J. Chem. Thermodynamics 57 (2013) 276–285

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J. Chem. Thermodynamics

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Advanced calibration, adjustment, and operation of a density and soundspeed analyzer q

Tara J. Fortin ⇑, Arno Laesecke, Malte Freund 1, Stephanie OutcaltNational Institute of Standards and Technology, Material Measurement Laboratory, Applied Chemicals and Materials Division, 325 Broadway, Boulder, CO 80305, USA

a r t i c l e i n f o

Article history:Received 14 May 2012Received in revised form 1 September 2012Accepted 6 September 2012Available online 26 September 2012

Keywords:DensityIsooctaneSpeed of soundTolueneUncertaintyVibrating tube densimeter

0021-9614/$ - see front matter Published by Elsevierhttp://dx.doi.org/10.1016/j.jct.2012.09.009

q Contribution of the National Institute of Standardsto Copyright � in the USA.⇑ Corresponding author. Tel.: +1 303 497 5044; fax

E-mail address: tfortin@boulder.nist.gov (T.J. Forti1 Current address: Germanischer Lloyd SE, Enginee

D-20457 Hamburg, Germany.

a b s t r a c t

Benchtop measurement systems have emerged as powerful tools in the ongoing quest for thermophysicalproperty data. We demonstrate that these instruments can yield results of high quality if operated in aninformed manner. The importance of sample purity, reproducibility over repeatability, expanded calibra-tion and adjustment protocols, and rigorous uncertainty estimates are emphasized. We report measure-ment results at ambient atmospheric pressure and temperatures from 343 K to 278 K, includingexpanded uncertainty estimates, for the density and speed of sound of isooctane and for the speed ofsound of toluene. These data are useful for validating the performance of such instruments.

Published by Elsevier Ltd.

1. Introduction

Reliable thermophysical property data, such as density andspeed of sound, are essential for industrial process design, optimi-zation, and implementation. For example, density information isrequired for a variety of applications including, but not limitedto, flow metering, quality control, and fluid custody transfer [1].Similarly, the speed of sound is important in a number of technicalapplications such as flow measurements and production monitor-ing [2,3], but the primary interest in this property arises from itsrelation to other fluid properties (e.g., compressibility and heatcapacity) [4,5]. Presently, thermodynamic properties are most reli-ably calculated from Helmholtz equations of state; accurate den-sity and speed of sound data are essential to the developmentand validation of such equations [6].

Improvements in instrument technology have allowed bench-top instruments to emerge as potentially powerful measurementtools. Advances such as miniaturized sensors and thermoelectricthermostating have resulted in instruments that are largely auto-mated and are capable of rapid measurements over a wide rangeof temperatures. As these benchtop instruments are increasingly

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: +1 303 497 5044.n).ring Services, Brooktorkai 18,

utilized for property measurements at atmospheric pressure, it isimportant to bear in mind that their ability to yield high qualitydata requires that they be calibrated, adjusted, and operated inan informed manner.

To illustrate this point, we will discuss our long-term experi-ences with one such commercial instrument, a combination den-sity and sound speed analyzer. First, we will describe theexperimental apparatus. Then, we will present measurement re-sults for a variety of liquids (water, toluene, isooctane, aviationfuels, biofuels, etc.) to illustrate our key themes: the significanceof sample purity, the importance of reproducibility over repeat-ability, the need for expanded calibration and adjustment proto-cols, and the merit of rigorous uncertainty estimates.

2. Instrumentation

Over the last few years, commercial instruments have gainedpopularity within the thermophysical properties research commu-nity. The instrument used in this work, the DSA 5000§ from AntonPaar USA Inc, combines two miniaturized inline cells to simulta-neously measure the density and sound speed of liquid samples atambient atmospheric pressure. The arrangement of the two

§ In order to describe materials and experimental procedures adequately, it isoccasionally necessary to identify commercial products by manufacturers’ names orlabels. In no instance does such identification imply endorsement by the NationalInstitute of Standards and Technology, nor does it imply that the particular product orequipment is necessarily the best available for the purpose.

FIGURE 1. Schematic diagram of the measuring cells in the density and soundspeed analyzer.

TABLE 1Manufacturer’s specifications for the density and sound speed analyzer [7].

Density (q) Speed of sound (w)

Pressure range 0–0.3 MPaTemperature range 273–343 KMeasurement range 0–3000 kg�m�3 1000–2000 m�s�1

Measurement time 1–4 minTotal sample volume �3 cm3

Repeatability 0.001 kg�m�3 0.1 m�s�1

Uncertaintya 0.005 kg�m�3 0.5 m�s�1

a Referred to as ‘‘accuracy’’ by manufacturer.

FIGURE 2. Schematic diagram of the speed of sound cell including streamlinesrepresenting sample flow.

T.J. Fortin et al. / J. Chem. Thermodynamics 57 (2013) 276–285 277

measurement cells is illustrated in figure 1, and the instrument spec-ifications, as quoted by the manufacturer [7], are listed in table 1.Both measurement cells are housed in a thermostated block, thetemperature of which is controlled with a combination of thermo-electric Peltier elements and an integrated Pt-100 resistancethermometer. Although the manufacturer quotes an operating tem-perature range of 273 K to 343 K (table 1), the practicable lower tem-perature limit of the instrument is 278 K due to a significantdecrease in the cooling rate of the Peltier elements below this tem-perature. The practicable upper temperature limit is determined bythe boiling point of the liquid under study. To make a measurement,liquid sample is injected into the instrument using a syringe with aLuer tip. As is shown in figure 1, the sample first fills the sound speedcell and then the U-shaped density cell.

The speed of sound is measured using a propagation time tech-nique [2,5]. The sound speed cell (see figure 2) consists of a circularcavity 8 mm in diameter and 5 mm deep. The sample is sand-wiched between two piezoelectric ultrasound transducers. Onetransducer emits sound waves through the sample-filled cavityat a frequency of approximately 3 MHz; the second transducer re-ceives those waves. Thus, the speed of sound (w) is obtained bydividing the known distance between transmitter and receiver bythe measured propagation time of the sound wave. The equationused by the manufacturer to determine the speed of sound is

W ¼ l� ð1þ ð1:6� 10�5Þ � DTÞPS

512� s� f3; ð1Þ

where l is the path length of the sound speed cell at 293 K (�5 mm),DT is the temperature deviation from 293 K, PS is the measuredwave propagation time, s is an apparatus constant representingthe time delay associated with the instrument’s electronics, and f3

is a temperature correction term for s [8]. Therefore, the numeratorof equation (1) is the cell path length corrected for temperatureeffects, and the denominator is the propagation time from the

transmitter to the receiver after accounting for inherent delaysassociated with the instrument’s electronics. Measurements of airand water performed at 293 K, 313 K, and 333 K are required to ad-just the apparatus constants s and f3 in equation (1). In accordancewith the International Vocabulary of Metrology [9], this is referred toby the manufacturer as an adjustment procedure.

Density is measured using a vibrating tube densimeter. Sincethe technique was introduced by Kratky et al. in 1969 [10] anextensive body of literature covering principles of operation,instrument design, and calibration procedures has been accumu-lated [10–21]. Briefly, the density is derived from the resonantfrequency of a sample-filled U-shaped tube as it vibrates perpen-dicular to its plane in an electromagnetic field. The vibration canbe regarded as a simple harmonic oscillation, thus allowing thedensity (q) to be expressed as

q ¼ Ks2 þ L; ð2Þ

where s is the period of oscillation and K and L are defined as

K ¼ C4p2Vt

ð3Þ

and

L ¼ mt

Vt: ð4Þ

In equations (3) and (4), Vt is the inner volume of the tube, mt isits mass, and C is the force constant, which depends on the tube’ssize and shape and is proportional to the Young’s modulus of thetube material. In the density and sound speed analyzer, the tubeis made of borosilicate glass, a material whose high stiffness resultsin greater instrument sensitivity compared to tubes made of stain-less steel or hastelloy. Because the mechanical properties of thetube (e.g., length, radius, and stiffness) are temperature and pres-sure dependent, K and L must be determined via calibration withone or more liquids whose densities are well known.

The equation used by the manufacturer to determine density isa modification of equation (2). Specifically, density is obtainedfrom

q ¼ KA� Q 2 � f1 � KBþ f2; ð5Þ

TABLE 2Measured density (q) and speed of sound (w) data for isooctane and toluene attemperature (T) and 83 kPa.

Isooctane Toluene

T/(K)

q/(kg�m�3)

Uqa/

(kg�m�3)w/(m�s�1)

Uwa/

(m�s�1)w/(m�s�1)

Uwa/

(m�s�1)

343.15 649.40 0.06 900.0 0.4 1117.0 0.6338.15 653.81 0.06 919.7 0.4 1137.2 0.5333.15 658.19 0.06 939.7 0.4 1157.7 0.6328.15 662.52 0.06 959.7 0.4 1178.2 0.6323.15 666.81 0.07 980.0 0.4 1198.9 0.6318.15 671.07 0.07 1000.5 0.4 1219.9 0.6313.15 675.28 0.06 1020.9 0.4 1240.9 0.6308.15 679.48 0.06 1041.6 0.5 1262.2 0.6303.15 683.64 0.06 1062.4 0.4 1283.6 0.6298.15 687.77 0.06 1083.1 0.4 1305.1 0.5293.15 691.89 0.06 1104.3 0.4 1326.9 0.6288.15 695.98 0.06 1125.4 0.4 1349.1 0.6283.15 700.05 0.06 1146.8 0.4 1371.5 0.6278.15 704.10 0.06 1168.4 0.4 1394.1 0.6

a Uq and Uw are expanded uncertainties at 95% confidence level for density andspeed of sound, respectively.

FIGURE 3. Speed of sound (w) as a function of temperature (T) for a binary mixturewith a nominal composition of 0.6 mol/mol n-hexadecane + 0.4 mol/mol butylbenzoate [22] at 83 kPa. Measurements made on separate days in 2006 are shownas symbols: -d-, 01 May; -N-, 02 May; , 12 May; �, 09 June; , 12 June. Referencevalues for water [23] are also shown ( ).

278 T.J. Fortin et al. / J. Chem. Thermodynamics 57 (2013) 276–285

where KA and KB are apparatus constants, f1 and f2 are correctionterms for temperature, viscosity, and nonlinearity, and Q is a quo-tient of the periods of oscillation of two tubes [8]. The densityand sound speed analyzer employs a reference oscillator that is alsomade of borosilicate glass, is filled with a known reference sub-stance, and is subjected to the same conditions as the measurementoscillator. By dividing the period of oscillation of the measuring cellby the period of oscillation of the reference cell, certain thermal ef-fects are compensated for. The correction for viscosity is requiredbecause sample viscosity can have a dampening effect on the periodof oscillation, which leads to an error in the density determination.Typically, the viscosities of our samples are low and the resultantcorrections are small; corrections for isooctane densities reportedhere (table 2) ranged from +0.007 kg�m�3 to �0.002 kg�m�3. As withthe sound speed cell, an adjustment procedure performed withwater and air at 293 K, 313 K, and 333 K is required to determinethe apparatus constants in equation (5).

3. Sample purity

Before and after measurements are performed on a given sam-ple, it is important to clean and dry the measurement cells thor-oughly to avoid sample contamination. This is of particularconcern for the sound speed cell where we have found that sampleliquids can become trapped. Figure 3 shows results for speed ofsound measurements of a binary mixture of n-hexadecane and bu-tyl benzoate with a mole fraction of 0.6 n-hexadecane [22]. Foreach measurement series, an aliquot of sample was injected andmeasurements proceeded from 343 K to lower temperatures indecrements of 10 K. For clarity, the results shown in figure 3 areaverages of at least two measurement series, except for that la-beled 02 May, which is the result of a single measurement series.Initially, the measured speed of sound values dropped by approx-imately 300 m�s�1 between 333 K and 323 K and then increasedwith decreasing temperature. In addition to the measured binarymixture data, sound speeds for water derived from the 1995 For-mulation of the International Association for the Properties ofWater and Steam (IAPWS-95) [23] are shown in figure 3 for com-parison. The initial binary mixture data are clearly consistent withthe sound speed of water, which had been in the instrument forwater checks prior to the sample measurements. Consultation withthe manufacturer revealed that the sound speed cell has a flowgeometry that can result in sample liquid becoming trapped. Thisis illustrated in figure 2. Sample liquid enters the circular cavity

through a pinhole at the bottom and exits through a pinhole di-rectly opposite at the top. With this geometry, it is possible for li-quid entering the cell to exit without flowing through the entirecavity. Thus, the sound speed cell may be divided into two regionsby the formation of vortices of opposite rotation, and any materialrotating in the vortices may not be flushed out.

This realization of the potential trapping of sample within thesound speed cell prompted the implementation of rigorous clean-ing procedures. Specifically, the cells are cleaned with two sol-vents; the first solvent removes the previously measured sampleand the second solvent removes any residues that may have beenleft behind by the first solvent. Typically, we use hexanes followedby acetone, but ultimately the choice of solvents depends on thesample that is being removed. It is crucial that the primary solventbe completely miscible with the sample that is to be removed andthat the second solvent be completely miscible with the first sol-vent. Furthermore, care must be taken to select solvents that willnot react to form insoluble residues. Typically, five injections ofeach solvent are made at an elevated temperature to aid in clean-ing; for the case of hexanes and acetone that temperature is 313 K,but generally a temperature slightly below the boiling point of agiven solvent is used. Finally, dry air is pumped through the cellsat 343 K for one hour to ensure that the solvents have completelyevaporated.

The manufacturer recommends performing a single watercheck before each series of measurements to verify that the mea-surement cells are clean and to validate the adjusted apparatusconstants in equations (1) and (5). During the water check proce-dure, degassed ultra-pure water is injected and the density andspeed of sound are measured at 293 K. The measured values arecompared with reference values [24,25] stored in the instrument’sinternal memory. By default, the instrument’s software designatesa water check as ‘‘valid’’ if the relative deviation is within±0.000100. If the deviation exceeds this limit for either cell, it islikely that some sample residue remains, and a second cleaningof the cells is recommended, followed by another water check.According to the manufacturer, a second invalid water check indi-cates that an instrument adjustment is required. However, we have

FIGURE 4. Relative deviations of density (q, A) and speed of sound (w, B) for a seriesof water checks performed at 293 K on 14 Jan 2009 (I), 27 Jan 2009 (II), 28 Jan 2009(III), and 29 Jan 2009 (IV). (Note the abbreviated U.S. date convention along the x-axis as day, month, year.) A water check is valid if the calculated deviation is withinthe manufacturer’s limits of ±0.000100, represented by the dashed lines ( ).

FIGURE 5. Repeatability of water measurements for density (q, A) and speed ofsound (w, B) represented as the standard deviation (r) of a minimum of tenconsecutive measurements made on a single sample injection.

T.J. Fortin et al. / J. Chem. Thermodynamics 57 (2013) 276–285 279

found with our density and sound speed analyzer that a singlewater check is often not sufficient to make a determination aboutthe cleanliness of the cells or the need for an adjustment.

Figure 4 shows relative deviations of the density (A) and speedof sound (B) for a series of water checks performed over severaldays. The density results, with the exception of a single outlier thatcan be attributed to the presence of an air bubble, show that thedensity cell is easily cleaned. In contrast, the sound speed cell isroutinely problematic; this is a consequence of the trapping ofsample within the cell as discussed previously. For example, aftermeasurements of a sample of soy-based biodiesel the instrumentrequired repeat cleanings over several days using various solventsbefore the water checks indicated a clean cell (figure 4B, sectionsII–IV). Furthermore, these results demonstrate that a single watercheck is insufficient to draw a reliable conclusion. Even a soundspeed cell that is not clean may yield a single valid water check re-sult; however, multiple consecutive water checks will more reli-ably indicate problems. Of course, the opposite situation ispossible as well. This is demonstrated in section I of figure 4Bwhere the results of the first water check alone could indicate acontaminated cell or a problem with the adjustment, but subse-quent water check results reveal that neither possibility explainsthe observations. In this case, the errant deviation results are mostlikely due to air bubbles; even though attempts are made to degasthe water before use, any remaining dissolved air can be releasedfrom the solution by sonication. As a result of these accumulatedexperiences, we have adopted a stricter requirement of three con-secutive valid water checks before the sound speed cell is consid-ered clean. If after several cleaning attempts with appropriatesolvents it is still not possible to meet this requirement, an instru-ment adjustment should be performed.

4. Repeatability vs. reproducibility

The repeatability [9,26,27] of the density and sound speed ana-lyzer is indicated by the standard deviation of the average of con-secutive measurements made on a single injection of sample. A test

of the repeatability was performed with degassed ultra-pure waterat temperatures from 278 K to 343 K. A minimum of ten consecu-tive measurements was made at each temperature; the averagesand standard deviations were then calculated. The standard devia-tion results are shown in figure 5. For comparison, the manufac-turer’s specifications for repeatability are shown in table 1. Inthis example, the repeatability of the density measurements(figure 5A) matches the manufacturer’s specifications of±0.001 kg�m�3 and the repeatability of the sound speed measure-ments (figure 5B) exceeds the manufacturer’s specifications of±0.1 m�s�1 by an order of magnitude. The repeatability that isshown in figure 5 is typical; a significant departure from thisbehavior would therefore indicate a major problem with theinstrumentation.

More informative than the repeatability is the reproducibility[9,26,27], which is indicated by deviations between measurementsmade on consecutive injections of a given sample. Poor reproduc-ibility can be an indication of sample contamination and/or of theneed to perform a new instrument adjustment. For example, weshow deviations from IAPWS-95 reference values [23] for the den-sity (figure 6) and speed of sound (figure 7) of water under contam-inated conditions in October 2008 (A) and under clean conditionsin December 2008 (B). Despite the fact that water checks per-formed prior to the October 2008 measurements met our prerequi-site of three consecutive valid checks, the maximum spreadbetween individual series is large with �0.08% for density (figure6A) and �0.6% for speed of sound (figure 7A). Further cleaningdid not entirely rectify the situation, indicating that an instrumentadjustment was also needed. After completion of the adjustmentprocedure, the maximum spread between individual measurementseries in December 2008 improves to �0.005% for density (exclud-ing series 1 due to the presence of air bubbles) (figure 6B) and�0.09% for speed of sound (figure 7B). Also shown in figures 6and 7 are the expanded (k = 2) uncertainties for the IAPWS-95 ref-erence values (dotted lines), which are equal to ±0.0002% and±0.01% for density and speed of sound, respectively [23]. It shouldbe noted that nearly all measured values exceed these uncertaintylimits under both contaminated (A) and clean (B) conditions. This

FIGURE 6. Reproducibility of water density (q) measurements at 83 kPa for fiveconsecutive injections of sample represented as percent deviation from IAPWS-95reference values [23] under contaminated conditions (October 2008, A) and cleanconditions (December 2008, B). Individual measurement series are shown assymbols: d, series 1; j, series 2; N, series 3; , series 4; �, series 5. Expanded(k = 2) uncertainties for the IAPWS-95 reference values ( ) and combinedinstrument and IAPWS-95 reference uncertainties ( ) are also shown.

FIGURE 7. Reproducibility of water sound speed (w) measurements at 83 kPa forfive consecutive injections of sample represented as percent deviation from IAPWS-95 reference values [23] under contaminated conditions (October 2008, A) andclean conditions (December 2008, B). Individual measurement series are shown assymbols: d, series 1; j, series 2; N, series 3; , series 4; �, series 5. Expanded(k = 2) uncertainties for the IAPWS-95 reference values ( ) and combinedinstrument and IAPWS-95 reference uncertainties ( ) are also shown.

FIGURE 8. Density (q) as a function of temperature (T) for a variety of sampleliquids at 83 kPa. Lines represent reference values for water ( ) [23], air ( )[31], toluene ( ) [32], and isooctane ( ) [34]. Symbols represent theaveraged results of measurements made with the present instrument: d, water;j, toluene; N, isooctane; �, animal biodiesel [28]; , anhydrous ethanol [28]; .,methylcyclohexane [29]; , jet fuel [30].

280 T.J. Fortin et al. / J. Chem. Thermodynamics 57 (2013) 276–285

observation is not entirely surprising since the estimated uncer-tainties for the IAPWS-95 density and speed of sound values arequite small; they are in fact significantly smaller than the uncer-tainties associated with these properties for practically any otherliquid that one might use to validate an instrument such as this.Therefore, we recommend using an estimate of combinedreference and instrument uncertainties as a more reasonablebenchmark when trying to determine whether the instrument isperforming within specifications. Using the reported instrumentspecifications (table 1) as an initial estimate of instrument

uncertainty, we calculated an expanded (k = 2) uncertainty limitthat combines instrument and reference uncertainties. This com-bined uncertainty limit is also shown in figures 6 and 7 (dashedlines). For densities (figure 6), essentially all of our measured devi-ations exceed combined uncertainties under contaminated condi-tions (A), but there is an improvement under clean conditions(B), although outliers remain. For sound speeds (figure 7), severalmeasured deviations are within combined uncertainties undercontaminated conditions (A), but there is additional improvementunder clean conditions (B) where almost all deviations are withincombined uncertainties.

5. Calibration and adjustment

As was previously mentioned, the apparatus constants in theworking equations (i.e., equations (1) and (5)) of the density andsound speed analyzer are determined by performing an adjust-ment procedure. The instrument’s built-in adjustment protocoluses water and air at 293 K, 313 K, and 333 K. Periodic calibrationsare necessary to verify that the instrument’s adjustment has notdrifted. Calibrations are performed by measuring a reference fluidand comparing the results to the known density and/or speed ofsound values [9]. Deviations exceeding the combined instrumentand reference uncertainties likely indicate a problem with the cur-rent adjustment.

Water is an obvious candidate for a calibration fluid becauseboth its density and speed of sound are well known [23], and infact we often use deviations from water reference values as a pri-mary indicator of instrument performance issues (see e.g., figures 6and 7). However, as can be seen in figure 8, many of the liquids thatwe have measured with this instrument [28–30] have densitiesthat are lower than water [23] and significantly higher than air[31]. This is a concern because it is preferable to calibrate theinstrument with a reference standard whose properties are similarto those of the measurement sample of interest.

FIGURE 9. Percent deviations of density (q) measurements of SRM 211d toluenefrom reference values [32,33]. Symbols are averaged measurements for consecutivesample injections: j, Feb. 2006; �, Oct. 2008; , Dec. 2008; d, Feb. 2009. Dottedlines ( ) represent expanded uncertainties as reported on the SRM 211dcertificate [33]. Dashed lines ( ) represent estimates of expanded combinedreference and measurement uncertainties where reference uncertainties werecalculated for extended range SRM 211d [32].

T.J. Fortin et al. / J. Chem. Thermodynamics 57 (2013) 276–285 281

As shown in figure 8, extended range Standard Reference Mate-rial (SRM) 211d toluene [32,33] and SRM 2214 isooctane(2,2,4-trimethylpentane) [34] are suitable calibration fluid candi-dates because their density values bracket those of our typicalsample liquids. Extended range SRM 211d toluene allows for cali-bration over the instrument’s full temperature range, while SRM2214 isooctane is currently only certified over the limited rangeof 288 K to 298 K. It should be noted that prior to the extendedrange certification, SRM 211d was also only certified over this lim-ited temperature range. Figure 9 shows deviation results for cali-bration measurements using SRM 211d toluene. In this figure,each data point represents an average of the calculated percentdeviation for several consecutive measurement series. Addition-ally, the measurements shown were made using both the morelimited temperature range SRM 211d (2006) and the extendedrange SRM 211d (2008 and later). In February 2006, the instrumentreproduced the certified reference values within the reported ex-panded (k � 2) uncertainty limits [33] (dotted line). However, mea-surements made in October 2008 show that the instrumentperformance in this density range had degraded over time; thedeviations are significantly larger than what is expected based onexpanded (k � 2) combined reference and instrument uncertain-ties (dashed line). Combined uncertainties are calculated using re-ported extended range SRM uncertainties [32] and estimatedinstrument uncertainties (see Section 4). In addition to the magni-tude of the measured deviations, there is an apparent temperaturedependence that is not being accounted for with the instrument’sfactory adjustment. The instrument was readjusted, and additionaltoluene measurements were performed in December 2008. Thepreviously observed temperature dependence improved somewhatwith the new adjustment; the magnitude of the deviations also im-proved, but the instrument still did not reproduce the certified val-ues within expanded combined uncertainties. The situationremained unchanged for measurements made in February 2009.

The observed deviations for SRM 211d toluene are in contrastwith calibration measurements made with water (e.g., figure 6B)and SRM 2214 isooctane around the same time. The reference den-sity values of water [23] and isooctane [34] were both reproducedwithin ±0.003% on average with maximum deviations of 0.005% forwater and �0.006% for isooctane. These deviations exceed ex-panded (k = 2) combined reference and instrument uncertainties

for water (±0.001%) but are within combined uncertainties for iso-octane (±0.006%). The �0.009% to �0.014% offset observed withtoluene indicates a systematic deviation of the densimeter at thatdensity range. This variation in densimeter performance depend-ing on density could be accounted for if a more comprehensiveinstrument adjustment were possible, specifically one that allowedfor the use of two or more reference liquids over a range of temper-atures. The user would be able to choose the specific reference liq-uids so that they more closely bracket the density range of interest.The instrument firmware of the density and sound speed analyzerdoes not currently allow for this. Therefore, at a minimum, werecommend that similar commercial instruments should becalibrated regularly using several reference liquids that span thedensity and temperature range of sample measurements. Further-more, the results of those calibrations should be used to helpformulate a reasonable and comprehensive uncertainty estimate(see Section 6).

For such comprehensive calibrations and uncertainty estimatesto be possible, additional reference materials of more moderatedensities that are certified over larger temperature ranges are re-quired. As seen with the extended range toluene (SRM 211d)(e.g., figure 9), access to reliable reference data that covers wideranges of density and pressure aids in the full characterization ofan instrument over all measurement conditions. Such a character-ization is essential to verify the linearity of an instrument’s re-sponse or to elucidate conditions where there are deviationsfrom linearity that need to be accounted for. We suggest isooctaneas the next liquid density reference material to be certified over anextended range because its density is lower than that of toluenebut is still high enough to be similar to many common measure-ment samples, including various fuels and fuel components (seefigure 8).

Ultimately, additional extended range reference materials willrequire comprehensive and careful absolute density measure-ments such as the work that was done by McLinden and Splett[32] for SRM 211d toluene and by Schilling et al. [35] for n-heptane,n-nonane, 2,4-dichlorotoluene, and bromobenzene. In the absenceof extended range reference materials for isooctane, access to reli-able data that include comprehensive uncertainty estimates andexpand the coverage of pressure and/or temperature conditionscan help experimentalists better characterize their instruments.Therefore, table 2 includes our measurement results for the densityof degassed SRM 2214 isooctane from 343 K to 278 K at atmo-spheric pressure (�83 kPa in Boulder, CO). These density data rep-resent the average of four measurement series, and the reporteduncertainty represents the expanded (k � 2) uncertainty associ-ated with a 95% confidence interval (see Section 6). We compareour density values to those calculated from a preliminary equationof state (EOS) for isooctane [36]. It should be noted that the currentdensity measurements were among the experimental data consid-ered during the development of the preliminary EOS. Figure 10shows relative deviations between the experimental and the calcu-lated data as function of temperature. Our measured values agreewith EOS values within 0.03%.

To evaluate further our isooctane density results, we searchedthe ThermoData Engine (TDE) database [37] for available literaturedata and found a total of 201 references and 388 data points thatoverlap our experimental conditions. For clarity, we have includeddeviation results for just nine of those sources [38–46] in figure 10.These nine sources were selected because they constitute the mostcomprehensive data sets available and/or because a similar com-mercial instrument was utilized to make the measurements. Theremaining available sources can be represented by the TDE densitycorrelation, the calculated deviations for which are shown in figure10 as a dashed line. All of the literature data shown in figure 10agree with EOS values within 0.1%, except those of Gómez-Díaz

FIGURE 10. Percent deviations of density (q) measurements of isooctane from apreliminary equation of state [36]. Our data (d) are averaged measurements forconsecutive sample injections of SRM 2214. Available literature data are includedfor comparison; only data for overlapping experimental conditions are shown.Select data sets are shown as symbols (., Belonenko et al. [38]; j, Dymond et al.[39]; , Gómez-Díaz et al. [40]; , Gonzalez-Olmos et al. [41]; , Malhotra andWoolf [42];J, Morávková et al. [43]; , Pádua et al. [44]; �, Papaioannou et al. [45]; ,Smyth and Stoops [46]), while the majority of available literature data isrepresented by the TDE correlation ( ) [37]. FIGURE 11. Speed of sound (w) as a function of temperature (T) for a variety of

sample liquids at 83 kPa. Lines represent reference values for water ( ) [23] andair ( ) [47]. Symbols represent the averaged results of measurements madewith the present instrument: d, water; j, toluene; N, isooctane; �, animal biodiesel[28]; , anhydrous ethanol [28]; ., methylcyclohexane [29]; , jet fuel [30].

FIGURE 12. Percent deviations of speed of sound (w) measurements of toluenefrom the equation of state [48] as implemented in REFPROP [49]. Our data (d) areaveraged measurements for consecutive sample injections of SRM 211d. Three datasets selected from the available literature data ( , Muringer et al. [50]; �, Okhotinet al. [51]; J, Verveiko et al. [52]) and one unpublished data set from Meier (j) [53]are included for comparison; only data for overlapping experimental conditions areshown.

282 T.J. Fortin et al. / J. Chem. Thermodynamics 57 (2013) 276–285

et al. [40], which are lower by as much as 0.44%. Interestingly, thedata set of Gómez-Díaz et al. [40] was one of the three shown thatwere measured with the same model of commercial instrumentused in this work; the other two agreed within 0.02% and0.08% for Gonzalez-Olmos et al. [41] and Morávková et al. [43],respectively.

The need for certified reference materials for speed of soundmeasurements is even more pronounced since none currentlyexist. Water is the commonly used reference fluid because it isparticularly well characterized. However, as shown in figure 11,the temperature dependence of its speed of sound is opposite ofthat observed for many sample liquids that we have measured[28–30]; the speed of sound of water increases with temperaturefrom 278 K to 343 K, while that of other liquids decreases withtemperature. Furthermore, as was the case with density, thespeeds of sound of water [23] and air [47] are drastically differentin magnitude from those of our typical sample liquids. The mea-surement results in figure 11 demonstrate that SRM 211d tolueneand SRM 2214 isooctane are suitable calibration fluid candidatesfor sound speed measurements. Characterizing their speeds ofsound over an expanded temperature range would be invaluablein the effort to provide reliable sound speed data using a high-throughput, benchtop instrument such as the density and soundspeed analyzer used in this work.

A search of TDE [37] shows that there are fewer sound speeddata that cover a wide range of temperature and/or pressure foreither toluene or isooctane than what is available for their density.Therefore, table 2 includes our measurement results for the speedof sound of SRM 2214 isooctane and extended range SRM 211d tol-uene at ambient atmospheric pressure (�83 kPa). Both fluids weredegassed prior to measurement. For both fluids, the measurementscover temperatures from 343 K to 278 K. The sound speed data re-ported in table 2 represent the average of four measurement seriesfor isooctane and five measurement series for toluene, and the re-ported uncertainty represents the expanded (k � 2) uncertaintyassociated with a 95% confidence interval (see Section 6). We com-pare our sound speed values to those obtained using the corre-sponding equation of state [36,48]; calculated relative deviationsare shown in figure 12 for toluene and in figure 13 for isooctane,both as a function of temperature.

For toluene (figure 12), our measured values agree with theequation of state [48] as implemented within the Reference FluidThermodynamic and Transport Properties (REFPROP) database[49] within 0.3%, well within the reported expanded (k � 2) uncer-tainty of 1% [48]. Of the 69 references for toluene speed of sounddata found in TDE [37], only three include data at atmosphericpressure. We have compared those three data sets [50–52] to val-ues calculated from the EOS and have included the deviation re-sults in figure 12. Also included in figure 12 are deviations ofunpublished data measured by Meier [53] with a double path pulseecho instrument [54]. For all four of the data sets selected for com-parison, only data that overlap with our experimental conditions

FIGURE 13. Percent deviations of speed of sound (w) measurements of isooctanefrom a preliminary equation of state [36]. Our data (d) are averaged measurementsfor consecutive sample injections of SRM 2214. Available literature data areincluded for comparison; only data for overlapping experimental conditions areshown. Select data sets are shown as symbols (j, Aminabhavi et al. [55]; , Gómez-Díaz et al. [40]; , Gonzalez-Olmos et al. [41]; J, Morávková et al. [43]; , Plantierand Daridon [56]), while the majority of available literature data is represented bythe TDE correlation ( ) [37].

T.J. Fortin et al. / J. Chem. Thermodynamics 57 (2013) 276–285 283

are shown and all agree with the EOS values within 0.3%. Althoughthe magnitudes of the deviations are within reported uncertainties,both the literature data and our data show clear temperaturedependence in figure 12.

For isooctane (figure 13), our measured values agree with thepreliminary equation of state [36] within 0.1% and no significanttemperature dependence is observed. It should be noted that thecurrent sound speed measurements were among the experimentaldata considered during the development of the preliminary EOS. Aswith toluene, we have selected a subset of the 25 literature refer-ences found in TDE [37] for isooctane speed of sound data for com-parison. Specifically, we selected the five data sets [40,41,43,55,56]that contained the largest number of points at overlapping exper-imental conditions and/or were also measured using a similarcommercial instrument. The remaining available literature dataare represented by the TDE sound speed correlation. Deviation re-sults for the literature data are also shown in figure 13. All of theliterature data shown agree with the preliminary EOS within0.4%. It is worth noting that the lowest deviations (<0.2%) are ob-served for the three data sets that were measured with the samemodel of commercial instrument used in this work [40,41,43]. Nosignificant temperature dependence is observed for the five se-lected data sets, but there is a temperature dependence observedfor the TDE correlation where deviations from the preliminaryEOS increase with decreasing temperature.

6. Uncertainty assessment

Table 1 shows that the manufacturer reports an uncertainty of±0.005 kg�m�3 and ±0.5 m�s�1 for density and speed of sound,respectively. However, it is not sufficient to quote values fromthe instrument manual as an estimate of uncertainty. We presenthere an approach to a comprehensive uncertainty assessment forthe density and sound speed analyzer as a guideline for other usersof similar commercial instruments. A similar approach is describedin Laesecke et al. [28], and additional details can be found therein.

The combined standard uncertainty for the average of n densitymeasurements ð�qÞ can be expressed as

uð�qÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n

S2q þ u2

c þ u2i þ u2

T

r; ð6Þ

where sq is the standard deviation of the average, uc is the uncer-tainty due to the resolution of the instrument, ui is the uncertaintydue to the instrument’s varied response with density range, and uT

is the contribution due to the uncertainty in measured temperature.From the manufacturer’s repeatability specifications (table 1),uc = 0.001 kg�m�3. To estimate ui we assume that the true densitylies between an upper (a+) and lower (a-) limit and that all valuesbetween those two limits are equally possible (i.e., rectangular dis-tribution). The resulting expression [26] is

ui ¼ðaþ � a�Þ

2ffiffiffi3p ; ð7Þ

where a+ and a- can be estimated from the observed deviations be-tween measured and certified densities for appropriate referenceliquids. For example, if SRM 211d toluene and SRM 2214 isooctaneare used as calibration liquids, the maximum observed toluenedeviation and the minimum observed isooctane deviation can beused as estimates for a+ and a-, respectively. Currently, the uncer-tainty in measured temperature is estimated at ±0.03 K, which cor-responds to uT = ±0.03 kg�m�3. This is a fairly conservative estimateof the temperature uncertainty. However, there is still some ques-tion surrounding the reliability of this estimate for uT, particularlywhen running the instrument in a temperature scan mode as wetypically do; additional experiments are planned to further addressthis issue.

Once uð�qÞ has been calculated, the Welch-Satterthwaiteapproximation [26] can be used to calculate the effective degreesof freedom (dfq) using the expression

dfq ¼u4ð�qÞ

ð1ns2qÞ

2

n�1 þu4c

dfcþ u4

idfiþ u4

TdfT

; ð8Þ

where n � 1, dfc, dfi, and dfT are the degrees of freedom associatedwith sq, uc, ui, and uT, respectively. If we assume the uncertaintyin the uncertainty is 25%, the degrees of freedom for dfc, dfi, anddfT are each equal to 30 [26]. The effective degrees of freedom (fromequation (8)) and the combined standard uncertainty (from equa-tion (6)) are then employed to determine the expanded uncertainty(Uq) using the expression

Uq ¼ tpðdfqÞ � uð�qÞ; ð9Þ

where tp(dfq) is taken from the t-distribution for dfq degrees of free-dom and a p percent level of confidence (typically 95%). The corre-sponding value of tp(dfq) can be found in table G.2 of the Guide to theExpression of Uncertainty in Measurement [26] by interpolation or bytruncating dfq to the next lower integer. Using the t-distributionyields a better approximation than simply assuming a normal dis-tribution and using the coverage factor kp (kp = 2 at p = 95%).

The equations used in the uncertainty approximation for thespeed of sound are the same as those used for density (equations(6)–(9)). However, the lack of sound speed reference liquids makesit difficult to estimate ui. It is possible to therefore ignore all termsrelated to ui in equations (6)–(9) when calculating sound speeduncertainties. Alternatively, one can use the observed minimumand maximum deviations for water to estimate ui instead. Forthe sound speed measurements, uc = 0.1 m�s�1 and uT = 0.13 m�s�1

(for a ±0.03 K temperature uncertainty). The approach we haveoutlined results in a reliable estimate of the statistical uncertaintyfor data measured with the density and sound speed analyzer.However, this work also shows that contributions arising from sys-tematic effects may substantially increase the overall uncertainty.

7. Conclusions

Benchtop instruments are capable of high quality thermophys-ical property measurements, but only if they are calibrated,

284 T.J. Fortin et al. / J. Chem. Thermodynamics 57 (2013) 276–285

adjusted, and operated in an informed manner. We have presentedexamples of our long-term experience with a commercial densityand sound speed analyzer to illustrate four key themes. First, dueto the design of the sound speed cell in particular, careful cleaningof the measurement cells is required to ensure sample purity. Wehypothesize that if the sound speed cell were to be redesigned tohave more than one inlet and outlet, sample removal could be im-proved. In the absence of such changes, multiple consecutive validwater checks, instead of a single valid check, are a more reliableindicator of whether the cleaning procedure has been successful.Second, the reproducibility of measurements made on consecutivesample injections is a better indicator of instrument performancethan the repeatability of measurements made on a single injection.Specifically, issues such as sample contamination and/or inade-quate instrument adjustment will be more readily apparent whenthe reproducibility is considered. Third, a more comprehensive andflexible adjustment procedure could improve the instrument’s per-formance, but this would require changes to the instrument’s firm-ware. Alternatively, frequent calibration measurements are a goodmethod to verify the instrument’s performance over specific mea-surement ranges. The use of two or more reference liquids thatspan the measurement range of interest can elucidate variationsin the instrument’s performance that would otherwise remainundetected. However, more reference materials, certified overwider temperature ranges, are needed to fully realize a more com-prehensive approach to both calibration and adjustment, particu-larly for sound speed measurements. In the meantime, access toreliable data that expand the coverage of pressure and/or temper-ature conditions can help experimentalists to characterize theirinstruments more comprehensively. Therefore, we have includedambient atmospheric pressure (�83 kPa) measurement resultsfor the density and speed of sound of SRM 2214 isooctane andfor the speed of sound of SRM 211d toluene, all over the tempera-ture range 343 K to 278 K. Finally, a comprehensive and reasonableuncertainty estimate is needed for the data measured with theseinstruments. We have outlined an approach that yields a reason-able estimate of uncertainty, and we have utilized that approachto calculate expanded uncertainties for the isooctane and toluenedata presented here.

Acknowledgments

The authors thank Mr. Darren Wilson of Anton Paar USA Inc. forproviding additional information about the instrument discussedin this work. The authors also thank Dr. Karsten Meier and Dr. EricLemmon for generously providing access to their unpublishedtoluene speed of sound data and isooctane equation of state,respectively.

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JCT 12-298