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

A new apparatus for measuring both the thermal conductivity and thermal diffusivity of fluids at temperatures from 220 to 775 K at pressures to 70 MPa is described. The instrument is based on the step-power-forced transient hot-wire technique. Two hot wires are arranged in different arms of a Wheatstone bridge such that the response of the shorter compensating wire is subtracted from the response of the primary wire. Both hot wires are 12.7 µm diameter platinum wire and are simultaneously used as electrical heat sources and as resistance thermometers. A microcomputer controls bridge nulling, applies the power pulse, monitors the bridge response, and stores the results. Performance of the instrument was verified with measurements on liquid toluene as well as argon and nitrogen gas. In particular, new data for the thermal conductivity of liquid toluene near the saturation line, between 298 and 550 K, are presented. These new data can be used to illustrate the importance of radiative heat transfer in transient hot-wire measurements. Thermal conductivity data for liquid toluene, which are corrected for radiation, are reported. The precision of the thermal conductivity data is ± 0.3% and the accuracy is about ±1%. The accuracy of the thermal diffusivity data is about ± 5%. From the measured thermal conductivity and thermal diffusivity, we can calculate the specific heat, Cp, of the fluid, provided that the density is measured, or available through an equation of state.

A new apparatus for measuring both the thermal conductivity and thermal diffusivity of fluids at temperatures from 220 to 775 K at pressures to 70 MPa is described. The instrument is based on the step-fwwer-forced transient hot-wire technique. Two hot wires are arranged in different arms of a Wheatstone bridge such that the response of the shorter compensating wire is subtracted from the response of the primary wire. Both hot wires are 12.7 (im diameter platinum wire and are simultaneously used as electrical heat sources and as resistance thermometers. A microcomputer controls bridge nulling, applies the power pulse, monitors the bridge response, and stores the results. Performance of the instrument was verified with measurements on liquid toluene as well as argon and nitrogen gas. In particular, new data for the thermal conductivity of liquid toluene near the saturation line, between 298 and 550 K, are presented. These new data can be used to illustrate the importance of radiative heat transfer in transient hotwire measurements. Thermal conductivity data for liquid toluene, which are corrected for radiation, are reported. The precision of the thermal conductivity data is ±0.3% and the accuracy is about ±1%. The accuracy of the thermal diffusivity data is about ±5%. From

Introduction
The transient hot-wire method is widely accepted as the most accurate technique for fluid thermal conductivity measurements at physical states removed from the critical region proper [1], The method is very fast relative to steady state techniques. The duration of a typical experiment is about 1 s when 250 temperature rises are measured. Normally the experiment is completed before free convection can develop in the fluid. If free convection is present, it is easy to detect be-' Also Centro de Quimica Estrutural, Complexo I, 1ST, 1096 Lisboa Codex, Portugal.
cause it results in a pronounced curvature in the graph of temperature rise versus the logarithm of time.
In addition to the thermal conductivity, thermal diffusivity can be measured with transient hot-wire instruments. With an appropriate design of the instrument [2], measurements of fluid thermal diffusivity can be made with reasonable accuracy over wide ranges of density. The heat capacity of a fluid can then be obtained from the measurements of thermal conductivity and thermal diffusivity, provided that the density is known or available from an equation of state.

Method
The transient hot-wire system is considered to be an absolute primary instrument [1]. The ideal working equation is based on the transient solution of Fourier's law for an infinite linear heat source [3]. The temperature rise of the fluid at the surface of the wire, where r =ro, at time / is given by ATi, ideal' (-0=4^1n(i)=^ln(i^) -*-4lx'"('). (1) In eq (1), q is the power input per unit length of wire, \ is the thermal conductivity, a = X/pQ is the thermal diffusivity of the fluid, p is the density, Q, is the isobaric heat capacity, and C = e^ = 1.781... is the exponential of Euler's constant. We use eq (1) and deduce the thermal conductivity from the slope of a line fit to the ATjdeai versus ln(f) data. The working equation for the thermal diffusivity is At (2) The thermal diffusivity is obtained from X and a value of Aridcai, from the fit line, at an arbitrary time t'. We normally select f' to be 1 s in our data analysis, as discussed in reference [2].
The thermal conductivity is reported at the reference temperature T, and density p, defined in eq (3) below. The thermal diffusivity calculated from eq (2) must be referred to zero time, that is, the equilibrium or cell temperature. In summary, the thermal conductivity and the thermal diffusivity evaluated by the data reduction program are related to the reference state variables and to the zero time cell variables as follows: where To is the equilibrium temperature and Pa is the equilibrium pressure at time t =Q.
The experimental apparatus is designed to approximate the ideal model as closely as possible. There are, however, a number of corrections which account for deviations between the ideal linesource heat transfer model and the actual experimental heat transfer situation. The ideal temperature rise is obtained by adding a number of corrections to the experimental temperature rise as ATjdeal -AT'experimental + 2j S^'- (4) These temperature rise corrections are described in references [2,4]. Our implementation of the corrections follows these two references with the exception of the thermal radiation corruption. This correction is dependent on the optical properties of the fluid and the cell, and is discussed in more detail below.

The Radiation Correction
If the fluid is transparent to infrared radiation, then this correction is only a function of the cell geometry and the optical properties of the materials used in its construction. The radiation correction described in references [2,4] assumes that all of the surfaces in the cell are blackbodies. The blackbody radiation correction is given by 8757 = SirroaTo^AiT^ (5) where CT is the Stefan-Boltzmann constant. In practice, many experimenters assume that this correction is negligible and neglect the correction. We have found that this correction changes the reported thermal conductivity of argon at 300 K by about 1% for our geometry, so it is not appropriate to ignore it. A more accurate correction can be obtained by considering the optical properties of the surfaces in the hot-wire cell. For this analysis we consider the cell surfaces to be diffuse gray surfaces and follow the analysis presented in reference [5]. We consider the cell to be an infinitely long hot wire in a concentric cylindrical cavity. Thus, two surfaces are involved in the heat transfer. Surface 1 is the hot wire whose temperature is a function of time, and surface 2 is the cylindrical cavity surrounding the hot wire which remains at the initial equilibrium temperature. The net radiative heat flux for the hot wire, using the tabulated view factors in reference [5], is

AMTj-Tj)
'"-■^t(--l)' (6) where Ai is the area, 7} is the temperature, and e,-is the emissivity of surface /. The ratio of the surface areas ^i/y42 which is present in the denominator of eq (6) is quite small since very thin hot wires are used. In our cell this surface area ratio is AJ >42=0.001. The inverse emissivity of the hot wire 1/ei varies from 10 to 25 for platinum and l/e2 is approximately 2. Therefore, the second term in the denominator of eq (5) is negligible to within 0.1% in Qi, and we are left with Qi=Aieia{Tt-T^).

(7)
Because the surface area of the cavity surrounding the hot wire is so much larger than the surface area of the hot wire, to a first approximation the heat transfer is not a function of the emissivity of the cavity.^ The cavity appears to be a blackbody, and the heat transfer is only a function of the emissivity of the platinum hot wire. Following the analysis of reference [4], the resulting correction to the experimental temperature rise in a transparent fluid is The emissivity of platinum, epiatinum, is a function of temperature and is tabulated in reference [6]. At 300 K the emissivity of platinum is 0.0455 relative to an emissivity of 1 for a blackbody. The blackbody radiation correction of eq (5) is roughly 20 times larger than the real case, eq (8), when platinum hot wires are used. For fluids which absorb infrared radiation, the technique described in reference [7] works well. The technique is based on the numerical simulations of transient conduction and radiative heat transfer from a hot wire in an absorbing medium. Since the emissivity of the platinum hot wire is so small, the radiative heat flux from the wire is negligible in the simulations. The primary mechanism for radiative losses is from emission from the fluid at the boundary of the expanding conduction front. This analysis [7] yields a radiation correction for absorbing media which is given by 57'5A = 4ITX ri ,(4at\ rS (9) ^This is possible because, as shown later, 21/^9=2x10"^ for the transient hot-wire instrument and, therefore, an error of 0.1% in Qi produces an error of 0.002% in q, well beyond the experimental accuracy.
The radiation parameter B is related to the fluid properties by B = pCp (10) where K is the mean extinction coefficient of the fluid and n is its refractive index. These fluid properties are a function of the fluid density and temperature and are not generally available. The procedure described in reference [7] allows B to be estimated from the experimental temperature rise data. Equation (9) indicates that the radiation correction introduces a term which is a direct function of time into the temperature rise equation. When the radiation correction is added to the ideal temperature rise, we obtain ^^-iLb^m$)-^.^^. + . (11) Thus, we correct the experimental data with all the other corrections and fit the resulting temperature rise to a function of the form AT = Ciln(0 + C2f+C3. The experimental radiation parameter B is determined from coefficient C2 using B <^y (13) Once B is determined, we use eq (9) to correct for radiation in the absorbing fluid. This technique allows us, as shown later, to use our experimental data to determine whether there is a significant thermal radiation correction in an absorbing fluid and to correct for the radiation. No prior knowledge of the optical properties of the fluid is required.

Apparatus
The apparatus is quite similar to a previously described low temperature system [8] which is used from 80 to 320 K. The new apparatus is designed to operate from 220 to 750 K at pressures to 70 MPa. A preliminary version of the new instrument has been described elsewhere [9]. Improvements have been incorporated into the new system to improve the precision and accuracy of the thermal conduc-tivity measurement and to enable measurement of the thermal diffusivity. They were based on modifications introduced in the low temperature system which are fully described in references [10] and [11].

Hot Wires
The hot wires are selected to conform to the ideal line-source model as closely as possible. The line-source model assumes that the wire has no heat capacity and that it is infinitely long, so there is no axial heat conduction. The wire diameter is 12.7 (xm in this instrument to minimize effects due to its finite heat capacity while retaining good tensile strength and uniformity. A two-wire compensating system is used in order to eliminate effects due to axial heat conduction. The arrangement of the two wires is shown in figure 1. The two wires have different lengths and are arranged in a modified Wheatstone bridge where the thermal response of the short wire is subtracted from the response of the long wire. The resulting response from a finite length of wire approximates that of an infinitely long hot wire. The length of the equivalent wire is the difference in the lengths of the long and short hot wires.
The hot wires are used simultaneously as electrical heat sources and as resistance thermometers.  Platinum wire is used in this instrument because its mechanical and electrical properties are well known over a wide temperature range, and it is resistant to corrosion up to 750 K. As shown above, platinum has the added advantage of low emissivity. The length of the long hot wire is about 19 cm. The length of the short hot wire is about 5 cm. The platinum hot wires are annealed after they are installed, so that their resistance will be stable during high temperature operation. The resistance of the annealed hot wires is about 20% less than the harddrawn platinum wire. The resistance of the hot wires is calibrated in situ as a function of temperature and pressure [12].
The wires are welded to rigid upper suspension stirrups and weighted lower suspension stirrups. The floating lower weights are used to tension the wires and to allow for thermal expansion. There are fine copper wires welded between the bottom weights and the massive bottom leads. These fine wire leads are flexible so that they do not introduce significant stress on the platinum hot wires. This arrangement provides both current and potential leads to both ends of each hot wire. Thus, four-terminal resistance measurements can be made on both the long and short hot wires, eliminating uncertainty due to lead resistances.

Hot-Wire Cell
The two platinum hot wires are contained in a pressure vessel which is designed for 70 MPa at 750 K. The cell is connected with a capillary tube to a sample-handling manifold. This sample-handling manifold allows evacuation of the cell, charging and pressurization of liquids with a screw pump, and pressurization of gases with a diaphragm compressor. There are seven electrical leads into the pressure vessel to enable four-terminal resistance measurements of both hot wires. The electrical leads pass through a 6.25 mm O.D. pressure tube which connects the bottom of the pressure vessel to the lead pressure seal. The pressure seal for the electrical leads is made at ambient temperature for improved reliability. The vessel access tube is located on the bottom of the vessel so that there is always a positive temperature gradient with respect to height to eliminate free convective driving forces. The entire pressure system is constructed of 316 stainless steel for corrosion resistance.
The thermal conductivity cell is shown in its temperature control environment in figure 2. The cell pressure vessel is surrounded by a 12 mm thick cylindrical aluminum heat shield. The aluminum  has a high thermal conductivity and provides a nearly isothermal environment for the pressure vessel. There is an air gap between the vessel and the heat shield. This air gap isolates the pressure vessel from temperature fluctuations in the heat shield. Tubes are silver-soldered to the outside of the pressure vessel which enclose the reference standard platinum resistance thermometer (PRT) and two smaller platinum resistance probes (RTDs). The two RTDs can be moved axially along the vessel to detect temperature gradients. Normally, one RTD is located near the top of the vessel, and the other RTD is located near the bottom of the vessel. This configuration allows us to measure the cell temperature at the center of the vessel with the reference standard PRT and temperature gradient in the cell with the two RTDs for each thermal conductivity measurement.
For experiments from ambient temperature to 750 K, the vessel and heat shield are placed in a cylindrical furnace constructed of heating elements cast in fibrous ceramic insulation. These heating elements are shown in figure 2 and are separated from the aluminum heat shield by a second air gap. An additional platinum RTD is located on the top of the aluminum heat shield. This probe provides the feedback signal for the furnace temperature control system. The main power supply is under computer control and is connected to the bottom end heating element and the tubular heating elements. The second trim power supply is manually controlled to eliminate axial gradients in the thermal conductivity cell. The heating elements are driven with dc power supplies to minimize electromagnetic noise in the thermal conductivity instrument. Temperature fluctuations in the cell are normally less than 0.01 K.
For experiments between 220 and 300 K, the electrical heaters are replaced by a copper cooling coil enclosed in polystyrene insulation. A refrigerant with a low freezing point is pumped through the cooling coil by a recirculating temperature control bath. This recirculating bath controls the fluid temperature to within 0.01 K. The aluminum heat shield and air gap further reduce the temperature fluctuations in the cell to less that 0.01 K.

Wheatstone Bridge Circuit
This instrument uses a Wheatstone bridge circuit to monitor the resistance changes of the hot wires during the step-power pulse. The two hot wires are set up in opposing legs of the Wheatstone bridge as shown in figure 3. The drive voltage is applied across points A and B. The bridge response is monitored by a high speed digital multimeter across points C and D. The bridge is initially balanced with a 100 mV drive voltage. There is negligible heating of the hot wires with this small balance voltage. The four legs of the Wheatstone bridge are designated Rl, R2, R3, and R4. Each of the four legs contains a variable decade resistor. The smallest step on these decade resistors is 0.01 fl. These four decade resistors are adjusted so that the bridge imbalance signal is 0 and the total resistance of each leg is the same.
There are two current paths between points A and B. Each current path contains a calibrated 100 n standard resistor in order to determine the current flowing through that path during the balancing procedure. Figure 3 shows a number of voltage taps on the Wheatstone bridge which allow the multiplexed digital multimeter to measure the voltage drops across all of the resistances in the bridge. Using the current, provided by the voltage drop across the standard resistors, we can obtain the resistance of all of the components of the bridge.
These resistances must be known very precisely, and the bridge must be balanced very closely, in  order to obtain accurate thermal diffusivities from the experiment. Thermal voltages from the components of the bridge have a significant impact on the balancing of the bridge. In order to eUminate errors from thermal voltages, the bridge is alternately measured with a positive and negative drive voltage with a reversing relay. During the balancing procedure, 10 alternating drive voltage cycles are measured. During each cycle the digital multimeter monitors the voltage across all of the voltage taps. These values are subsequently averaged and displayed by the system computer.
When a satisfactory bridge balance is obtained, we are ready to begin the transient hot-wire experiment. The power supply is switched to a dummy resistor and the drive voltage is set to a level which will produce the desired heating of the hot wires. The experiment begins when the power supply is switched from the dummy resistor to the Wheatstone bridge. During the experiment the multimeter records the bridge voltage as a function of time across points C and D. This signal is proportional to the differential resistance change of the two hot wires. This differential resistance change of the two wires is related to the temperature changes of the two hot wires by the wire calibration which is described below. The experiment normally lasts 1 s with a bridge response voltage recorded every 4 ms.

Data Acquisition and Control
Data acquisition and control are coordinated by a personal computer. The computer controls the cell temperature, synchronizes the experimental timing, records the data, and provides a graphical display of the data. The computer has an analogto-digital interface board which generates the timing signals based on the computer's internal quartz crystal oscillator and controls the system voltage multiplexers. The computer is also equipped with an IEEE-488 interface which allows communication with a dedicated digital temperature controller, a digital nanovoltmeter, and the high speed digital multimeter.
The cell PRT and the two gradient RTDs are connected in series with a standard resistor and a precision 1 mA current source. The computer controls a multiplexer which allows the nanovoltmeter to measure the voltage drops across the three resistance thermometers and the calibrated standard resistor. Using the current which is determined by the voltage drop across the standard resistor, we can obtain the resistances of the three thermometers.
A second multiplexer is connected to the input of the high speed digital multimeter. This multiplexer allows sampling of all the voltage taps on the Wheatstone bridge during bridge balancing. Since standard resistors are included in both current paths of the bridge, we can obtain accurate measurements of all the resistances in the bridge. The resistance of the two hot wires is used in conjunction with the PRT temperature to obtain the calibrations for the hot wires. In addition, the multiplexer allows us to measure the drive voltage and the resistance of the power switching relay for an accurate determination of the power applied to the hot wires.
During the experiment, there are two parallel systems measuring the bridge response. A 16 bit analog-to-digital converter directly monitors the bridge response, while the high speed digital multimeter monitors the response of an instrumentation amplifier which is also connected across points C and D. The instrumentation amplifier has a fixed gain of 100 and also has an analog filter built in. This filter significantly reduces the noise of the bridge response but introduces a time lag which we must account for. The noise of the raw signal is 25 |JLV but is reduced to 3 |JLV by the filter. The experimental timing is fixed by the raw signal which is monitored by the analog-to-digital converter. The relatively noisy raw signal is used to adjust the timing of the filtered bridge response which is recorded by the high speed digital multimeter.

Hot-Wire Calibration
The electrical resistance of pure platinum as a function of temperature is very well characterized because of its widespread use in thermometry. In most thermometry applications the platinum is maintained at ambient pressure. In transient hotwire instruments, however, the platinum is immersed directly in the fluid of interest. Roder et al. [12] showed that the effect of pressure on the resistance of the platinum hot wires must be accounted for. The functional form of our calibration is given by where R is the wire resistance, T is the temperature, and P is the applied pressure.
We have found that an in situ calibration provides the most reliable measurements possible. In practice, we obtain the resistance of both hot wires at the cell temperature and pressure for every experiment. The calibration process is an integral part of balancing the bridge. As described above, we have the capability to make a four-terminal resistance measurement of each hot wire without errors from the temperature-dependent lead resistance. When we have completed all measurements on a given fluid, we do a surface fit of the resistance of each wire using the functional form above. Examining trends in deviations from this surface fit helps us to detect inconsistent data. Slow changes in the calibration usually indicate changes in the physical condition of the hot wires, such as contin-ued annealing of the platinum at high temperatures. Sudden changes in the wire calibration provide an indication of mechanical damage to the wires. In addition, the capability to generate an in situ calibration provides freedom to use materials other than platinum for the hot wires.

Performance Verification
Toluene was selected to verify the instrument performance in the liquid phase since it has been recently recommended as a thermal conductivity reference standard [13]. Argon and nitrogen were selected to verify performance of the apparatus in the gas phase since they have been widely studied with both steady-state techniques and transient hot-wire instruments. In addition, they have been studied with our low temperature instrument so that discrepancies between the two instruments can be detected and resolved.

Toluene
The thermal conductivity of liquid toluene has been widely studied with both steady-state and transient hot-wire instruments for a number of years. Early steady-state experiments on toluene were often plagued by free convection. Free convection is easily avoided in a transient hot-wire instrument, but, if present, is easily detected due to deviations from the ideal line-source model. The contribution of thermal radiation to the apparent thermal conductivity of toluene has also been of much concern since toluene is not transparent in the infrared. Nieto de Castro et al. [7] have made an extensive study of thermal radiation and concluded that the radiative contribution to heat transfer is very small for toluene at temperatures up to 370 K. Above 370 K, it was estimated that the contribution of heat transport by radiation to the measured value of thermal conductivity would increase with temperature resulting in nonzero values of the quantity B in eq (13). Toluene was selected to verify both the performance of the new instrument in the liquid phase and the size and effect of the radiative contribution at the higher temperatures.
The spectroscopic grade toluene used in our verification measurements was dried over calcium hydride and distilled to remove a trace of benzene impurity. The purified toluene was analyzed by gas chromatography and found to have less than 50 parts per billion (ppb) benzene and less than 100 ppb water. The results of the saturated liquid toluene tests are provided in table 1. In order to   obtain the isobaric heat capacity from the measured thermal diffusivity, we have calculated the density with the equation of state of Goodwin [14]. Figure 4 shows a typical deviation plot of the experimental temperature rises from the full heat transfer model for a liquid phase toluene point (number 1202) at a temperature of 324 K. The deviations from linearity are less than 0.04%. The deviations show that much of the noise is due to 60 Hz electromagnetic interference, but the noise is acceptably small. Table 1 shows two additional statistics which reflect nonlinearity of each data set relative to the ideal line source model, eq (1), after correcting according to eq (4). The first term is "STAT" which reflects the uncertainty in the slope of the regression line at a confidence level of 2 times the standard deviation (2«T). The term "DSTAT" reflects the uncertainty in the intercept of the regression line at a 2a confidence level. For instance, a value of "STAT" or "DSTAT" of O.OOl indicates the 2CT uncertainty is 0.1%. As discussed earlier, we expect the thermal radiation correction to affect the measured thermal conductivity of toluene more and more as the temperature is increased above 370 K. The effect can be seen in the statistic "STAT" which is a numerical description of a deviation plot such as figure 4. Graphically, the deviation plots are no longer random but become systematically curved, as predicted by eq (11). Consequently, the thermal conductivities ob-  tained from the usual linear fit are larger than they should be. To obtain correct results, we apply eq (12) to the experimentally measured temperature rises and evaluate B for every individual point. Next, the experimentally determined values for B are fit to a linear function in temperature. The resulting expression is B = -0.0685 + 2.310 x lO"" To (15) where 5 is in s"^ and To is in K. The values given by eq (15) are used to re-evaluate the radiation correction, 8T5, for each data point. The results corrected in this fashion are given in table 1. Figure 5 shows the deviation plot for the temperature rises for a toluene data point (2105) at To = 548.140 K and P = 2.686 MPa, before and after the radiation correction 575 has been applied. The deviation "STAT" has decreased from 0.002 to 0.001 and the curvature has been eliminated. These a) before application of the radiation correction, eq (9), "STAT" is 0.002. b) after application of the radiation correction, eq (9), "STAT" is 0.001. results support the model developed by Nieto de Castro et al. [7] to account for the effect of radiation in absorbing media, and suggest that the instrument with a revised 87$ is operating in accordance with its mathematical model. Figure 6 shows both the uncorrected and the radiation corrected thermal conductivity values of toluene near the saturation line as a function of temperature. The standard reference data correlation of Nieto de Castro et al. [13], which is valid to 360 K, is a line shown in figure 8. The measurements of Fischer and Obermeier [15] are also displayed. These were obtained with a rotating concentric-cylinder apparatus, operating in steadystate mode, for different gaps between the cylinders. We have included their extrapolation to zero gap, which is considered to be their radiation-corrected thermal conductivity. Figure 6 shows that our transient hot-wire instrument has a smaller radiation contribution than the steady-state measurements. However, the transient hot-wire radiation contribution becomes significant at elevated temperatures, 3.1% at 550 K. The larger radiation contribution in steady-state methods produces much larger uncertainty in the extrapolated radiation-corrected thermal conductivity data obtained with steady-state instruments. The temperature dependence along the saturation boundary, shown in figure 6, is similar to the trend reported in reference [13] with respect to the thermal conductivity data of Nieto de Castro et al. [7]. The data above 370 K show the presence of radiative effects. Also shown in figure 6, as an insert, are the compressed-liquid data at 550 K, which correspond to the shaded area of the diagram.
Deviations between the toluene thermal conductivity data and the correlation by Nieto de Castro et al. [13] are shown in figure 7 for temperatures up to 380 K. All of the data are within 1% of the correlation from 300 to 372 K; however, the deviations are systematic. We suggest that a higher-order temperature-dependent term might be added to the correlation in order to extend its temperature range. Figure 8 displays the deviations between the heat capacity of toluene obtained from the measured thermal diffusivity and thermal conductivity using the density from the equation of state of Goodwin [14], versus the Cp value calculated by this equation of state. The data, uncorrected for radiation, show systematic departures from the equation-of-state prediction above 370 K, with deviations of 30% at 550 K. After the adjusted radiation correction BTs is applied, the deviations decrease to less than 10% at the highest temperature, falling in a band of ±5% Temperature, K 500 550 Up to 500 K. The larger deviations above 500 K are still within the combined uncertainties of our diffusivity measurements and the equation of state of Goodwin [14]. Figures 6 and 8 demonstrate the performance of the instrument for the measurement of both thermal conductivity and thermal diffusivity at high temperatures in infrared absorbing fluids when the radiation correction, given by eqs (9) to (13) and (15), is applied.

Argon
We have previously reported two sets of transient hot-wire measurements of argon's thermal conductivity near 300 K [16,17]. Both of these data sets were made with the low temperature instrument described by Roder [8]. Thermal conductivity measurements on argon have also been reported by a number of other researchers [18][19][20][21][22]. Table 2 provides the results for the present measurements near 300 K. Younglove's equation of state [23] is used to obtain the densities reported in the table 2. The purity of the argon used in these measurements is better than 99.999%. Argon is transparent to thermal radiation, and the radiation correction at 300 K is negligible.
Deviations between the present thermal conductivity data and the new surface fit of Perkins et al. [24] as a function of density are shown in figure 9. The maximum deviation between our present measurements and the correlation is 1.2% at the highest densities. The present data were not, however, used in the development of the thermal conductivity surface [24]. The same trend of deviations relative to the correlation is exhibited by the other available data. Our thermal conductivity data agree with the results of the other data within ± 1%. All of the other data were made with transient hotwire instruments, with the exception of data from Michels et al. [19], which was obtained with a steady-state parallel-plate instrument.

Nitrogen
For the present instrument, table 3 provides the results on nitrogen for temperatures near 425 K. Younglove's equation of state [23] is used to obtain the densities reported in the table 3. The purity of the nitrogen used in these measurements is better than 99.999%. Nitrogen is transparent to thermal radiation, and the radiation correction at 425 K is negligible.
Deviations between our thermal conductivity data and the correlation of Stephan et al. [25] as a function of density are shown in figure 10. The maximum deviation between our measurements and the correlation is 2%. Nitrogen thermal conductivity measurements have also been reported by several other researchers [21,22,26]. The same trend of deviations relative to the correlation is exhibited by the other available data. Our thermal conductivity data agree with those results to 1%, except for values from reference [22] for densities above 9 mol-L"'. All of the other data were ob-tained with transient hot-wire instruments, with the exception of data from le Neindre [22], which were obtained with a steady-state concentric-cylinder instrument. The dilute gas value of Millat and Wakeham [27] is also plotted in this figure and agrees with the extrapolation of the present data within 0.5%. There is both theoretical [27] and experimental [28] evidence that the low density values of the Stephan et al. correlation [25] need to be revised. The correlation given by Younglove [23] has a completely different curvature as already shown in reference [28]. Figure 11 shows heat capacities of nitrogen given in table 3 for the isotherm at 425 K. The values are derived from the measured values of thermal conductivity and thermal diffusivity taking the densities from the equation of state [23]. They are compared to values calculated from the equation of state, and they are systematically higher than the equation-of-state predictions by about 5% except for the highest densities. We assign an estimated error of ±5% to our measured heat capacities; the   error estimated for the specific heats from the equation of state is also 5%. Thus, the agreement between the two sources is within their mutual uncertainties even at the higher densities.

Repeatability Tests
In addition to comparisons of our thermal conductivity data with the data and correlations of other researchers, we have made many measurements to assess the repeatability of the instrument. The temperature assigned to a given thermal conductivity measurement is a function of the fluid temperature rise during the experiment. As a result, each power represents a different and independent temperature rise and experimental temperature. For a given cell temperature, we routinely make measurements at many powers not only to verify the instrument performance but also to check on the presence of convection. To check repeatability, results at different powers are compared in terms of deviations from a correlation of the thermal conductivity surface. Figure 12 shows deviations of the liquid toluene thermal conductivity data for four cell temperatures as a function of the applied power. There are from five to eight different powers for each cell temperature. The maximum difference between the deviations for each cell temperature is about 0.3%, which is equivalent to the experimental precision in X. The deviations do not appear to have any power dependence.
The power dependence of the isobaric heat capacity of liquid toluene is shown in figure 13. The maximum difference between the deviations for each temperature is 2.6%. Again there is no discernable trend in the deviations of the heat capacity with respect to the applied power. Figure 14 shows a deviation plot of 40 argon thermal conductivity data points relative to the correlation of Younglove et al. [29]. The applied power ranges from 0.11 to 0.42 W/m for a range of final temperature rises from 0.8 to 5 K. The data were obtained in four different sequences over 2 days. The four measurement sequences are shown -Ref. [18] oRef. [22] -Ref. [21] -Ref. [20] -Ref. [19] -Ref. [16] «Ref. [17] %^^^ ° •present work v «" . with different plot symbols. The deviations from the correlation range from about -0.1% to -0.7%. Thus, the set of 40 measurements are consistent with each other and fall within a band of ±0.3%. The instrument's response is shown to be independent of applied power over a very wide range of temperature rises. The instrument's performance is also very repeatable over an extended period.

Summary
A new transient hot-wire thermal conductivity instrument for use at high temperatures is described. This instrument has an operating range from 220 to 750 K at pressures to 70 MPa. Thermal conductivity can be measured over a wide range of fluid density, from the dilute gas to the compressed liquid. The thermal conductivity data have a precision of ±0.3% and an accuracy of ±1%. The instrument is also capable of measuring the thermal diffusivity with a precision of ± 3% and an accuracy of ±5%, Given accurate fluid densities, we can obtain isobaric heat capacities from the data. This instrument complements our low temperature instrument [8] which has a temperature range from 80 to 325 K at pressures to 70 MPa, A detailed analysis of the influence of radiative heat transfer in the transient hot-wire experiment has been performed, and radiation-corrected thermal conductivities are reported for liquid toluene near saturation at temperatures between 300 and 550 K. In addition, new measurements of the thermal conductivity and thermal diffusivity of argon and nitrogen verify the performance of the apparatus. -Ref. [23] ■Ref. [27] V Ref. [22] -Ref. [26] «Ref. [21] •present work  Figure 11. Nitrogen isobaric heat capacity rela;ive to values calculated (solid line) from the equation of state of Younglove [23]. Dashed line is a 5% offset from [23].   Figure 14. Deviations in the thermal conductivity of argon gas as a function of applied power. Baseline is the correlation of Younglove et al. [29]. Dashed lines show 95% uncertainty band.