U3l-=’

——

FORAERONAUTICS

-ia

CALORIMETRIC

TECHNICALNOTE2838

DETERMINATIONOF CONSTANT-PRESSURE

.—

SPECIFIC

HEATSOF CARBONDIOXIDEAT ELEVATED

PRESSURESANDTEMPERATURES

By Virgil E. Schrock

Universityof Caltiornia

-

WashingtonDecember1952

....-+ .. .._ . ----- . .

lB

..

.

1Cbrl LlnnAn 1n-l--s . ,~,

Iu!ulllllllllll!nllnljUb5132J

NATIONALADVISORYCOMMITTEEFORAERONAUTICS

TECHNICALNOTE2838

CALORIMETRICDETERMINATIONOFCONSTANT-PRESSURESPECIFIC .

HEATSOFCARBONDIOXIDEATELEVATED

PRESSURESANDTmmRmmEsByVirgilE. Schrock

. SUMMARY

Theconstant-pressurespecificheatof carbondioxidehasbeenmeasuredovertherangeofpressures,andtemperaturesfromambientcondi-tionsto1000poundspersquareinchgageand1000°F usinga steady-flowcalorimeteroperatingonanopencycle.Itappearsthattheappa-ratusasusedinthisdeterminationwillyieldvalueswitha probableerrorof0.5percentatthehighesttemperaturelevelconsidered.Theresultsofthesetestscheckthewidelyacceptedspectroscopicdatawithin1 percent.Thevaluesatelevatedpressuresareinreasonableagreementwiththosederivedfromthezero-pressurespectroscopicvaluesand

but

theapplicationoftheBeattie-Brid&maneqyationof st@e.

Onlyverylimitedcalorimetricdataareavailableintheliteraturesubstantialagreementexistswiththoseconsideredreliable.

INTRODUCTION

ThepresentinvestigationwasconductedattheUniversityofCaliforniaunderthesponsorshipandwiththefinancialassistanceoftheNationalAdvisoryCommitteeforAeronautics.

ObjectiveandScopeofInvestigation

Inthepresentresearchprogramtheuseofa steady-flowcalorimeterforthemeasurementof specificheats”ofgasesathightemperaturesandpressureshasbeeninvestigatedto determinethevalidityandlimita-tionsofthemethod.Thepurposeofthisreportistopresenttheresultsoftestsmadeon carbondioxideintherangefromambientconditionsupto1000poundspersquareinchand1000°F. Forthesetestsa calorti-eterbuiltof Inconelandoriginallydesignedtooperatewitha closed

.

.-. ———.—— ———— — --- ———-- — ——...———— --

2 NACATN 283

cyclewasused,butbecauseofdifficultiesinmetering,pumping,andregulatingtheflowitwaselectedto operatewithan opencycle.Certainlya closedcyclewouldhavesomeadvantageinthatitwouldallowlongerrunsata singlecondition.It seemedadvisabletomaketestsusingtheopencyclebeforeexpendinganygreateffortin solvingproblemsconnectedwiththeclosedcyclethatwerenotassociatedwiththeformer.

Of considmableimportancetotheengineersrethespecificheatsoftheconstituentsoftheproductsofcombustion.Becausecarbondioxideisa prominentconstituentinmostcombustiongasesitwasselectedforthesetests.Otherfactorsinfluencingtheselectionofthisgaswere: (a)Itsspecificheatisaffectedto greatextentbypressure,whichappesredtobe desirableforthepurposesoftheinves-tigation,(b)itis quiteinert,and(c)itisavailableatlowcostandhigh

Theas:

(1)

(2)

(3)

(4)

purity.

MethodsforDeterminingSpecificHeats

methodsofobtainingspecificheatsof gasesmaybe classified

Directmeasurement

Determinationofratio 7 = c-p/cv ●

DeterminationofJoule-Thomsoncoefficients ,

Spectroscopicmeasurements

directmeasurementoftheconstant-volumespecificheatofgasesusinga nonflowcalorimeterisimpracticalbecauseofthehighcapacityofthecontainingvesselcomparedwiththegascontained.Thiswasusedonlybyveryearlyexperimenters.Themeasurementoftheconstant-pressurespecificheatusinga flowcalorimetercan,however,bemadewitha highdegreeofprecision.

Themethodsof determiningtheratioof specificheatsby themeasurementofthespeedof soundorthereversibleadiabaticexpansionmethodhavedefiniteshortcomings.E&h requireaccuratepressure,volume, andtemperaturerelationsoranappropriateequationof stateforthegas. ConsiderforandNewtonshowedthatthe

examplethevelocity-of-soundmethod.Maxwelllocalacousticveloci@is

a=E=E(1)

●

NACATN2838 3

where k isthebulkmodulusofthegasand p isthemassdensity.LaplaceandPoissonsuggestedthatthesoundcompressionwaveisisentropic,hence,

pvy= Constant= c

and

k=- <)b~ isentropic

.()=(-v)= =7p~7+1

then

(2)

(3)

andfora perfectgas

a= E7 (4)

Theperfect-gaslawdoesnotapplyfortherealgasexceptatzeropressuresothetrueequationof statemustbe knowninordertoputequation(3) intermsofthetemperature.Thatis, p, v, and T datamustbe availablefromwhich p maybe determinedfrommeasurementsofpressureandtemperature.

Whenthevalueof 7 fromthemeasurementoftheacousticveloci~hasbeenobtained,thespecificheatsmaybe determinedfromthethermo-dynamicidentities,usingtheappropriateequationof state.Forexample,

% 00ap NJ-Cv= ~v--p

andtherefore

(H)apavCV=(7:1)’12%V%P

(5)

(6)

—.—— .—— — _ . _ —-——— .- ——

4 NACATN 2833

Knowingthevalueof 7 thespecificheatsmaybe determinedifthederivatescanbe evaluated.Notehowever,thevalue 7 - 1 willbesmallerthan 7 andthereforethevalueof specificheatwillbe less ~accuratethanthevalueof 7 measured.Sincethespecific-heatdataobtainedinthisindirectmannerrequiretheuseofanequationofstateintwowaysandtheresultsarelessaccuratethanthevalueof 7obtained,itisprobablyoflessimportancethantheothermethods.

High-pressurespecificheatsmaybe determinedfromJoule-Thomsonmeasurementsifthezero-pressuredataareavailable.Thepressure-temperaturerelationshipisdeterminedby allowingthegasto expandadiabaticallywithoutdoingworkandwithnochangeinkineticenergy.Dataobtainedarelinesofconstantenthalpyona temperature-presmreplot. Theconstant-pressurespecificheatisgivenby

Cp = ()&@p

orfora smalltemperatureinterval

fromwhichitisevidentthatthespecificheatsatvariouspressuresareproportionalto the AT spacingoftheconstantenthalpylinesandmaybe calculatedfrom AT betweenthesametwoenthalpylinesandtheknow valuesof Cp atzeroPressure.

.Thedifficultiesinvolvedinthismeasurementarethemaintenance

ofadiabaticconditionsandprecisemeasurementofthetemperature.Ityieldsthepressureeffectbutisnotdirectlya measureofthespecificheat.A numberofauthors(references1 to 3) haveusedthismethodwithsuccess.

Thevaluesobtainedspectroscopicallyarethezero-pressureconstant-volumespecificheats.Sincegasesobeytheperfect-gaslawatzeropres-suretheconstant-pressurevaluescanbe obtainedby addingthegascon-stant.Specificheatscalculatedfromspectroscopicdataassumingasimpleoscillatorarespecificheatsmaybedynamicidentitiesas

consideredaccurateto0.5 percent.High-pressureobtainedfromthespectroscopicdataandthethermo-follows(reference4):

(7)

—.———.

NACATN 2838

and

whereagainthe

Cp-cv=

equationof stateGay(reference5)havecalculated

(8)

mustbe known.Ellenwood,Kulik,andthehigh-pressurevaluesof specific

heatsforeightcomon gasesu8ingthespectroscopicdataofJohnston(reference6) andtheBeattie-Bridgemanequationof state(reference7).

At presenttheBeattie-Bridgemanequationisbeingusedinan extra-polatedform(references5 and8). Theconstantsgivenby theauthorsofreference7 wereevaluatedfromtheavailabledataon carbondioxideinthetemperaturerangefrom-lm” to 430° F. All ofthesedataweredeterminedintheperiodfrom1869to 1903exceptthoseatlessthan1 atmospherewhichwereobtainedimx6. The equationtiththecon-stantspresentedby theauthorschecksthedatawithanaveragedevia-tionof0.2percent.Themaximumdeviationforcarbondioxidefo&d intheirtableofcomparisonvalue~was1.3 percentwhichoccursnearthecriticalpoint.

Useofthesecondderivativesofthe13eattie-Bridgemanequationprobablyplacesconsiderablestrainonitsaccuracy,andcertainlyitsextrapolationtotemperaturesof 4000°F is somewhatquestionable.Crown(reference8) statesthatthechiefjustificationof sucha pro-cedure,apartfromtheabsenceof a betterone)iSthegood%mementexistingintherangewhereexperimentaldatadoexistfora largenwnberofgasesevenapproachingthecriticalcon~tionsorliquefaction.Thereisan obviousneedformoreextensivepressure,volumejandtemperaturedata.

An abundanceofempiricalequationsareavailableintheliterature(referencesgto 14). Theseequationsarebaseduponthespectroscopicdata.Heckgivestabularthermodmc properties,inengineeringunits,fromthespectroscopicdata(reference15).

Thedirectmeasurementofspecificheats’has,inthepast,beenseriouslylimitedinrangebecauseoftheinabilityofavailablemate-rialsofconstruction.tosustainhighstressat”hightemperatures.Inrecentyearsmetallurgicaladvanceshavebeenmadeto a pointwheresustainedstressesup toabout10,~0poundspersquareincharenowpossibleat2000°F,makinga high-temperaturehigh-pressurecalorimeterfeasible.Sincetheonlyextensivespecific-heatvaluesavailableintherecentliterature,thespectroscopicvalues,areessentiallyindi-rectlymeasured,thereseemsa needforconfirmationby directmeasurement.

_.— .—...— —.——_.— —— —.—

Y

R

a

k

P

P’

v

T

Tm

P

c

w

v

Q

Qnet

t

A

specificheat

meanvslueof

specificheat

specificheat

gasconstant,

\

SYMBOLS

atconstantpressure,Btu/(lb)(%)

~, Btu/(lb)(%)

atconstantvolume,Btu/(lb)(%)

ratio,%/%

ft-lb/(lb)(%)

NACATN2838

speedof sound,ft/8ec

hulkmodulus,lb/sqft

massdensity;lbsec2/ftk

weightdensi@,lb/cuft

gravitationalacceleration,ft/sec2

specificvolume,I/pr,CU ft/lb

absolutetemperature,‘R

meantemperature,OF

pressure,lb/sqft

constant,pv7

weightrateofflow,lb/hr

volumetricrateofflow,cuft/min

rateofheataddition,Btu/hr

netheataddedto gas

time,min

precedinganysymboldenotesa changeinthatquantity

heat-tramfercoefficientforradiation,Btu/(hr)(sqft)(%)

enthal~,Btu/lb

.- —

- NACATN2838 7

G emissivity

M molecularweight

%? heatduetoradiation,Btu/br

Fe emissivityfactor

Fa geometricshapefactor

D1,D2 diametersofflowtubeandradiationshield,respectively,ft

DESCRIPTIONOFAPPARATUSANDTESTPROCEDURE

Theprimarycomponentsofthesystemusedinthisinvestigationare(fig.1)thegassupply,theheaterstobringthetemperatureofthegastothetestlevel,thecalorimeter,theaftercooler,andthemeter.Schematicdiagramsandsectionaldrawingsappearinfiguree1 to4.

.

Calorimeter

Thecalorimeterconsistsofa shieldedInconeltubewithl-inchinsidediameterhousinganelectricalheateranddifferentialthermo-coupleswhichareshieldedfromtheheater.Oneradiationshield,madeof sheetInconel,surroundsthetesttubeoveritsentirelength,andacoiloffourZ/k-inchInconeltubessurroundstheshield..Thegasentersthroughthecoiledtubingandpassesbackthroughthetesttube.Thisentireassemblyiscontainedinanevacuatedcasingmadeofa l-footlengthof8-inchInconeltubing.Thecasingvacuumwasproducedby aHy-Vacvacuumpumpratedat0.10micron,thuseliminatingconvectionwithinthecalorimetercasing.A sectionaldrawingofthecalorimeterisshowninfigure2. Detailofthetesttubeisalsoshowninthisdrawing.

Thermocoupleswereattachedto thetesttubeandthecalorimetercasinginorderto determinesteady-stateconditionsandestimateradia-tionlosses.Thecasingofthecalorimeterandtubingleadingto itwerewrappedwithasbestoscloth.Guardheaterswerewrappedasuniformlyaspossibleontheasbestosclothtoeliminateheatlossfromthecalorim-eter.Twolayersofpipeinsulationconsistingof2 inchesofhigh-temperatureand5 inchesof standardinsulationwerethenapplied.

.

—---- ——-——.--——---- -. .———— ---———

,NACATN 2838

TestGas.

Gassupply.-Commercialcarbondioxidewasobtainedin~-pound wcylindersfromthePureCarbonicCo. Purityoftheliguefiedcarbondioxideisclaimedtobe 99.5percentorbetter.Threecylindersweremanifoldedtogethertoconstitutethesupplyreservoir.Eachcylinderwaswrappedwithanelectricalheaterofl-kilowattcapacityandinsulatedwithasbestoscloth.Heatingofthecylinderswasnecessarytoobtainpressuresabove950poundspersquareinchabsolute,.thevaporpressureatroomtemperature,andtomaintainthepressureasthegaswasboiledoff. Tobe effective,theheatingmustbe donemostlyatthelowerportionofthecylinder.

Controlofthegaspressurein thecalorimeterwasaccomplishedbyGrovepressureregulators.Thelinestoandfromtheregulatoraswellasitsbodywerewrappedwitha resistanceheatertopreventtheregulatotmm icing.Theflowwascontrolledbya high-pressurestainless-steelneedlevalve.

Heatingofgas.-Inadditiontotheheatingat therese~oirjthegaswaspassedthrougha 3-inch-diametercoilof20turnsofheavy-wallMoneltubing.Heatingwasprovidedby a forcedprimaryairgasburner.

-

Close-fittingguidesdirectedthehotfluegasesoverthecoiledtubing.Finalheatingandclosecontrolofthegastesttemperaturewereprovidedby a seriesofeightcross-wireelectricalheatershavinga totalcapac-ityof 4 Hlowattsat110volts.Thedesignwaschosensoasto givethemaximumheatingina minimumof space.Theseheaterswerecontrolledby a variableautotransformer.

Thetest-gasheatinginthecalorimet=wasprovidedby an elec- .tricalheater(fig.3)ofthesametypeasthosejustdescribed.

Meteringofgas.-Therateofgasflowwasmeasuredbymeansofa10-cubic-footmeterprover.A watermanometerconnectedto theinlet. tothetankindicatedtheincreaseinpressurenecessaryto overcomethefrictioninthebalanceassemblywasonly0.2to0.3inchofwater.Thiswasconsitiednegligible.

ThehotgaS leavingthecalorimeterwascooledandh~~fied beforebeingpassed.to thevolumetricmeter.Coolingwasaccomplishedby a two-passshellandtube@at exchangercontainingninety-sixl/4-inch-diameterbrasstubes.Watersurroundingthetubeswasusedto coolthegasflowingthroughthetubes.

Humidificationwasnecessarytopreventtheevaporationofthewater.inthevolumetrictank.Thegaswaspassedthroughtwobottlescontainingceramic-beadcolumnpacldng.Onlybubblesofappro-tely 1 centimeter

2B

..

NACATN 2838

indiameteror smallerwereobserved,withno channelingoftheflow.Thegasleavingthehumidifyingbottleswasassumedsaturatedwithwatervapor.

9

Applyingthevolumetricmeasurementtothedeterminationoftheweightrateofflow,thedensityusedwasobtainedfromreference16at1 atmosphereand32°F, thisvaluebeingcorrectedfortemperatureandpressureby theperfect-gaslaw. Thecorrectionis quitesuitableinviewofthesmalldeviationofthemetercon~tionsfromthestandard.Thecalculationisgivenin appendixA.

Instrumentation

Temperaturedetermination.-Theinstrumentationfortemperaturedeterminationwasasfollows:

(a)Thetemperatureriseusedinthecalculationofthespecificheatwasmeasuredby differentialiron-constant-anthermocouplestogetherwitha Whitedoublepotentiometer.Leeds&I?orthrupthermocouplewireandcalibrationslopes(fig.5) wereused.Allthermocoupleswerecheckedatthemeltingpointofpureleadandattheicepoint.ThemaximumvsriationoftheelectromotiveforceofthevariouscoupleswasO.O3Omillivoltatthemeltingpoint,621.6°F. To obtainthetempera-turedifference,thedifferenceinelectromotiveforcewasrecordedwiththetwojunctionsatthesametemperature(fig.6) andagainaftertheadditionofheat.Netelectromotiveforceswerethenusedto calculatethetemperaturedifferential.A Leeds&NorthruptypeR galvanometerswasusedwiththeWhitedoublepotentiometer.Thiscombinationallowedobservationoftheelectromotiveforcewitha precisionof0.5 microvolt.IntermsoftemperaturethisrepresentsapproximatelyO.OIPF. Inorderto insureaccuratemeasurementsofelectromotiveforcetheEppleystandardcell,usedto standardizethepotentiometercurrent,waskeptina thermostaticallycontrolledbathwitha differentialof0.5° F.

Thedifferentialthermocoupleswerearrangedsothattheupstresmthermocouplecouldbe usedto determinethetemperatureofthegasenteringthetestsection.Thesethermocouplesweremountedindouble-boreceramicinsulatorsandcenteredinthetesttube.

(b)Othertemperatfiemeasurementsweremadeusingiron-constantanthermocoupleswitha Leeds&NorthrupModel8662potentimneter.Acommoncoldjunctionwasused;thethermocoupleswereconnectedthrougha selectorswitch.

(c)Thermocoupleleadswerebroughtoutofthehigh-pressurecalorim-eterthrougha sealassembly(fig.4). Eightwireswerebroughtthrougha singleseal.Theleadswerestrungthrougha 2-footlengthof

- .—. ——— ———-— .— -—

10 NACATN2838

l/4-inch-diameterstainless-steeltubinginorderto getthesealaway ‘fromthehigh-temperatureregion.Theinnerlayerof glassinsulationwasleftonthewiresas’theywerepassedthroughtheseal.ThesealwasmadewithSauereisenLiquidPorcelaincement.

Pressuredetermination.-Test-gaspressurewasmeasuredwitha@ad-weightgagetester.A Bourdontypepressuregagewasusedforvisualobservationofthepressurelevel.

Electricalheaterinput.-Heataddedto causea riseintemperatureofthetestgaswasdoneelectricallyby theheateralreadydescribed.Theinputtotheheaterwasmeasuredwitha WestonstandardwattmeterNo.326,havinga precisionof1/750ofthefull-scaledeflection,uniformoverthescalerange.Accuracyis claimedby themanufacturertobe betterthan0.1percentofthefull-scalereading.Supplyvoltagewasregulatedby a voltagestabilizertoeliminatevsriationoftheheating.

#

ExperimentalProcedure

Preparationof systemandpreliminarytests.-As thecalorimeterwasassembledallpartswerecleanedaswellaspossibleusingcarbontetra-chlorideinordertoremoveoiland.dirtleftafterthemachiningopera-tions.Thebindingmaterialontheglassthermocouplewireinsulationwasremovedfromallleadswithinthecalorimeterbyburningitawaywitha smalloxidizingflame.Carewastakentoavoidfusingtheglassinsulation.Thisprocedureleftthewiresinsulatedwithclean,white,andflexibleglassinsulation.

Allsealswerepressure-testedwitha soapsolutionpriortoinsulatingthecalorimeter.A negligibleleakagecouldbe detectedfromthetest-gasheaterleadsealsbutnoneco~d be detectedfromthethermocouplesealsoranyfittingsonthecalorimeterordownstreamfromit.

Thesystemwaspressurizedto1000poundspersqusreinchgageandallowedto standfor24 hours.A lossofonlySOpoundspersquareinch “occurredduringthistime.This’rateofleakageisnegligiblefortheflowsusedandintiewoftestsmentionedabuveitappearsthatthemajorportionofthisoccurredupstreamfromthecalorimeterattheelectricalheaters,wherethegreatestdifficultyineffectinga sealwasencountered.Onlyleakagefromthecalorimeterandpartsdownstreamwouldaffecttheresults.

Preparationfortests.-Theguardcontinuedbringingthecalorimeterand

heaterswereturnedonandheatingtubingleadingto ittothedesired

.

.— .—

..

NACATN 2838

testtemperaturelevelandthensupplyingthemaintainthattemperaturelevel.A periodof

I-1

heatlossnecesssryto24hourswasallowedfor

thisoperation,ontheaverage.Heatingofthereservoircylinderswas

begunabout~ hoursbeforethe”establislunentofthegasflowandwas

continueduntil.apressureof18OOto2000poundspersquareinchgagewasreached.Heatwasthensuppliedtoafterestablistientofflow.

Tests.- Whenthetemperaturelevelthedesiredconditionsthegasflowwas1000poundspersquareinchgagein theadjusteduntilthegasenteredthetest

maintainthereservoirpressure

andresenroirpressurewereatestablishedata pressureofcalorimeter.Heatingwassectionatthetemperatureof

thecalorimeter.Afterobservingthereadingofthedifferentialthermo-coupleforisothermalconditionsatthattemperaturelevelthetest-gasheatingwasstartedandadjustedtoproduceatemperatureriseofthegasof20°to 35° F.

DatawererecordeduntiltheconditionsremainedunchangedforaTeriodofabout20minutes;thusa valueof specificheatwasobtainedata particularteweratureandat1000poundspersqusreinchgage.

. Thepressurewasthenreducedbuttheweightrateofflowmaintainedconstant.Followingthisprocedurethesteady-stateconditionswereaffectedonlyby theinfluenceofpressureuponthespecificheatanda newsteady-statecontitioncouldbe reachedmuchmorerapidlythanthefirst.Inthiswaya seriesofmeasurementswasmadeateachtempera-turelevelandvariouspressures.Inmostcasesdatawereobtainedatfourpressurelevelsateachtemperature.

DISCUSSION

ValidityofResults

Specificheatsobtainedhereinaremeanvaluesfora temperaturerangeof20°to 35° F andwereobtainedfrom

~ _%etP WAT

Thenetheataddedwasobtainedfromthewattagesuppliedandthecalculatedheatlossfromthetestsection.Intwocasesthelossincludeda smallcorrectionduetoa slighttransientcondition.Ithasbeenpointedoutthattheveloci~of soundandspectroscopicmethodshavetheadvantageofyieldinginstantaneousvalues,whereastheflow

..——.— —— —-. —. —

12 NACATN 2833

calorimetergivesa meanovera temperaturerange.Thevaluesobtainedinthisinvestigationarereportedatthearithmeticmeantemperature,whichisequivalenttoassumingthatthespecificheatisa linearfunc-tionofthetemperatureinthatrange.Therateof changeofthespecificheatwithtemperatureovera 20°to 35°F rangeissufficientlyconstantsothatno seriouserrorwilJ-resultfromthisassumption.

An analysisoferror(appendixB) indicatesa maximumerrorof0.42percentanda probableerrorof0.25percent.InviewofotheruncertaintiessuchastheaccuracyofthecorrectionappliedtoheatinputtheresultsareconsideredaccuratetoonlyO.~percent.Themaximumcorrectionappliedwas4.3percentandwasatthemaximumtem-perature,950°F. At the685°F levelthecorrectionwasonly2.0per-cent.Becauseofthedependenceofradiationuponthefourthpoweroftheabsolutetemperaturetheheat-lossuncertaintywouldbecomesignif-icantabove1000°F. Additional.shielding,theuseofa higherflowrate,anda lowertemperaturedifferentialshouldmentsupto2000°F.

PresentationofResults

allowaccuratemeasure-

Theexperimentalvaluesofthespecificheatsareplottedinfig-ures7 to 12asa functionofpressureat eachtemperaturelevelemployedduringthetests.In eachcasethedatahavebeenshownin comparison .

withthoseofEllenwood,Kulik,andGaysincetheirdataarethemostextensiveandprobablythemostreliableto tite.Otherlow-pressure‘data(references17 and18) areinagreementwiththoseofJohnstonetalii(reference6).

Figures13 to 18 sh~ thespecificheatsasa functionoftempera-tureforconstantpressuresandwereobtainedby interpolationbetweenpointsandextrapolationto zeropressure.Pointswereshownonthecurvesofexperimentaldatainorderto indicatethemagnitudeofthedeviationfromthemeanlines.Experimentalcurvesfromfigures13to 17have beenplottedtogetherinfigure18 to showtheeffectsoftempera-tureandpressuresimultaneously.TheresultsaretabulatedintableI.

A comparisonoftheexperimentalresultswithdataofGmdenoughandFelbeck(reference19), Partin@onandSchilling(reference20),andJohnston(reference6) is showninfigure19. These dataareforlowpressure.Theeffectofa pressureof1 atmosphereinthistempera-turerangeisverysmall.Twopoints,thedataofSwarm(reference21)at1 atmosphere,wereincludedin-thiscomparisonbecausetheyrepresentaccuratecalortietricmeasurementsandarein goodagreementwiththeresultsofthesetests,especiallyintrend.

— —

NACATN2838 13

ThedataofPartingtonandSchil.lingrepresenttheaverageofalargecollectionof dataobtainedbyvariousmethods,themajoritybeingfromveloci@-of-soundmeasurements.No comparisonsoftheearlierhigh--pressuremeasurementsinconsistent,showing

Factorsinvolved

havebeenincludedsincethosedatawerefewandonlyqualitativelytheeffectofpressure.

LimitationsofCalorimeter

intheoptiqumcalorimeterdesignconditionsare:

(1)Limitationoftemperaturerisetoallowaccuraterepresentationofthedatabymeanvalues,butlargeenoughto allowaccuratemeasurement

(2)L@Ltationoftheflowveloci~toeliminaterecoveryinte~er-aturemeasurements

(3) A highratio

(4)A largeheat

ofgascapacitytocontainercapacity

inputcomparedwiththelosses

Unfortunatelythesefactorsopposeoneanother,requiringa com-promisecondition.IthasalreadybeenpointedoutthatthetemperaturedifferentialusedwasZ13°to 35°F andthatthissatisfiesthefirstcondition.~hiswasconsideredtobe anindependentrequirementandtheotherconditionsselectedonthisbasis.

Theflowveloci~duringthesetestsvariedwithpressureandtem-peraturesincetheweightrateofflowwasmaintainedconstant,forthereasonspreciouslystated.Themaximumveloci~obviouslyoccurredatthe “ temperatureandminimumpressure.Approximatecalculations,basedontheassumptionofa perfectgas,indicatethatthemaximumllachnumberwas0.026wl$chcorrespondstoa stagnationtemperatureriseofonlyO.O1°F.

Thethirdconditionisnecessarytominimizetheeffectoftransientconditions.A highweightrateofflowandasthina tubeaspossible=e desired.Condition(4)alsorequiresa highwei~t rateofflowandminimizationof theheatlosses.Boththeseconditionsweremetsatis-factorily.However,foranextendedtemperaturerangea higherflowrateandadditionalshieldingseemadvisable.It appearsthata practicallimitofthetemperaturerangewillbe dictatedby theradiationlossbecauseofitsrapidincreasewithtemperature.

—----—— ——. —

14 N/MITli2838

CONCLUSIONS

Thefollowingconclusionsweredrawnfroman investigationofthecalorimetricdeterminationoftheconstant-pressurespecificheatsofcarbondioxideatelevatedpressuresandtemperatures:

1.Theresultsarea reasonableconfirmationofthespecific-heatvaluesof carbondioxideobtainedspectroscopicallyforthezero-pressurestateandovertherangeoftemperaturesfrom100°to700°F. Theexperi-mentaldataareapproximately1 percentlowerthanthespectroscopicdata.Thissmalldifferencemaybe dueto lackof completeequilibrium;thatis,thevibrationalenergymaynotbe fullyactivatedatthepointwherethetemperatureriseisobserwed.

2.Greaterdifferenceexistsbetweenthehigh-pressurevaluesmeasuredandthosecomputedbyEllenwood,Kulik,andGay. Themaximumdeviationisapprod.mately3 percentandoccursata pressureof1000poundspersguareinchabsoluteandwOO F. Theagreementismuchcloseratthispressureforbothhigherandlowertemperatures.Thisdetiationmaybe e~lainedby thestressplacedontheBeattie-Bridgemanequationh obtainingthesecondderivatives.

3. A singlemeasurementat 950°F and1000poundspersquareinch .gageseemsto offerconfirmationofthespectroscopicdataatthishighertemperaturelevel.

4.Theresultsshowthattheeffectofpresswquponthespecificheatbecomeslesssignificantathighertemperatures,aspredictedbythethermodynamicidentitiesandtheBeattie-Bridgemanequat~onofstate.

5. Theeqtipmentshouldbemodifiedtoreducetheradiationlossfurtherwhenusedathighertemperatures.

UniversityofCaliforniaBerkeley,Cslif.,January31,1952

——z. —-

NACAm 2838 15

AH?ENmxA

CALCULATIONS

Thespecificheatsweredeterminedfrom:

CP= (E)p = (Z)p ‘%

Flow

Sincetheflowratewasmetereddeterminationwasnecessary.Itwas

Rate

volumetricallydeterminedfrom

reference16at0°C and1 atmosphereasfollows:

~nsi~ = ~.g769gram/liter

1 wuu = 0.002205lb

1 liter= 0.03531Cuft

fromwhich

and

ThisiE

0.002205P! =1.9769x o 03531.

R=~= 14.6g6X 144P’T 0.1235X 491.6

notthetrueularweight),butitsuseaccurateresultsthan

gasconstant

inaccuratedensi~thevaluegivenin

= 0.1235lb/cuft

= 34.88 ft-lb/(lb)(%)

154-4/M(whereM isthemolec-nearthestandardconditionswillyieldmore-

R = 1544/M= 35.11

——. .——— ——. ..

16

Thethe

useofthevslue34.88smalldeviationofthe

saturationpressureofthe

yACATN2838

foot-poundsperfootperOFis justifiedby.

meterconditionsfromthestandard.Thewatervaporwassubtractedfromthebarometric

toobtainthepartialpressureofthecarbondioxideatthemeter.

TemperatureRise

Readingsoftheelectromotiveforceofthedifferentialthermo-coupleswerecorrectedby subtractingtheelectromotiveforceobservedwiththetwojunctionsatthesame,temperature.A curveoftheisothermaldifferenti~isgiveninfigure$6.Thenetdifferentialwasconvertedtotemp~atureby usingtheLeeds& Northrupcalibrationslopes(forstandardlJ.031thermocouples)giveninfigure5.

Net

Thenetheataddedtothelossesasfollows:

HeatAddition

gaswasfoundby correctingfortheheat

.’(a)Measurementofwalltemperaturesindicatesthatnonetheat

lossoccurredbecauseofconductionalongthetestsection.Apparentlyheatwasconductedbackintothedownstreamendatthesamerateitleft .theupstreamend,withintheaccuracyofexperimentalmeasurements.

(b)Theradiationlos~wascalculatedfromtheasfollows:

Stefan-Boltzmann

wherethesubscriptr referstofactor,and Fa isthegeometrictheform

radiation,Fe istheemissivityshapefactor.Thiscanbewritten

law

in

where ~ istheheat-transfercoefficientforradiationandisa func-tionofthetemperaturelevelandthedifferenceT1 - T2. TheshapefactorFa = 1. Theemissivityfactorforthisgeometryisgivenby

—..—— .—. ——

3B IUCATN283gI ‘.

17

andactud-~ssionlinearvariationof

Theuseoftheshieldcalculation;

inwhich 6 istheemissivityand D1 and D2 arethediametersoftheflowtubeandtheradiationshield,respectively.

Theemissivitywasobtainedfromspectralmeasurementsmadeonanequivalentnickel-chromealloy(fig.20). Totalemissivitieswereobtainedby graphical,integrationofthecurvesofPlankianradiation

atvarioustemperatures.Theresultsindicateatotalemissivitywithtemperature(fig.21).

linearrelationshipforradiationsimplifiesthethatis,

.F=6,-2 1-+($(+)

.,2-3 ‘++ (-($-‘)then

theresultsofthiscalculationaregiveninfigure22.

Values.ofhr werecomputedatvarioustemperaturesusingthemeantemperatedifference(tableII)andthesevaluesusedtocomputetheradiationlossfromthetestsectionperhourperdegreemeantemperaturedifference(fig.23).

(c)Usingheatcapaciwanddensitydatafurnishedby theInternationalNickelCo.,producersofInconel,thecapacityofthetestsectionwas-determinedanda correctionappliedbecauseofa slighttransientcondi-tionduringtwooftheruns.Thiscorrectionwas2.8percentoftheheataddedforrun1 and1.0percentforrun5.

.

-..—- -.—— —..——_ .- -— .—..—— —..—— — -_ __

.

18 NACATN 2838

.

Theerrorsofwhere

APPENDIXB

ANALYSISOFERROROFOBSERVATION

observationinrun16,

Q. 229.3——WAT 30.19X33.55=

whichisusedasanexample,

0.2263Btu/(lb)(%)

aregivenbelow.

Errorin Q (Q= 229.3Btu/hrreadto ii/kwattwithscalefactor1/4):

i~X~X 3.413= *0.21Btu/hr

+“”~ – M0091percent’229.3

Errorin AT (AT= Potentiometerindication/Calibrationslope):

potentiometerindication= 1.2065t 0.0005mv

Calibrationslope= 0.03063* 0.00005mv/OF

, AT = 33.55°F

Errorduetopotentiometertolerance:.

0.0005= 0.000411.=65

Errordueto slopetolerance:

o.moos = 0.00160.0306C,

*

4

NACATN2838

. Maximumerror:

3.44(o.cm6+0.00041)=to.067

T = 33.55 i 0.067° F

Probableerror:

●

(33.44x0.0016)2+ (33.55x0.00041)2=io.0555

AT=33.55* 0.056°F

[6op’vErrorin w W=7=

)30.19lb/hr

P’=&

No errorresultedfrom p or R.

Ap’. p’~=o.1089x~ = 0.000051

v= 9.82 tO.0025 tuft

t = 2.126”t0.oo2min

Maximumerrorin w:

Aw( )

.w~+~+$

(. 30.19~ +3+

w = 30.19 t 0.05

)0.002izzm = 0.05

19

—.— ..—.—..

20 NAC!Am 283a

l%robableerrorin w:

(30.19X 0.0047)2 + (30.19X 0.00025)2+ (30.19 x 0.00094)2

w= 30.19 2 0.032

Maximumerrorin Cp:

[ 1AW+AB.+A~=cyy AT

( 0.056=o.2263&+— )0.21

33.55— = 0.00095. + 229.3

“ ~ .0.2263 t 0.00095Btu/lb/°For tO.@ percent

4Probableerrorin Cp: .

%—= 0.001652+0.001652+ 0.000912= to.oo25or to.25percent‘P

CustomarilyitisfeltthattheprobableerrorascalculatedHereismoreapplicable,butinviewofotheruncertaintiessuchascalculat-ion ofradiantlossesandpossibilityofa slighttransientconditiona morepessimisticviewshouldhe taken.Theresultsarebelievedtobe accurateto0.5percent.

.

,

.

.

.

.—

NACAm 2838

REFERENCES

21

1.

2.

3.

4.

5.

6.

‘7.

8.

9.

10.

Keenan,J.H.: ProgressReportontheDevelopmentofSteamChartsandTablesfromtheHarvardThrottlingExperiments.Mech.Eng.,vol.48,no.2,Feb.26, 1926,Pp.14-4-151.

Roebuck,J.R.: TheJoule-ThomsonEffectinAir. Proc.Am.Acad.Artsanasci.,vol.60,no.13,Dec.1925,Pp.537-596;vol.64jno.9, Aug.1930, PP. ~7-334=

Sage,B.H:,Kennew,E. R.)and~cy~ W“N“: PlymeEquilibriainHydrocarbonSystems.Ind.andEng.Chem.,vol.28,no.5,my 1936, pp. 60L604.

Dodge,BarnettFred: ChemicalEngineeringThermodynamics.Firstcd.,McGraw-HillBookCo.,Inc.,1944.-

Ellenwood,I!YankO.,Kulik,Nicholas,andGay,NormanR.: TheSpecificHeatsofCertainGasesoverWideRangesof~ressuresandTemperatures.Air,CO,C02,CH4,C@2, H2,N2,and02. Bull.No.30,Eng.Exp.Station,CornellUniv.,Oct.1942.

Johnston,H. L.,Davis,C.O.,Chapman,A. T.,Walker,M. K.,andDawsonjD.H.: HeatCapacityCurvesoftheShplerGases.Jour.Am.Chem.SOC.,ser.A, vol.55,no.1,Jan.1933,pp.153-186; no.7,July1933, PP.27W2753; VO1.56j no. 2>Feb.1934>PP.z71.-276;VO1.57sno.4)April1935,PP.@2-684.

BeattiejJ.A.,andBridgeman,O.C.: A NewEquationofState.Proc.Am.Acad.ArtsandSci.,vol.63,no.5,Dec.19~, pp.229-308~

Crown,J.C.: Flowofa GasCharacterizedbytheBeattie-BridgemanEqyationofStateandVariable.SpecificHeats.Memo.No.9619,NavalOral.Lab.,April1949.

Bryant,W.M. D.: RnpiricalMolecularHeatEquationsfromSpec-troscopicData. IntLandEng.Chem.,VO125,no.7,July1933,pp.8~-823. ~ “

Chipman,J.,andFontana,M. G.: A NewCapacityatHighTemperatures.Jour.no.1,Jan.193>,pp.48-51.

ApproximateEquationforHeatAm.Chem.Sot.,vol.57,

— .. ..—_ ..—

22 2!338

11.

12.

13.

14.

16.

17.

18.

19.

20.

21.

22.

23.

Eastman,E.D.: SpecificHeatsofGasesPaper445,Bur.Mines,Dept.Commercej

NACATN

atHighTemperatures.1929.

Tech. .

Spencer,H.M.,andJustice,J.L.: RnpiricalHeatCapacityEquationsforSimplerGases.Jour.Am.Chem.SOC., vol. ’56, no.~, Nov.1934, pp. 2311-2312.

Smallwood,J. C.: EquationsfortheSpecificHeatsofGases.Ind.andEng:chem.,vol.34,no.7,July194-2,PP.863-864.

Sweigert,R.L.,andBeardsley,M.W.: EmpiricalSpecificHeatEquationsBaseduponSpectroscopicData. Bull.No.2,Eng.Exp.Station,Ga.SchoolofTech.,vol.1,no.8,June1938.

Heck,R. C.E.: TheI?ewSpecificHeats.Mech.Eng.,vol.62,no.1,Jan.1940,PP.9-W.

Washburn,EdwardW. (cd.):InternationalCriticalTables.Vol.III.McGraw-HillBookCo.,Inc.,1928,p. 3.

KAssel,L.S.: ThermodynamicFunctionsofNitrousOxideandCarbonDioxide. Jour.A.m.Chem.SOC.,vol.56,no.9,Sept.1934,pp.1838-1842.

Woolley,HaroldW.: C“arbonDioxide(IdealGasState).NBS-NACATablesofThermalRcopertiesofGases,Table13.10,July1950.

Goodenough,G.A.,andFelbeck,G.T.: An InvestigationoftheMaximumTemperaturesandPressuresAttainableintheCombustionofGaseousandLiquidFuels.Bull.No.139,Eng.Exp.StationjUniv.ofIll.,March17,1924.

Part@ton,J.R.,andSchilling,W. G.: TheSpecificHeatsofGases.ErnestBerm(London),1924.

Swarm,W.F. G.: SpecificHeatsofAirandC02atOneAtmosphere,by a ContinuousElectricalMethod.fioc.Roy.Sot.(Iondon),ser.A, vol.82,no.553,nay6,1909,PP.147-149.

Henry,P. S.H.,Blackett,P.M. S.,andRideal,E. K.: A FlowMethodforComparingtheSpecificHeatsofGases.Proc.Roy.Sot.(London),ser.A, vol.126,no.801,Jan.1,1930,pp.319-333.

Osborne,NathanS.,Stimson,H. F.,andSlight,T.S.,Jr.: A FlowCalorimeterforSpecificHeatsofGases.Sci..PaperNo.503,Bur.Standards,vol.20,April4,1925,pp.498-523.

.

—— ——

NACAm 2838

,

23

Run

B123

:

789

10u.121314151617181920212223242526

Flowrate

(lb/hr)

30.71;;.:;31:4528.7528.1331.2133.4030.4229.1032.7137.5828.1032.6730.3830.1928.0829.9328.9230.1232.7831.1030.0030.4230.6830.23

Netheatinput(Btu/hr)

174.2252.5217.4200.7213.2208.2208.4207.5425.9286.7283.3264.1259.9234.5234.0229.3234.8234.2233.1232.2251.8264.7263.5279.2279.1282.0

TABLEI

TABULATEDRESULTS

Temperaturerise(OF)

21.2331.5725.6827.8328.5028.8226.4025.08“38.1034.3236.8234.5034.4028.4031.8233*5532.u30.6232.0531.4031.5231.2032.6334.7835.1032.70

Meantemperature

(OF)

339.0338.0339.0339.0540.5537.5535.5533.5145.0101.599.599.5

297.0292.0293.0293.0456.o453.0453.0454.0 ‘455

%686687951

%orrectedfora slighttransientcondition.

Pressure(psia)

101571541520

101571541520

101551531520

101571541520

101571541521520

101571541520

1015

Btu/;b)(%

0.2669.2537.2435.2293.26r2.2569.2531.2475.3672.2870.23TL.2038.2687.2530.2420.2263.2605.2555.2514.2457.2435.2727.2691.2683.2589.2853

(SeeappendixA.)

~

.,

—_______ .—. - ———— ——— .—-—— —=. ——

24 NAC!.ATN 2838

TABLEII

VALUESCOMPUTED‘US~GMEAN~ DIFFERENCE

Temperature % % Qg(%) ~AT m

100 1.40 0.0186 0.0260200 2.00 .0210 .0420400 4.40 .0260 .1144600 8.20 .0310 .25ti800 14.0 .0360 .4890

1000 22.0 .0410 .9020

.

.

.

—

0-300 Psl

>cREGULATORS

T

300-1000 Psl

Coz CYLINDERS

—

VOLUMETRIC

DISPLACEMENT

METER

IT6AS HEATER ELECTRIC HEATERS

tzI

f In

— c T@.“’c :; ,=11%2\

I Ill\ \ I

CALORIMETER ~ HEATER :

I

-–HUMIDIFIERS C OLER

Figure1.- Schematic layout of sy8tem. 0

(“73’)o

0 0

0 O*

00oo~fi$o

,.

@ /

Vm AA

--?

L-

F@re 2.- Calorimeter detail.

r , , ,

t

?’”2 ‘n”11PK!F “

I

!]IUDI H!r

Heater Wound With 14.3 ft ofNo.26 Kanthal Wire

@

IiFigure3.-Test-gas electrical heater. Twice full scale.

I

28 NAC!.ATN 2838

.

COMs

FILLEDWITH

ISENCEMENT

1/4 in

.

Figure4.-Thermocoupleleadsealassembly.Twicefullscale.

———— .———— .—

.033C

.0320

,0310

.0”300

.0290

,0280=%%=.

100200300400500600 700~9001000

TEMPERATURE, 0 F

Figure .5.- Slope of calibration curve for Leeds & Northrup standard 11031iron-conatantanthermocouple.

30

,04

,03

*O2

,01

00

/’

200 4 o E

NACATN 23*

Zj7

‘o 1000

TEMPERATURE, 0F

Figure6.- Isothermaldifferentialfordifferentialthermocouple.

.

.

,— . .

31

ILo

.

..

.360

,340

,320

.300

,280

,260

.24C

.220

.2000

/

ELLENWOOD,KULIK, .4100° Fa GAY

+

/ ELLENWOOD,_

. .

. .. .

III EXP. DATA 145 ‘Fo E)(P, DATA. 100° F.

200 “400 600 ‘ 800 1000PRESSURE,psia ‘ . .

Fi@re 7.- Effectofpressureuponconstant-pressurespecificheatofcar~ondioxideat 100°andlw” F.

———— —.— .—. .._ .

32 NACAm 2838

.

.280

,270

260

,250

,240

,230

0220

ELLENWOOD,KULIK,& GAY

/ - EXPERIMENTALDATA

=@=

—-- ----

.

0 200 400 600 800 1000

PRESSURE,psia

Figure8.- Effectofpressureuponconstant-pressurespecificheatofcarbondioxideat295°F.

.

.

.

5B NACATN2838 33

.280

.270

,260

,250

no

.240

,230

,220

ELLENWOOD,KULIK,

8 “y -L .

- 200 400 t

1 /

4“

- EXPERIMENTALDATA

10 1000

PRESSURE,psia

Figure9.- Effectofpressureuponconstant-pressurespecificheatofcarbondioxideat 3400-F.

.

— —— — ——.— — –———

34. NACA m 2838

,280

.270

.260

,240

ELLENWOOD,KULIK

.2300 200

Figure10.- Effectof

EXPERIMENTAL DATA

400 600 800

PRESSURE,psia

pressureuponconstant-pressurecarbondioxideat455°F.

specific

.

.

—

35

..

.

,290

,280

,270

0260

250

,24C

ELLENWOOD;KULIK8 GAY ~

0 200

Figure11.- Effectof

/

EXPERiMENTA DATA —

400 600 800 1000

PRESSURE,psia

pressureuponconstant-pressurespecificheatofcarbondioxideat535°F.

—-— –——— —

36

.290

NAC!Am 2838

ILo

,280

La)

Q .27031-m

.

0= ,260

,250

,240

I ELLENWOOD,KULIK

‘ ‘“y-=-.-.-,EXPERiMENTAL DATA

o. 200

Figure1$’.- Effectof

400 600 800 1000

PRESSURE,psia

pressureuponconstant-pressurespecificheatofcarbondioxideat 685°F.

.

———

.28C

IL .2600LQJn

uc

s.240

a.

I

3

1- .220m

.Q

0

.200

.180

I ELLENWOOD, KULIK I8 GAY-

\

A

‘o 100 200 300 400 500

~ EXPERIMENTAL DATA I

TEMPERATURE , “F600 700

Figure 13. - Effect of temperatureof csxbon dioxide

upm constant-pressurespecific heatat zero pressure.

800

I

.300

IL0 ,280

=1-a! ,24C

“n

0

.220

.20C

%

ELLENWOOD, KULIK

~ GAY

\

EXPERIMENTAL DATA

/

v

100 200 300 400 500 600 700 800

TEMPERATURE ‘F

Figure 14.- Effect of temperature upon constant-pressme specific heatof carbon dioxide at 100 pounds per square inch absolute.

I

I

1

1

.320

.30C

L0La)n .280~zn

9 .26C?m.a

“ .240

.2200,

.,

?

ELLENWOOD, KULIK8 GAY

\

\ /

100 200 300 400 500 600

EXPERIMENTAL DATA .

T=J==700

TEMPERATURE, “F

Figure 15.- Effectoftemperature u~n constant-pressure specific heatof carbon dioxide at 300 pounds per square inch absolute.

\

Boo

IL0kaln

,340

.320

.300 1

\

280 :

.260

.240

‘ EXPERIMENTAL DATA

T

o 100 200 300 400 - 500 600 700 000TEMPERATURE, 0 F

Figure16.- Effect of temperature upon constant-pressurespecific heatof carbon.dioxide at ~ wunm per square Inch absolute.

I

I

I

I

1,

(

i

I

(

I

Lmn

3!-m

.

on

.360

.340

.320.

.300.

,280.

.260,100 2(

ELLENWOOD, KULIK& GAY

/

3 300 400 500 600 7TEMPERATURE, “F

I I

EXPERIMENTAL DATA .

/

*

10 800 900

Figure 17.- Eflect of tem~rature upon constant-pressurespecific heatof carbon dioxide at 1000 pounds per square Inch absolute.

I

360

340

3?0

\1000

.300 PUIQu.●

,

2)

~~ ~

,280 \, / fg

/

ka

/ / ‘MO

E/ ‘ ZERO-PRESSURE DATA d

JOHNSTON .j

\240 \ /

\ 300 & /

220100pnb

AT

.2000 I(XY 200 300 w 500 600 Too 800 Soo 1000 1100 1200

TEMPERATURE, ‘F

Figure 18.- Specific heat of carbon dioxide from experimentalresults.

-wm

.

I

i

i

I

II

,

140

u50n

“

s

,280

260

JOHNSTON

,240 \y /

SWANN ‘,220 , % GOODENOUGH a FE -BECK

PARTINGTON 8 SCHILLING

,200 EXPERIMENTAL

=s=

.180, “o 100 200 300 400 , 500 600 700 800

.

., TEMPERATURE, “F

Figore 19. - Comparison of low-pressure data for carbon dioxide.

I

F4=

I

I

10090

/ ~80

// ‘

70

/60 )

50

40 ‘

30

2 0

10-=%=-

0 I

0 2 4 6 8 10 12 14 16 18 20

WAVE LENGTH, microns

Figure 20.- S~ctral reflectivity of Inconel.

7B

.

NACATN2838

30

20

10

c)

.05

.04

.03

1-& 4..z .02

,01

0

2

TEMPERATURE, ‘F .

Figure21.- TotalemissivityofInconel.

/

/

/

J__b!ico 200 400 600 800 1000 1200 IL

TEMPERATURE,“F

Figure22.- PlotoftemperatureagainstQr/h#T.

45

00

~—. . ..-—

L20

LOO

0.80

0.60 /

Q40/

020 ‘ /

—o

I

—

—

—

—

—

—

o 100 200

Figure 23.-

300 400 500 600 700 800 900 1000

TEMPERATURE, ‘F

Radiant heat loss fran test section.