yk rao_part 1

8/2/2019 YK Rao_Part 1

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Stoichiometry andthermodynamics of_metallurgical processes

-Y. K.RAOProjessoro] MeJa((urgicol Engin . - li"J"~HI I ! oo : .J , ., . . ,~!..-J~',:r~I~";.''''...:.Jlr

CAMBRI DG E UN IVERS ITY PRESSCambridgeLondoo New York New RochelleMelbourne Sydney


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CONTFNTS

Preface

Chapter I . In troduct ion1.1 Definitions1.2 Measurement of quanti ties: unit s and d imensions1.3 Gram-mole, kilogr am-mole , pound-mo le, and gram-atom1.4 Composition1.5 Behavior of gases and vapors1.6 Gaseous mixtures

Worked .examplesProblems. References

Chapt er 2. Sto ichi omet ry: material balance s in metal lurgical processes2.1 Stoichiometry2.2 Law of conservation of mass2.3 Method of calcu la tion2.4 Blast-furnace charge-balance calculations2.5 Materi a! balan ces in copper smeltin g and converting2.6 Continuous coppe r-sme ll ing process es2.7 Unsteady-stat e operat ion s: th e basic oxygen pro cess

Worked examples ,ProblemsReferences

Chap ter 3. First law of thermodynamics3.1 . Work3.2333.43.5363.73 1 ' .3.9

HeatFirst law of thermodynamicsHeal and work changes in reversible processesHeal capacityCalculat ion o f e nthal py chang esRevers ib le adiabat ic processEnergy balances in simple systemsEnergy balances in complex systemsWorked examplesProblemsReferences

vu

page xiii

466S1317) 9

201021222426272730525 . : 1

55555757606 36 8717373768487


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Vlll

Chapter 4 . Fuels and combus ti on4 J Energy resources4 .2 C o~1 resources-1 3 C las sifica tio n of coal4 .4 Iv \et allu rg lca l coke4.5 Gaseous fuels46 Gasif icat ion or" sol .d fue l>4.7 L iquid fuels..).8 C om bu stion

Worked examplesProblemsReferences

Chapter 5. Energy balances5.1 Appii ca ti on of energy balances5.2 TIT in a blast furnace53 Roast ing of copper sul fide concentrates5.4 Fluid-bed roasung of zinc concentrates5.5 Heal balance In a n iro n blast furnace5.6 Energy consumption in metallurgical processes

Worked examplesProblemsReferences

Chapter 6. Second law of thermodynamics6.] Introduction6.2 Statement of the second law63 Effic iency of 3 heal engmt6.4 The Carner cycle6.56.66. 76.86. 96.106.116.]26.136.146156.16617

Some consequences of the second lawThe concept of entropyEnt ropy changes i n typic al revers ible proce ssesEntropy changes In some ir rever si bl e processesEntropy change of the universe in a reversible processEntropy change of the universe in an irrevers.ble processThe Clausius inequal ityCombined statement of first and second lawsSome useful thermodynamic relat ionshipsDifference between h ea r c ap ac i. ie s CI' and C vEntropy of an Ideal gasAbsolute value of the entropy of a substanceEntropy change f o r i r reve rs i b le chemical reactionsProblemsReferences

Chapter 7. AUXil iary funct ions7.] The Helmholtz free energ\' and the GIbbs free energy7.2 Free-energy equal ions in differential form

Contents888 88 89 6

] 0 211 1]1313 113 314717718 218 518518 518518 6]8618 7] 8 82052072082082082092 0 921 32162] 82 1 922]22222622722823 223 323 6238239 I.'242

, I243243244

____ .. _ _ _Coruents7_37A

Free-energy changes for an ideal gasThermodynamic potentialsThe Maxwell relat ionsCriteria of equilibriumCriteria of spontaneity (or irreversibility).The Gibbs-Helmhol tz equat ionThe Gibbs f ree-energy changes In typical reversible processesThe Gibbs free-energy changes in typical Irreversible processesThe thi rd l aw of thermodynamicsEvalua ti on of abso lu te en tropyProblemsReferences

r .7_67.87.97_107_117_12

Chapter 8. Theory of solutions I8_1 The Gibbs free energy (If an ideal gas8.2 Mixtures of idea l gases8_3 The fugacity function8_ 4 Evalua tion o f the fugacity o r a real gas8.5 Mixtures of real gases8_6 Fugacities of condensed substances8.7 Definition of activity8-8 Partial molar quant it ies8.9 The partial molar Gibbs free energy8.10 Other partial molar quantities 8.1 I Par tia l molar quanti ties of idea l-gas mix tures8.12 Integral molar quant it ies8.13 Method of determining partia l molar quantities from integral

molar quantities8.14 Integra tion of the Gibbs-Duhem equation8.15 Relative partial molar quantities8.16 Relative integral molar quantities .

Tempe ra ture dependence of act ivi tyRaoults law and idea l sbl uti ons

8.178_188.19 Dilute solut ions and Henry 's law

Determination of activity by integration of the Gibbs-Duhem equat ionDetermination of H'l' and HM from data on HrDeviations from the ideal: excess thermodynamic quantitiesRegular solutionsProblemsReferences

8.2]lOU2iU3

Chapter 9. The Gibbs free-energy change and the equilibrium constant9_] Introduction9'_2939-49_ 5

Equil ibrium constantEquilibrium constant fo r an all-gas rea ction: ideal ga sesEquilibrium constant for an all-gas reaction: real gasesLe Chatc lie rs princLple

, _IX24524624 824 825025225 425 525626226 32652 6 726 726827]2 7 22752772 7 82 8 028228328428528528828928929 22 9 429729 9

30430 730 831431 932 132 132232433033 2


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x9.6 Heterogeneous reacuons9.7 Temperature dependence of t.co and K9.8 free-energy equation for formation of MgO9.9 Sources of thermodynamic data9.10 Simpli fied th ree-term and two-term free-energy equ atio ns9.11 Free energy of formation for inorganic substances9.1~ Free-energy charts and Ellingham diagrams9 .1 3 E xp erim en ta l methods for determining LlG T f or r eact ions . a t

high temperatures9 . 1 4 Systematic thermodynamic treatment of experimental data on Kand . : : . G - ' j -9.lS Electrochemical systems916 Highre rnperature gahanic cells9.17 Electrolysis9.18 Dilute solutions of gases in condensed phases9.19 Alternative standard states9.20 Activity data from experimental measurements9.21 Interaction coefficients in rnuhicomponent systems

ProblemsReferences

Chapter 10 . Phase equilibria10.1 Definition of terms102 Phase equilibria and equality of chemical potentials in all phases1 0 ..3 N o ne q ui li br ium systems and phase stabi lit y10.4 The phase ru le for nonreactiv e component s10.5 The phase rule fo r reactive components10.6 Phase changes in sin gle-compone nt systems10.7 Effects of pressure on the Gibbs free energy and activity of a pure

condensed phase10.8 The Gibbs free-energy change accompanying vaporization of

a condensed phase10.9 Temperature dependence of LlGo for phase transformations10.10 Experiment al dat a on v apor pressures: sy st emat ic t reatment10.11 Phase equilibria and chemica l equ il ib ri a10.12 P- T - x equili bria invo lvi ng condensed ph ases10 .13 Frec-en ergy+cornpos.u on cu rves and equi librium phase d iagrams]0. [4 Examples of construction of binary phase diagrams10 15 Thermodynamic data from phase diagramslU.16 The iron-carbon system10. J 7 Systems with intermediate compounds of v ar ia bl e c om p os it io n10.18 Met al- oxygen syst ems wi: h intermediate compounds o f variabl e

composition]0.19 The iron-oxygen sys.crn10 .20 Thermodynamic quanti ties for homogeneous met al~gas sol utio ns10.21 The uranium+carhon svstern ..10.22 Further comments on phase equilibria in oxide systems10.~3 Met al- su lfu r-oxygen systcrns: st abil ity di agrams

Contents C0l11enlS33 834234 5360363366371

10.2410..2510.2610.27] ( 1 . 2 H

The lead - sulfur - oxygen systemThe coppcr-sulfur-oxygen systemThe COppCT- hydrogen +chlcr inc systemIsot hermal-stabil ity diag ram for the Cu - H - CI- 0 systemEqui l ibr ium and sroichiorncrric calcu la tions in chloride svst emsProhlemsReferences

388 Chapter I I. Equilibria in complex systems11.1 Heterogeneous reaction systems .11.2 Conventio nal methods in equ ili bri um calcu lati ons11.3 Stoichiometry of chemical reactions11 .4 Analysis o f typi cal meta llurgical syst ems11.5 Complex equilibria: modern methods ..11 . 6 Computation of complex equilibria on a high-speed digital

computer by t he i terat ive method11.7 Complex equilibria in crystal growth systems: iterative method11.8 Vapor ization equil ibria11.9 Convergence aids11.10 free-en ergy-minimi zation method11.11 Ad iabat ic syst ems

ProblemsAppendixReferences

39 040141742 843443 84444674785035085085U 9510511516520

Chapter 12 . Theory of solutions II .:12.1 Composition dependence of activities in binary solutions12.2 Statistical thermodynamics of solutions12.3 Mixtures of fused salts12.4 Reuular-solution model for fused-salt mixtures12.5 Ap;lication of the Gibbs-Duhem equation to complex systems12.6 Chemical-species m~dels applied to associated solutions12.7 Thermodvnarrncs and consmuuon of slag systems12.8 Flood-GrJotheim treatment of ionic melts

ProblemsAppendixReferences

52 853053454 255256256857758258~601

Appendix A: Units and conve rs ion tab le sAppendix B. Program FUELGASAppendix C: Thermochemical clawAppend ix D: Vapor-p ressure equat ionsAppendix E: Mal .r ices and vec to rs04bOt)

61n6i962()6 26

Answers IIIproblemsNomcnclai UT


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PREFACE

This text book is wnt ten primar ily for s tudents in metallurgy and in al lied f ieldssuch as mater ia ls science, physical chemist ry, chemica l engineering, and fueitechnology. The intent isto introduce the student early on tothe fundamentals ofthe physical chemistry and the thermodynamics of metallurgical processes andthen gradually expand the treatment into progressively more advanced areas.At one t ime. instruc tion in extrac tive (process Or chemical) metallurgy con-

sis ted sole ly of studying process descript ions and opera tional de tai ls . At a fewplaces this approach may sti ll be in vogue , but for the most par t, a much sounderapproach has taken root, with emphasis on quantitative analysis of metallurgicalprocesses. At the minimum, this latter approach should prov ide instruc tionIn topics such as stoichiometric principles, material balances of metallurgicalreactors, the laws of thermodynamics, energy consumption inmetallurgical pro-cesses, chemical equilibrium, phase equilibrium, heterogeneous systems. andsolution theory. Such a wide range of topics obviously cannot be covered in asingle course, unless one compromises the quality of instruction severely.This text provides a comprehensive t rea tment of these and a var iety of othertopics. The material presented here has formed the basis of three sequential

courses offered by the author fOT some years at the University ofWashington andat Columbia University. The suggested course organization is as follows:Stoichiometry: material and energy balances: Chapters I through 5lntroduction to thermodynamics: Chapters 3,6,7,8,9 (Sections 9.1-9.7, 9.9,

9.12, and 9.15), and )0 (Se~tions 10.1, 10.2, lOA, 10.6, 10.7, and 10.23)Advanced thermodynamics: Chapters 9 (Sections 9.8-9.11, 9.13, 9.14. and

9.16-9.21). 10 (Sections 10.3, 10.5, 10.8-10.22, and 10.24-10.28). 11. and12

The first 'twocourses are to be offered at the undergraduate (junior-senior) level,and the final course, which draws heavily from the last three chapters, best f its thegrcduare curriculum.Each chapter coruains a substantial number of illustrative examples. the pur-

poses of which are to demonstrate the application ofthe theoretical principles andto provide further elaboration of the text. In Chapters I-5, the examples havebeen separa ted from the main body of the text and grouped together at the end ofeach chapter. This is because most of these examples are unusually long andwould tend to in terrupt the f low of the theore tica l discussion. In the remain ingchapters . the examples blend well wi th the textua l material.XIII


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XI V Preface Preface XV

Group l : Simple examples and problems that relate to idealized conditions andprocesses. O ften these involve on ly strai ghtforward applicati on of the formu-la s gi ven in t he text

Group 11 :Project-type examples and p rob lems that require in-depth analysis andmay draw on materi al from several chapters.

publ ication s, have profoundl y alt ered and en riched t he l andscape of metal lurgicalthermodynamics ..Many influences h ave helped to mold my vi ews and understanding o f thermo-

dynamics. I am pl eased 1


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IINTRODUCTION

1.1 DefinitionsA system is a port ion of the universe that we have chosen for st udy. The remainderof the universe is called the surroundings.A closed system is e nclosed by an impermeable boundary or wall thai does not

permit the transfer of mailer but allows transfer of energy. The mass of a closedsystem rema ins constan t.An open system is bounded by permeable walls that allow the transfer of both

matter and energy across the walls.An isolated system IS a system enclosed by impermeable walls that permit

neither exchange o f e nergy nor transfer of matter. Such wal ls a rc termed adiabaticwalls.A homogeneous sy stem is made up of a single phase; a heterogeneous sys tem

consists of two or more phases.A reactor is t he physi cal app aratus in which chemical reacti ons take place. The

reaction mixture is t he entire material with in the reactor. It consists o f reactant andproduct species, and in some instances it may include catalytic substances or inertspecies.The state of a sys tem is defined by speci fy ing SIGle variables or s t at e p r op e rt i es ,

namely, temperature, T, pressure, P, volume, V, and composi tion . When dea lingwith heterogeneous systems it is necessary to specify additional parameterssuch as the particle size distribution or the surface area of the particulatematter.

1.2 Measurement of quantities: units and dimensionsSeveral different kinds of units have been in use for measuring mass, length.volume, pressure. and temperature in a system. Some of the most commonly usedsets of uni ts are listed in Table 1- J The factors used for converting from one sciof units to another arc provided in Table 1- 2 and in Appendix A. The units ofmass. length. and volume require no fu rther d iscussion.

Pressure measurementPressure IS defined 3S force per u nit a re a. It may he expressed in pascal, (P:I).millimeters of mercury (rnrn Hg = Torr). feet of water. pounds of force persquare inch (Ibf/in.~). o r standnrd arrncsphcres. The pressure measured maybe obsolute or relativc. Measurement ag~inst a perfect vacuum yields absoluu:pressure, Gl1f1gepressure, on the other hand, is a relative quantity obtuincd whenthe measurement has been made against aunosphcric pressure. Thus,


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-2Table 1-J Mas! com mall uni ts

A b so lu te u nitsQuantity 51 MKS CGS FPSLength m m em flTime sec sec secMass k o kg g Ihe-Moles mol kgmolc gmole lh-rnolcTernperat.ure K K(ol K) "C OFVolume liter m'(orclIm) ml (or em') fl'Forc~ newt on (N) N dyne poundalPressure pascal (Pa) Nlm: dyne/crrr' ooundal/tt?Energy Joule (J) J erg ftpounda:

--1 IntroductionE ng in ee ri ng u ni tsEnglish Americanf l f lsec secslug Ibmlbmole lb-rnoleOF offr' ft'lb wt. Ib,Ib,tfr' Ib,/ft2B I U B l u . h p - h r

Multiple-unit prefixes:nano (n) = IO-~micro ( JL ) = 10-"milli. (rn) = 10)

centi (e ) = 111'kilo (k ) = IO J

mq:" (M ) = 10"

absolute pressure =gauge pressure + atmospheric pressure (1-1)Atmospheric pressure is the pressure 01 air that is around us; this pressure,although it changes from one day to the next, does not deviate great ly from 760mm Hg (or Torr). The unit standard atmosphere or simply atmosphere, unlikeatmospheric pressure. is a fixed quantity; il is defined as the pressure exerted,under standard gravi tational condi tions, by a column of mercury 760 mm high at atemperature of DoC. This ma y be expressed in various units, as follows:1.000 atmosphere (atrn) = J01,325 pascals (Pa)

760.000 millimeters of mercury (mm Hg, or Torr)29.921 inches of mercury (in Hg)33.910 feet of water (f: H20)14.696 pounds per square inch (lbr/in.2}The most ccrnrnonly used engineering units for pressure are pounds per squareinch (psi) and inches of mercury (In. Hg]. Absolute pressure IS abbreviated as"psia (pounds per square inch absolute). Gauge pressure is abbreviated as"psig" (pounds per square inch gauge).Temperature measurementThe temperature of a system can be measu red eit her i n deg rees centigrade (alsoknown as Celsius'; Of III degrees Fahrenheu, The most common scientific scale isthe ccnr igr adc sca le. 111 which ( J o e is t he ice point of water and 1o o o e i s the normalboiling point of Willer. In daily life. and In some engineering applications, theFahrenheit scale is preferred. lr this scale. 32F represents the icc point and 212Fdenotes the normal bolling POIl)1 ulwctcr The Kelvin (or absolllr~) and Rimkinesca les are rel ated to these as fol luws:

- ------1.2 Measurement of quantities 3Length

Table 1 -2. Conversion [actors and units

Volume

TimeMass

Force

Pressure

Ternper aturc

Energy

Power

1 m = 3.2R08 1" 1 = 3'1.37 in1 ern = 111-' m = D.3 I Irnrn = I no "' mmicron l~) = 1 micrometer 1 ~ f 1 1 1 = IW'" rn3ngSlrom (.A) = ]0-'" mIller = i O O O em'

J cubic meter (rn') = 35 . .3 J 5 f1'I gal (u.S.) = 231 in) .I gal (U.K.) = 277.42 in.) = 4546 liters = IUI04546 rn1 nr = 60 min = 36()!l sec1 kg = ](~)()g = 2.2046 pounds ma~5 (Ihn) = 6.852l x ]0- slugs1 Ihm = 16 ounce, (oz) = (J.4535Y237 kg = 7()()()grams (Troy)I 1011 = 224() Ib", = 10]6 kgI m etric IO n = 1000 kg = nO.:).6 lb.,I short Ion = 2000 Ib m = 907.2 kgI newton [N) = 1 k g-m/sec ' = 10:\ dynesI dvne = I g {'m/scc~blogram force (kg .] = 980665 Npound force (Ib r) =4 .44~ x 10" dynes = 4 .44~ N

I poundal = 13.826 dynes = 0.13826 NI pasca I ( P O l ) = I N/m2 = !O dynes/em'I aim = 14.696 Ib,/in.~ = 760 Tor r = 1 ,( 11 32 5 x lU" dynes/em'Illill H~ = I Tor r = 0.01934 Ibr/in.' = 1,33322 X 10' dvncs/cm 'bar = 1 0 " dynes/em' =JO' Pa = O.9S692 aim

I Ib,i in. ' = 61i.941> dynes/em' = 7 ln. I kg,lm'I rmcron (IL) = HI-" rn Hg = 10-\ mill Hg = 0. 13 33 22 PaT degrees Kelvin = Idegrees ccnt igrade + 273 15, degrees Fahrenheit =1.8/ degrees centigrade +32T degree, Rankine = f degrees Fahrenhen + 459.67I Joule {Jl = 1 kg'm'/sec' = Ill' gcm'lscc' = 10' ergsI cal (thermochemical) = 4.184 JI cal ( ;nlCr ~" li on, Ji st eam rabl c ) = 4.1868 JI B tu = 7 7K [ \' 11 0 , = 105435 J = 2 52 ( ,I II kca l (thcr rnochc mical ) = I(lO() (ill = 3 .96~ BtuI e l ec t ron "011 leV) = 1~61122 X 10""! JI ""III (W) = I kgm~/scC"' = I Jisec1 ho rs epower (h p) = 'i~O fllhrlsec = 74fl Wk il uwat t (kW) = ]()Oll \V = }414 Bru/hr

T (OK ) ICC) 7 ::m.I:'i(DK) (1-2)nOR) I(F) + 45Y.67(DR) (1-3)

I ( O F ) I.X r (DC ) + .1 2 (1-4)TI"K) T(OR);IX ( 1-5)


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4 1 Introduction

GOIC mett sSilver melts

K C,'::;r ~0662- . 10' 130 4.525 2.2:2255 118.fj4 )574 x 10' 140' 5881 2.8H:-;60 149.3& 1.992 X 10' ISO 7.569 3.71765 In.54 2.500 " 10 160 '9.652 4.74170 :m.70 3.116 " 10' 170 12.199 5 .91 )275 2R9. IO 3.854 X 10' 18 0 15.291 7.51180 355.10 4 .734 " 10' 190 19.0)4 1 ) .33985 433.60 5.781 >- . 10' 200 23.467 11.52690 525.76 7.010 >- . 10' 212 29.922 14.6%95 633.90 8.451 ).. IU' 220 3 4. Y 9 2 17.11;6100 760.00 1.013 x I()' 230 42.3liR 2[1779lOS 90607 1 .2 08 )- . 10' 240 50.837 24.\l6~110 J074.56 1.433 " 10' 250 61l.725 29.825115 1267.9S 1.691 ) 10' 261l 72.134 35.42~120 1489.14 1.985 x 10' 270 85.225 41.85R125 1740.93 2.321 " 10' 21:\0 lOll 18 49.20J130 2026.16 2.701 >- . 10' 29() 117.19 57.557135 2347.26 3.129 ,. Ill' 30 0 136.44 67f112Sources. Data from AlP (reference 2) and Keenan and Keyes (reference 3).

where PHQ i s t he partial pressure of water vapor in the gas m ixture and V11 .[) isthe partial pressure of w ater vapor in the gas m ixtu re if the g , 1 5 m i xt ur e i s s at ur nt cow ith vapor at the given te m pcruturc. T he percentage relative hum idity can beobtained hy m u lti pl yin g th e rel.u ive satu ration by !O()

A nothe r im po rta nt co nc ep t rb.u must be consid ered is ihar of dew {WIlli. L eI u ssu pp ose that the unsaturated 'lif-w aler vap or rmxturc is s lowly coo led. If thetotal p ressu re of the system is kept constant, then ihc p artial ju cssurc of the w atervapor w ill nOL be changed bv the cooling process. With continued cooling,h ow e ve r. t he t em p er at ur e will r cach a value at which the p ar ti al p re ss ur e of w.ucrvap or in the m ixture w ill become equal to the eq uilib riu m v ap or pressure o f p urewater A t this rcrnperarurc , then. th e m ix tu re has become t ho ro ug hl y s at ur at edw ith w ate r v ap or, , I I l U a ny f ur th er coolir.g w ill only result in condensation of thewater vapor. This ternpc rnturc is known ,IS the de w point of the g;\S m ixtu re. T hed ew p oint of a system depend s' on the kind of vapor p resent in the gas m ixture.

VVorked exor.nples 13WORKED EXAMPLESExample I-I. The bar, a u ni t of pr es su re IS defined as HY'dynes/em'- Express onestandard atmosphere (760 mm Hg) of pressure in bars. The density of rnercurv is1 3 .5 95 1 g/cm'.The pressure. P. can be calculated using the following formula:

P =hdgwhere h is the height of the mercury column (76 em). d is the de ns ity of mer cur y(13 .595 I g/crrr'). and g i s t h e a cc el er at ion du e 10 gravity (981 em/sec"). Subst itut ion g ivesP = 76 (13.5951 )(981) = 1.013.596 dynes/em'orP = J . O J 3596 barsExarriple 1- 2. Th e specific heal of o-iron at 298K is 0.108 cal lgoK. Convert this 10t he uni ts Btu/ lboR.(0.108 cal/gf()(453.6 gllb)(l Btu/252 cal)( 10KJLg'R) = O . J 0 8 BJullbOT.714 x ic:'

I-I:The pressure in an evacuated vessel was recorded as j_2 dynes/em' Express thisvalue in microns of mercury at 25C.1-2: An open-end manometer connected to a tank indicates 28.56 in. Hg a t 25'C.The barometer re adi ng is 14 .5 83 psia. The density of Hg is 13.59 g!cm> What is thepressure inside the tank"1-3: Compute the missing tempera\ures in the following table:

(a) (b) (e) (d) (e)D C 659 (f) (g)3380'KOFO R

9 02 16.8456 1664.61012

1-4: The flux of radiant energy emitted by a black body is given hI'Q = a(T4 - r: )

The de gre e o f di ss oci at ion i ncr eas es wi th temperature. Figure \-7 shows the degree ofdi ss oci at ion as " f un ct io n of tempe ra tu re.Ex.ample 1-8. The moist blast used in an iron blast lurn.ice cor n. un s 7. 2 ! tr ams of wat ervapor per cubic foot .u 77F. Determine rhe ternpe rutu-e t n which t hc hl;t,t rnuxt hepreheated in order that its relative saturation will become 1I.12.Consider I ft' of moist bias! as the basis.

where Q i s the nux of radiant energy (ergs/cm'-sec). {T i s t he S te fa n-Bol tzman n c ons ta nt1 5 735 x 10-< ergs/cm2scc('K)"I. T is the temperature of the hOI black body (OK ) .and T,. is Ihe temperature of the surroundings (OK ) . What is the value of a i n Bt u!ft'hr(OR}"?1-5: How marty gr"m-mok~

yk rao_part 1

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