the datu datum m chos chosen. en. However Howe ver, , the same enthalpy enth alpy datu datum m shou should ld be used ffor or all com compone ponents nts in any on one e calculation.

24-6 and  and 24-7 24-7,, the m mixture ixture compositi composition on must b be e To use use Fi Figs. gs. 24-6 known. The mole fra fraction ction av average erage (p (pseudo) seudo) ccritical ritical tempe temperarature and pres pressure sure are calcu calculated lated using Kay Kay’s ’s Rule4 as illu illussThe e mol mole e trated in Fig. 23-6 (TCm = ΣyiTCi and PCm =  ΣyiPCi). Th fraction average mixture enthalpy is calcu calculated lated from:

This website stores data such as cookies to enable site CHANGE OFessential OF ENTHALPY WITH PRE SSURE SURE functionality, as well as marketing, For purposes purposes and of correlatio correlation n and calculation,, the ideal and personalization, analytics. Youcalculation real re al gas ga s beh behav avior iors s are tr treat eated ed se sepa parat rately ely. The mix mixtu ture re idea ideall may change your settings at any time gas enthalpy at a specified tempera temperature ture is calcul calculated; ated; the e ennorthalp accept thegedefault settings. thalpy y chan change of the the real gas mixture mixture is ccalcu alculate lated d from a cor-

0 Hm = ΣyiH0i

E q 24-5

The valu alues of H0i are obtai obtained ned by m multip ultiplyin lying g th the e enth enthalpy alpy value valu e from Figs. Figs. 24-4 and 24-4 and 24-5 by 24-5 by the molecul molecular ar weight of the individual component.

relation prepared prepared from experim experimental ental enthalp enthalpy y measurem measurements ents on a variety of mixtures. This relation can be expressed as:

E q 24-1

The mole mole fraction av average erage ac acentric entric factor is calculated:   E q 24 24-6 -6 ω m   = Σyi ω i

(H0T − H00) the idea0l gas state enthalpy above the da-

The info informa rmation tion nece necessary ssary to ev evalua aluate te e enthal nthalpies pies for the 24-7  is now known known.. Use of th the e mixture from Figs. 24-4  24-4  to 24-7  method will be cleare clearerr after study of the followin following g illustrativ illustrative e calculation.

Privacy HPTPolicy − H00 =   (H0T − H00) − (H0T − HPT) where:

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tum, H , at the the des desir ired ed tem tempe pera ratur ture e (su (subbPersonalization scr script ipt T), Btu/ Btu/lb lb mol mole e

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24-2

 

EXAMPLE CALCULATION USING US ING ENTHALPY CORRE LATION

EXAMPLE EXAMPL E C ALCUL ATION USING USING ENTROPY CORREL CORRE L ATION TI ON

Fig. g. 24 24-8 -8 is at 12 120°F 0°F  A gas with the compositi composition on shown in Fi 24-6   and 24-7  24-7  calcul calculate ate the enand and 1010 1010 psia psia.. Us Usin ing g Figs Figs..  24-6 thalpy thalp yo off the gas. Fol Followin lowing g the exa example mple in Fig. Fig. 23-6 23-6,, the mol mole e fraction average critical critical temperature temperature is calculated as 370.7°R, and the the pse pseudo udo ccriti ritical cal pre pressur ssure e as 670 670.0 .0 psi psia. a. Foll Followi owing ng the the

The same gas as in the e enthalpy nthalpy exam example ple (shown in Fig. 24-18) is at 12 24-18) 120 0°F and 1010 psia. psia. Th The e pse pseudo udo crit critical icals, s, acen acentric tric factor,, reduced tempera factor temperature, ture, and reduced p pressure ressure ha have ve the same sam e valu values es as in tthe he en enthalp thalpy y exam example ple.. The mixt mixture ure idea ideall gas stateentrop stateentropy y is 52. 52.2 2 Btu Btu/(lb /(lb mole•°R). The value value read from

same procedure, procedure, the mixture acentric factor is 0.0264 an and d the molar enth enthalpy alpy 4885.7 Btu Btu/lb /lb m mole ole.. Wi With th a redu reduced ced tem tempera pera-ture of 1.564 and a reduced pressure of 1.493, the reading from Fig. 24-6 -6   is is 0.73 0.730 0 and and from from Fig. Fig. 24 24-7 -7 is 0.02 0.020, 0, whic which h gi give ve a Fig. 24 mixture enthalpy at 120°F and 1010 psia of 43 4347.6 47.6 Btu/l Btu/lb b mole.

Fig. 24-20 is 0.34 0.3 45 and that th fr Fi Fig. g. 24 24-2 -21 isatmospheres) 0.065. 0.065. The These se 24-20 combine to is give give (rememb (remember erat P from inom   l nP must be1in a real gas entropy of 44.05 Btu/(lb mole•°R).

REFERENCES 1. API Researc Research h Pro Projec jectt 4 44, 4, “Data “Data on Hydroc Hydrocarb arbons ons and Rel Relate ated d Compounds,” A & M Press, College Station, Texas. Texas.

The tot total al ent enthalp halpy y char charts ts show shown n in Fig Figs. s. 24-9 to 24-17 offer 24-17 offer a rap rapid id mean meanss of calc calculati ulating ng enthalpy enthalpy chang changes es on essent essentially ially the same basis as previous previously ly describe described. d. They m may ay be used instead of carrying carryingout out the detailed compon component-wise ent-wise calculations for mixture enthalpies. The charts cover the range of composit sitio ions, ns, pr press essure uress and te temp mper eratu atures res en enco count untere ered d in mo most st natural natur al gas syst systems. ems.

2. Curl, Curl, R. F., Jr Jr. an and d Pit Pitzer zer,, K. K. S., Ind Ind.. Eng. Eng. Ch Chem., em., 50, 1958, 1958, p. 265. 265. 3. Chao, Chao, K K.. C. and Gre Greenko enkorn, rn, R. A., A., GP GPA A Rese Researc arch h Report Report RR-3 RR-3,, Gas Pro Process cessors ors Associa Associatio tion, n, Tuls ulsa, a, Oklaho Oklahoma, ma, April April 1971. 1971. 4. Kay Kay, W W.. B., Ind. Ind. En Eng. g. Ch Chem em., ., 2 28, 8, 19 1936 36,, p p.. 10 1014 14.. 5. Jacoby Jacoby, R. H. and Yarborou arborough, gh, L., Tech echnic nical al Report Report to GPA, 196 1966. 6.

The total enthalpy charts were develop developed ed from results calculated for synthesized synthesized binary mixtures of the pure compon component ent normal norm al paraf paraffin fin hyd hydrocar rocarbon bonss next lig lighter hter and hea heavie vierr than th the e mixtu mixture re mo mole le we weigh ights ts ind indica icate ted. d. The calcu calculat lation ionss wer were e carried carr ied out by a compute computerr progr program am whic which h interp interpolate olated d between adjacent adjacent values in the tabulated values of enthalpy de-

6. ASME ASME S Ste team am Tab able les, s, 3r 3rd d Ed Ed., ., Amer Amer. Soc Soc.. of Me Mech ch.. Eng., Eng., Ne New w  Y  York, ork, N.Y., N.Y., 1967. 7. Keena Keenan, n, J. H. H.,, Ke Keye yes, s, F. G., G., Hil Hill, l, P. G. an and d Mo Moor ore, e, J. G., G., “Ste “Steam am Tables, ables,”” John Wi Wiley ley & Sons, Inc., New York, York, N.Y., N.Y., 1969. 8. Ely, J. F F., ., Priva Private te Communi Communicat cation ion,, 1985. 1985.

pa partu rture re repo report rted ed by Cu Curl rl an and d Pit Pitzer zer..2 Ideal Ide al gas enth enthalpy alpy values values for each pu pure re nor normal mal pa paraffi raffin n component compone nt were calculated and used to calculate the ideal gas mixture mixtu re enth enthalpy alpy. The ide ideal al gas state enth enthalpy alpy eq equatio uation n used for methane, methane, etha ethane ne and p propane ropane was a curv curve e fit of the d data ata 24-3.. For butane butane and h heavier eavier com components ponents,, a show shown n in Fig. 24-3 fourth order polynomial was used with coeffi coefficients cients taken from the API Data Book, Table A1.2. 9 The fifth coefficient reported in the the API table was d drop ropped ped to cconver onvertt to th the e 0°R 0°R,, 0 psi psia a enthalpy datum.

9. “T “Techni echnical cal Data Data Book — Petr Petroleum oleum Refining Refining,” ,” 3rd Ed., Ed., American Petroleum Petro leum Institute, Institute, Washington, ashington, D.C., 1977. 10 10.. So Soav ave, e, G., G., “Equi “Equili libr briu ium m Const Constan ants ts from from a Modif Modifie ied d Redli Redlich ch-Kwong Equati Equation on of State,” Che Chem. m. Eng. Sci., Vol. 27, No. 6, pp. 1197-1203, 1972. 11 11.. Ma Maddo ddox, x, R.N.and Moshfe Moshfeghi ghian,M., an,M., Privat Private e Communi Communicati cation,1996 on,1996..

BIBLIOGRAPHY  1. “Tech “Technic nical al Data Data Book—Pe Book—Petro troleu leum m Refinin Refining,” g,” 3rd Ed., Ed., American American Petroleum Petro leum Institute, Institute, Washington Washington,, D.C., 1977. 2. Reid, Reid, R. D. D.,, Pr Prausn ausnitz itz,, J. M. M. and Sherwoo Sherwood, d, T. K., K., “The Propert Properties ies of Gases Gases and Liquid Liquids,” s,” 3rd Ed., McG McGraw raw-Hi -Hill ll Book Co. Co.,, New York ork,, N.Y., 1977.

Ideal gas enthalpies were correcte corrected d for pressu pressure re changes by interpolating interpol ating the ta tabular bular dat data a used to compile Figs. 24-6 and 24-6 and 24-7. Pressure calculations calculations were made from reduced press pressures ures of 0.2 to 3,000 psi psia. a. Tempe emperatur ratures es ranged ranged from -300°F or Tr = 0.35 minimu minimum m to 600°F max maximum. imum.

3. Kesler, Kesler, M. G. and and Lee, Lee, B. I., “Impro “Improve ve Predict Prediction ion of Enthal Enthalpy py of  Fractions,” Hydrocarbon Processing, 55, 1976, pp. 153-158. 153-158.

Caution. Some mixtures mixtures encou encountered ntered in the calcula calculations tions  fell inside the phase enve envelopes lopes of Figs. Figs. 24-6  24-6 and  and 24-7   24-7   , Rather

4. Wormald, ormald, C. J., “Thermo “Thermo D Data ata for Steam/Hydro Steam/Hydrocarbon carbons,” s,” HydroHydrocarbon Processing, May 1982, pp. 137-141.

 24-6 and than. extra extrapolat polate e into the phas phase e enve envelopes lopes Figs. 24-6 Figs.  24-7  for entha en thalpy lpy p pres ressu sure re co corre rrecti ctions ons, , theofto tota tall enth en thalp alpies ies were first generat generated, ed, plott plotted, ed, and then extrapolated. extrapolated.

5. Lee, Lee , M. C., Ratcl Ratclif iffe, fe,Capacity A. E., Maddo Ma ddox, x, R.ed D., Parham, am,Fractions,” W. W. F. F. and Maddox, R. N., “Heat Determined Determin forParh Crude Hydrocarbon Hydro carbon Process Processing ing,, June 1978, 1978, pp. 18 187-18 7-189. 9.

 Vapor  Vapor enthalpies at 150 psia were extended to lower tem-

6. Yu, W. C., Lee, H. H. M. and Ligon, Ligon, R. M., “Predic “Predicted ted Hig High h Pressure Pressure Properties, Prope rties,”” Hydrocarbon Hydrocarbon Processing Processing,, Jan. 1982, pp. 171-178. 171-178.

This website stores data such as the relative peratur pera tures es by assu assuming ming relative enth enthalpy alpy chan change ge wit with h cookies to enable essential site temperat temp erature ure tto o be the sa same me as for an idea ideall gas. functionality, as well as marketing, CORRE LATION personalization, andENTROPY analytics. YouCORRELATION Entrop Enyour tropy ysettings is mos mostt usedas gui guide de for inte interpre rpretingthe tingthe behavior behavior may change at any atime of gase gases s and liqui liquids ds in comp compress ression ion and expa expansio nsion n pro process cesses. es. or accept the default settings.

7. “Properties “Properties for Light Light Petrol Petroleum eum Systems,” Systems,” Gulf Publi Publishing shing Co., Houston, Houst on, Texas, 1973. 8. Canjar Canjar,, L. N. a and nd Mann Manning ing,, F. S., “Thermod “Thermodyna ynamic mic Properti Properties es and and ReducedCorrelations Correlationsof Gases,” Gases,” GulfPublishing GulfPublishingCo., Houston, Houston, Texas,1967. 9. Weber, eber, J. H., “Predict “Predict Latent Latent Heats Heats of of Vaporiza Vaporization, tion,”” Chemical Chemical Engineerin Engi neering, g, Jan. 14, 1980.

The entropy entropy of a m multicompo ulticomponent nent m mixture ixture may be calculated by co comb mbin ing g id idea eall ga gass stat state e entro entropi pies es fr from om API API 441  with the 2 Curl and Pitzer  tables of values for the change of entropy with with pressure. Entropy equations for undefined mixtures (pseudo Privacy Policy compone comp onents) nts) are not avai available lable but, for mos mostt uses uses wher where e th the e pseud pse udo o com compo ponen nents ts ar are e pr prese esent nt in sm small all conc co ncent entrat ration ion, , they th ey Marketing can satisfacto satisfactorily rily be ap approx proximat imated ed by the near nearest est mole molecula cularr weight paraffin hydrocarbon. Personalization

10. St Starl arling ing,, K. E., “Fluid “Fluid Thermod Thermodyna ynamic mic Pr Prope operti rties es for Light Light PePetroleum troleu m Systems,” Systems,” Gulf Publishi Publishing ng Co., Houst Houston, on, Texas 1973. 11. Mad addo dox, x, R. N. an and d L. Lill Lilly y, “Gas “Gas Co Cond ndit itio ioni ning ng an and d Proc Proces essi sing ng,” ,”  V  Vol. ol. 3, 3, Campbell Campbell Petroleum Petroleum Series Inc., Norman, Norman, Oklahoma, Oklahoma, 1990. 12. Van Ness Ness,, H. C. and and Abb Abbott ott,, M. M. M.,, “Class “Classica icall Thermod Thermodyna ynamic micss of Non-Electrolyte Solutions,” McGraw-Hill, McGraw-Hill, N.Y., N.Y., 1982.

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24-3

 

   0    0  .    0    0    0  ,    2

  s   m   a   e   r    t    S   s   a    G    l   a   r   u    t   a    N    l   a   c    i   p   y    T    2   -   r   o    4   f    2   y  .   p    l    G    I   a    F   h    t   n    E   n   o   e   r   u   s   s   e   r    P    f   o   e   c   n   e   u    l    f   n    I

   A    I    S    P  ,   e   r   u   s   s   e   r    P

   2

  e   n   a    h    t   e    M   —

  s   a    G    l   a   r   u    t   a    N   —

   O    C    %    0    1    h    t    i   w   s   a    G    l   a   r   u    t   a    N   —

   t   n   e   n   o   p   m   o    C   e   r   u    P    d    i   u   q    i    L   —

  e   r   u    t   x    i    M    d    i   u   q    i    L   —

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  e  l    o    M    b  l /   U    T    B    M  ,  y    p  l  a   h   t  n    E

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FIG. 24-3 Ideal-Gas-State Enthalpy of Pure Components

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24-5

 

FIG. 24-4 Ideal-Gas-State Enthalpy of Pure Components

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24-6

 

FIG. 24-5 Ideal-Gas-State Enthalpy of Petroleum Fractions

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24-7

 

FIG. 24-6 Effect of Pressure on Enthalpy (Simple Fluid)

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24-8

 

FIG. 24-7 Effect of Pressure on Enthalpy (Correction for Real Fluids)

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24-9

 

FIG. 24-8 Example Enthalpy Calculation

Com Co mponent

Mole Fraction

Molecular Weight

Critical Temp. R.

Critical Pressure psia

Acentric Factor

Ideal Ga Idea Gas s Enthalpy Btu/lb

Methane

0.9010

16.04

343.0

667.8

0.0126

292

Carbon Dioxide

0.0106

44.01

547.5

1071.0

0.2667

100

Ethane

0.0449

30.07

549.8

707.8

0.0978

189

Propane

0.0187

44.1

665.7

616.3

0.1541

162

i-Butane

0.0065

58.12

734.6

529.1

0.1840

151

n-Butane

0.0045

58.12

765.3

550.7

0.2015

162

i-Pentane

0.0017

72.15

828.7

490.4

0.2286

151

n-Pentane

0.0019

72.15

845.3

488.6

0.2524

158

Hexane

0.0052

86.18

912.0

470.0

0.2900

139

IDEAL GAS STATE ENTROPY ENTROPY PSEUDO PSE UDO CRI CRITICA TICAL L TEMPER TEMPERATU ATURE RE

Btu/lb Btu/lb mol

4885.7

°R

370.7 370.7

REDUCED REDUCE D TEMPERATURE TEMPERATURE PSEUDO PSE UDO CRI CRITIC TICAL AL PRE PRESSU SSURE RE

1.564 1.56 4 psia psia

670.0 670.0

RE REDU DUCED CED PR PRES ESSU SURE RE

1. 1.49 493 3

MOLE FRACTIO FRACTION N AVERAGE ACENTRIC ACENTRIC FACTOR FACTOR

0.0264

[(H0 –H) / RTC](0)  from Fig. 24-6 0

0.730

(’)

[(H  –H) / RTC] from Fig. 24-7

 

[(H0 –H)m / RTC] = [(H0 –H –H)) / RTC](0) + [wm [(H0 –H –H)) / RT RTC] (’)

0.7305

(H0 –H)m, Btu/lb mole

538.1

H, Btu/lb mole

4347.6

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24-10

 

FIG. 24-9 Total Enthalpy of Paraffin Hydrocarbon Vapor

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24-11

 

FIG. 24-10 Total Enthalpy of Paraffin Hydrocarbon Vapor

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24-12

 

FIG. 24-11 Total Enthalpy of Paraffin Hydrocarbon Vapor

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24-13

 

FIG. 24-12 Total Enthalpy of Paraffin Hydrocarbon Vapor

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24-14

 

FIG. 24-13 Total Enthalpy of Paraffin Hydrocarbon Vapor

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24-15

 

FIG. 24-14 Total Enthalpy of Paraffin Hydrocarbon Vapor

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24-16

 

FIG. 24-15 Total Enthalpy of Paraffin Hydrocarbon Vapor

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24-17

 

   d    i   u   q    i    L   n   o    b   r   a   c   o   r    d   y    6    H    1   -   n    4    i    f    2    f  .   a   r    G    I   a    F    P    f   o   y   p    l   a    h    t   n    E    l   a    t   o    T

   8    1      4    2

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   d    i   u   q    i    L   n   o    b   r   a   c   r    d   y    7    H    1   -   n    4    i    f    2    f  .   a   r    G    I   a    F    P    f   o   y   p    l   a    h    t   n    E    l   a    t   o    T

   9    1      4    2

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FIG. 24-18 Example Exam ple Entropy Calculation Calculation

Com Co mponent

Mole Fraction

Molecular Weight

Critical Temp. Temp. °R.

Critical Pressure psia

Acentric Factor

Ideal Ga Idea Gas s Entropy Btu/lb

Methane

0.9010

16.04

343.0

667.8

0.0126

3.150

Carbon Dioxide

0.0106

44.01

547.5

1071.0

0.2667

1.176

Ethane

0.0499

30.07

549.8

707.8

0.0978

2.036

Propane

0.0187

44.1

665.7

616.3

0.1541

1.624

i-Butane

0.0065

58.12

734.6

529.1

0.1840

1.400

n-Butane

0.0045

58.12

765.3

550.7

0.2015

1.338

i-Pentane

0.0017

72.15

828.7

490.4

0.2286

1.260

n-Pentane

0.0019

72.15

845.3

488.6

0.2524

1.245

Hexane

0.0052

86.18

912.0

470.0

0.2900

1.198

IDEAL IDE AL GAS GAS STATE STATE ENTROP ENTROPY Y PSEUDO PSE UDO CRI CRITICA TICAL L TEMPER TEMPERATU ATURE RE

Btu/lb Btu/lb mol °R

REDUCE RED UCED D TEMPER TEMPERATU ATURE RE PSEUDO PSE UDO CRI CRITIC TICAL AL PRE PRESSU SSURE RE

52.2 370 370.7 .7 1.564 1.56 4

psia psia

670 670.0 .0

RE REDU DUCED CED PR PRES ESSU SURE RE

1. 1.50 507 7

MOLE FRACTIO FRACTION N AVERAGE ACENTRIC ACENTRIC FACTOR FACTOR

0.0264

( )

24-20 20 Fig. 24[(S0 −S) /   R] o  from Fig.

0.345

[(S0 −S) /  R]( ′ )   from Fig. 24-21  

0.065

In P (P in atmosp atmosphere heres) s)

4.2301 4.23 01

o

S − Sdata such as This website stores   ) (o) + [(S0 −S) =  R [ ( cookies to enableR essential site functionality, aso well as marketing, S − S   ) (analytics. o) +  I  In n P You w ( personalization, and R may change your settings at any time RΣyi lnyi or accept the default settings.

9.094 -0.9404

So m = (Σ yiSoi   − RΣyi lnyi) 

Privacy Policy Sm = [S 0  – (S0 m

m

53.14

– Sm)]

44.05

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24-20

 

  s    t   n   e   n   o   p   m   o    C   e   r   u    P    9    f    1      4   o    2   y  .   p   o    G   r    I    t    F   n    E   e    t   a    t    S   s   a    G    l   a   e    d    I

   1    2      4    2

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FIG. 24-20 Effect of Pressure on Entropy (Simple Fluid)

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24-22

 

FIG. 24-21 Effect of Pressure on Entropy (Correction for Real Fluids)

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  m   a   r   g   a    2    i    2    D      4    H    2    .    P    G    I   n    F   e   g   o   r    t    i    N

   4    2      4    2

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  m   a   r   g   a    i    D    3    H      2      4    P   e    2    d  .    i    G    I   x   o    F    i    D   n   o    b   r   a    C

   5    2      4    2

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  m   a   r   g   a    4    i    2   -    D    4    H    2    .    P    G    I   e    F   n   a    h    t   e    M

   6    2      4    2

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  m   a   r   g    5    i   a    2   -    D    4    2    H  .      P    G    I   e    F   n   a    h    t    E

   7    2      4    2

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  m   a   r   g   a    6    i    2    D      4    H    2    .    P    G    I   e    F   n   e    l   y    h    t    E

   8    2      4    2

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  m   a   r   g   a    7    i    2   -    D    4    H    2    .    P    G    I   e    F   n   a   p   o   r    P

   9    2      4    2

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  m   a   r   g   a    8    i    D    2      4    H      2    P  .   e    G    I   n    F    l   e   y   p   o   r    P

   0    3      4    2

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  m   a   r   g   a    9    i    2   -    D    4    H    2    .    P    G    I   e    F   n   a    t   u    B      i

   1    3      4    2

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  m   a   r   g   a    0    i    3   -    D    4    H    2    .    P    G    I   e    F   n   a    t   u    B     n

   2    3      4    2

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  m   a   r   g   a    1    i    D    3      4    H      2    P  .    G    I   e    F   n   a    t   n   e    P      i

   3    3      4    2

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  m   a   r   g   a    2    i    D    3      4    H      2    P  .   e    G    I   n    F    t   a   n   e    P     n

   4    3      4    2

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  m   a   r   g   a    3    i    3   -    D    4    H    2    .    P    G    I   n    F   e   g   y   x    O

   5    3      4    2

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FIG. 24-34 Thermodynamic Properties of Water

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  r   e    t   a    W    f   o   s   e    i    t    5   r   e    3   -   p    4   o   r    2    P  .   c    G    I    i    F   m   a   n   y    d   o   m   r   e    h    T

   7    3      4    2

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  e   r   u   s   s   e   r    P   n   o    i    t   a   r   u    6   t    3   -   a    4   S    2   t  .   a    G    I   s   e    F   i    t   r   e   p   o   r    P   r   e    t   a    W

   8    3      4    2

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FIG. 24-37 Saturated Steam: S team: Temperature Ta Table ble Temp., °F

Pressure, psia

32.018 35

Enthalpy, Btu/lb

Entropy, Btu/(lb °F) L iqui d Vapor

L iqui d

Vapor

L iqui d

Vapor

0.08865 0.09991

0.016022 0.016020

3302.4 2948.1

0.000 3.002

1075.5 1076.8

0.0000 0.0061

2.1872 2.1767

40 45 50

0.12163 0.14744 0.17796

0.016019 0.016020 0.016023

2445.8 2037.8 1704.8

8.027 13.044 18.054

1079.0 1081.2 1083.4

0.0162 0.0262 0.0361

2.1594 2.1426 2.1262

55 60 65 70 75

0.21392 0.25611 0.30545 0.36292 0.42964

0.016027 0.016033 0.016041 0.016050 0.016060

1432.0 1207.6 1022.1 868.4 740.3

23.059 28.060 33.057 38.052 43.045

1085.6 1087.7 1089.9 1092.1 1094.3

0.0458 0.0555 0.0651 0.0745 0.0839

2.1102 2.0946 2.0794 2.0645 2.0500

80 85 90 95 100

0.50683 0.59583 0.69813 0.81534 0.94294

0.016072 0.016085 0.016099 0.016114 0.016130

633.3 543.6 468.1 404.4 350.4

48.037 53.027 58.018 63.008 67.999

1096.4 1098.6 1100.8 1102.9 1105.1

0.0932 0.1024 0.1115 0.1206 0.1295

2.0359 2.0221 2.0086 1.9954 1.9825

110 120 130 140 150

1.2750 1.6927 2.2230 2.8892 3.7184

0.016165 0.016204 0.016247 0.016293 0.016343

265.39 203.26 157.33 122.98 97.07

77.98 87.97 97.96 123.00 117.95

1109.3 1113.6 1117.8 1122.0 1126.1

0.1472 0.1646 0.1817 0.1985 0.2150

1.9577 1.9339 1.9112 1.8895 1.8686

160 170 180

4.7414 5.9926 7.5110

0.016395 0.016451 0.016510

77.27 62.08 50.225

127.96 137.97 148.00

1130.2 1134.2 1138.2

0.2313 0.2473 0.2631

1.8487 1.8295 1.8111

1 29 00 0

191..354206

0..0 01 16 66 53 77 2 0

43 0..6 93 59 7 3

16 58 1 8..0 04 9

1 11 14 42 6..1 0

0 0..2 27 98 47 0

1 1..7 79 73 64 4

210 212 220 230 240

14.123 14.696 17.186 20.779 24.968

0.016705 0.016719 0.016775 0.016849 0.016926

27.816 26.799 23.148 19.381 16.321

178.15 180.17 188.23 198.33 208.45

1149.7 1150.5 1153.4 1157.1 1160.6

0.3091 0.3121 0.3241 0.3388 0.3533

1.7600 1.7568 1.7442 1.7290 1.7142

250 260 270 280 290

29.825 35.427 41.856 49.200 57.550

0.017066 0.017089 0.017175 0.017264 0.01736

13.819 11.762 10.060 8.644 7.4603

218.59 228.76 238.95 249.17 259.4

1164.0 1167.4 1170.6 1173.8 1167.8

0.3677 0.3819 0.3960 0.4098 0.4236

1.7000 1.6862 1.6729 1.6599 1.6473

300 320 340 360 380

67.005 89.643 117.992 153.01 195.73

0.01745 0.01766 0.01787 0.01811 0.01836

6.4658 4.9138 3.7878 2.9573 2.3353

269.7 290.4 311.3 332.3 353.6

1179.7 1185.2 1190.1 1194.4 1198.0

0.4372 0.4640 0.4902 0.5161 0.5416

1.6351 1.6116 1.5892 1.5678 1.5473

400 420 440 460 480

247.26 308.78 381.54 466.87 566.15

0.01864 0.01894 0.01926 0.01961 0.02000

1.8630 1.4997 1.2169 0.99424 0.81717

375.1 396.9 419.0 441.5 464.5

1201.0 1203.1 1204.4 1204.8 1204.1

0.5667 0.5915 0.6161 0.6405 0.6648

1.5274 1.5080 1.4890 1.4704 1.4518

500 520 540 560 580

680.86 812.53 962.79 1133.38 1326.17

0.02043 0.02091 0.02146 0.02207 0.02279

0. 67492 0.55956 0.46513 0.38714 0.32216

487.9 512.0 536.8 562.4 589.1

1202.2 1199.0 1194.3 1187.7 1179.0

0.6890 0.7133 0.7378 0.7625 0.7876

1.4333 1.4146 1.3954 1.3757 1.3550

0.02364 0.02466 0.02595 0.02768 0.03037

0.26747 0.22081 0.18021 0.14431 0.11117

617.1 646.9 679.1 714.9 758.5

1167.7 1153.2 1133.7 1107.0 1068.5

0.8134 0.8403 0.8686 0.8995 0.9365

1.3330 1.3092 1.2821 1.2498 1.2086

0.03662 0.03824 0.04108 0.05078

0.07519 0.06997 0.06300 0.05078

825.2 835.0 854.2 906.0

991.7 979.7 956.2 906.0

0.9924 1.0006 1.0169 1.0612

1.1359 1.1210 1.1046 1.0612

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Volume cu ft/lb

700 702 704 705.47

3094.3 3135.5 3177.2 3208.2

Marketing  Data in the steam tables abstracted abstracted by permission permission from "Thermodynamic "Thermodynamic Properties of Steam Steam"" by J.H. Keenan and F.G. Keyes, published by John W Wiley iley & Personalization Sons, Inc. 1936

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FIG. 24-37 (Cont’d) Saturated Steam: Pressure Table Volume, cu ft/lb

Enthalpy, Btu/lb

Entropy, Btu/(lb °F) L iquid Vapor

Pressure, psia

Temp., °F

L iquid

Vapor

L iquid

Vapor

0.10 0.20

35.02 53.16

0.016020 0.016025

2945.5 1526.3

3.03 21.22

1076.8 1084.7

0.0061 0.0422

2.1766 2.1060

0.30 0.40 0.60

64.48 72.87 85.22

0.016040 0.016056 0.016085

1039.7 792.1 540.1

32.54 40.92 53.25

1089.7 1093.3 1098.7

0.0641 0.0799 0.1028

2.0809 2.0562 2.0215

0.80 1.0 2.0 3.0 4.0

94.38 101.74 126.07 141.47 152.96

0.016112 0.016136 0.016230 0.016300 0.016358

411.69 333.60 173.76 118.73 90.64

62.39 69.73 94.03 109.42 120.92

1102.6 1105.8 1116.2 1122.6 1127.3

0.1195 0.1326 0.1750 0.2009 0.2199

1.9970 1.9781 1.9200 1.8864 1.5626

6 8 10 20 30

170.05 182.80 193.21 227.96 250.34

0.016451 0.016527 0.016592 0.016834 0.017009

61.984 47.345 38.420 20.087 13.744

138.03 150.87 161.26 196.27 218.9

1134.2 1139.3 1143.3 1156.3 1164.1

0.2174 0.2676 0.2836 0.3358 0.3682

1.8294 1.8060 1.7879 1.7320 1.6995

40 50 60 70 80

267.25 281.02 292.71 302.93 312.04

0.017151 0.017274 0.017383 0.017482 0.017573

10.4965 8.5140 7.1736 6.2050 5.4711

236.1 250.2 262.2 272.7 282.1

1169.8 1174.1 1177.6 1180.6 1183.1

0.3921 0.4112 0.4273 0.4411 0.4534

1.6765 1.6586 1.6440 1.6316 1.6208

90 100 150 200

320.28 327.82 358.43 381.80

0.017659 0.017740 0.01809 0.01839

4.8953 4.4310 3.0139 2.2873

290.7 298.5 330.6 355.5

1185.3 1187.2 1194.1 1198.3

0.4643 0.4743 0.5141 0.5438

1.6113 1.6027 1.5695 1.5454

250 300 350 400 450 500

400.97 417.35 431.73 444.60 456.28 467.01

0.01865 0.01889 0.01912 0.01934 0.01954 0.01975

1.84317 1.54274 1.32554 1.16095 1.03179 0.92762

376.1 394.0 409.8 424.2 437.3 449.5

1201.1 1202.9 1204.0 1204.6 1204.8 1204.7

0.5679 0.5882 0.6059 0.6217 0.6360 0.6490

1.5264 1.5105 1.4968 1.4847 1.4738 1.4639

600 700 800 900 1000

486.20 503.08 518.21 531.95 544.58

0.02013 0.02050 0.02087 0.02123 0.02159

0.76975 0.65556 0.56896 0.50091 0.44596

471.7 491.6 509.8 526.7 542.6

1203.7 1201.8 1199.4 1196.4 1192.9

0.6723 0.6928 0.7111 0.7279 0.7434

1.4461 1.4304 1.4163 1.4032 1.3910

1200 1400 1600 1800 2000

567.19 587.07 604.87 621.02 635.80

0.02232 0.02307 0.02387 0.02472 0.02565

0.36245 0.30178 0.25545 0.21861 0.18831

571.9 598.8 624.2 648.5 672.1

1184.8 1175.8 1164.5 1152.3 1138.3

0.7714 0.7966 0.8199 0.8417 0.8625

1.3683 1.3474 1.3274 1.3079 1.2881

2200 2400 2600 2800 3000

649.45 662.11 673.91 684.96 695.33

0.02669 0.02790 0.02938 0.03134 0.03428

0.16272 0.14076 0.12110 0.10305 0.08500

695.5 719.0 744.5 770.7 801.8

1122.2 1103.7 1082.0 1055.5 1020.3

0.8828 0.9031 0.9247 0.9468 0.9728

1.2676 1.2460 1.2225 1.1958 1.1619

3100 3200 3208.2

700.28 705.08 705.47

0.03681 0.04472 0.05078

0.07452 0.05663 0.05078

824.0 875.5 906.0

993.3 931.6 906.0

0.9914 1.0351 1.0612

1.1373 1.0832 1.0612

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FIG. 24-38 Properties of Superheated Steam bs. Press.,  A bs. P, psia (Sat. Temp.)

Temperature, °F 200

300

400

500

600

700

800

900

1000

1100

1200

1400

1600

v... h...

392.6 1150.4

452.3 1195.8

512.0 1241.7

571.6 1288.3

631.2 1335.7

690.8 1383.8

750.4 1432.8

809.9 1482.7

869.5 1533.5

929.1 1585.2

988.7 1637.7

1107.8 1745.7

1227.0 1857.5

s... v... h... s...

2.0512 78.16 1148.8 1.8718

2.1153 90.25 1195.0 1.9370

2.1720 102.26 1241.2 1.9942

2.2233 114.22 1288.0 2.0456

2.2702 126.16 1335.4 2.0927

2.3137 138.10 1383.6 2.1361

2.3542 150.03 1432.7 2.1767

2.3923 161.95 1482.6 2.2148

2.4283 173.87 1533.4 2.2509

2.4625 185.79 1585.1 2.2851

2.4952 197.71 1637.7 2.3178

2.5566 221.6 1745.7 2.3792

2.6137 245.4 1857.4 2.4363

10 (193.21)

v... h... s...

38.85 1146.6 1.7927

45.00 1193.9 1.8595

51.04 1240.6 1.9172

57.05 1287.5 1.9689

63.03 1335.1 2.0160

69.01 1383.4 2.0596

74.98 1432.5 2.1002

80.95 1482.4 2.1383

86.92 1533.2 2.1744

92.88 1585.0 2.2086

98.84 1637.6 2.2413

110.77 1745.6 2.3028

122.69 1857.3 2.3598

14.696 (212.00)

v... h... s...

.... .... ....

30.53 1192.8 1.8160

34.68 1239.9 1.8743

38.78 1287.1 1.9261

42.86 1334.8 1.9734

46.94 1383.2 2.0170

51.00 1432.3 2.0576

55.07 1482.3 2.0958

59.13 1533.1 2.1319

63.19 1584.8 2.1662

67.25 1637.5 2.1989

75.37 1745.5 2.2603

83.48 1857.3 2.3174

20 (227.96)

v... h... s...

.... .... ....

22.36 1191.6 1.7808

25.43 1239.2 1.8396

28.46 1286.6 1.8918

31.47 1334.4 1.9392

34.47 1382.9 1.9829

37.46 1432.1 2.0235

40.45 1482.1 2.0618

43.44 1533.0 2.0978

46.42 1584.7 2.1321

49.41 1637.4 2.1648

55.37 1745.4 2.2263

61.34 1857.2 2.2834

40 (267.25)

v... h... s...

.... .... ....

11.040 1186.8 1.6994

12.628 1236.5 1.7608

14.168 1284.8 1.8140

15.688 1333.1 1.8619

17.198 1381.9 1.9058

18.702 1431.3 1.9467

20.20 1481.4 1.9850

21.70 1532.4 2.0212

23.20 1584.3 2.0555

24.69 1637.0 2.0883

27.68 1745.1 2.1498

30.66 1857.0 2.2069

60 (292.71)

v... h... s...

.... .... ....

7.259 1181.6 1.6492

8.357 1233.6 1.7135

9.403 1283.0 1.7678

10.427 1331.8 1.8162

11.441 1380.9 1.8605

12.449 1430.5 1.9015

13.452 1480.8 1.9400

14.454 1531.9 1.9762

15.453 1583.8 2.0106

16.451 1636.6 2.0434

18.446 1744.8 2.1049

20.44 1856.7 2.1621

80 (312.03)

v... h... s...

.... .... ....

.... .... ....

6.220 1230.7 1.6791

7.020 1281.1 1.7346

7.797 1330.5 1.7836

8.562 1379.9 1.8281

9.322 1429.7 1.8694

10.077 1480.1 1.9079

10.830 1531.3 1.9442

11.582 1583.4 1.9787

12.332 1636.2 2.0115

13.830 1744.5 2.0731

15.325 1856.5 2.1303

100 (327.81)

v... h... s...

.... .... ....

.... .... ....

4.937 1227.6 1.6518

5.589 1279.1 1.7085

6.218 1329.1 1.7581

6.835 1378.9 1.8029

7.446 1428.9 1.8443

8.052 1479.5 1.8829

8.656 1530.8 1.9193

9.259 1582.9 1.9538

9.860 1635.7 1.9867

11.060 1744.2 2.0484

12.258 1856.2 2.1056

120 (341.25)

v... h... s...

.... .... ....

.... .... ....

4.081 1224.4 1.6287

4.636 1277.2 1.6869

5.165 1327.7 1.7370

5.683 1377.8 1.7822

6.195 1428.1 1.8237

6.702 1478.8 1.8625

7.207 1530.2 1.8990

7.710 1582.4 1.9335

8.212 1635.3 1.9664

9.214 1743.9 2.0281

10.213 1856.0 2.0854

140 (353.02)

v... h... s...

.... .... ....

.... .... ....

3.468 1221.1 1.6087

3.954 1275.2 1.6683

4.413 1326.4 1.7190

4.861 1376.8 1.7645

5.301 1427.3 1.8063

5.738 1478.2 1.8451

6.172 1529.7 1.8817

6.604 1581.9 1.9163

7.035 1634.9 1.9493

7.895 1743.5 2.0110

8.752 1855.7 2.0683

160 (363.53)

v... h... s...

.... .... ....

.... .... ....

3.008 1217.6 1.5908

3.443 1273.1 1.6519

3.849 1325.0 1.7033

4.244 1375.7 1.7491

4.631 1426.4 1.7911

5.015 1477.5 1.8301

5.396 1529.1 1.8667

5.775 1581.4 1.9014

6.152 1634.5 1.9344

6.906 1743.2 1.9962

7.656 1855.5 2.0535

180 (373.06)

v... h... s...

.... .... ....

.... .... ....

2.649 1214.0 1.5745

3.044 1271.0 1.6373

3.411 1323.5 1.6894

3.764 1374.7 1.7355

4.110 1425.6 1.7776

4.452 1476.8 1.8167

4.792 1528.6 1.8534

5.129 1581.0 1.8882

5.466 1634.1 1.9212

6.136 1742.9 1.9831

6.804 1855.2 2.0404

200 (381.79)

v... h... s...

.... .... ....

.... .... ....

2.361 1210.3 1.5594

2.726 1268.9 1.6240

3.060 1322.1 1.6767

3.380 1373.6 1.7232

3.693 1424.8 1.7655

4.002 1476.2 1.8048

4.309 1528.0 1.8415

4.613 1580.5 1.8763

4.917 1633.7 1.9094

5.521 1742.6 1.9713

6.123 1855.0 2.0287

220 (389.86)

v... h... s...

.... .... ....

.... .... ....

2.125 1206.5 1.5453

2.465 1266.7 1.6117

2.772 1320.7 1.6652

3.066 1372.6 1.7120

3.352 1424.0 1.7545

3.634 1475.5 1.7939

3.913 1527.5 1.8308

4.191 1580.0 1.8656

4.467 1633.3 1.8987

5.017 1742.3 1.9607

5.565 1854.7 2.0181

240 (397.37)

v... h... s...

.... .... ....

.... .... ....

1.9276 1202.5 1.5319

2.247 1264.5 1.6003

2.533 1319.2 1.6546

2.804 1371.5 1.7017

3.068 1423.2 1.7444

3.327 1474.8 1.7839

3.584 1526.9 1.8209

3.839 1579.6 1.8558

4.093 1632.9 1.8889

4.597 1742.0 1.9510

5.100 1854.5 2.0084

.... .... ....

2.063 1262.3 1.5897

2.330 1317.7 1.6447

2.582 1370.4 1.6922

2.827 1422.3 1.7352

3.067 1474.2 1.7748

3.305 1526.3 1.8118

3.541 1579.1 1.8467

3.776 1632.5 1.8799

4.242 1741.7 1.9420

4.707 1854.2 1.9995

.... .... ....

1.9047 1260.0 1.5796

2.156 1316.2 1.6354

2.392 1369.4 1.6834

2.621 1421.5 1.7265

2.845 1473.5 1.7662

3.066 1525.8 1.8033

3.286 1578.6 1.8383

3.504 1632.1 1.8716

3.938 1741.4 1.9337

4.370 1854.0 1.9912

1 (101.74) 5 (162.24)

This website stores data such as v... . . .site . .... cookies to enable essential 260 h... .... .... functionality,(404.42) as wells . as . . marketing, .... .... v . .analytics. . . . . . You. . . . personalization, and 280 h... .... .... may change(411.05) your settings at any time s... .... .... or accept the default settings. v... .... .... 300 (417.33)

350 Privacy Policy (431.72)

Marketing 400 (444.59)

h... s...

.... ....

.... ....

.... .... ....

1.7675 1257.6 1.5701

2.005 1314.7 1.6268

2.227 1368.3 1.6751

2.442 1420.6 1.7184

2.652 1472.8 1.7582

2.859 1525.2 1.7954

3.065 1578.1 1.8305

3.269 1631.7 1.8638

3.674 1741.0 1.9260

4.078 1853.7 1.9835

v... h... s...

.... .... ....

.... .... ....

.... .... ....

1.4923 1251.5 1.5481

1.7036 1310.9 1.6070

1.8980 1365.5 1.6563

2.084 1418.5 1.7002

2.266 1471.1 1.7403

2.445 1523.8 1.7777

2.622 1577.0 1.8130

2.798 1630.7 1.8463

3.147 1740.3 1.9086

3.493 1853.1 1.9663

v... h... s...

.... .... ....

.... .... ....

.... .... ....

1.2851 1245.1 1.5281

1.4770 1306.9 1.5894

1.6508 1362.7 1.6398

1.8161 1416.4 1.6842

1.9767 1469.4 1.7247

2.134 1522.4 1.7623

2.290 1575.8 1.7977

2.445 1629.6 1.8311

2.751 1739.5 1.8936

3.055 1852.5 1.9513

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FIG. 24-38 (Cont’d) Properties of Superheated Steam bs. Press.,  A bs. P, psia (Sat. Temp.) v... 450 h... (456.28) s...

500

550

600

620

640

660

680

700

800

900

1000

1200

1400

1600

1.1231 1238.4 1.5095

1.2155 1272.0 1.5437

1.3005 1302.8 1.5735

1.3332 1314.6 1.5845

1.3652 1326.2 1.5951

1.3967 1337.5 1.6054

1.4278 1348.8 1.6153

1.4584 1359.9 1.6250

1.6074 1414.3 1.6699

1.7516 1467.7 1.7108

1.8928 1521.0 1.7486

2.170 1628.6 1.8177

2.443 1738.7 1.8803

2.714 1851.9 1.9381

500 (467.01)

v .. . h... s...

0.9927 1231.3 1.4919

1.0800 1266.8 1.5280

1.1591 1298.6 1.5588

1.1893 1310.7 1.5701

1.2188 1322.6 1.5810

1.2478 1334.2 1.5915

1.2763 1345.7 1.6016

1.3044 1357.0 1.6115

1.4405 1412.1 1.6571

1.5715 1466.0 1.6982

1.6996 1519.6 1.7363

1.9504 1627.6 1.8056

2.197 1737.9 1.8683

2.442 1851.3 1.9262

550 (476.94)

v... h... s...

0.8852 1223.7 1.4751

0.9686 1261.2 1.5131

1.0431 1294.3 1.5451

1.0714 1306.8 1.5568

1.0989 1318.9 1.5680

1.1259 1330.8 1.5787

1.1523 1342.5 1.5890

1.1783 1354.0 1.5991

1.3038 1409.9 1.6452

1.4241 1464.3 1.6868

1.5414 1518.2 1.7250

1.7706 1626.6 1.7946

1.9957 1737.1 1.8575

2.219 1850.6 1.9155

600 (486.21)

v... h... s...

0.7947 1215.7 1.4586

0.8753 1255.5 1.4990

0.9463 1289.9 1.5323

0.9729 1302.7 1.5443

0.9988 1315.2 1.5558

1.0241 1327.4 1.5667

1.0489 1339.3 1.5773

1.0732 1351.1 1.5875

1.1899 1407.7 1.6343

1.3013 1462.5 1.6762

1.4096 1516.7 1.7147

1.6208 1625.5 1.7846

1.8279 1736.3 1.8476

2.033 1850.0 1.9056

700 (503.10)

v... h... s...

.... .... ....

0.7277 1243.2 1.4722

0.7934 1280.6 1.5084

0.8177 1294.3 1.5212

0.8411 1307.5 1.5333

0.8639 1320.3 1.5449

0.8860 1332.8 1.5559

0.9077 1345.0 1.5665

1.0108 1403.2 1.6147

1.1082 1459.0 1.6573

1.2024 1513.9 1.6963

1.3853 1623.5 1.7666

1.5641 1734.8 1.8299

1.7405 1848.8 1.8881

800 (518.23)

v... h... s...

.... .... ....

0.6154 1229.8 1.4467

0.6779 1270.7 1.4863

0.7006 1285.4 1.5000

0.7223 1299.4 1.5129

0.7433 1312.9 1.5250

0.7635 1325.9 1.5366

0.7833 1338.6 1.5476

0.8763 1398.6 1.5972

0.9633 1455.4 1.6407

1.0470 1511.0 1.6801

1.2088 1621.4 1.7510

1.3662 1733.2 1.8146

1.5214 1847.5 1.8729

900 (531.98)

v... h... s...

.... .... ....

0.5264 1215.0 1.4216

0.5873 1260.1 1.4653

0.6089 1275.9 1.4800

0.6294 1290.9 1.4938

0.6491 1305.1 1.5066

0.6680 1318.8 1.5187

0.6863 1332.1 1.5303

0.7716 1393.9 1.5814

0.8506 1451.8 1.6257

0.9262 1508.1 1.6656

1.0714 1619.3 1.7371

1.2124 1731.6 1.8009

1.3509 1846.3 1.8595

1000 (544.61)

v... h... s...

.... .... ....

0.4533 1198.3 1.3961

0.5140 1248.8 1.4450

0.5350 1265.9 1.4610

0.5546 1281.9 1.4757

0.5733 1297.0 1.4893

0.5912 1311.4 1.5021

0.6084 1325.3 1.5141

0.6878 1389.2 1.5670

0.7604 1448.2 1.6121

0.8294 1505.1 1.6525

0.9615 1617.3 1.7245

1.0893 1730.0 1.7886

1.2146 1845.0 1.8474

1100 (556.31)

v... h... s...

.... .... ....

.... .... ....

0.4532 1236.7 1.4251

0.4738 1255.3 1.4425

0.4929 1272.4 1.4583

0.5110 1288.5 1.4728

0.5281 1303.7 1.4862

0.5445 1318.3 1.4989

0.6191 1384.3 1.5535

0.6866 1444.5 1.5995

0.7503 1502.2 1.6405

0.8716 1615.2 1.7130

0.9885 1728.4 1.7775

1.1031 1843.8 1.8363

1200 (567.22)

v... h... s...

.... .... ....

.... .... ....

0.4016 1223.5 1.4052

0.4222 1243.9 1.4243

0.4410 1262.4 1.4413

0.4586 1279.6 1.4568

0.4752 1295.7 1.4710

0.4909 1311.0 1.4843

0.5617 1379.3 1.5409

0.6250 1440.7 1.5879

0.6843 1499.2 1.6293

0.7967 1613.1 1.7025

0.9046 1726.9 1.7672

1.0101 1842.5 1.8263

1400 (587.10)

v... h... s...

.... .... ....

.... .... ....

0.3174 1193.0 1.3639

0.3390 1218.4 1.3877

0.3580 1240.4 1.4079

0.3753 1260.3 1.4258

0.3912 1278.5 1.4419

0.4062 1295.5 1.4567

0.4714 1369.1 1.5177

0.5281 1433.1 1.5666

0.5805 1493.2 1.6093

0.6789 1608.9 1.6836

0.7727 1723.7 1.7489

0.8640 1840.0 1.8083

1600 (604.90)

v... h... s...

.... .... ....

.... .... ....

.... .... ....

0.2733 1187.8 1.3489

0.2936 1215.2 1.3741

0.3112 1238.7 1.3952

0.3271 1259.6 1.4137

0.3417 1278.7 1.4303

0.4034 1358.4 1.4964

0.4553 1425.3 1.5476

0.5027 1487.0 1.5914

0.5906 1604.6 1.6669

0.6738 1720.5 1.7328

0.7545 1837.5 1.7926

1800 (621.03)

v... h... s...

.... .... ....

.... .... ....

.... .... ....

.... .... ....

0.2407 1185.1 1.3377

0.2597 1214.0 1.3638

0.2760 1238.5 1.3855

0.2907 1260.3 1.4044

0.3502 1347.2 1.4765

0.3986 1417.4 1.5301

0.4421 1480.8 1.5752

0.5218 1600.4 1.6520

0.5968 1717.3 1.7185

0.6693 1835.0 1.7786

2000 (635.82)

v... h... s...

.... .... ....

.... .... ....

.... .... ....

.... .... ....

0.1936 1145.6 1.2945

0.2161 1184.9 1.3300

0.2337 1214.8 1.3564

0.2489 1240.0 1.3783

0.3074 1335.5 1.4576

0.3532 1409.2 1.5139

0.3935 1474.5 1.5603

0.4668 1596.1 1.6384

0.5352 1714.1 1.7055

0.6011 1832.5 1.7660

2500 (668.13)

v... h... s...

.... .... ....

.... .... ....

.... .... ....

.... .... ....

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.... .... ....

0.1484 1132.3 1.2687

0.1686 1176.8 1.3073

0.2294 1303.6 1.4127

0.2710 1387.8 1.4772

0.3061 1458.4 1.5273

0.3678 1585.3 1.6088

0.4244 1706.1 1.6775

0.4784 1826.2 1.7389

3000 (695.36)

v... h... s...

.... .... ....

.... .... ....

.... .... ....

.... .... ....

.... .... ....

.... .... ....

.... .... ....

0.0984 1060.7 1.1966

0.1760 1267.2 1.3690

0.2159 1365.0 1.4439

0.2476 1441.8 1.4984

0.3018 1574.3 1.5837

0.3505 1698.0 1.6540

0.3966 1819.9 1.7163

.... .... ....

.... .... ....

.... .... ....

.... .... ....

.... .... ....

0.1583 1250.5 1.3508

0.1981 1355.2 1.4309

0.2288 1434.7 1.4874

0.2806 1569.8 1.5742

0.3267 1694.6 1.6452

0.3703 1817.2 1.7080

.... .... ....

.... .... ....

.... .... ....

.... .... ....

0.0306 780.5 0.9515

0.1364 1224.9 1.3241

0.1762 1340.7 1.4127

0.2058 1424.5 1.4723

0.2546 1563.3 1.5615

0.2977 1689.8 1.6336

0.3381 1813.6 1.6968

.... .... ....

.... .... ....

.... .... ....

0.0287 763.8 0.9347

0.1052 1174.8 1.2757

0.1462 1314.4 1.3827

0.1743 1406.8 1.4482

0.2192 1552.1 1.5417

0.2581 1681.7 1.6154

0.2943 1807.2 1.6795

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