A High-Temperature Transient Hot-Wire Thermal Conductivity Apparatus for Fluids

Transcription

1 [J. Res. Natl. Inst. Stand. Technl. 96, 247 (1991)] A High-Temperature Transient Ht-Wire Cnductivity Apparatus fr Fluids Vlume 96 Number 3 May-June 1991 R. A. Perkins and H. M. Rder Natinal Institute f Standards and Technlgy, Bulder, CO and C. A. Niet de Castr' Departament de Quimica, Universidade de Lisba, R. Ernest Vascncels, Blc Cl, 1700 Lisba, Prtugal A new apparatus fr measuring bth the thermal cnductivity and thermal diffusivity f fluids at temperatures frm 220 t 775 at pressures t 70 MPa is described. The instrument is based n the step-fwwer-frced transient ht-wire technique. Tw ht wires are arranged in different arms f a Wheatstne bridge such that the respnse f the shrter cmpensating wire is subtracted frm the respnse f the primary wire. Bth ht wires are 12.7 (im diameter platinum wire and are simultaneusly used as electrical heat surces and as resistance thermmeters. A micrcmputer cntrls bridge nulling, applies the pwer pulse, mnitrs the bridge respnse, and stres the results. Perfrmance f the instrument was verified with measurements n liquid tluene as well as argn and nitrgen gas. In particular, new data fr the thermal cnductivity f liquid tluene near the saturatin line, between 298 and 550, are presented. These new data can be used t illustrate the imprtance f radiative heat transfer in transient htwire measurements. cnductivity data fr liquid tluene, which are crrected fr radiatin, are reprted. The precisin f the thermal cnductivity data is ±0.3% and the accuracy is abut ±1%. The accuracy f the thermal diffusivity data is abut ±5%. Frm the measured thermal cnductivity and thermal diffusivity, we can calculate the specific heat, Cp, f the fluid, prvided that the density is measured, r available thrugh an equatin f state. ey wrds: argn; heat capacity; nitrgen; radiatin crrectin; thermal cnductivity; thermal diffusivity; tluene; transient ht-wire. Accepted: March 5, Intrductin The transient ht-wire methd is widely accepted as the mst accurate technique fr fluid thermal cnductivity measurements at physical states remved frm the critical regin prper [1], The methd is very fast relative t steady state techniques. The duratin f a typical experiment is abut 1 s when 250 temperature rises are measured. Nrmally the experiment is cmpleted befre free cnvectin can develp in the fluid. If free cnvectin is present, it is easy t detect be- ' Als Centr de Quimica Estrutural, Cmplex I, 1ST, 1096 Lisba Cdex, Prtugal. 247 cause it results in a prnunced curvature in the graph f temperature rise versus the lgarithm f time. In additin t the thermal cnductivity, thermal diffusivity can be measured with transient ht-wire instruments. With an apprpriate design f the instrument [2], measurements f fluid thermal diffusivity can be made with reasnable accuracy ver wide ranges f density. The heat capacity f a fluid can then be btained frm the measurements f thermal cnductivity and thermal diffusivity, prvided that the density is knwn r available frm an equatin f state.

2 2. Methd The transient ht-wire system is cnsidered t be an abslute primary instrument [1]. The ideal wrking equatin is based n the transient slutin f Furier's law fr an infinite linear heat surce [3]. The temperature rise f the fluid at the surface f the wire, where r =r, at time / is given by ATi, ideal' (-0=4^1n(i)=^ln(i^) -*-4lx'"('). (1) In eq (1), q is the pwer input per unit length f wire, \ is the thermal cnductivity, a = X/pQ is the thermal diffusivity f the fluid, p is the density, Q, is the isbaric heat capacity, and C = e^ = is the expnential f Euler's cnstant. We use eq (1) and deduce the thermal cnductivity frm the slpe f a line fit t the ATjdeai versus ln(f) data. The wrking equatin fr the thermal diffusivity is At (2) The thermal diffusivity is btained frm X and a value f Aridcai, frm the fit line, at an arbitrary time t'. We nrmally select f' t be 1 s in ur data analysis, as discussed in reference [2]. The thermal cnductivity is reprted at the reference temperature T, and density p, defined in eq (3) belw. The thermal diffusivity calculated frm eq (2) must be referred t zer time, that is, the equilibrium r cell temperature. In summary, the thermal cnductivity and the thermal diffusivity evaluated by the data reductin prgram are related t the reference state variables and t the zer time cell variables as fllws: X = X(rr,pr), rr=r+.5(ari i,ii+arfi a,), Pr = p(rr,/'),. x(rfl,p) a =fl(p,7): (3) PO(CP)Q ' p = p(r/'), and (C;,)=Q(r A), where T is the equilibrium temperature and Pa is the equilibrium pressure at time t =Q. The experimental apparatus is designed t apprximate the ideal mdel as clsely as pssible. There are, hwever, a number f crrectins which accunt fr deviatins between the ideal linesurce heat transfer mdel and the actual experimental heat transfer situatin. The ideal temperature rise is btained by adding a number f crrectins t the experimental temperature rise as ATjdeal AT'experimental + 2j S^'- (4) These temperature rise crrectins are described in references [2,4]. Our implementatin f the crrectins fllws these tw references with the exceptin f the thermal radiatin crruptin. This crrectin is dependent n the ptical prperties f the fluid and the cell, and is discussed in mre detail belw. 2.1 The Radiatin Crrectin If the fluid is transparent t infrared radiatin, then this crrectin is nly a functin f the cell gemetry and the ptical prperties f the materials used in its cnstructin. The radiatin crrectin described in references [2,4] assumes that all f the surfaces in the cell are blackbdies. The blackbdy radiatin crrectin is given by 8757 = SirraT^AiT^ (5) where CT is the Stefan-Bltzmann cnstant. In practice, many experimenters assume that this crrectin is negligible and neglect the crrectin. We have fund that this crrectin changes the reprted thermal cnductivity f argn at 300 by abut 1% fr ur gemetry, s it is nt apprpriate t ignre it. A mre accurate crrectin can be btained by cnsidering the ptical prperties f the surfaces in the ht-wire cell. Fr this analysis we cnsider the cell surfaces t be diffuse gray surfaces and fllw the analysis presented in reference [5]. We cnsider the cell t be an infinitely lng ht wire in a cncentric cylindrical cavity. Thus, tw surfaces are invlved in the heat transfer. Surface 1 is the ht wire whse temperature is a functin f time, and surface 2 is the cylindrical cavity surrunding the ht wire which remains at the initial equilibrium temperature. The net radiative heat flux fr the ht wire, using the tabulated view factrs in reference [5], is AMTj-Tj) '"- ^t(--l)' (6) 248

3 where Ai is the area, 7} is the temperature, and e,- is the emissivity f surface /. The rati f the surface areas ^i/y42 which is present in the denminatr f eq (6) is quite small since very thin ht wires are used. In ur cell this surface area rati is AJ >42= The inverse emissivity f the ht wire 1/ei varies frm 10 t 25 fr platinum and l/e2 is apprximately 2. Therefre, the secnd term in the denminatr f eq (5) is negligible t within 0.1% in Qi, and we are left with Qi=Aieia{Tt-T^). (7) Because the surface area f the cavity surrunding the ht wire is s much larger than the surface area f the ht wire, t a first apprximatin the heat transfer is nt a functin f the emissivity f the cavity.^ The cavity appears t be a blackbdy, and the heat transfer is nly a functin f the emissivity f the platinum ht wire. Fllwing the analysis f reference [4], the resulting crrectin t the experimental temperature rise in a transparent fluid is 875T = SlTreplatinumO'T' Ar (8) The emissivity f platinum, epiatinum, is a functin f temperature and is tabulated in reference [6]. At 300 the emissivity f platinum is relative t an emissivity f 1 fr a blackbdy. The blackbdy radiatin crrectin f eq (5) is rughly 20 times larger than the real case, eq (8), when platinum ht wires are used. Fr fluids which absrb infrared radiatin, the technique described in reference [7] wrks well. The technique is based n the numerical simulatins f transient cnductin and radiative heat transfer frm a ht wire in an absrbing medium. Since the emissivity f the platinum ht wire is s small, the radiative heat flux frm the wire is negligible in the simulatins. The primary mechanism fr radiative lsses is frm emissin frm the fluid at the bundary f the expanding cnductin frnt. This analysis [7] yields a radiatin crrectin fr absrbing media which is given by 57'5A = 4ITX ri,(4at\ rs (9) ^This is pssible because, as shwn later, 21/^9=2x10"^ fr the transient ht-wire instrument and, therefre, an errr f 0.1% in Qi prduces an errr f 0.002% in q, well beynd the experimental accuracy. The radiatin parameter B is related t the fluid prperties by B = pcp (10) where is the mean extinctin cefficient f the fluid and n is its refractive index. These fluid prperties are a functin f the fluid density and temperature and are nt generally available. The prcedure described in reference [7] allws B t be estimated frm the experimental temperature rise data. Equatin (9) indicates that the radiatin crrectin intrduces a term which is a direct functin f time int the temperature rise equatin. When the radiatin crrectin is added t the ideal temperature rise, we btain ^^-ilb^m$)-^.^^. +. (11) Thus, we crrect the experimental data with all the ther crrectins and fit the resulting temperature rise t a functin f the frm AT = Ciln(0 + C2f+C3. (12) The experimental radiatin parameter B is determined frm cefficient C2 using B <^y (13) Once B is determined, we use eq (9) t crrect fr radiatin in the absrbing fluid. This technique allws us, as shwn later, t use ur experimental data t determine whether there is a significant thermal radiatin crrectin in an absrbing fluid and t crrect fr the radiatin. N prir knwledge f the ptical prperties f the fluid is required. 3. Apparatus The apparatus is quite similar t a previusly described lw temperature system [8] which is used frm 80 t 320. The new apparatus is designed t perate frm 220 t 750 at pressures t 70 MPa. A preliminary versin f the new instrument has been described elsewhere [9]. Imprvements have been incrprated int the new system t imprve the precisin and accuracy f the thermal cnduc- 249

4 tivity measurement and t enable measurement f the thermal diffusivity. They were based n mdificatins intrduced in the lw temperature system which are fully described in references [10] and [11]. 3.1 Ht Wires The ht wires are selected t cnfrm t the ideal line-surce mdel as clsely as pssible. The line-surce mdel assumes that the wire has n heat capacity and that it is infinitely lng, s there is n axial heat cnductin. The wire diameter is 12.7 (xm in this instrument t minimize effects due t its finite heat capacity while retaining gd tensile strength and unifrmity. A tw-wire cmpensating system is used in rder t eliminate effects due t axial heat cnductin. The arrangement f the tw wires is shwn in figure 1. The tw wires have different lengths and are arranged in a mdified Wheatstne bridge where the thermal respnse f the shrt wire is subtracted frm the respnse f the lng wire. The resulting respnse frm a finite length f wire apprximates that f an infinitely lng ht wire. The length f the equivalent wire is the difference in the lengths f the lng and shrt ht wires. The ht wires are used simultaneusly as electrical heat surces and as resistance thermmeters. Pint F Lng Ht-Wire Pint E Pint G Shrt Ht-Wire Pint H High Pressure Cell Bundary Figure 1. Arrangement f current leads (i) and ptential taps (P) within the pressure cell. Bridge pints crrespnd t thse in figure 3. Platinum wire is used in this instrument because its mechanical and electrical prperties are well knwn ver a wide temperature range, and it is resistant t crrsin up t 750. As shwn abve, platinum has the added advantage f lw emissivity. The length f the lng ht wire is abut 19 cm. The length f the shrt ht wire is abut 5 cm. The platinum ht wires are annealed after they are installed, s that their resistance will be stable during high temperature peratin. The resistance f the annealed ht wires is abut 20% less than the harddrawn platinum wire. The resistance f the ht wires is calibrated in situ as a functin f temperature and pressure [12]. The wires are welded t rigid upper suspensin stirrups and weighted lwer suspensin stirrups. The flating lwer weights are used t tensin the wires and t allw fr thermal expansin. There are fine cpper wires welded between the bttm weights and the massive bttm leads. These fine wire leads are flexible s that they d nt intrduce significant stress n the platinum ht wires. This arrangement prvides bth current and ptential leads t bth ends f each ht wire. Thus, fur-terminal resistance measurements can be made n bth the lng and shrt ht wires, eliminating uncertainty due t lead resistances. 3.2 Ht-Wire Cell The tw platinum ht wires are cntained in a pressure vessel which is designed fr 70 MPa at 750. The cell is cnnected with a capillary tube t a sample-handling manifld. This sample-handling manifld allws evacuatin f the cell, charging and pressurizatin f liquids with a screw pump, and pressurizatin f gases with a diaphragm cmpressr. There are seven electrical leads int the pressure vessel t enable fur-terminal resistance measurements f bth ht wires. The electrical leads pass thrugh a 6.25 mm O.D. pressure tube which cnnects the bttm f the pressure vessel t the lead pressure seal. The pressure seal fr the electrical leads is made at ambient temperature fr imprved reliability. The vessel access tube is lcated n the bttm f the vessel s that there is always a psitive temperature gradient with respect t height t eliminate free cnvective driving frces. The entire pressure system is cnstructed f 316 stainless steel fr crrsin resistance. The thermal cnductivity cell is shwn in its temperature cntrl envirnment in figure 2. The cell pressure vessel is surrunded by a 12 mm thick cylindrical aluminum heat shield. The aluminum 250

5 Pressurizatin Blts Cntrl RTD Tp RTD Cylindrical Heater Pressure Cell Cell Wrk Space Cell Clsure Supprt and Leveling Screws the feedback signal fr the furnace temperature cntrl system. The main pwer supply is under cmputer cntrl and is cnnected t the bttm end heating element and the tubular heating elements. The secnd trim pwer supply is manually cntrlled t eliminate axial gradients in the thermal cnductivity cell. The heating elements are driven with dc pwer supplies t minimize electrmagnetic nise in the thermal cnductivity instrument. Temperature fluctuatins in the cell are nrmally less than Fr experiments between 220 and 300, the electrical heaters are replaced by a cpper cling cil enclsed in plystyrene insulatin. A refrigerant with a lw freezing pint is pumped thrugh the cling cil by a recirculating temperature cntrl bath. This recirculating bath cntrls the fluid temperature t within The aluminum heat shield and air gap further reduce the temperature fluctuatins in the cell t less that Cell Access, Wires and Sample Figure 2. High-pressure cell, shield, and furnace. has a high thermal cnductivity and prvides a nearly isthermal envirnment fr the pressure vessel. There is an air gap between the vessel and the heat shield. This air gap islates the pressure vessel frm temperature fluctuatins in the heat shield. Tubes are silver-sldered t the utside f the pressure vessel which enclse the reference standard platinum resistance thermmeter (PRT) and tw smaller platinum resistance prbes (RTDs). The tw RTDs can be mved axially alng the vessel t detect temperature gradients. Nrmally, ne RTD is lcated near the tp f the vessel, and the ther RTD is lcated near the bttm f the vessel. This cnfiguratin allws us t measure the cell temperature at the center f the vessel with the reference standard PRT and temperature gradient in the cell with the tw RTDs fr each thermal cnductivity measurement. Fr experiments frm ambient temperature t 750, the vessel and heat shield are placed in a cylindrical furnace cnstructed f heating elements cast in fibrus ceramic insulatin. These heating elements are shwn in figure 2 and are separated frm the aluminum heat shield by a secnd air gap. An additinal platinum RTD is lcated n the tp f the aluminum heat shield. This prbe prvides 3.3 Wheatstne Bridge Circuit This instrument uses a Wheatstne bridge circuit t mnitr the resistance changes f the ht wires during the step-pwer pulse. The tw ht wires are set up in ppsing legs f the Wheatstne bridge as shwn in figure 3. The drive vltage is applied acrss pints A and B. The bridge respnse is mnitred by a high speed digital multimeter acrss pints C and D. The bridge is initially balanced with a 100 mv drive vltage. There is negligible heating f the ht wires with this small balance vltage. The fur legs f the Wheatstne bridge are designated Rl, R2, R3, and R4. Each f the fur legs cntains a variable decade resistr. The smallest step n these decade resistrs is 0.01 fl. These fur decade resistrs are adjusted s that the bridge imbalance signal is 0 and the ttal resistance f each leg is the same. There are tw current paths between pints A and B. Each current path cntains a calibrated 100 n standard resistr in rder t determine the current flwing thrugh that path during the balancing prcedure. Figure 3 shws a number f vltage taps n the Wheatstne bridge which allw the multiplexed digital multimeter t measure the vltage drps acrss all f the resistances in the bridge. Using the current, prvided by the vltage drp acrss the standard resistrs, we can btain the resistance f all f the cmpnents f the bridge. These resistances must be knwn very precisely, and the bridge must be balanced very clsely, in 251

6 "Dummy Figure 3. The Wheatstne bridge schematic fr the transient ht-wire apparatus. Ptential taps are indicated by pints A-L. rder t btain accurate thermal diffusivities frm the experiment. vltages frm the cmpnents f the bridge have a significant impact n the balancing f the bridge. In rder t euminate errrs frm thermal vltages, the bridge is alternately measured with a psitive and negative drive vltage with a reversing relay. During the balancing prcedure, 10 alternating drive vltage cycles are measured. During each cycle the digital multimeter mnitrs the vltage acrss all f the vltage taps. These values are subsequently averaged and displayed by the system cmputer. When a satisfactry bridge balance is btained, we are ready t begin the transient ht-wire experiment. The pwer supply is switched t a dummy resistr and the drive vltage is set t a level which will prduce the desired heating f the ht wires. The experiment begins when the pwer supply is switched frm the dummy resistr t the Wheatstne bridge. During the experiment the multimeter recrds the bridge vltage as a functin f time acrss pints C and D. This signal is prprtinal t the differential resistance change f the tw ht wires. This differential resistance change f the tw wires is related t the temperature changes f the tw ht wires by the wire calibratin which is described belw. The experiment nrmally lasts 1 s with a bridge respnse vltage recrded every 4 ms. 3.4 Data Acquisitin and Cntrl Data acquisitin and cntrl are crdinated by a persnal cmputer. The cmputer cntrls the 252 cell temperature, synchrnizes the experimental timing, recrds the data, and prvides a graphical display f the data. The cmputer has an analgt-digital interface bard which generates the timing signals based n the cmputer's internal quartz crystal scillatr and cntrls the system vltage multiplexers. The cmputer is als equipped with an IEEE-488 interface which allws cmmunicatin with a dedicated digital temperature cntrller, a digital nanvltmeter, and the high speed digital multimeter. The cell PRT and the tw gradient RTDs are cnnected in series with a standard resistr and a precisin 1 ma current surce. The cmputer cntrls a multiplexer which allws the nanvltmeter t measure the vltage drps acrss the three resistance thermmeters and the calibrated standard resistr. Using the current which is determined by the vltage drp acrss the standard resistr, we can btain the resistances f the three thermmeters. A secnd multiplexer is cnnected t the input f the high speed digital multimeter. This multiplexer allws sampling f all the vltage taps n the Wheatstne bridge during bridge balancing. Since standard resistrs are included in bth current paths f the bridge, we can btain accurate measurements f all the resistances in the bridge. The resistance f the tw ht wires is used in cnjunctin with the PRT temperature t btain the calibratins fr the ht wires. In additin, the multiplexer allws us t measure the drive vltage and the resistance f the pwer switching relay fr

7 an accurate determinatin f the pwer applied t the ht wires. During the experiment, there are tw parallel systems measuring the bridge respnse. A 16 bit analg-t-digital cnverter directly mnitrs the bridge respnse, while the high speed digital multimeter mnitrs the respnse f an instrumentatin amplifier which is als cnnected acrss pints C and D. The instrumentatin amplifier has a fixed gain f 100 and als has an analg filter built in. This filter significantly reduces the nise f the bridge respnse but intrduces a time lag which we must accunt fr. The nise f the raw signal is 25 JLV but is reduced t 3 JLV by the filter. The experimental timing is fixed by the raw signal which is mnitred by the analg-t-digital cnverter. The relatively nisy raw signal is used t adjust the timing f the filtered bridge respnse which is recrded by the high speed digital multimeter. 4. Ht-Wire Calibratin The electrical resistance f pure platinum as a functin f temperature is very well characterized because f its widespread use in thermmetry. In mst thermmetry applicatins the platinum is maintained at ambient pressure. In transient htwire instruments, hwever, the platinum is immersed directly in the fluid f interest. Rder et al. [12] shwed that the effect f pressure n the resistance f the platinum ht wires must be accunted fr. The functinal frm f ur calibratin is given by R(T,P)=A+BT + CT^ + (P+ET)P, (14) where R is the wire resistance, T is the temperature, and P is the applied pressure. We have fund that an in situ calibratin prvides the mst reliable measurements pssible. In practice, we btain the resistance f bth ht wires at the cell temperature and pressure fr every experiment. The calibratin prcess is an integral part f balancing the bridge. As described abve, we have the capability t make a fur-terminal resistance measurement f each ht wire withut errrs frm the temperature-dependent lead resistance. When we have cmpleted all measurements n a given fluid, we d a surface fit f the resistance f each wire using the functinal frm abve. Examining trends in deviatins frm this surface fit helps us t detect incnsistent data. Slw changes in the calibratin usually indicate changes in the physical cnditin f the ht wires, such as cntin- 253 ued annealing f the platinum at high temperatures. Sudden changes in the wire calibratin prvide an indicatin f mechanical damage t the wires. In additin, the capability t generate an in situ calibratin prvides freedm t use materials ther than platinum fr the ht wires. 5. Perfrmance Verificatin Tluene was selected t verify the instrument perfrmance in the liquid phase since it has been recently recmmended as a thermal cnductivity reference standard [13]. Argn and nitrgen were selected t verify perfrmance f the apparatus in the gas phase since they have been widely studied with bth steady-state techniques and transient ht-wire instruments. In additin, they have been studied with ur lw temperature instrument s that discrepancies between the tw instruments can be detected and reslved. 5.1 Tluene The thermal cnductivity f liquid tluene has been widely studied with bth steady-state and transient ht-wire instruments fr a number f years. Early steady-state experiments n tluene were ften plagued by free cnvectin. Free cnvectin is easily avided in a transient ht-wire instrument, but, if present, is easily detected due t deviatins frm the ideal line-surce mdel. The cntributin f thermal radiatin t the apparent thermal cnductivity f tluene has als been f much cncern since tluene is nt transparent in the infrared. Niet de Castr et al. [7] have made an extensive study f thermal radiatin and cncluded that the radiative cntributin t heat transfer is very small fr tluene at temperatures up t 370. Abve 370, it was estimated that the cntributin f heat transprt by radiatin t the measured value f thermal cnductivity wuld increase with temperature resulting in nnzer values f the quantity B in eq (13). Tluene was selected t verify bth the perfrmance f the new instrument in the liquid phase and the size and effect f the radiative cntributin at the higher temperatures. The spectrscpic grade tluene used in ur verificatin measurements was dried ver calcium hydride and distilled t remve a trace f benzene impurity. The purified tluene was analyzed by gas chrmatgraphy and fund t have less than 50 parts per billin (ppb) benzene and less than 100 ppb water. The results f the saturated liquid tluene tests are prvided in table 1. In rder t

8 Table 1. cnductivity, thermal diffusivity, and heat capacity f liquid tluene frm 300 t 550 Run Pt. Pressure MPa Temperature Density ml/l Pwer W/m cnductivity W/(m-) STAT Cell temperature diffusivity m% DSTAT Specific heat J/(ml-) x10-' X10-' X10-' x10-' x10-' x10-' X10-' X10-' X10-' X10-' x10-' X10-' X10-' X10-' x10-' x10-' X10-' X10-' x10-' x10-' x10-' X10-' X10-' X10-' X10-' X10-' X10-' X10-' x10-' X10-' X10-' x10-' X10-' x10-' x10-' x10-' x10-' X10-' X10-' x10-' x10-' X10-' X10-' x10-' X10-' x10-' x10-' x10-' , x10-' X10-' X10-' x10-' x10-'

9 Table 1. cnductivity, thermal diffusivity, and heat capacity f liquid tluene frm 300 t 550 Cntinued Run Pt. Pressure MPa Temperature Density ml/l Pwer W/m cnductivity W/(m-) STAT Cell temperature diffusivity m% DSTAT Specific heat J/(ml-) x10-' x10-' X10-' X10-' x10-' x10-' X10-' X10-' x10-' x10-' x10-' X10-' X10-' X10-' x10-' x10-' x10-' x10-' J X10-' x10-' x10-' X10-' x10-' x10-' x10-' x10-' X10-' X10-' X10-' x10-' x10-' X10-' X10-' X10-' 0.0O X10-' X10-' X10-' x10-' x10-' x10-' x10-' X10-' x10-' x10-' x10-' x10-' X10-' X10-' x10-' x10-' x10-' 0.0O X10-'

10 Table 2. cnductivity, thermal diffusivity, and heal t capacity f argn gas near 300 Run Pt. Pressure MPa Temperature Density ml/l Pwer W/m cnductivity W/(m-) STAT Cell temperature diffusivity m^/s DSTAT Specific heat J/(ml-) X10-' X10-'' x10-'' X10-' X10-'' X10-' x10-' X10-' X10-' x10-' x10-' X10-' X10-' X10-' x10-' x10-' X10-' X10-' x10-' x10-' X10-' X10-' X10-' x10-' x10-' X10-' x10-' x10-' X10-' X10-' x10-' S X10-' X10-' x10-' X10-' x10-' X10-' x10-' x10-' X10-' x10-' x10-' x10-' X10-' X10-' x10-' X10-' x10-' x10-' x10-' losl X10-' x10-' X10-'

11 Table 2. cnductivity, thermal diffusivity, and heat capacity f argn gas near Cntinued Run Pt. Pressure MPa Temperature Density mi/l Pwer W/m cnductivity W/(m-) STAT Cell temperature diffusivity m^/s DSTAT Specific heat J/(ml-) x10-' X10-' X10-' x10-' x10-' X10-' x10-' x10-* X10-' X10-' X10-* X10-* x10-* X10-' X10-' X10-* x10-* X10-* x10-* x10-* x10-* X10-* x10-* X10-* X10-* X10-* O.OOl X10-* X10-* x10-* X10-* x10"* X10-* x10-* x10-* X10-* X10-* x10-* x10-* X10-* X10-* x10-* X10-* X10-* x10-* x10-* X10-* X10-* x10-* x10-* X10-* X10-* x10-* x10-*

12 Table 2. cnductivity, thermal diffusivity, and heal : capacity f argn gas near Cntinued Run Pt. Pressure MPa Temperature Density ml/l Pwer W/m cnductivity W/(m-) STAT Cell temperature diffusivity m% DSTAT Specific heat J/(ml-) x10-" X10-' x10-^ X10-' X10-' x10-' X10-' x10-' X10-' x10-' X10-' X10-' X10-' x10-' x10-' X10-' X10-' x10-' x10-' x10-' X10-' X10-' x10-' X10-' X10-' x10-' X10-' X10-' X10-' x10-' x10-' X10-' ,77, X10-' x10-' x10-' x10-' X10-' X10-' Table 3. cnductivity, thermal diffusivity, and heat capacity f nitrgen gas near 425 Run Pt. Pressure MPa Temperature Density mi/l Pwer W/m cnductivity W/(m-) STAT Cell temperature diffusivity m^/s DSTAT Specific heat J/(ml-) X10-' X10-* x10-" X10-" X10-' x10-' X10-'

13 Table 3. cnductivity, thermal diffusivity, and heat capacity f nitrgen gas near 425 Run Pt. Pressure MPa Temperature Density ml/l Pwer W/m cnductivity W/(m-) STAT Cell temperature diffusivity m% DSTAT Specific heat J/(ml-) X10-* x10-* x10-* X10-* X10-* X10-* x10-* x10-* x10-* X10"* X10-* x10-* x10-* x10-* x10-* X10-* X10-* x10-* x10-* x10-* x10-* X10-* x10-* x10-* x10-* x10-* x10-* x10-* x10-* X10-* X10-* X10-* x10-* x10-* X10-* X10-* x10-* x10"* x10-* x10-* X10-* X10-* x10-* x10-* X10-* X10-* x10-* x10-* X10-* x10-* x10-* x10"* x10"*

14 Table 3. cnductivity, thermal diffusivity, and heat capacity f nitrgen gas near 425 Cntinued Run Pt. Pressure Temperature Density Pwer MPa ml/l W/m cnductivity W/(m-) STAT Cell temperature diffusivity m^s DSTAT Specific heat J/(ml-) x10-' X10-" x10-" x10-' x10-' x10-' x10-* X10-* X10-' x x10-' X10-' btain the isbaric heat capacity frm the measured thermal diffusivity, we have calculated the density with the equatin f state f Gdwin [14]. Figure 4 shws a typical deviatin plt f the experimental temperature rises frm the full heat transfer mdel fr a liquid phase tluene pint (number 1202) at a temperature f 324. The deviatins frm linearity are less than 0.04%. The deviatins shw that much f the nise is due t 60 Hz electrmagnetic interference, but the nise is acceptably small. Table 1 shws tw additinal statistics which reflect nnlinearity f each data set relative t the ideal line surce mdel, eq (1), after crrecting accrding t eq (4). The first term is "STAT" which reflects the uncertainty in the slpe f the regressin line at a cnfidence level f 2 times the standard deviatin (2«T). The term "DSTAT" reflects the uncertainty in the intercept f the regressin line at a 2a cnfidence level. Fr instance, a value f "STAT" r "DSTAT" f O.OOl indicates the 2CT uncertainty is 0.1%. As discussed earlier, we expect the thermal radiatin crrectin t affect the measured thermal cnductivity f tluene mre and mre as the temperature is increased abve 370. The effect can be seen in the statistic "STAT" which is a numerical descriptin f a deviatin plt such as figure 4. Graphically, the deviatin plts are n lnger randm but becme systematically curved, as predicted by eq (11). Cnsequently, the thermal cnductivities b- es > Q \f O.OB Time, s 0.75 Figure 4. Typical deviatins f experimental temperature rises frm the calculated straight line versus the lg f time fr liquid tluene data pint 1202 at T = and P = MPa. 260

15 tained frm the usual linear fit are larger than they shuld be. T btain crrect results, we apply eq (12) t the experimentally measured temperature rises and evaluate B fr every individual pint. Next, the experimentally determined values fr B are fit t a linear functin in temperature. The resulting expressin is B = x lo"" T (15) where 5 is in s"^ and T is in. The values given by eq (15) are used t re-evaluate the radiatin crrectin, 8T5, fr each data pint. The results crrected in this fashin are given in table 1. Figure 5 shws the deviatin plt fr the temperature rises fr a tluene data pint (2105) at T = and P = MPa, befre and after the radiatin crrectin 575 has been applied. The deviatin "STAT" has decreased frm t and the curvature has been eliminated. These V.., Time, s Figure 5. Liquid tluene data pint 2105 at T = and P = MPa. a) befre applicatin f the radiatin crrectin, eq (9), "STAT" is b) after applicatin f the radiatin crrectin, eq (9), "STAT" is (b) results supprt the mdel develped by Niet de Castr et al. [7] t accunt fr the effect f radiatin in absrbing media, and suggest that the instrument with a revised 87$ is perating in accrdance with its mathematical mdel. Figure 6 shws bth the uncrrected and the radiatin crrected thermal cnductivity values f tluene near the saturatin line as a functin f temperature. The standard reference data crrelatin f Niet de Castr et al. [13], which is valid t 360, is a line shwn in figure 8. The measurements f Fischer and Obermeier [15] are als displayed. These were btained with a rtating cncentric-cylinder apparatus, perating in steadystate mde, fr different gaps between the cylinders. We have included their extraplatin t zer gap, which is cnsidered t be their radiatin-crrected thermal cnductivity. Figure 6 shws that ur transient ht-wire instrument has a smaller radiatin cntributin than the steady-state measurements. Hwever, the transient ht-wire radiatin cntributin becmes significant at elevated temperatures, 3.1% at 550. The larger radiatin cntributin in steady-state methds prduces much larger uncertainty in the extraplated radiatin-crrected thermal cnductivity data btained with steady-state instruments. The temperature dependence alng the saturatin bundary, shwn in figure 6, is similar t the trend reprted in reference [13] with respect t the thermal cnductivity data f Niet de Castr et al. [7]. The data abve 370 shw the presence f radiative effects. Als shwn in figure 6, as an insert, are the cmpressed-liquid data at 550, which crrespnd t the shaded area f the diagram. Deviatins between the tluene thermal cnductivity data and the crrelatin by Niet de Castr et al. [13] are shwn in figure 7 fr temperatures up t 380. All f the data are within 1% f the crrelatin frm 300 t 372 ; hwever, the deviatins are systematic. We suggest that a higher-rder temperature-dependent term might be added t the crrelatin in rder t extend its temperature range. Figure 8 displays the deviatins between the heat capacity f tluene btained frm the measured thermal diffusivity and thermal cnductivity using the density frm the equatin f state f Gdwin [14], versus the Cp value calculated by this equatin f state. The data, uncrrected fr radiatin, shw systematic departures frm the equatin-f-state predictin abve 370, with deviatins f 30% at 550. After the adjusted radiatin crrectin BTs is applied, the deviatins decrease t less than 10% at the highest temperature, falling in a band f ±5% 261