conductivity

InternationalJournalofThermophysics,VoL10,No.4,1989

AbsoluteMeasurementsoftheThermalConductivity

ofMixturesofAlcoholswithWater

,idou,~m1"2

ReceivedAugust10,1988

Newabsolutemeasurementsofthethermalconductivityofmixturesof

methanol,ethanol,surements

wereperformedinatantalum-typetransienthot-wireinstrumentatatmospheric

pressure,ralluncertaintyofthe

reportedvaluesistimatedtobelessthan_+0.5%,anestimateconfirmedby

tureswithwater

studiedhavecompositionsof25,50,and75%,byweight,ofmethanoland

ethanoland50%,byweight,tlypropodmiempirical

schemeforthepredictionofthethermalconductivityofpureliquidsixtended

toallowthepredictionofthethermalconductivityofthemixturesfromthe

purecomponents,asafunctionofbothcompositionandtemperature.

KEYWORDS:ethanol;methanol;mixtures;propanol;thermalconductivity;

transienthot-wiremethod;water.

UCTION

Intheprecedingpaper[1],anewmiempiricalschemeforthecorrelation

andpredictionofthethermalconductivityofawiderangeofliquidsis

emeisbadonanextensionofconceptsderivedfrom

therigid-spheremodelofden-fluidtransportproperties[2-6]andwas

ted

valuesofthethermalconductivityareshowntodifferlessthan_+4%from

accurateexperimentalvaluesoverthetemperaturerange110-370Kandat

pressuresupto600MPa.

1DepartmentofChemicalEngineering,AristotleUniversity,GR54006Thessaloniki,Greece.

2Permanentaddress:DepartmentofChemicalEngineeringandChemicalTechnology,

ImperialCollege,LondonSW72BY,UnitedKingdom.

793

0195-928x/89/.00/091989PlenumPublishingCorporation

794Assael,Charitidou,andWakeham

Fewaccuratemeasurementsofthethermalconductivityofliquid

ntriesofmeasurementswasperformedinorder

toexaminetheapplicationofthisschemetomixtures.

MENTAL

Inariesofrecentpapers[7-9],acomputer-controlledtransient

hot-wireinstrumenthasbeendescribed,andmeasurementsofthethermal

conductivityofwater[-8]andthealcohols,methanoltohexanol[8,9],

surementswereshowntodisplayan

uncertaintyof+0.5%.Fortheheatsource,twoanodizedtantalumwires

of25-#mdiameterwereud,inordertopreventpolarizationof25-#m

diameterwereud,inordertopreventpolarizationoftheelectrically

prentmeasurements,theinstrumenthasbeen

surementswerecarriedoutatatmospheric

hod

oftreatingtheeffectofradiativeheattransportadoptedisthesameasthat

propodbyLietal.[10]andNietodeCastroetal.[11].Asacheckof

thecontinuinggoodoperationoftheinstrument,waterwasmeasured

uesobtainedforwaterwereinfull

agreementwiththoreportedearlier[-8].

alsLtd.

withanominalpurityof99.8%formethanol,99.7%forethanol,and

99.8%amplesweretreatedforalongperiodoftime

uentgas

chromatographyanalysisshowedapurityofbetterthen99.9%forall

pleofwaterudwasalsosuppliedbythesamecompany

(HPLCgrade).Themixtureswerepreparedgravitationallyandtheuncer-

taintyinthecompositionwaslessthan0.005%.Threecompositionsfor

methanolandethanolmixtureswithwaterwerestudied,25,50,and75%,

aofpropanolandwatermixture,a50%,byweight,

compositionwaxamined.

S

InTablesI,II,andIIItheexperimentalthermalconductivityvalues

ofmethanol,ethanol,propanol,andtheirmixtureswithwaterarepren-

e-componentvalueshavebeenreportedinearlierpapers[8,9]

surements

wereperformedatatmosphericpressureandthetemperaturerange

suredthermalconductivityvalues,

ThermalConductivityofAlcohol-WaterMixtures795

rmalConductivityofMixturesofMethanolandWaterasa

FunctionofTemperatureatAtmosphericPressure

(CompositionsinWeightPercentageofMethanol)

100%75%50%25%

T),T

(K)(mW.m-~.K-')(K)

2T2T2

mW,m-~.K-~)(K)(mW,m-~.K-~)(K)(mW-m-~-K~)

301.30198,3304.03261.2304.26342,8305.19453.6

304.28197.8307,10262,3308.02344.9308,83459.4

306.32197.4310.70262.6311.18346.4311.02461.1

310,37197.5313.71263.9315.33348.5315.21467.8

313.07197,1317.25264.2317.85350.5319.64472.5

316.01197.4320,32265.2320,59352,3323.45477.2

318.97196.9323.67265.5326,72357,0326.29480,3

323,07196.0326.56267.5328,92358,4328.59483.2

325.41196.4

2,werefittedasafunctionoftheabsolutetemperature,T,tothelinear

function

2=ao+~lT(1)

Thevaluesofthecoefficients~oand~1,forthepurecomponentsandthe

mixtures,areshownisTableIVtogetherwiththeirvariancesandthe

Table1I.

TheThermalConductivityofMixturesofEthanolandWaterasa

FunctionofTemperatureatAtmosphericPressure

(CompositionsinWeightPercentageofEthanol)

100%75%50%25%

T2T2T2,T2

(K/(-K-l)(K)(rnW-rn-I-K-I)(K)(-I-K-j)(K)(,Ki)

305.74160,7300.98227.0302.12311.5301.52434.9

311.13160.0307,46228.5305,80314.5306.17440.5

312.69160.1310,48228,5310.13315.9310.20444.7

316.15159.6315.79229.2315,57318.5315.57451.7

319,87159.1318,68228,3320,07320.6319.67455.2

323.96159,0322.3228,9325.51322.9322.54459.4

325.82158.8326,27230,1333.16326.1327,64465.1

328.95159.0327,67229.8336.17326.8332.61472,7

331.43158.3332.54230,6339.03328.8

335.06158,0

796Assael,Charitidou,andWakeham

TableIlLTheThermalConductivityofMixturesofPropanolandWateras

aFunctionofTemperatureatAtmosphericPressure

(CompositionsinWeightPercentageofPropanol)

100%50%0%

T2

(K)(mW.m-1.K-1)

T2T).

(K)(roW.m-1.K-1)(K)(mW.m-1.K-~)

300.44149.1307.10312.3303.85614.4

304.59148.9310.16314.3306.98623.3

309.87148.0313.09316.3313.56631.3

312.18148.2316.35318.6317.75635.0

316.12147.4319.96320.3318.79635.7

322.01147.3323.36322.0319.81640.6

326.43146.0331.46326.0323.50642.7

331.22146.0334.82328.5325.74646.7

335.26145.4326.79648.9

340.74145.6327.51648.0

330.79652.7

332.71655.3

TableIuCoefficientsoftheLeast-SquaresStraight-LineFitof

theThermalConductivityasaFunctionofTemperature

(CompositionsinWeightPercentageofAlcohol)

(X0O{I(7

(mW.m1.K-l)(#W.m-l.K-1)(%)

Methanol/water

100%

75%

50%

25%

0%

Ethanol/water

100%

75%

50%

25%

0%

Propanol/water

100%

50%

0%

220.7+3.7-75___11+0.1

185.5-+6.2249+20+0.1

147.6___7.2639-+23-+0.1

73.7-+7.91247+24+0.1

209.2_+15.41342_____48+0.2

186.4+2.2-84+6+0.1

198.7+5.095+15+0.2

178.5-+3.8443___+12__0.1

75.8-+7.51190_____24__0.1

209.2+15.41342-+48-+0.2

179.2+2.4-100+7__+0.2

139.2___4.9565_____15__0.1

209.2_+15.41342__48+0.2

15

330K

840/10/4-3

g

o

r<

L

o

r<

i

x

-15

15

,-*mido-~--~--~-~-~o,~-

6.O

~~JJII

9290K

99

qD~O0~~~qDql)ql)

(

~U99tl

.0

O-6.6.~0

-i~iii)(ik

lO0

WEIGHTOFMETHANOL,%

ionsofexperimentalthermalcon-

ductivityvaluesofmethanol/watermixtures,from

theprentwork,at290and330K.(O)Prent

work;(mm)Ref.12;(O)Ref.13;(ID)Ref.14.

g

x

o

o

,-<

Icl

x

cu

,.<

15

-15

15

-15

330K

%-

6.

6.

4)-

,,,,.

0

@

6.9-6'

I,i

9290Km

It)I)(qD

,I)o_o,~@-o_ol)o_~,.~o.e_~_q

%IF--

0

43"

6.

6.9"49_6.

rInnrnI

100

WEIGHTOFETHANOL,~

ionsofexperimentalthermalcon-

ductivityvaluesofethanol/watermixtures,fromthe

prentwork,at290and330K.(O)Prentwork;

(m)Ref.12;(O)Ref.13;(ID)Ref.14;(())

Ref.15;(~)Ref.16.

798Assael,Charitidou,andWakeham

eenthatthestandarddeviation

ofthefitsislessthan_+0.2%.Figure1showsaplotofthedeviationsof

thethermalconductivityofotherinvestigatorsat290and330Kfor

mixturesofmethanolwithwater,2shows

aratusudbythe

aretheplots,

asmallamountofinterpolationwasudfortheotherinvestigators,

producinganerrorofabout_+0.5%.Itcanbeeninthefiguresthat

deviationxtendto_+15%,inthemeasurementsofBatesandHazzard

[12]andFilippov[13].ThevaluesofRiedel[14],Tdeberg[15],and

PopovandMalov[16]arewithin_+5%

thecaofthe50%,byweight,propanol-watermixture,thevaluesof

Riedel[14]arewithin-+3%oftheprentmeasurements.

ENTATIONOFTHEMIXTURETHERMAL

CONDUCTIVITY

Inariesofrecentpapers[24]onconceptsrelatedtotheapplica-

tionoftheEnskogtheorytothevanderWaalsmodelofadenfluid

[5,6],ithasbeenshownthattheexperimentalquantity,

2*=1.9362x107(M/RT)1/22V2/3(2)

foraparticularliquidisafunctiononlyoftheratioofthemolarvolume,

V,toacharacteristicmolarvolumeVo[4],sothat

2*=F(V/Vo)(3)

Here,Misthemolecularweight,Rthegasconstant;Ttheabsolute

temperature,andVoacharacteristicmolarvolumedisplayingaweak

on(3)impliesthatitshouldbe

possibletosuperimpoplotsofexperimentalcurvesof2"againstInVfor

asinglefluidatariesoftemperaturesmerelybyimposingrelativeshifts

ingareferencevaluetoVoforonefluidatthe

lowesttemperatureforwhichaccuratemeasurementsofthethermalcon-

ductivityexist,theamountofshiftrequiredwillproducethevaluesofVo

.[3]udtheaccuratemeasurementsof11

hydrocarbonliquidsoverthetemperaturerange110-370Kandfor

pressuresupto600MPatodeterminethefunctionF(V/Vo)ofEq.(3).

Thesinglecurveof2*asafunctionofreducedmolarvolumecanbe

reprentedbytheequation,

In2*=4.8991-2.2595In(V/Vo)(4)

ThermalConductivityofAlcohol-WaterMixtures799

Adoptingthehypothesisthattheuniversalityofthefunction2*extends

beyondthenormalalkanes,andinparticulartothealcohols,Eqs.(2)and

(4)maybeemployedtoevaluatethecharacteristicmolarvolumes,V0,for

uesofVothuscalculatedcanbe

reprentedasafunctionoftheabsolutetemperaturebythelinear

function,

Vo=b0+blT(5)

Thevaluesofthecoefficientsboandbtformethanol,ethanol,propanol

andwaterhavebeenreportedearlier[4]andareshowninTableV.

Inordertocorrelatethemixturesthermalconductivity,theprocedure

adoptedwastheoneudtocorrelateourearliermeasurementsof

mixturesofethyleneandpropyleneglycolswithwater[17].According

tothisprocedure,itwasbeenpostulatedthatthemixturewillbean

equivalentliquidwithamolefractionaveragemolecularweight,amass

fractionaveragedensity,andacharacteristicmolarvolume,mix

Vo,givenby

thefollowingmixingrule;

V~TM=XVI+(1-X)VII-X(1-X)C(6)

whereV~andVnarethecharacteristicmolarvolumesofthepure

components,undtobeaconstant

characteristicofthepurecomponents,independentoftemperatureand

composition,ue

-tforthe

methanolwatermixtures,-tfortheethanolwater

-~

Fig.3thedeviationsoftheexperimentalthermalconductivitiesofthe

mixturesfromthocorrelatedbytheschemeofEq.(2)andEqs.(4)-(6)

eenthatthemaximumdeviationofallmixturesis

oneof_+2.2%.Theadvantagesofthisschemeisthatitissimpletouand

cientsoftheLeast-SquaresStraight-LineFitofthe

CharacteristicMolarVolumeasaFunctionofTemperature,Eq.(5)

bobl

(-l)(10-gm3-mol1.K-l)

Water6.2286.238

Methanol12.4951.187

Ethanol20.7621.556

Propanol31.2221.568

800Assael,Charitidou,andWakeham

C3

C3

x

L_

9

L3

,-<

L

O

tD

,-<

I

~<

0J

,.<

-Z

[]

9A

aa

~BIAQI

rl

01A

riir

29035c

T,K

ionsoftheexperimentalthermalconductivityvaluesfrom

thecorrelatingscheme,Eq.(2)andEqs.(4)-(6).(0)Methanol;(11)

ethanol;(A)propanol;((3)ol/water:(@)75%;(~)

50%;(~)25%.Ethanol/water:(~il)75%;(rl)50%;(t~)25%.

Propanol/water:(A)50%.

thevalueofCforaparticularmixturecanbedeterminedfromjustone

measurementofthethermalconductivityofasinglemixtureatonetem-

rmore,itemsthatitmightbepossibletocorrelatethe

heme,however,hasnopredictivepower

becauthethermalconductivitiesofthepurecomponentsarenecessaryto

derivethecorrespondingvaluesofV~andV~I.

TION

Inarecentpaper[4],amolecular-groupcontribution-badscheme

wasdevelopedforthepredictionofthecharacteristicmolarvolume,Vo,

alequationforthetotalcharacteristic

molarvolumeofthepureliquids,expresdasgroupcontributions,is

where

=Vlollv2OHVoVo1B+-o+

23

106VNo(O,nc)=~~aijnSri

i=0j=O

11

106V~B(0,rtc)=~~bijrtjOi

i=oj=O

(7)

ThermalConductivityofAlcohol-WaterMixtures801

and

12

106V~~nc)=2Zcon{Oi

i=Oj=0

1

106V02~2djn~

j=0

0=T/273.15

where0isanondimensionaltemperaturedefinedforcomputationalcon-

valuesofthecoefficientsaij,bij,cij,

equationforthetotalcharacteristicmolarvolume,thefirsttermreprents

thecontributiontoVoifthechainwereastraightchainofnccarbon

ondtermreprentsanadditivecontribution,ifsixofthe

rdterm

reprentsanadditivecontributionforthecawhereonehydrogenatom

issubstitutedbyanOH-group,whilethefourthtermisrefferedtothe

schemedescribedbyEq.(7)andEqs.(2)and(4)wasshowntobeableto

predictvaluesofthethermalconductivitywithin_+4%inthetemperature

range110-370Kandforpressuresupto600MPa.

Applyingthisgroup-contributionscheme,Eq.(7)canbeudto

obtainthecharacteristicmolarvolumesofthepurecomponentsdirectly

withouttheneedformeasurementsofthepurecomponentsproperties.

fficientsao,bo,c~,anddjofEq.(7)

m39tool-1

ijagbqcijdj

00+6.3918-14.700-0.1630+4.40

01+9.7389--2.8280-4.5280+0.70

02+0.84785--+0.7807--

03-0.013132------

100+8.1945+1.7209--

11-4.57722-0.52991+4.4797--

120---0.69653--

130------

200------

21+1.40555------

220------

230------

802Assael,Charitidou,andWakeham

O

O

x

9

S

r-(

x

0

-4

000O0O0

~;~~~n~nun~

[][]~-i9

A

A

290351

T,K

ionsoftheexperimentalthermalconductivityvaluesfrom

thepredictivescheme,Eqs.(2),(4),(6),and(7).(O)Methanol;(ll)

ethanol;(A)propanol;(ol/water:(~)75%;(~)

50%;(~)25%.Ethanol/water:([~)75%;(Pll)50%;(/~)25%.

Propanol/water:(A)50%.

Subquently,Eqs.(2),(4),and(6)canbeemployedtocalculatethether-

malconductivityofthemixturesapplyingthesamemixingruleasinthe

evaluesoftheconstantCwerefoundtofitthe

4showsthedeviationsoftheexperimental

thermalconductivitiesofthepurecomponentsandthemixturesfromtheir

eenthatthemaximumdeviationis+_4%.The

advantageofthisschemeinrelationtothepreviousonediscusdisthat

measurementsofthethermalconductivityofthepurecomponentsarenot

inglemeasurementofamixtureatonetemperatureis

requiredtocalculatethevalueoftheconstantCinEq.(6),althoughfor

mixturesofcompoundsinahomologouschemicalries,itemsthatit

shouldbepossibletocorrelatethevalueofthisconstant.

SIONS

Newmeasurementsofthethermalconductivityofthemixtures

ofmethanol,ethanol,

measurementswereperformedatatmosphericpressureinatantalum-type

transienthot-wireinstrument,inthetemperaturerange300-345K,withan

uncertaintyof_+0.5%.

Acorrelatingschemeforthethermalconductivityofmixturesbad

eme

ThermalConductivityofAlcohol-WaterMixtures803

wasfoundtocorrelatethethermalconductivityofthemixtureswithan

uncertaintyof_+2.2%.Analternativereprentationwithmorepredictive

power,badonarecentlydevelopedmolecular-groupcontribution

scheme,wasfoundtoreprentthethermalconductivityofthemixtures

withanuncertaintyof+_4%.

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