NISTIR 6640

Thermochemical and 

Thermophysical

Properties of JP-10

Thomas J. Bruno

Marcia L. Huber

Arno Laesecke

Eric W. Lemmon

Richard A. Perkins

NISTIR 6640

Thermochemical and 

Thermophysical

Properties of JP-10

Thomas J. Bruno 

Marcia L. Huber 

Arno Laesecke 

Eric W. Lemmon 

Richard A. Perkins 

Physical and Chemical Properties Division 

Chemical Science and Technology Laboratory 

325 Broadway 

Boulder, CO 80305 

Report Prepared for: 

Fuels Branch, Turbine Engine Division 

Propulsion Directorate, AFRL 

Wright Patterson Air Force Base, Ohio 45433 

June 2006

U.S. Department of Commerce 

Carlos M. Gutierrez, Secretary 

Technology Administration 

Robert Cresanti, Under Secretary of Commerce for Technology 

National Institute of Standards and Technology 

William A. Jeffrey, Director 

Contents 

Introduction............................................................................................................ 1 

Chemical Analysis ................................................................................................. 2 

Thermal Decomposition of JP-10 .......................................................................... 7 

Instrumentation for Density, Viscosity, and Speed of Sound Measurements........ 14 

Density Measurements for JP-10........................................................................... 17 

Viscosity Measurements for JP-10 ........................................................................ 21 

Viscosity Correlation ............................................................................................. 24 

Sound Speed Measurements and Derived Adiabatic Compressibilities of JP-10.. 27 

Thermal Conductivity for JP-10 ............................................................................ 29 

Distillation Curve for JP-10................................................................................... 32 

Model Development for the Thermodynamic and Transport Properties for JP-10 34 

Thermodynamic Properties of JP-10 ..................................................................... 35 

Transport Properties of JP-10 ................................................................................ 45 

Viscosity Model..................................................................................................... 45 

Thermal Conductivity Model................................................................................. 47 

References.............................................................................................................. 51 

Appendix 1. Thermal Conductivity Measurements of Liquid JP-10.................... 54 

iii

Thermochemical and Thermophysical 

Properties of JP-10

MIPR F4FBEY5102G001

Report Prepared for: 

Dr. Tim Edwards 

Fuels Branch, Turbine Engine Division 

Propulsion Directorate, AFRL 

Wright Patterson Air Force Base 

Ohio, 45433-7103 

By: 

Physical and Chemical Properties Division 

National Institute of Standards and Technology 

Boulder, CO 80305 

October 2005 

Technical Contact: Administrative Contact: 

Dr. Thomas J. Bruno Ms. Beverly Armstrong 

303-497-5158 (office) 303-497-3868 (office) 

303-497-5927 (fax) 303-497-5044 (fax) 

303-497-5978 (laboratory) beverly@boulder.nist.gov 

bruno@boulder.nist.gov
Executive Summary: 

• Report of the chemical analysis of JP-10, on the sample received from AFRL. 

• Report of chemical decomposition kinetics of JP-10, on the sample received from AFRL. 

• Report of density survey measurements of JP-10, on the sample received from AFRL. 

• Report of viscosity survey measurements of JP-10, on the sample received from AFRL. 

• Report of speed of sound survey measurements of JP-10, on the sample received from AFRL. 

• Report of thermal conductivity survey measurements of JP-10, on the sample received from 

AFRL. 

• Report of the distillation curve of JP-10, on the sample received from AFRL. 

• Report on model development for JP-10. 

Technical Contact: Administrative Contact: 

Dr. Thomas J. Bruno Ms. Beverly Armstrong 

303-497-5158 (office) 303-497-3868 (office) 

303-497-5927 (fax) 303-497-5044 (fax) 

303-497-5978 (laboratory) beverly@boulder.nist.gov 

bruno@boulder.nist.gov
1

Thermochemical and Thermophysical 

Properties of JP-10 

Thomas J. Bruno 

Physical and Chemical Properties Division 

National Institute of Standards and Technology 

Boulder, CO 80305 

This report describes measurement and modeling efforts performed on the missile 

fuel, JP-10. Measurements* include chemical analysis, thermal decomposition 

kinetics, density, viscosity, speed of sound, thermal conductivity and vapor 

pressure (distillation curve measurement). These measurements and data from the 

literature were then used in the formulation of a Helmholtz energy model to 

describe the equilibrium (thermodynamic) properties, and a corresponding states 

model for the transport properties. 

Keywords: density, distillation curve, Helmholtz energy model, JP-10, speed of 

sound, thermal conductivity, thermal decomposition, vapor pressure, viscosity 

Introduction 

The Fuels Branch of AFRL (Wright Patterson Air Force Base) required physical property 

measurement and modeling on an aviation turbine fuel, JP-10. This fluid is essentially a pure 

component: exo-tetrahydrodicyclopentadiene (tricyclo[5.2.1.02,6]decane, CAS No. 2825-82-3). 

This fluid has an appreciable density (0.94 g/cm3), and produces a specific impulse of 297.4 s 

(the thrust per mass flow rate at the nozzle). These characteristics, as well as the very low 

freezing point of the fluid (−79 °C) has made this fluid the only air- breathing missile fuel used 

by the United States at the present time. The chemical structure of this fluid is shown in Figure 

1. To achieve the goal of producing a provisional or preliminary physical property model, 

measurements of chemical composition, thermal decomposition, density, viscosity, thermal 

conductivity, speed of sound, and vapor pressure were carried out. These data were then used, 

along with evaluated data from the literature, to develop the model. The major accomplishments 

of this project are summarized in this report. 

Note: 

In order to describe materials and experimental procedures adequately, it is occasionally 

necessary to identify commercial products by manufacturers’ names or labels. In no instance 

does such identification imply endorsement by the National Institute of Standards and 

Technology, nor does it imply that the particular product or equipment is necessarily the best 

available for the purpose. 
2

Chemical Analysis of JP-10 

Two containers of JP-10 were obtained from AFOSR, Fuels Branch, for testing. There were no 

identifying marks or numbers listed on the containers beyond the chemical name and contact 

information of Tim Edwards, Fuels Branch, AFOSR. 

A 1 mL aliquot was withdrawn from one of the containers for analysis. Sample was not 

permitted to come into contact with the can exterior. The sample was maintained in a sealed 

scintillation vial throughout the course of this work. Exposure of the sample to ambient air was 

minimized to prevent oxidation and the uptake of moisture. Although the vial was stored at 7 °C 

when not in use, the sample was permitted to attain room temperature before the vial was opened 

for use. 

A gas chromatography-mass spectrometry method was used for the analysis. A 30 m capillary 

column with a 0.1 μm coating of 5 % phenyl polydimethyl siloxane was chosen as the stationary 

phase. This phase provides separations based upon boiling temperature and also on polarity. It 

is considered a weakly polar stationary phase. Sample was injected manually via 

chromatographic syringe into a split/splitless injector that was set with a 100 to 1 split ratio. The 

injector was operated at a temperature of 350 °C and held to a constant head pressure of 68.77 

kPa (10 psig). The column was temperature programmed to provide complete and rapid elution 

with minimal loss of peak shape. Initially, the temperature was maintained isothermally at 60 °C 

for 2 min, followed by a 2 °C/min ramp to 90 °C, followed by a 10 °C/min ramp to 250 °C. 

Although the analysis was allowed to run for 40 min, all peaks of interest were eluted after 

approximately 7 min. These conditions proved to be suitable for most of the constituents, which 

produced sharp, clearly defined peaks. 
4

Figure 1. The chemical structure of JP-10, exo-tetrahydrodicyclopentadiene 

(tricyclo[5.2.1.02,6]decane), depicted in a traditional planar format and a three-dimensional ball 

and stick format. 
5

The total ion chromatogram for this analysis is presented in Figure 2. The major constituent of 

the sample is exo-tetrahydrobicyclopentadiene, or JP-10. In addition, two major related 

impurities were identified. Both elute after the main peak of JP-10. The first impurity is 

identified as adamantane, and the second is identified as the endo- isomeric modification of JP10 (hereafter referred to as endo-). The approximate (uncalibrated) composition is: 

Table 1. Major components identified in sample of JP-10 provided by Wright Laboratory. 

____________________________________ 

Constituent Percent, mass/mass 

 JP-10 96.5 

 adamantane 1.0 

 endo- 2.5 

There is a peak whose mass spectrum is consistent with decahydronaphthalene that elutes 

immediately before the main JP-10 peak. It was not quantitated separately because it was not 

base-line resolved from the main JP-10 peak. It is possible to magnify the very light components 

that elute before the major constituents. The magnified section of the total ion chromatogram is 

presented in Figure 3. Numerous additional peaks can be seen, not all of which can be identified. 

The following table provides the likely identities of some of the larger minor constituents: 

 

Table 2. Early eluting components in the analysis of JP-10. 

____________________________________________________________ 

 Peak Name 

 A 2-methyl-bicyclo[3.2.1]octane 

 B 2-ethyl-bicyclo[2.2.1]heptane 

 C endo-2,2,3-trimethyl-bicyclo[2.2.1]heptane 

 D cis-1-methyl-4-(-1-methylethenyl)cyclohexane 

 E 2,6-dimethyl-bicyclo[3.2.1]octane 

The peak labels correspond to the identified peaks of Figure 3. 
6

Figure 2. Total ion chromatogram of a sample of pure JP-10, as received from Wright 

Laboratory. 

Figure 3. Total ion chromatogram, magnified, for the light components (early eluting peaks).

See light see light components 

JP-10 

Endoadamantane 

decahydronaphthalene 

A 

B D 

E 

C 
7

Thermal Decomposition of JP-10 

Several studies have been done to address the thermal decomposition of JP-10[1-8]. These 

studies have been done in various test rigs that have been designed to mimic conditions that are 

applicable in engines. Typically, residence times are very short, in the range of milliseconds to 

several min. The longer residence times (between 1 and 48 hours) normally associated with the 

measurement of thermophysical properties required us to address the topic of thermal 

decomposition from a more fundamental standpoint. We must approach the question of thermal 

decomposition in such a way as to provide a predictive capability for property measurement time 

scales[9,10]. 

For a simple reaction in which a starting material (A) thermally decomposes into a product (eq. 

1), perhaps the best description of the decomposition is the fundamental rate equation. For a 

model reaction where starting material A decomposes into product B (eq. 1), the rate law can be 

written as eq. (2) or (3): 

 A → B (1) 

 Rate = −d[A]/dt (2) 

 Rate = d[B]/dt, (3) 

where [A] is the concentration of A, [B] is the concentration of B, and t is the time. As the 

reaction proceeds, the decrease in A (denoted by the negative sign) is accompanied by a 

corresponding increase in B, and a rate equation can be expressed in terms of the reaction 

products as: 

 d/dt [B] = k[B]n

, (4) 

where k is the reaction rate constant and n is the order of the reaction. If we integrate the 

equation and assume first order, we obtain: 

ln[B] – ln[Bo] = kt, (5) 

where [Bo] is the initial product concentration, which at the start of a decomposition reaction, is 

zero. A plot of ln[B] as a function of time will provide a straight line with a zero intercept, the 

slope of which is k. 

An inherent limitation in defining the rate constant in terms of B occurs for disproportionate 

reactions, where each molecule of starting material decomposes to generate more than one 

molecule of product. A disproportionate reaction can be written as: A → ΣBi, where Bi is the 

number of individual products formed in the reaction. In the thermal decomposition of a 

complex fluid, the potential for such a situation is clear. Furthermore, the decomposition rate of 

a single component can be significantly altered in the presence of the mixture compared to the 

pure component [3]. Nevertheless, insight can be gained into the overall fluid stability against 

thermal stress by focusing instead on the global behavior of the bulk fluid. Then, if the trends in 

the measured data are appropriate, the decomposition can be approximated as first-order 

decomposition [11]. Thus, rather than describing the decomposition of each component in the 

mixture, a global rate constant can be used to describe the bulk behavior of the complex fluid 
8

[12,13]. This is the approach we have taken in the assessment of the thermal decomposition of 

JP-10. 

The simple apparatus assembled to make the thermal decomposition kinetics measurements 

consists of a 304L (AISI designation) stainless-steel thermal block that is heated to the desired 

experimental temperature. In the work reported here, temperatures between 350 and 425 °C 

were used. Stainless-steel was chosen for the block because of its favorable mechanical and 

corrosion resistance properties at high temperature. The block is supported in an insulated box 

with carbon rods, which were chosen for low thermal conductivity. The temperature is 

maintained and controlled (by a PID controller) to within 0.1 °C in response to a platinum 

resistance sensor embedded in the thermal block and sealed with ceramic adhesive. The cells 

consist of 6.4 cm lengths of ultrahigh pressure 316L stainless steel tubing (0.64 cm external 

diameter, 0.18 cm internal diameter) that are sealed on one end with a stainless-steel plug welded 

by a clean tungsten-inert-gas (TIG) process. Each cell is connected to a high-pressure valve at 

the other end with a short length of 0.16 cm diameter 316 stainless steel tubing with an internal 

diameter of 0.02 cm. This length of tubing is also TIG welded to the cell. Each cell and valve is 

capable of withstanding a pressure in excess of 105 MPa at the desired temperature. Although 

not used in the experiments described here, an impact agitator is attached to the heating block for 

use when heterogeneous systems are investigated. 

The internal volume of each cell (including the short length of connecting tubing, and the small 

dead volume of the valve) was determined by gravimetric gasometry using liquid carbon dioxide. 

This procedure consisted of filling a cell of known mass with carbon dioxide to a predetermined 

pressure (20.68 MPa) and at a constant temperature. The cell mass was measured again and the 

increase in mass allowed calculation of the cell volume using an accurate equation of state for 

the density of carbon dioxide [14]. Cell volumes were measured three times and averaged to 

yield 0.210 ± 0.002, 0.226 ± 0.001, and 0.235 ± 0.003 cm3

 for the three vessels. 

The cell filling procedure was a critical step since we desired to mimic the conditions that might 

be encountered in our physical property measurement apparatus. We modified a computer 

program that provides the necessary fluid mass to achieve a selected pressure at the desired 

temperature [14]. This program allowed us to determine the target mass to place in the evacuated 

cell, given the cell volume, to achieve a nominal 34.5 MPa at temperatures between 350 and 425 

°C. A simple predictive equation of state for exo-tetrahydrobicyclopentadiene (JP-10) was used 

to estimate the pressure in each cell at the decomposition temperature [14]. 

The calculated mass of JP-10 was added to the cell with a syringe equipped with an ultra fine 

needle, and the mass of the cell was measured to within ±0.0001 g. The valve was then affixed 

to the cell and sealed. Sample masses were typically on the order of 0.1 g and varied depending 

on the experimental temperature and cell volume. Cells were then chilled to −196 °C in liquid 

nitrogen and subsequently evacuated to 10 Pa through the valve to remove air from the cell. The 

valve was then closed and the cell was warmed to room temperature, at which time the mass of 

the entire cell-valve assembly was recorded. 

 

Loaded cells were then inserted into the stainless steel thermal block that was heated to the 

desired experimental temperature. The cells were maintained at the reaction temperature for a 

specified period of time ranging from 4 min to 20 h. After the desired time period, the cells were 
9

removed from the thermal block and quenched in water at room temperature. The cells were 

dried and the mass was measured to ensure that no leakage had occurred over the course of the 

experiment. The thermally stressed JP-10 was then recovered from the cells and analyzed. 

After each run, the cells and valves were solvent-rinsed with hexanes, toluene, acetone, and 

finally methanol using an ultra fine needle. Solvent rinsing was performed until each solvent 

was colorless as it exited the cell. Cleaned cells and valves were heated to 150 °C for at least 30 

min to remove residual solvent. 

A blank experiment was performed to investigate any possible artifacts introduced in the 

experiment such as residual solvent in the cell or possible catalytic behavior of the cell materials. 

The cells were loaded and evacuated as described above, then maintained at room temperature 

for 65 h. The liquid sample was then removed and analyzed in the same manner as the samples 

that had been exposed to elevated temperature. 

The purpose of the analytical procedure mentioned above was to measure the decomposition 

kinetics of the thermally stressed JP-10. As such, a detailed identification of each product is 

unnecessary; only the rate of change is required. A liquid sampling procedure was developed to 

minimize sample loss when the cells were opened. A short length of stainless steel tubing was 

connected to the valve outlet and placed inside a pre-chilled (at 7 °C) glass vial. The valve was 

slowly opened and the reacted JP-10 was expelled and collected in the vial. The cell was then 

removed from the valve, and any sample remaining in the cell was transferred to the glass vial 

using a syringe equipped with an ultra-fine needle. Samples were refrigerated (at 7 °C) until the 

analysis was performed. Liquid samples were prepared for gas chromatographic analysis by 

dilution in n-dodecane. The resulting solution was typically 8 % reacted JP-10, mass/mass. The 

uncertainty in the mass measurement was 0.0001 g. Sample vials were crimp sealed and the 

contents were mixed using a vortex mixer. 

Aliquots (2 μL) of the sample were injected into a gas chromatograph equipped with an 

automatic sampler and a flame ionization detector. Research-grade nitrogen was used as the 

carrier and make-up gas. The split/splitless injection inlet was maintained at 300 °C and samples 

were separated on a capillary column (30 m column coated with a 1 μm film of 100 % 

dimethylpolysiloxane). A temperature program was used consisting of an initial isothermal 

separation at 100 °C for 2 min followed by a 7 °C/min gradient to 225 °C. This final 

temperature was held constant for 15 min. 

Chromatographic analysis was performed on a suite of emergent decomposition peaks. These 

were peaks corresponding to products formed during the thermal stress; they were not present in 

the unreacted JP-10. Retention times from a standard solution of n-alkanes were used to account 

for the day-to-day variations in the retention times of the decomposition products. This was 

done with a mixture of n-hexane, n-heptane, n-octane and n-nonane that was analyzed before and 

after each JP-10 sample. Retention times of the reference alkanes were used to bracket and 

predict the retention times of the major decomposition products, and were remarkably consistent 

throughout this study. A linear regression was used to fit the data and typically yielded 

correlation coefficients greater than 0.99999, and predicted retention times were typically within 

±0.01 min of the measured product retention times. This procedure ensured that no extraneous 

peaks were used in the chemical analyses upon which the reaction kinetics were based. 
10

An external standard of n-hexane in a solution of n-tetradecane was used to account for variation 

in sample response from day to day. This external standard was injected before and after each 

set of analytical samples of thermally stressed JP-10. The chromatographic areas adjusted with 

this calibration are represented as Ac. A plot of ln(Ac) against time for each temperature was 

used to determine the rate constants for the decomposition. 

The thermal decomposition peaks that were obtained with the ampoule procedure described 

above were, in general, faster-eluting than the main JP-10 peaks. Some later eluting peaks were 

found. Among the later eluting peaks that were not part of the starting material were: 1,1’-

bicyclopentyl, 1-cyclopentylcyclopentene, and 2,3-dihydro-5-methyl-1H-indene. These are not 

considered further since they were not used in determining the thermal decomposition rate. 

The major early eluting peaks are shown in the total ion chromatogram that is presented as 

Figure 4. These measurements were made after the sample was maintained at 425 °C and 34 

MPa for 90 min. The labels on this figure correspond to the components identified in Table 3. 

Table 3. A listing of the components labeled on the total ion chromatogram presented in Figure 

4. These components have been identified on the basis of their mass spectra, after a sample of 

JP-10 was maintained at 425 °C and 34 MPa for 90 min. 

 ______________________________________________________ 

 Component Name 

 1 n-propane 

 2 n-butane 

 3 cyclopentane 

 4 methyl cyclopentane 

 5 1-methyl cyclopentene 

 6 benzene 

 7 ethyl cyclopentane 

 8 ethylide cyclopentane 

 9 toluene 

 10 n-propyl cyclopentane 

 11 cis-bicyclo[3.3.0]oct-2-ene 

 12 ethyl benzene 

 13 o-xylene 

14 octahydropentylene 

 15 3-methyl cyclo octane 

As an example of the decomposition data, the plot of lnAc against time for 375 °C is provided in 

Figure 5. 

The preliminary results for the decomposition reaction rate constants are provided in Table 4. 

These rate constants may change as the data analysis is finalized. In this table, k is the pseudo 

first-order rate constant given in min-1. The uncertainty, obtained from linear regression of ln Ac 

against time, and the coefficient of variation in percent is also provided. 
11

Table 4. Thermal decomposition reaction rate constants for JP-10. 

Temp, °C Temp, K k, min-1 std. error CV, % 

425 698 0.01518 0.00302 19.9 

400 673 0.00437 0.00039 9.02 

375 648 0.00111 0.00016 14.4 

350 623 0.00024 0.00004 17.46 

The curvature that can be seen in the measurements of Figure 5 is indicative of disproportination, 

or the subsequent reaction of reaction products. This invalidates a strictly first order approach to 

the analysis of the rate, but it does not affect the interpretation in the context of this study. 

Recall that our purpose here is to delineate the regions in which thermophysical properties can be 

measured in laboratory apparatus. 

Figure 4. A total ion chromatogram showing the early eluting peaks of decomposed JP-10, 

harvested after 90 min at 425 °C and 34 MPa. 

 

1 1 2 

3 

4 

5 

6 

7 

8 9 

10 

11 

12 

13 

14 

15 
12

12.2

12.4

12.6

12.8

13

13.2

13.4

13.6

13.8

14

0 200 400 600 800 1000 1200 1400 1600

Time, min

Ln Ac

Figure 5. Representative measurements of the decomposition of JP-10, measured at varying 

times at a temperature of 375 °C. Ln(Ac) is the natural logarithm of the calibrated 

chromatographic area measured for each ampoule sample. 
13

0.00000

0.00200

0.00400

0.00600

0.00800

0.01000

0.01200

0.01400

0.01600

0.00142 0.00144 0.00146 0.00148 0.0015 0.00152 0.00154 0.00156 0.00158 0.0016 0.00162

(1/T)K

k, min-1

Figure 6 Temperature dependence of the measured thermal decomposition rate constants. 

The temperature dependence of the measured rate constants is provided in Figure 6. Here again 

the curvature is indicative of disproportionation. 

It is difficult or impossible to directly compare the thermal decomposition results presented here 

with previous results since most previous studies used very short residence times. Previous 

studies employed residence times as short as milliseconds to as long as 4 s. In this work, the 

residence times were much longer, since the context of these measurements was indeed different. 

Here, at the highest temperature studied (425 °C), the shortest residence time was 2220 s. At the 

lowest temperature studied, 350 °C, the longest residence time used was 241,000 s. 

For the purpose of thermophysical property measurement, residence time in instrumentation is 

not expected to be a factor unless the fluid is exposed to temperatures between 375 and 400 °C. 

All of the measurements in this work were made at temperatures considerably below this 

temperature. Thus, we may conclude that thermal decomposition is not an issue with these 

measurements. 

The onset of thermal decomposition does not necessarily preclude measurements at higher 

temperatures. It simply means that above 375 °C, explicit consideration must be given to the 

potential of sample decomposition. Test samples must be analyzed after each measurement, and 

residence times must be limited. 
14

Instrumentation for Density, Viscosity, and Speed of Sound Measurements 

The density, viscosity, and speed of sound of a JP-10 sample from Wright Laboratory were 

measured in two commercial rapid characterization instruments. A Stabinger viscodensimeter 

(Anton Paar SVM 3000) was used to determine the density and the absolute and kinematic 

viscosity in the temperature range from −40 °C to 100 °C (233.15 K to 373.15 K) at atmospheric 

pressure. A sound-speed analyzer (Anton Paar DSA 5000) was used to measure the speed of 

sound and the density of the JP-10 samples at atmospheric pressure (84 kPa at 1654.7 m altitude 

of Boulder, Colorado) in the temperature range from 5 °C to 70 °C (278.15 K to 343.15 K). 

The measurements with the Stabinger viscodensimeter were carried out according to ASTM 

Standard D 7042 – 04 Standard Test Method for Dynamic Viscosity and Density of Liquids by 

Stabinger Viscometer (and the Calculation of Kinematic Viscosity). The following instrument 

description is partly excerpted from ASTM Standard D 7042 – 04. The viscometer part of the 

instrument uses a rotational coaxial cylinder measuring system. The outer cylinder (tube) of 

Hastelloy is driven by a motor at a constant and known rotational speed. The low-density inner 

cylinder (rotor) of titanium is held in the axis of rotation by the centrifugal forces of the higher 

density sample and in its longitudinal position by the magnet and the soft iron ring. 

Consequently, the system works free of bearing friction as found in rotational viscometers. A 

permanent magnet in the inner cylinder induces eddy currents in the surrounding copper casing. 

The rotational speed of the inner cylinder establishes itself as the result of the equilibrium 

between the driving torque of the viscous forces and the retarding eddy current torque. This 

rotational speed is measured by an electronic system (Hall effect sensor) that counts the 

frequency of the rotating magnetic field (see Figures 7 and 8). 

The digital density analyzer in the viscodensimeter uses a U-shaped vibrating sample tube and a 

system for electronic excitation and frequency counting. The density of the sample liquid in the 

vibrating tube is obtained from the resonant frequency of the vibrating system relative to the 

resonant frequency with a calibration liquid of known density. 

The combination of a viscometer and a densimeter makes it possible to obtain absolute viscosity 

η as well as kinematic viscosity ν of a sample because ν = η/ρ, where ρ is the density. The 

amount of sample needed for both measuring cells is less than 5 mL. 

The assembly is thermostatted by a copper block that surrounds both the viscosity and the 

density measuring cells and keeps both cells at the same temperature. A thermoelectric heating 

and cooling system ensures the temperature stability of the copper block within 0.005 °C from 

the set temperature at the position of the viscosity cell over the whole temperature range. At 

temperatures below 0 °C the viscodensimeter was cooled with an additional external circulator. 

The uncertainty (k = 2; 95 % confidence level) of the temperature calibration is no more than 

0.03 °C over the range from 15 to 100 °C. Outside this range the calibration uncertainty is no 

more than 0.05 °C. 
15

Figure 7. Main components of the Stabinger viscodensimeter SVM 3000. 

1 – Thermostatting Peltier block, 2 – Concentric cylinder viscometer, 3 – Vibrating tube 

densimeter. 

Figure 8. Assembly of the concentric cylinder viscometer in the Stabinger viscodensimeter 

SVM 3000. 

The uncertainty of the viscosity measurement is stated by the manufacturer as 0.35 % of the 

measured value and that of the density measurement at 0.5 kg·m-3, while the repeatabilities are 

0.2 % of the measured value and 0.2 kg·m-3, respectively. However, wide-ranging comparisons 

of measured viscosities with reference values of viscometer calibrating liquids both in this 

laboratory and elsewhere have shown that the uncertainty of the viscosity measurements as 

stated by the manufacturer is not maintained throughout the entire advertised measuring range of 

the instrument (0.2 to 10,000 mPa·s in absolute viscosity and 0.2 to 10,000 mm2

·s

-1 in kinematic 

viscosity) with one calibration. The actual uncertainty in these measurements has been assessed 
16

by benchmark measurements on two standard oils. These tests will be discussed in the section 

on JP-10 viscosity measurements. 

Density and the speed of sound in liquid samples of JP-10 were measured with a sound-speed 

analyzer DSA 5000 that is similar to the SVM 3000 viscodensimeter in design and appearance. It 

includes also a vibrating U-tube densimeter and a pulse-echo speed of sound measurement cell 

that is illustrated below. However, the temperature range is limited from 0 °C to 70 °C. The 

measurement uncertainty is stated for both properties as 0.01 % to 0.1 %, with repeatabilities of 

0.001 kg·m-3 in the density and 0.1 m·s-1 in the speed of sound measurement. The density 

measurement in the DSA 5000 is more accurate than that in the viscodensimeter. By design, the 

densimeter in the viscodensimeter was made only as accurate as necessary in view of the higher 

uncertainty of the viscosity measurement. 

Combining a densimeter with a speed of sound measurement (Figure 9) makes it possible to 

obtain the adiabatic compressibility κs = –(∂V/∂p)s/V = 1 / (ρ w

2

) where V denotes volume, p is 

pressure, and w the speed of sound. Subscript s indicates “at constant entropy s.” 

Transmitter

Length

~ 5mm

Receiver

Period of the

sound speed cell

Electronics

Figure 9. Schematic of the sound speed measurement in the DSA 5000. 
17

Density Measurements for JP-10 

The density of JP-10 was measured in both instruments, the Stabinger viscodensimeter SVM 

3000 as well as the Sound Speed Analyzer DSA 5000. The results are tabulated in Table 5 and in 

Table 6, and illustrated in Figure 10. 

860

880

900

920

940

960

980

1000

220 240 260 280 300 320 340 360 380

DSA 5000 Sample 1

DSA 5000 Sample 2

SVM 3000 Sample 1

Run 1

SVM 3000 Sample 1

Run 2

SVM 3000 Sample 2

Run 2

SVM 3000 Sample 3

Run 1

ρ / kg·m3

T / K

Figure 10. Densities of JP-10 measured in the Stabinger viscodensimeter and in the sound speed 

analyzer DSA 5000. 

The experimental data were correlated by a quadratic polynomial in reduced temperature 

ρ = a0 + a1Tr + a2Tr

2

, (6) 

where ρ is the density in kg·m-3 and Tr = T / (273.15 K) is the reduced absolute temperature. The 

values of the parameters a0 to a2 were determined by linear least squares regression. They are 

listed with their standard deviations in Table 7. The experimental density data are represented by 

eq. (6) with a maximum negative deviation of −0.02 % and a maximum positive deviation of 

0.04 %. These deviations are within the estimated uncertainty of the data. The percent deviations 

are illustrated in Figure 11, which gives also an indication of the repeatability of either 
18

instrument and of their mutual agreement. The data show the higher repeatability and lower 

uncertainty of the vibrating tube densimeter in the sound speed analyzer DSA 5000. 

Table 5. Densities of JP-10 measured in the Stabinger viscodensimeter SVM 3000. The ambient 

pressure during the measurements was 84 kPa. 

Temperature 

T

Density 

ρ

Temperature 

T

Density

ρ

Temperature 

T

Density

ρ

Temperature 

T

Density 

ρ

K kg·m-3 K kg·m-3 K kg·m-3 K kg·m-3

Sample 1 

Run 1 

Sample 2 

Run 1 

Sample 2 

Run 2 

Sample 3 

Run 1 

353.15 

348.15 

343.15 

338.15 

333.15 

328.15 

323.15 

318.15 

313.15 

308.15 

303.15 

298.15 

293.15 

288.15 

283.15 

278.15 

273.15 

888.7 

892.8 

896.7 

900.6 

904.6 

908.6 

912.5 

916.3 

920.2 

924.1 

928.0 

931.8 

935.7 

939.6 

943.4 

947.3 

951.2 

373.15 

368.15 

363.15 

358.15 

353.15 

348.15 

343.15 

338.15 

333.15 

328.15 

323.15 

318.15 

313.15 

308.15 

303.15 

298.15 

293.15 

288.15 

283.15 

278.15 

273.15 

872.6 

876.4 

880.5 

884.5 

888.5 

892.5 

896.4 

900.4 

904.4 

908.3 

912.2 

916.2 

920.1 

924.0 

927.9 

931.8 

935.7 

939.6 

943.5 

947.3 

951.2 

283.15 

278.15 

273.15 

268.15 

263.15 

258.15 

253.15 

248.15 

243.15 

238.15 

233.15 

943.4 

947.2 

951.1 

954.9 

958.8 

962.6 

966.5 

970.3 

974.1 

977.9 

981.7 

283.15 

278.15 

273.15 

268.15 

263.15 

258.15 

253.15 

248.15 

243.15 

238.15 

233.15 

943.6 

947.5 

951.4 

955.2 

959.1 

962.9 

966.7 

970.6 

974.4 

978.3 

982.1 
19

Table 6. Densities of JP-10 measured in the Sound Speed Analyzer DSA 5000.The ambient 

pressure during the measurements was 84 kPa. 

Temperature 

T

Density 

ρ

Temperature

T

Density

ρ

K kg·m-3 K kg·m-3

Run 1 Run 2 

343.152 

338.151 

333.150 

328.151 

323.149 

318.150 

313.151 

308.151 

303.152 

298.152 

293.151 

288.151 

283.151 

278.147 

896.276 

900.235 

904.188 

908.134 

912.072 

916.002 

919.923 

923.837 

927.750 

931.664 

935.577 

939.491 

943.403 

947.315 

343.150 

338.150 

333.150 

328.151 

323.151 

318.150 

313.152 

308.151 

303.151 

298.151 

293.152 

288.151 

283.150 

278.143 

896.272 

900.232 

904.186 

908.129 

912.068 

915.999 

919.918 

923.833 

927.744 

931.659 

935.573 

939.486 

943.400 

947.311 
20

Table 7. Parameter values and associated standard deviations of the density correlation eq. (6). 

i

Parameter 

ai

Standard 

deviation si

0 

1 

2 

1153.0412 

−192.47447 

−9.3825928 

1.020 

1.868 

0.8485 

-0.05

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

220 240 260 280 300 320 340 360 380

DSA 5000 Sample 1 DSA 5000 Sample 2

SVM 3000 Sample 1 Run 1 SVM 3000 Sample 2 Run 1

SVM 3000 Sample 2 Run 2 SVM 3000 Sample 3 Run 1

T / K

100 ((ρexp/ρcorr) - 1)

Figure 11. Percent deviations of the measured densities of JP-10 relative to the correlation, eq. 

(6). 
21

Viscosity Measurements for JP-10 

The viscosity of JP-10 was measured with the Stabinger viscodensimeter SVM 3000 on three 

samples from the same stock to assess the repeatability of the instrument. Four runs were carried 

out in the combined temperature range from 233.15 K to 373.15 K. The measured absolute and 

kinematic viscosities are tabulated in Table 8 and illustrated in Figure 12. 

The viscosity of two certified viscosity standard calibrating liquids was measured to verify the 

performance of the viscometer. Calibrating liquids S3 and N1.0 were obtained from Cannon 

Instruments, Inc. This company has been delegated by NIST to provide U.S. national 

measurement standards and to issue calibration and measurement certificates for certified liquid 

viscosity reference standards. Figure 12 shows that the viscosity of standard calibrating liquid 

N1.0 is about three times lower than that of JP-10 while the temperature dependence is about the 

same for both liquids in the range where the viscosity of the standard calibrating liquid N1.0 is 

known. The viscosity of standard calibrating liquid S3 matches that of JP-10 at 373.15 K but 

increases faster with decreasing temperature and is four times higher at 233.15 K. Thus the 

viscosities of the two standard calibrating liquids bracket that of JP-10 and allow a rigorous 

uncertainty assessment of the instrument during these measurements. 

Table 8. Absolute and kinematic viscosities of JP-10 measured in the Stabinger viscodensimeter 

SVM 3000. The ambient pressure during the measurements was 84 kPa. 

Temperature 

T

Absolute 

viscosity 

η

Kinematic 

viscosity 

v

Temperature 

T

Absolute 

viscosity 

η

Kinematic 

viscosity 

v

K mPa·s mm2·s-1 K mPa·s mm2·s-1

Sample 1 Run 1 Sample 2 Run 1 

353.15 

348.15 

343.15 

338.15 

333.15 

328.15 

323.15 

318.15 

313.15 

308.15 

303.15 

298.15 

293.15 

288.15 

283.15 

278.15 

273.15 

1.1619 

1.2411 

1.3284 

1.4252 

1.5321 

1.6515 

1.7848 

1.9343 

2.1034 

2.2957 

2.5153 

2.7673 

3.0582 

3.3963 

3.7915 

4.2564 

4.8078 

1.3074 

1.3901 

1.4815 

1.5825 

1.6937 

1.8177 

1.9560 

2.1109 

2.2858 

2.4843 

2.7105 

2.9697 

3.2684 

3.6148 

4.0188 

4.4932 

5.0547 

373.15 

368.15 

363.15 

358.15 

353.15 

348.15 

343.15 

338.15 

333.15 

328.15 

323.15 

318.15 

313.15 

308.15 

303.15 

298.15 

293.15 

288.15 

283.15 

0.91482 

0.97140 

1.0325 

1.0989 

1.1713 

1.2507 

1.3381 

1.4347 

1.5419 

1.6612 

1.7948 

1.9449 

2.1147 

2.3080 

2.5287 

2.7823 

3.0752 

3.4161 

3.8149 

1.0483 

1.1084 

1.1726 

1.2424 

1.3184 

1.4014 

1.4927 

1.5934 

1.7049 

1.8289 

1.9674 

2.1229 

2.2984 

2.4978 

2.7251 

2.9859 

3.2865 

3.6358 

4.0435 
22

278.15 

273.15 

4.2857 

4.8444 

4.5240 

5.0930 

Temperature 

T

Absolute 

viscosity 

η

Kinematic 

viscosity 

v

Temperature 

T

Absolute 

viscosity 

η

Kinematic 

viscosity 

v

K mPa·s mm2·s-1 K mPa·s mm2·s-1

Sample 2 Run 2 Sample 3 Run 1 

283.15 

278.15 

273.15 

268.15 

263.15 

258.15 

253.15 

248.15 

243.15 

238.15 

233.15 

3.8094 

4.2790 

4.8364 

5.5038 

6.3083 

7.2898 

8.4955 

9.9955 

11.986 

14.474 

17.695 

4.0382 

4.5174 

5.0851 

5.7634 

6.5794 

7.5728 

8.7903 

10.302 

12.305 

14.801 

18.025 

283.15 

278.15 

273.15 

268.15 

263.15 

258.15 

253.15 

248.15 

243.15 

238.15 

233.15 

3.8165 

4.2932 

4.8572 

5.5321 

6.3476 

7.3450 

8.5365 

10.065 

11.993 

14.462 

17.671 

4.0446 

4.5312 

5.1056 

5.7915 

6.6186 

7.628 

8.8302 

10.37 

12.308 

14.783 

17.993 
23

1E-1

1E+0

1E+1

1E+2

220 240 260 280 300 320 340 360 380 400

JP-10 Sample 1 Run 1 JP-10 Sample 2 Run 1

JP-10 Sample 2 Run 2 JP-10 Sample 3 Run 1

Viscosity Standard S3 Viscosity Standard N1.0

 / mPa·s

T / K

Figure 12. Absolute viscosities of JP-10 and of certified viscosity standard calibrating liquids S3 

and N1.0 measured in the Stabinger viscodensimeter SVM 3000. 

The percent deviations of the measured viscosities of the calibrating standards relative to the 

certified reference values are shown in Figure 13. The measured values for calibrating standard 

N1.0 deviate systematically between −10.8 % and −8.7 % from the certified reference values. 

These deviations are clearly beyond the uncertainty of the viscometer as quoted by the 

manufacturer (0.35 %). They are consistent with our earlier performance validations and 

experiences of other users of the Stabinger viscodensimeter, which indicate that the manufacturer 

quoted uncertainty is reached only in a viscosity range from 1 mPa·s to 1 Pa·s. The viscosities of 

JP-10 are within this range. Note that the viscosity of calibrating standard N1.0 is about three 

times lower than that of JP-10. Figure 13 shows that the percent deviations of the measured 

viscosities of calibrating standard S3 agree with the certified reference values within 0.42 %. 

This deviation is consistent with the combined manufacturer quoted uncertainty of the 

viscometer and the uncertainty of the certified reference values. Since the viscosity of calibrating 
24

standard S3 matches that of JP-10 more closely, and based on the accumulated experience of this 

laboratory, the actual uncertainty of the viscosity measurements of JP-10 is estimated at ±1 %. 

-12

-10

-8

-6

-4

-2

0

2

220 240 260 280 300 320 340 360 380

N1.0 Sample 1

N1.0 Samlpe 2

S3 Sample 1

S3 Sample 2

T / K

100 ((ηexp/ηstd) - 1)

Figure 13. Percent deviations of the measured viscosities of the calibrating standards relative to 

the certified reference values. 

Viscosity correlation 

To facilitate the practical application of the measured viscosities, their temperature dependence 

was also correlated in this work. The curvature of the logarithmically scaled experimental 

viscosity data in Figure 12 indicates that simple exponential terms such as the Arrhenius ansatz

are insufficient to represent the data within their experimental uncertainty. The Vogel-TammannFulcher (VTF) equation is applicable over wider ranges of temperature but was also found 

inadequate for the wide-ranging JP-10 viscosity measured here. Adding two temperature terms to 

the VTF equation yielded a representation of the viscosity data well within their experimental 

uncertainty. The reduced absolute viscosity is expressed as a function of the reduced absolute 

temperature according to 

,(7) 

where η0 = 1 mPa·s is a dimensional reducing factor and Tr = T / (273.15 K) is the reduced 

absolute temperature. The values of the adjustable parameters β1 to β4 were determined by 

nonlinear least squares regression. They are listed with their standard deviations in Table 9. The 

η

η0

= exp β1

Tr + β 2

+ β 3Tr + β 4Tr

2 ⎛

⎝ ⎜ 

⎞ 

⎠ ⎟ 
25

experimental viscosity data are represented by eq. (7) with a maximum negative deviation of 

−0.62 % and a maximum positive deviation of 0.63 %. These deviations are within the estimated 

uncertainty of the data of 1 %. 

Table 9. Parameter values and associated standard deviations of the viscosity correlation eq. (7). 

i

Parameter 

βi

Standard 

deviation si

1 

2 

3 

4 

1.82400 

−0.430094 

−1.99450 

0.370442 

 0.0099 

 0.0013 

 0.025 

 0.014 

The percent deviations of the experimental viscosity data from the correlation are illustrated in 

Figure 14. The curvature of the deviations at either end of the temperature range should caution 

users of eq. (7) not to extrapolate the correlation beyond the temperature limits. The graph gives 

also an impression of the repeatability of the viscosity measurements in the Stabinger 

viscodensimeter with different samples from the same stock. 

-1.5

-1.0

-0.5

0.0

0.5

1.0

220 240 260 280 300 320 340 360 380

Sample 1 Run 1 Sample 2 Run 1

Sample 2 Run 2 Sample 3 Run 1

T / K

100 ((η exp/η std) - 1)

Figure 14. Percent deviations of the measured viscosities of JP-10 relative to the correlation, eq. 

(7). 
26

Sound Speed Measurements and Derived Adiabatic Compressibilities for JP-10 

The speed of sound in JP-10 was measured in the Sound Speed Analyzer DSA 5000 between 

278.15 K and 343.15 K. The results are tabulated in Table 10 and illustrated in Figure 15. Table 

10 includes also derived values of the adiabatic compressibility κs = − (∂V/∂p)s/V = 1 / (ρ

w

2

). These are illustrated in Figure 16. 

1200

1250

1300

1350

1400

1450

1500

1550

270 280 290 300 310 320 330 340 350

Sample 1

Sample 2

w / m·s-1

T / K

Figure 15. Speed of sound in JP-10 measured in the sound speed analyzer DSA 5000. 
27

Table 10. Speeds of Sound and derived Adiabatic Compressibilities of JP-10 measured in the 

Sound Speed Analyzer DSA 5000. The ambient pressure during the measurements was 84 kPa. 

Temperature TSpeed of 

sound w

Adiabatic 

compressibility κs

Temperature TSpeed of 

sound w

Adiabatic 

compressibility κs

 K m·s-1 GPa-1 K m·s-1 GPa-1

Run 1 Run 2 

343.152 

338.151 

333.150 

328.151 

323.149 

318.150 

313.151 

308.151 

303.152 

298.152 

293.151 

288.151 

283.151 

278.147 

1229.62 

1248.15 

1267.03 

1286.14 

1305.47 

1325.04 

1344.85 

1364.90 

1385.21 

1405.80 

1426.63 

1447.73 

1469.17 

1490.93 

0.737932 

0.713035 

0.688918 

0.665692 

0.643335 

0.621793 

0.601036 

0.581036 

0.561743 

0.543117 

0.525167 

0.507846 

0.491087 

0.474888 

343.150 

338.150 

333.150 

328.151 

323.151 

318.150 

313.152 

308.151 

303.151 

298.151 

293.152 

288.151 

283.150 

278.143 

1229.59 

1248.11 

1266.98 

1286.09 

1305.43 

1325.00 

1344.79 

1364.83 

1385.16 

1405.74 

1426.58 

1447.66 

1469.13 

1490.95 

0.737971 

0.713083 

0.688974 

0.665748 

0.643377 

0.621832 

0.601093 

0.581098 

0.561787 

0.543167 

0.525206 

0.507898 

0.491116 

0.474877 
28

0.4

0.5

0.6

0.7

0.8

270 280 290 300 310 320 330 340 350

Sample 1

Sample 2

κs / GPa-1

T / K

Figure 16. Adiabatic compressibilities of JP-10 derived from measurements in the sound 

speed analyzer DSA 5000. 

Thermal Conductivity of JP-10 

Transient hot-wire measurements of the thermal conductivity of the JP-10 liquid sample were 

made along 11 isotherms at temperatures from 300 to 500 K with pressures up to 30 MPa. The 

transient hot-wire instrument has been described in detail elsewhere[15]. The measurement cell 

is designed to closely approximate transient heating from a line source into an infinite fluid 

medium. The ideal (line source) temperature rise ΔTid is given by 

ln ln ,

10

1

w

0

2 id = T + T

r C

4a (t)+

4

q T = i

i=

δ

πλ

Δ ∑ ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ Δ (8) 

where q is the power applied per unit length, λ is the thermal conductivity of the fluid, t is the 

elapsed time, a = λ/ρCp is the thermal diffusivity of the fluid, ρ is the density of the fluid, Cp is the 

isobaric specific heat capacity of the fluid, r0 is the radius of the hot wire, C = 1.781... is the 

exponential of Euler's constant, ΔTw is the measured temperature rise of the wire, and δTi are 

corrections to account for deviations from ideal line-source conduction [15,16]. The only significant 
29

correction for the JP-10 measurements is for the finite wire dimensions. A plot of ideal temperature 

rise versus log of elapsed time should be linear, such that thermal conductivity can be found 

from the slope and thermal diffusivity can be found from the intercept of a linear fit to the data. 

At time zero, a fixed voltage is applied to heat the small diameter wire that is immersed in the 

fluid of interest. The wire is used as an electrical heat source while its resistance increase allows 

determination of the transient temperature rise as a function of elapsed time. A single anodized 

tantalum wire of 25 μm diameter and 10 cm length was used for the measurements. Short 

experiment times (nominally 1 s) and small temperature rises (nominally 1 to 4 K) are selected to 

eliminate heat transfer by free convection. Experiments at several different heating powers (and 

temperature rises) provide verification that free convection is not significant. Heat transfer due to 

thermal radiation is more difficult to detect and correct when the fluid can absorb and re-emit 

infrared radiation, as does JP-10. Thermal radiation heat transfer will increase roughly in 

proportion to the absolute temperature cubed and can be characterized from an increase in the 

apparent thermal conductivity as experiment time increases since radiation emission from the 

fluid increases as the thermal wave diffuses outward [16]. Measurements of toluene liquid made 

prior to the JP-10 measurements verified that the apparatus was performing correctly. The 

toluene verification measurements at 300 K and 320 K agreed with IUPAC recommendations 

within 1 % at a 95 % confidence interval. 

The results of 683 transient hot-wire measurements are given in Appendix 1 and shown in Figure 

17 at temperatures from 300 K to 500 K. Each experiment is characterized by the initial cell 

temperature T0 and the mean experiment temperature Te. There are generally five experiments at 

each initial cell temperature to verify that convection was not significant, since convection 

depends strongly on the temperature rise (ΔT = Te − T0). The conditions of the fluid during each 

measurement are given by the experimental temperature Te, pressure pe, and density ρe. The 

thermal conductivity without correction for thermal radiation is given by λe; the contribution of 

thermal radiation to the measured thermal conductivity is less than 0.5 % at the highest 

temperature of 500 K. The uncertainty of the measured thermal conductivity data is less than 1 % 

for temperatures from 300 to 500 K. 
30

0.085

0.090

0.095

0.100

0.105

0.110

0.115

0.120

5.5 5.7 5.9 6.1 6.3 6.5 6.7 6.9

ρ (mol.

L-1)

λ (W.

m-1K-1)

300 K

320 K

340 K

360 K

380 K

400 K

420 K

440 K

460 K

480 K

500 K

Figure 17. Thermal conductivity of JP-10 at pressures from 0.1 MPa to 30 MPa. 
31

Distillation Curve for JP-10 

One normally associates the distillation curve measurement with complex mixtures, such as 

crude oils, gasolines, and kerosenes. The distillation curve of what is nominally a pure fluid is 

really a measurement of a vapor pressure. Since several components were found in the sample of 

JP-10 that was used for all of the measurements discussed in this report, it was decided that the 

distillation curve would be instructive. 

The distillation curve of JP-10 was measured with a developmental apparatus that incorporates 

several important improvements over previous approaches [17]. The main improvement has 

been the introduction of a composition channel, allowing on-the-fly sampling of distillate for a 

quantitative analysis. In addition, there have been improvements in temperature measurement 

and control, and in the liquid volume measurement. 

The distillation curve that was measured for JP-10 is provided in Figure 18. This curve is 

presented as temperature (Tk, measured directly in the liquid) plotted against volume fraction. 

The temperatures were measured at an ambient atmospheric pressure of 84.06 kPa. These 

temperatures have been converted to what would have been measured at standard atmospheric 

pressure with the modified Sidney Young equation: 

Cc = C(760 – Pa)(273 + T) , (9) 

where Cc is the correction added to the observed temperature, C is a constant, Pa is the 

atmospheric pressure in mmHg, and T is the measured temperature in °C. In fact, the original 

Sidney Young equation specifies that C is dependent upon the average hydrocarbon chain length 

of the fluid, ranging from 0.000135 for a single carbon to 0.000119 for 8 carbons. A linear 

correlation of these factors can be used to predict a value for simple fluids. It should be noted 

that the Sidney Young equation may have significant limitations when applied to correct boiling 

point temperatures more than 5 kPa from standard atmospheric pressure [18]. 

It can be seen that this curve is indeed indicative of a single component fluid. Despite the seven 

identified components, the distillation properties of this fluid are best described as a vapor 

pressure, within a first approximation. The boiling temperature at 84.06 kPa was found to be 

180.8 °C, with an uncertainty of 0.2 °C. When corrected to standard atmospheric pressure with 

the Sidney Young equation, a boiling temperature of 187.2 °C is obtained, also with an 

uncertainty of 0.2 °C. Note that 18 separate measurements are used to calculate these values; the 

final inflection point represents lift-out of the sensing thermocouple, and the end of a 

measurement. 
32

170.0

180.0

190.0

200.0

210.0

220.0

230.0

240.0

250.0

260.0

270.0

0 10 20 30 40 50 60 70 80 90 100

Volume Fraction (%)

Temperature Tk (oC)

Figure 18. The distillation curve for JP-10, as received from Wright Laboratory. Tk represents 

the temperature measured directly in the liquid (the kettle) corrected with the Sidney Young 

equation. This curve is essentially the distillation curve of a pure fluid. Note that the inflection 

seen at the highest volume fraction is the result of the lift out of the measuring thermocouple, and 

is not part of the distillation curve proper. 
33

Model Development for the Thermodynamic and Transport Properties of JP-10 

In order to begin model development for the thermophysical properties of JP-10, we first 

collected data from the literature. The experimental data in the literature are very limited; a 

summary is presented in Table 11. There is no information on density, viscosity, heat capacity, 

sound speed, or thermal conductivity at pressures above the saturation boundary. The most 

comprehensive sets are those of Steele et al. [19] which provide the critical point, a vapor 

pressure curve, heat capacities and liquid densities at saturation conditions, and Moynihan et al. 

[20] which provides limited liquid density and viscosity data at atmospheric pressure. For this 

work it is therefore important to have NIST measurements of thermophysical properties to 

supplement the very limited information in the open literature. 

Table 11. Summary of literature data on the thermophysical properties of JP-10. 

Source Summary of properties 

Boyd et al., 1971 [21] Vapor pressure correlating equation only (358 ≤ T(K) ≤ 417) 

cp

0

, 5 points (200 ≤ T(K) ≤ 500) 

cp, 4 points (329 ≤ T(K) ≤ 390) 

Moynihan et al., 1977 [22] Correlating equations given for cp, density and viscosity of the 

liquid at atmospheric pressure 

Moynihan et al., 1978 [23] Repeats information in Moynihan et al., 1977 

Smith et al., 1978 [24] cp correlating equation only 

Smith and Good, 1979 [25] One experimental liquid density and cp point (298 K) 

Smith et al., 1980 [26] cp correlating equation only 

Gammon and Smith, 1982 

[27] 

Two experimental liquid density points (288 K, 298 K) 

Moynihan et al., 1982 [20] Liquid density and viscosity at atmospheric pressure, 17 points 

for (219 ≤ T(K) ≤ 322) 

Steele et al., 1989 [19] Critical point, Vapor pressure, 23 points (343≤T(K)≤507) 

Saturated liquid density, 3 points (690 ≤ T(K)≤698) 

Saturated vapor density, 4 points (681 ≤ T(K)≤698) 

csat, 39 points (300 ≤ T(K) ≤ 680) 

Chickos et al., 2002 [28] cp, 10 points (193 ≤ T(K) ≤ 273) 

Heat of vaporization, 1 point (298 K) 

CRC, Inc., 2004 [29] Provides graphical information only on liquid density at 

atmospheric pressure, kinematic viscosity at atmospheric 

pressure, surface tension, vapor pressure, specific heat and liquid 

thermal conductivity at atmospheric pressure, dielectric constant. 
34

Thermodynamic Properties of JP-10 

A fundamental equation of state for JP-10 has been developed, explicit in Helmholtz energy as a 

function of density and temperature. All single-phase thermodynamic properties can be 

calculated as derivatives of the Helmholtz energy. A preliminary equation of state for propane 

was used as the starting point for the equation of state developed here for JP-10. Unlike high 

accuracy equations, which generally use 20 to 50 fluid-specific terms to describe densities to the 

order of (0.01 to 0.1) %, the equation presented here has only 10 terms. For JP-10, there are not 

sufficient experimental data available to develop a high-accuracy fluid-specific model with 20 to 

50 terms similar to that done in other work. 

The extrapolation of the equation of state can be checked at low temperatures (as demonstrated 

by the curvature of the isobaric and isochoric heat capacities, and the speed of sound) and at high 

temperatures (as demonstrated by the ideal curves). In addition, the number of terms in the 

equation (10 terms for the real gas) was kept to a minimum, thus decreasing the correlation 

among terms and the possibility of over fitting. Although the smaller number of terms decreases 

the flexibility of the equation, and thus its ability to accurately represent a fluid’s properties, its 

rigid shape becomes more applicable to substances with limited data, and thus becomes a tool to 

fill in gaps in the thermodynamic surface, a key feature in modeling fluids such as JP-10. 

The critical temperature and pressure were taken from Steele et al. [19] Although Steele et al. 

reported a value for the critical density (2.092 mol/dm3

), this value appeared to be too low and 

was not used here, rather, the critical density was fitted simultaneously with the coefficients of 

the equation, resulting in a value of 2.16 mol/dm3

. Steele et al. did not actually measure the 

critical density, rather it was graphically selected by plotting a line through their seven critical 

region values of the saturated densities. The method used in this work to determine the critical 

density also uses these seven values, in additional to all of the other available data for JP-10, and 

is thus a more reliable technique for the critical density prediction. The values of the critical 

parameters reported below should be used for all property calculations from the equation of state. 

Tc = 698 K 

pc = 3.733 MPa 

ρc = 2.16 mol/dm3

 

The equation of state, expressed in a fundamental form explicit in the Helmholtz energy, has 

become the most widely used method for calculating thermodynamic properties with high 

accuracy for many fluids. The independent variables in the functional form are density and 

temperature, 

 , (10) 

where a is the Helmholtz energy, a

0

(ρ,T) is the ideal gas contribution to the Helmholtz energy, 

and ar

(ρ,T) is the real fluid Helmholtz energy that results from intermolecular forces. All 

thermodynamic properties can be calculated as derivatives of the Helmholtz energy. For 

example, the pressure derived from this expression is 

a( ) T a ( T) a ( T) r , , , 0 ρ = ρ + ρ
35

 

T

a

p ⎟

⎟

⎠

⎞ ⎜

⎜

⎝

⎛

∂ρ

∂ = ρ2 . (11) 

 

In practical applications, the functional form used is the dimensionless Helmholtz energy, α, as a 

function of a dimensionless density and temperature. The form of this equation is 

 ( ) α() () () δ τ α δ τ α δ τ ρ , , , , 0 r

RT

a T = = + , (12) 

where δ = ρ /ρc and τ = Tc / T. The Helmholtz energy of the ideal gas is given by 

 ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = + − − + − ∫ ∫ 0 0

0

0

0

0 0

0

0 d d ln 0 0 T

T T R

T

c

a h c T RT T s

T

T

p

T

T p ρ

ρ , (13) 

where ρ0 is the ideal gas density at T0 and p0 (ρ0 = p0/T0R) and T0 and p0 are arbitrary constants. 

The ideal gas Helmholtz energy is given in a dimensionless form by 

 ∫ ∫

τ

τ

τ

τ τ

τ

τ +

τ

τ − δ τδτ − − +τ

α = 0 0d 1 1 ln d

0

2

0

0

0

0

0

0

0 0 p p

c

c

R

c

R R

s

RT

h , (14) 

where δ0 = ρ0 / ρc and τ0 = Tc / T0. 

The calculation of thermodynamic properties from the ideal gas Helmholtz energy requires an 

equation for the ideal gas heat capacity, cp

0

. These values can be obtained from heat capacity 

measurements extrapolated to zero pressure, gaseous speed of sound measurements, or 

calculations from statistical methods using spectroscopically determined frequencies. In this 

work, we fitted the following equation simultaneously with the other parameters in the real gas 

part of the equation. 

 ( )

[ ] ( ) 2

3

3

2

3

2

0.85

0 1

0

exp / 1

exp /

− ⎟

⎠

⎞ ⎜

⎝

⎛ = + +

c T

c T

T

c

c c T c

R

c p , (15) 

Here, the molar gas constant, R, is 8.314472 J·mol–1·K–1 and the values of the coefficients are c0 

= 3.3218, c1= 0.07975, c2 = 27.6975, and c3 = 1470. The values of cp

0

 in Boyd et al. [21] 

supplemented at temperatures over 600 K with values for a similar compound, adamantine [21] 

were used in the fitting. The ideal gas Helmholtz energy equation, derived from eqs. (14) and 

(15), is 

( ) ( ) [ ] ( ) c

c c c T c T

a a c ln 1 exp /

0.85 1.85

ln 1 ln 2 3

0.85

0.85

1

1 2 0

0 α = + τ + δ + − τ − τ + − − τ − , (16) 
36

where a1 and a2 are arbitrary, and are conventionally chosen by the definition of the reference 

state for enthalpy and entropy. 

 

The common functional form used for the Helmholtz energy equation of state is 

 α ( ) δ τ = ∑ δ τ +∑ δ τ ( ) − δ k k k k k i j l

k

i j

k

r , , (17) N N exp

where each summation typically contains 4 to 20 terms and where the index k points to each 

individual term. The functional form used here is: 

 

( )

2

exp exp

exp exp exp

,

4 2.5

10

6 1.72

9

6 0.95

8

3 1.69

7

3 2.0

6

4

5

2 1.65

4

2 1.42

3

1.15

2

0.2

1

−δ −δ

−δ −δ −δ

+ δ τ + δ τ

+ δ τ + δ τ + δ τ

α δ τ = δτ + δτ + δ τ + δ τ + δ τ

n n

n n n

n n n n n r

 , (18) 

where the coefficients nk of the residual part of the equation of state are given in the table below. 

Table 12. Coefficients of the equation of state. 

k nk

1 1.64044 

2 –2.75277 

3 –1.04100 

4 0.909461 

5 0.0396564 

6 –0.429241 

7 1.21962 

8 0.0609974 

9 –0.0798114 

10 –0.0439556 

 

The functions used for calculating pressure (p), compressibility factor (Z), internal energy (u), 

enthalpy (h), entropy (s), Gibbs energy (g), isochoric heat capacity (cv), isobaric heat capacity 

(cp), and the speed of sound (w) are: 

 

τ

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂δ

∂α = + δ

ρ =

r

RT

p Z 1 (19) 

 ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂τ

∂α

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂τ

∂α = τ

δ δ

r

RT

u

0

 (20) 
37

 1

0

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂δ

∂α

+ δ

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂τ

∂α

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂τ

∂α = τ

δ δ τ

r r

RT

h (21) 

 r

r

R

s − α − α

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂τ

∂α

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂τ

∂α = τ

δ δ

0

0

 (22) 

 

τ

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂δ

∂α = + α + α + δ

r

r

RT

g 0 1 (23) 

 ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂τ

∂ α

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂τ

∂ α = −τ

δ δ

2

2

2

2 0

2

r

v

R

c (24) 

 

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂δ

∂ α

+ δ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂δ

∂α

+ δ

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂δ∂τ

∂ α − δτ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂δ

∂α

+ δ

= +

τ τ

τ

2

2

2

2

2

1 2

1

r r

r r

p v

R

c

R

c

 (25) 

 

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂τ

∂ α

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂τ

∂ α

τ

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

∂δ∂τ

∂ α − δτ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂δ

∂α

+ δ

− ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂δ

∂ α

+ δ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂δ

∂α = + δ

δ δ

τ

τ τ

2

2

2

2 0

2

2

2

2

2

2

2

1

1 2 r

r r

r r

RT

w M . (26) 

The derivatives of the ideal gas Helmholtz energy and the residual Helmholtz energy required by 

the equations for the thermodynamic properties are given in Lemmon et al. [30] 

 

In the development of equations of state, various data types are useful in evaluating other types 

of data. Since one equation is used to represent multiple properties, the accuracy of one property 

can influence the behavior of another. In particular, the availability of heat capacity data is 

fundamental in equation of state development. Without it, equations can inadvertently give 

negative heat capacities at low temperatures or show unrealistic curvature in certain areas of the 

thermodynamic surface. For JP-10, the differences in the heat capacities among the various data 

sets is large, and new measurements will help access the uncertainties in the data sets. Although 

the quantity of heat capacity data for a fluid may be limited, even a few values in the liquid phase 

can often be sufficient to tie down the equation of state when working with a fixed functional 

form. This can be confirmed by plotting various constant property lines over the surface of state, 

and by comparing the slopes of such lines to expected behavior. The extrapolation behavior of 

the functional form used here at low and high temperatures, pressures, and densities gives 

confidence in the equation of state in the absence of highly accurate experimental data over some 

areas of the thermodynamic surface. 
38

Nonlinear fitting techniques were used to fit the coefficients of the equation. The selected data 

used in fitting were a subset of the available database determined by the correlator to be 

representative of the most accurate values measured. The nonlinear algorithm adjusted the 

coefficients and temperature exponents of the equation of state to reduce the overall sum of 

squares of the deviations of calculated properties from the input data. Each data point was 

individually weighted according to type, region, and uncertainty. Additionally, the values of the 

first and second derivatives of pressure with respect to density at the critical point were forced to 

be near zero at the selected critical point. The final set of coefficients represented not only the 

fitted data, but also the consistent data available for JP-10. 

 

Figure 19 shows deviations in density from about 200 to 350 K (the range of the experimental 

data). Comparisons with the equation of state to the data measured in this work and the data of 

Moynihan et al. [20,23] are very consistent and are generally within 0.1 %. The equation of state 

was fitted to the data measured in this work and is generally within 0.04 %. There are no 

experimental measurements above atmospheric pressure, above 400 K, or in the vapor phase, 

except for seven saturated liquid or vapor points from Steele et al. [19] in the critical region. The 

deviations are much larger than those at lower temperatures, but this is to be expected due to the 

nature of the critical region. Figure 20 shows these seven points and their proximity to the 

calculated saturation line from the equation of state. The data point with the highest density may 

be in error, and was not used in fitting. One of the data points was reported by Steele et al. to be 

in the liquid phase. However, with the change of critical density in this work, that point is 

actually in the vapor phase. 
39

Figure 19. Density deviations of available experimental data from the model. 
40

Figure 20. Saturation boundary of JP-10. 

 

Figure 21 shows comparisons of the equation of state with vapor pressure measurements. There 

is a definite need for additional measurements due to the large scatter between the data sets. The 

equation was fit to the boiling point determined at 84.06 kPa, measured in this work. The values 

from Steele et al. 19 vary substantially from this, and are 3 to 6% off from the equation of state. 

Likewise the equation of Boyd et al.21 differs by –2 to –10 %. The deviation of the vapor 

pressure point measured in this work is less than 0.1 %, as is the deviation of the only available 

heat of vaporization point of Chickos et al.[28] 
41

Figure 21. Deviations of vapor pressure for JP-10. 

 

Figure 22 shows comparisons of the ideal gas heat capacity to the values given by Boyd et al. 

[21] The equation differs from the five points for JP-10 given by Boyd et al. by up to 0.4 %. For 

the high temperature points taken for the fluid adamantane, differences are similar, but rise to 0.8 

% at 1000 K. Figure 23 shows the large scatter between the equation of state and other data sets 

for the isobaric and saturation heat capacities available for JP-10. The data of Chickos et al. [28] 

and the equation of Moynihan et al. [23] are about 5 % below the equation of state. The data of 

Steele et al. [19] and Boyd et al. [21] are about 5 % above the equation of state. The 1980 data 

from Smith et al. [19] compare the best with the equation, but the 1978 data from Smith et al. 

[24] show the largest deviations. Additional measurements of either the isobaric heat capacity or 

the isochoric heat capacity are needed to decrease the uncertainties in the equation of state for the 

heat capacity. There is only one set of measurements of the speed of sound for JP-10, measured 

as part of this work. The equation shows deviations of less than 0.04 %, as shown in Figure 24. 

Additional independent measurements of the speed of sound would help determine the total 

uncertainty of these data and of the equation of state. 
42

Figure 22. Deviations of the ideal gas heat capacity of JP-10. 
43

Figure 23. Deviations of the isobaric and saturation heat capacities of JP-10. 
44

Figure 24. Deviations of the speed of sound for JP-10. 

The uncertainties of properties calculated using the new equations are 0.1 % in density and in the 

speed of sound for the liquid phase at temperatures below 400 K and at pressures below 0.2 

MPa. Elsewhere the uncertainty in density rises to 1 % or more; experimental data are needed to 

validate this estimate. The uncertainties are 5 % in heat capacities and 2 % in vapor pressure 

(where all of the uncertainties for the equation of state can be considered as estimates of a 

combined expanded uncertainty with a coverage factor of 2). Deviations in the critical region are 

higher for all properties. 
45

Transport Properties of JP-10 

Viscosity Model 

In this work, we apply the extended corresponding states (ECS) viscosity model as described in 

Ref. [31], where the viscosity of a pure fluid is a sum of a dilute gas and a residual contribution, 

and the corresponding states principle applies only to the residual contribution [32], 

 ( , ) ( ) ( , ) ( ) ( , ) ( , ), 0 0 0

* * η T ρ =η T + Δη T ρ = η T + Δη T ρ Fη T ρ (27) 

where the superscript * denotes a dilute gas value, and the subscript 0 denotes a reference fluid 

value. In this work we selected propane as a reference fluid, and use the formulations given in 

references [33-35] for the equation of state, viscosity, and thermal conductivity. The viscosity of 

the reference fluid is evaluated at a conformal temperature and density T0 and ρ0 given by 

 T T / f 0 = and (28) 

 ρ0 = ρh . (29) 

The quantities f and h are called equivalent substance reducing ratios, and relate the reference 

fluid to the fluid of interest using a ratio of critical parameters (denoted by the subscript c) and 

functions of temperature and density known as shape functions θ and Φ, 

 f

T

T

c

c

= 0θ and (30) 

 h c

c

= ρ

ρ φ 0 . (31) 

The shape factors can be considered functions of both temperature and density. For small, 

nonpolar, almost-spherical molecules they are nearly unity and can be thought of as functions to 

compensate for deviations from a spherical shape. In this work, we use a form of the “exact” 

shape factor method [36]. 

The dilute gas viscosity in eq. (1) is found by Chapman-Enskog theory 

 2 (2,2)

*

16

5 ( )

πσ Ω η = mk T

T B , (32) 

where the dilute gas viscosity is η*, m is the molecular mass, kB is the Boltzmann constant, and T

is the absolute temperature. We will further assume that a Lennard-Jones 12-6 potential applies, 

and use the Lennard-Jones collision diameter for σ. Neufeld et al. [37] gave the 

following empirical correlation for the calculation of the collision integral Ω(2,2) 

 

* * (2,2) 0.14874 0.77320 2.43787 1.16145( *) 0.52487 2.16178 T T T e e − − − Ω = + + , (33) 
46

with the dimensionless temperature T* = kBT/ε, and ε the minimum of the Lennard-Jones pairpotential energy. The range of validity of this empirical correlation is 0.3 < T* < 100, and we 

have used the truncated form that does not include a sinusoidal term. 

The factor Fη in eq. (27) is found from the expression 

 

1/ 2

0

1/ 2 2 / 3

⎥

⎦

⎤ ⎢

⎣

⎡ = −

M

M Fη f h , (34) 

where M is the molar mass of the fluid and M0 is the molar mass of the reference fluid. In order 

to improve the model, experimental viscosity data are used to determine an empirical correction 

factor, where one evaluates eq. (27) at ρ0,v instead of ρ0, with 

 ( , ) ( , ) ( ) ρ0,v T ρ = ρ0 T ρ ψ ρr , (35) 

and ψ is a polynomial in reduced density ρr = ρ/ρc of the form 

 2

0 1 2 ( )r r r ψ ρ = c + c ρ + c ρ , (36) 

where the coefficients c0, c1 and c2 are constants found from fitting the experimental viscosity 

data. We fit the experimental viscosity data from NIST determined in this work and obtained c0 = 

1.38384, c1 = −0.216585 and c2 = 0.037507. In addition, we used Lennard-Jones potential 

parameters kbT/ε = 554.3 and σ = 0.6325 nm, estimated using the method of Chung [38]. Figure 

25 gives comparisons with the experimental viscosity data. At present, all of the data are at 

atmospheric pressure. In the liquid phase, we estimate the uncertainty of the correlation to be 

approximately 2 %. The model is capable of predicting values at pressures above the saturation 

boundary, but data are not available for comparison. However, based on the behavior of this 

model with similar fluids, we estimate the uncertainty in the liquid phase at pressures to 10 MPa 

to be less than 5 %. 
47

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

200 250 300 350 400 450 500

T, K

100*(1-ηcorr/ηexp)

this work

Moynihan 1982

Handbook of Aviation Fuel Properties

Figure 25. Deviations of viscosity of JP-10 

Thermal Conductivity Model 

We start with the procedure of Ely and Hanley [39] and represent the thermal conductivity of a 

fluid as the sum of translational (from collisions between molecules) and internal (due to internal 

motions of the molecule) modes of energy transfer, 

 ) ( , ) ( ) ( , int λ T ρ = λ T + λ T ρ trans . (37) 

We use an Eucken correlation for the internal contribution 

 ⎥

⎦

⎤ ⎢

⎣

⎡ − η λ = c R

M

f T p 2

5 ( ) *

*

int int , (38) 

where cp

*

 is the ideal gas heat capacity in J/(mol·K), R is the molar gas constant [40], 8.314 472 

J/(mol·K), η*

 is the dilute-gas viscosity in μPa·s as given in eq. (32), fint is set to 1.32·10-3, and λ

is in W/(m·K). If sufficient dilute-gas thermal conductivity data are available, fint may be fit to a 

polynomial in temperature; however no data were available to do this so we have retained fint as a 

constant. 
48

The translational contribution may be further divided into a dilute-gas contribution (denoted here 

by a superscript *

) that is a function only of temperature, a residual contribution, and a critical 

enhancement, 

 ) ( , ) ( ) ( , ) ( , * λ T ρ = λ T + λ T ρ + λ T ρ trans r crit . (39) 

For the dilute-gas translational contribution (in W/(m·K)) we use 

 M

R T

4

15 10 ( )

3 *

* η λ

− ⋅ = . (40) 

The residual contribution is found using extended corresponding states: 

 λ T ρ = λ T ρ Fλ

r r ( , ) ( , ) 0 0 0 , with (41) 

 

1/ 2

1/ 2 2 / 3 0

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡ = −

M

M

Fλ f h . (42) 

In order to improve the representation of the thermal conductivity, an empirical correction factor 

may be used if there are experimental thermal conductivity data available. We then evaluate eq. 

(41) at ρ0,k instead of ρ0 , where 

 ) ( , ) ( , ) ( ρ0,k T ρ = ρ0 T ρ χ ρr , (43) 

and χ is a polynomial in reduced density ρr = ρ/ρc of the form 

 k

r

n

k

χ ρr = ∑bkρ =0( , (44) )

where the coefficients bk are found from fitting the experimental thermal conductivity data. We 

fit the experimental thermal conductivity data obtained as part of this work and obtained b0 = 

1.11831 and b1 = –0.0157596. 

We treat the final contribution, the critical enhancement, with a simplified crossover model 

developed by Olchowy and Sengers [41], 

 ( ) 0

0

6 ( , ) Ω − Ω

πηξ

ρ λ ρ = c R k T

T crit p B , (45) 

where the heat capacity at constant pressure, cp(T,ρ), is obtained from the equation of state, R0 = 

1.03 is a universal constant, and the viscosity, η(T,ρ), is from the method described earlier. The 

crossover functions Ω and Ω0 are determined by 
49

 

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

ξ + ξ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ −

π

Ω = arctan( ) ( ) 2

d

p

v

d

p

p v q

c

c

q

c

c c

, and (46) 

 

⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎣

⎡

⎟

⎟

⎟

⎟

⎟

⎠

⎞

⎜

⎜

⎜

⎜

⎜

⎝

⎛

⎟

⎟

⎠

⎞ ⎜

⎜

⎝

⎛

ρ

ξ ρ ξ +

− − π

Ω =

−

2

1

0

( )

3

1 ( )

1 1 exp2

d c

d

q q

. (47) 

The heat capacity at constant volume, cv(T,ρ), is obtained from the equation of state, and the 

correlation length ξ is given by 

 

γ γ

⎥

⎦

⎤ ⎢

⎣

⎡

∂

∂ρ ρ − ∂

∂ρ ρ ⎥

⎦

⎤ ⎢

⎣

⎡

Γρ

ρ ξ = ξ

/ /

0 2

( , ) ( , ) v

T

R R

T

v

c

c

p

T

T

T

p

p T . (48) 

The partial derivative ∂ρ/∂p|T, is evaluated with the equation of state at the system temperature T

and a reference temperature, TR. For the reference temperature, we select a value where the 

critical enhancement is assumed to be negligible: TR = 1.5Tc. The exponents γ = 1.239 and ν = 

0.63 are universal constants. The critical amplitudes Γ and ξ0 are system-dependent and are 

determined by the asymptotic behavior of the equation of state in the critical region. The thermal 

conductivity at the critical point itself is infinite. We have chosen to use fixed values that we 

consider reasonable, Γ = 0.0496 and ξ0 = 1.94·10-10 m. The only parameter left to be determined 

is the cutoff wavenumber qd (or alternatively, its inverse qd

-1). If there are sufficient data 

available in the critical region, we fit thermal conductivity data to determine the systemdependent cutoff parameter qd

-1

. Data were unavailable in the critical region so we have 

estimated the value of qd

-1 to be approximately 1.52·10-9 m; this is the same value we used for 

dodecane[42]. 

 

Figure 26 shows comparisons of the model with experimental thermal conductivity data obtained 

at NIST, and with values obtained from the graph presented in the Handbook of Aviation Fuel 

Properties [29] as a function of temperature. The values from the Handbook of Aviation Fuel 

Properties are approximately 5 to 7 % higher than the model predictions. The deviations with the 

NIST data are less than 2 %. The NIST data cover pressures up to 30 MPa, while the handbook 

data are for atmospheric pressure only. Figure 27 shows the deviations in thermal conductivity as 

a function of pressure. The deviations remain less than 2 % even at 30 MPa. We note however 

that density data at pressures above atmospheric were unavailable for the development of the 

equation of state and this could lead to uncertainties in the density at higher pressures; which in 

turn can lead to larger uncertainties in the transport properties at higher pressures. It is therefore 

important to obtain reliable measurements of the density at higher pressures to validate the 

behavior of both the equation of state and the transport properties at pressures above 

atmospheric. 
50

-2

-1

0

1

2

3

4

5

6

7

8

250 300 350 400 450 500 550

Temperature, K

100*(1-λcorr/λexp)

this work

Handbook of Aviation Fuel Properties

Figure 26. Thermal conductivity deviations as a function of temperature. 

-2

-1

0

1

2

3

4

5

6

7

8

0 5 10 15 20 25 30 35

Pressure, MPa

100*(1-λcorr/λexp)

this work

Handbook of Aviation Fuel Properties

Figure 27. Thermal conductivity deviations as a function of pressure.
51

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54

Appendix 1. Thermal conductivity measurements of liquid JP-10 

Point ID T0 Te Pe ρe λe 

 (K) (K) (MPa) (mol·L-1) (W·m-1K-1) 

1011 300.209 301.677 0.067 6.8157 0.11105 

1012 300.205 301.706 0.067 6.8156 0.11166 

1013 300.209 301.960 0.067 6.8141 0.11096 

1014 300.207 301.995 0.067 6.8139 0.11177 

1015 300.209 302.245 0.067 6.8125 0.11180 

1016 300.211 302.373 0.066 6.8117 0.11141 

1017 300.209 302.912 0.066 6.8086 0.11140 

1018 300.209 303.057 0.066 6.8078 0.11167 

1019 300.210 303.441 0.066 6.8056 0.11158 

1020 300.213 303.574 0.066 6.8048 0.11191 

1021 300.198 301.731 5.669 6.8419 0.11321 

1022 300.201 301.816 5.694 6.8415 0.11407 

1023 300.196 302.115 5.713 6.8399 0.11289 

1024 300.197 302.156 5.732 6.8398 0.11370 

1025 300.194 302.451 5.728 6.8381 0.11347 

1026 300.194 302.556 5.747 6.8376 0.11324 

1027 300.191 302.794 5.759 6.8363 0.11343 

1028 300.191 302.725 5.741 6.8366 0.11423 

1029 300.187 302.885 5.606 6.8351 0.11311 

1030 300.185 302.956 5.506 6.8342 0.11318 

1031 300.171 301.796 10.941 6.8656 0.11448 

1032 300.166 301.869 10.941 6.8652 0.11446 

1033 300.165 302.191 10.966 6.8635 0.11458 

1034 300.162 302.190 10.978 6.8636 0.11451 

1035 300.162 302.470 10.997 6.8622 0.11487 

1036 300.156 302.407 10.983 6.8624 0.11562 

1037 300.156 302.529 10.860 6.8612 0.11487 

1038 300.156 302.583 10.761 6.8605 0.11478 

1039 300.151 302.834 10.690 6.8588 0.11486 

1040 300.153 302.949 10.631 6.8579 0.11482 

1041 300.123 301.660 20.565 6.9085 0.11701 

1042 300.118 301.731 20.586 6.9083 0.11664 

1043 300.119 301.981 20.601 6.9070 0.11647 

1044 300.113 302.057 20.617 6.9067 0.11662 

1045 300.115 302.342 20.637 6.9053 0.11668 

1046 300.113 302.400 20.644 6.9050 0.11676 

1047 300.109 302.615 20.652 6.9039 0.11672 

1048 300.106 302.523 20.594 6.9041 0.11733 

1049 300.107 302.745 20.472 6.9024 0.11667 

1050 300.105 302.836 20.388 6.9016 0.11657 

1051 300.095 301.546 29.851 6.9479 0.11854 

1052 300.097 301.649 29.777 6.9471 0.11867 

1053 300.092 301.875 29.699 6.9456 0.11813 

1054 300.091 301.930 29.627 6.9450 0.11848 

1055 300.091 302.214 29.557 6.9433 0.11837 

1056 300.086 302.277 29.485 6.9427 0.11829 

1057 300.090 302.386 29.383 6.9417 0.11907 
55

Point ID T0 Te Pe ρe λe 

 (K) (K) (MPa) (mol·L-1) (W·m-1K-1) 

1058 300.085 302.376 29.172 6.9409 0.11961 

1059 300.087 302.619 28.981 6.9389 0.11826 

1060 300.085 302.680 28.824 6.9379 0.11830 

1061 300.029 301.290 0.299 6.8191 0.11174 

1062 300.031 301.458 0.316 6.8182 0.11157 

1063 300.024 301.764 0.335 6.8165 0.11232 

1064 300.029 301.920 0.349 6.8157 0.11191 

1065 300.023 302.139 0.359 6.8145 0.11226 

1066 300.027 302.273 0.369 6.8138 0.11225 

1067 300.017 302.590 0.378 6.8120 0.11207 

1068 300.022 302.662 0.386 6.8116 0.11233 

1069 300.024 303.033 0.393 6.8095 0.11211 

1070 300.024 303.112 0.399 6.8091 0.11206 

1071 320.274 321.984 0.174 6.6994 0.10937 

1072 320.269 322.013 0.182 6.6993 0.11017 

1073 320.268 322.346 0.188 6.6974 0.10956 

1074 320.266 322.379 0.194 6.6972 0.10991 

1075 320.259 322.702 0.199 6.6954 0.10986 

1076 320.258 322.773 0.203 6.6950 0.10959 

1077 320.255 323.057 0.207 6.6934 0.10985 

1078 320.252 322.920 0.207 6.6942 0.11008 

1079 320.245 323.141 0.205 6.6929 0.10996 

1080 320.242 323.214 0.203 6.6924 0.10948 

1081 320.240 322.193 1.549 6.7055 0.11000 

1082 320.243 322.212 1.545 6.7054 0.10978 

1083 320.247 322.497 1.543 6.7037 0.10965 

1084 320.247 322.247 1.555 6.7052 0.11016 

1085 320.251 322.454 1.525 6.7039 0.11097 

1086 320.249 322.410 1.393 6.7034 0.11056 

1087 320.247 322.664 1.291 6.7014 0.11036 

1088 320.253 322.778 1.231 6.7004 0.11088 

1089 320.254 323.077 1.194 6.6985 0.10987 

1090 320.260 323.191 1.163 6.6977 0.11005 

1091 320.253 322.018 1.445 6.7059 0.11065 

1092 320.251 321.881 1.355 6.7063 0.11085 

1093 320.250 322.079 1.254 6.7046 0.11047 

1094 320.248 322.122 1.190 6.7040 0.10994 

1095 320.248 322.404 1.139 6.7021 0.10999 

1096 320.253 322.440 1.092 6.7017 0.11099 

1097 320.242 322.746 1.053 6.6997 0.10960 

1098 320.245 322.995 1.091 6.6985 0.10928 

1099 320.247 323.386 1.183 6.6967 0.10962 

1100 320.246 323.620 1.241 6.6957 0.10971 

1101 320.257 321.740 5.037 6.7263 0.11052 

1102 320.259 321.908 5.115 6.7258 0.11053 

1103 320.257 322.266 5.177 6.7241 0.11078 

1104 320.253 322.312 5.209 6.7240 0.11099 

1105 320.254 322.641 5.232 6.7222 0.11102 

1106 320.253 322.735 5.242 6.7218 0.11090 

1107 320.255 322.990 5.250 6.7204 0.11098 
56

Point ID T0 Te Pe ρe λe 

 (K) (K) (MPa) (mol·L-1) (W·m-1K-1) 

1108 320.253 323.169 5.259 6.7194 0.11086 

1109 320.255 323.454 5.266 6.7178 0.11071 

1110 320.258 323.613 5.279 6.7170 0.11098 

1111 320.248 321.707 10.112 6.7523 0.11254 

1112 320.240 321.695 10.019 6.7519 0.11182 

1113 320.243 321.992 9.945 6.7499 0.11271 

1114 320.242 322.006 9.876 6.7494 0.11245 

1115 320.239 322.289 9.822 6.7476 0.11200 

1116 320.236 322.473 9.812 6.7465 0.11189 

1117 320.232 322.805 9.855 6.7449 0.11183 

1118 320.228 322.982 9.904 6.7442 0.11224 

1119 320.227 323.316 9.914 6.7424 0.11187 

1120 320.223 323.399 9.920 6.7420 0.11213 

1121 320.246 321.813 19.957 6.7994 0.11453 

1122 320.250 321.922 19.910 6.7986 0.11472 

1123 320.246 322.093 19.848 6.7974 0.11434 

1124 320.248 322.213 19.808 6.7966 0.11442 

1125 320.254 322.483 19.747 6.7949 0.11442 

1126 320.253 322.520 19.701 6.7945 0.11491 

1127 320.253 322.859 19.652 6.7924 0.11465 

1128 320.256 322.908 19.590 6.7919 0.11441 

1129 320.260 323.240 19.548 6.7899 0.11436 

1130 320.255 323.337 19.484 6.7891 0.11435 

1131 320.260 321.773 20.167 6.8006 0.11462 

1132 320.261 321.885 20.134 6.7999 0.11507 

1133 320.260 322.106 20.077 6.7984 0.11453 

1134 320.263 322.192 20.042 6.7978 0.11447 

1135 320.265 322.489 19.991 6.7960 0.11440 

1136 320.263 322.513 19.951 6.7957 0.11463 

1137 320.268 322.883 19.909 6.7935 0.11449 

1138 320.264 322.915 19.859 6.7931 0.11496 

1139 320.267 323.262 19.822 6.7911 0.11455 

1140 320.267 323.358 19.769 6.7904 0.11427 

1141 320.282 321.775 29.985 6.8455 0.11693 

1142 320.281 321.899 29.883 6.8444 0.11708 

1143 320.284 322.099 29.769 6.8429 0.11663 

1144 320.286 322.200 29.681 6.8420 0.11696 

1145 320.282 322.455 29.578 6.8403 0.11667 

1146 320.281 322.512 29.494 6.8396 0.11699 

1147 320.283 322.846 29.401 6.8375 0.11653 

1148 320.286 322.882 29.311 6.8369 0.11689 

1149 320.284 323.239 29.228 6.8347 0.11672 

1150 320.284 323.304 29.132 6.8339 0.11663 

1151 320.275 321.891 0.165 6.6999 0.10956 

1152 320.276 321.950 0.168 6.6995 0.10977 

1153 320.274 322.235 0.170 6.6979 0.10939 

1154 320.278 322.296 0.172 6.6976 0.11007 

1155 320.279 322.630 0.174 6.6957 0.10967 

1156 320.277 322.651 0.175 6.6955 0.11007 

1157 320.282 323.054 0.177 6.6932 0.10967 
57

Point ID T0 Te Pe ρe λe 

 (K) (K) (MPa) (mol·L-1) (W·m-1K-1) 

1158 320.283 323.090 0.178 6.6930 0.10962 

1159 320.282 323.472 0.180 6.6908 0.10969 

1160 320.279 323.541 0.181 6.6904 0.10957 

1161 320.292 322.013 5.127 6.7252 0.11093 

1162 320.294 322.009 5.120 6.7252 0.11113 

1163 320.296 322.326 5.118 6.7234 0.11107 

1164 320.297 322.346 5.103 6.7232 0.11105 

1165 320.299 322.661 5.104 6.7215 0.11100 

1166 320.302 322.723 5.086 6.7210 0.11077 

1167 320.299 323.045 5.088 6.7192 0.11085 

1168 320.302 323.145 5.072 6.7186 0.11072 

1169 320.299 323.419 5.071 6.7170 0.11087 

1170 320.300 323.569 5.052 6.7161 0.11067 

1171 340.586 342.092 5.500 6.6137 0.10872 

1172 340.584 342.237 5.514 6.6130 0.10897 

1173 340.584 342.455 5.526 6.6118 0.10829 

1174 340.580 342.540 5.538 6.6114 0.10914 

1175 340.584 342.843 5.544 6.6097 0.10837 

1176 340.582 342.885 5.553 6.6095 0.10878 

1177 340.586 343.218 5.555 6.6076 0.10862 

1178 340.589 343.285 5.555 6.6073 0.10872 

1179 340.583 343.611 5.563 6.6054 0.10873 

1180 340.588 343.735 5.557 6.6047 0.10854 

1181 340.560 341.797 1.344 6.5913 0.10824 

1182 340.556 341.840 1.274 6.5906 0.10823 

1183 340.551 342.040 1.218 6.5891 0.10742 

1184 340.543 342.067 1.164 6.5887 0.10751 

1185 340.540 342.343 1.120 6.5868 0.10747 

1186 340.530 342.410 1.086 6.5862 0.10751 

1187 340.524 342.815 1.121 6.5841 0.10714 

1188 340.522 343.019 1.186 6.5833 0.10711 

1189 340.517 343.288 1.223 6.5819 0.10716 

1190 340.510 343.468 1.260 6.5811 0.10757 

1191 340.573 341.986 10.530 6.6425 0.11016 

1192 340.568 342.067 10.530 6.6421 0.11018 

1193 340.574 342.260 10.525 6.6410 0.11006 

1194 340.574 342.355 10.519 6.6404 0.11053 

1195 340.574 342.444 10.449 6.6395 0.10998 

1196 340.571 342.441 10.335 6.6389 0.10936 

1197 340.579 342.730 10.257 6.6369 0.11010 

1198 340.579 342.794 10.193 6.6362 0.11071 

1199 340.576 343.102 10.148 6.6342 0.10967 

1200 340.575 343.206 10.113 6.6335 0.11002 

1201 340.584 341.824 20.016 6.6940 0.11309 

1202 340.582 341.783 19.885 6.6935 0.11403 

1203 340.582 341.992 19.747 6.6917 0.11249 

1204 340.589 342.042 19.641 6.6909 0.11316 

1205 340.587 342.284 19.538 6.6891 0.11255 

1206 340.591 342.345 19.446 6.6883 0.11237 

1207 340.598 342.633 19.374 6.6864 0.11229 
58

Point ID T0 Te Pe ρe λe 

 (K) (K) (MPa) (mol·L-1) (W·m-1K-1) 

1208 340.594 342.838 19.347 6.6851 0.11183 

1209 340.596 343.189 19.376 6.6834 0.11231 

1210 340.596 343.362 19.366 6.6824 0.11223 

1211 340.604 341.833 29.990 6.7438 0.11526 

1212 340.599 341.928 29.916 6.7430 0.11502 

1213 340.597 342.110 29.846 6.7417 0.11507 

1214 340.595 342.242 29.775 6.7407 0.11544 

1215 340.595 342.435 29.694 6.7393 0.11494 

1216 340.596 342.556 29.632 6.7384 0.11518 

1217 340.594 342.771 29.541 6.7369 0.11516 

1218 340.595 342.939 29.482 6.7358 0.11509 

1219 340.596 343.190 29.400 6.7341 0.11499 

1220 340.595 343.332 29.339 6.7331 0.11498 

1221 340.613 341.737 30.277 6.7457 0.11488 

1222 340.609 341.841 30.176 6.7447 0.11523 

1223 340.616 342.060 30.086 6.7432 0.11529 

1224 340.611 342.184 30.009 6.7421 0.11566 

1225 340.606 342.393 29.922 6.7407 0.11533 

1226 340.609 342.509 29.851 6.7397 0.11529 

1227 340.611 342.766 29.748 6.7379 0.11477 

1228 340.614 342.876 29.671 6.7370 0.11488 

1229 340.616 343.203 29.581 6.7349 0.11491 

1230 340.608 343.262 29.502 6.7342 0.11524 

1231 340.595 341.936 0.498 6.5855 0.10753 

1232 340.595 342.092 0.511 6.5846 0.10703 

1233 340.595 342.274 0.503 6.5835 0.10705 

1234 340.597 342.398 0.517 6.5829 0.10737 

1235 340.600 342.673 0.512 6.5813 0.10715 

1236 340.598 342.776 0.523 6.5807 0.10730 

1237 340.604 343.095 0.523 6.5789 0.10708 

1238 340.602 343.118 0.527 6.5788 0.10748 

1239 340.602 343.505 0.530 6.5765 0.10703 

1240 340.604 343.558 0.525 6.5762 0.10716 

1241 340.615 341.991 0.046 6.5825 0.10694 

1242 340.618 342.057 0.047 6.5821 0.10737 

1243 340.616 342.338 0.047 6.5804 0.10712 

1244 340.621 342.381 0.047 6.5802 0.10757 

1245 340.615 342.700 0.048 6.5783 0.10717 

1246 340.616 342.760 0.048 6.5780 0.10694 

1247 340.616 343.057 0.048 6.5762 0.10732 

1248 340.616 343.154 0.048 6.5757 0.10729 

1249 340.620 343.458 0.048 6.5739 0.10716 

1250 340.622 343.623 0.048 6.5729 0.10718 

1251 361.305 362.909 0.820 6.4646 0.10439 

1252 361.298 363.027 0.877 6.4643 0.10466 

1253 361.293 363.299 0.908 6.4629 0.10490 

1254 361.284 363.383 0.929 6.4626 0.10442 

1255 361.278 363.640 0.942 6.4611 0.10462 

1256 361.265 363.736 0.954 6.4606 0.10476 

1257 361.250 364.006 0.963 6.4591 0.10464 
59

Point ID T0 Te Pe ρe λe 

 (K) (K) (MPa) (mol·L-1) (W·m-1K-1) 

1258 361.244 364.111 0.972 6.4586 0.10474 

1259 361.229 364.413 0.980 6.4568 0.10459 

1260 361.214 364.508 0.985 6.4563 0.10474 

1261 361.152 362.500 5.605 6.4981 0.10639 

1262 361.168 362.579 5.557 6.4973 0.10711 

1263 361.183 362.882 5.522 6.4954 0.10574 

1264 361.207 362.986 5.518 6.4948 0.10599 

1265 361.226 363.412 5.583 6.4927 0.10578 

1266 361.240 363.624 5.655 6.4920 0.10621 

1267 361.260 363.960 5.705 6.4904 0.10588 

1268 361.277 364.106 5.740 6.4898 0.10613 

1269 361.291 364.429 5.768 6.4881 0.10599 

1270 361.307 364.571 5.792 6.4874 0.10629 

1271 361.293 363.324 10.944 6.5267 0.10713 

1272 361.288 363.367 10.959 6.5265 0.10803 

1273 361.288 363.645 10.973 6.5251 0.10792 

1274 361.279 363.663 10.981 6.5250 0.10813 

1275 361.280 363.763 10.912 6.5241 0.10754 

1276 361.276 363.796 10.820 6.5233 0.10819 

1277 361.281 364.057 10.755 6.5215 0.10755 

1278 361.281 364.146 10.703 6.5207 0.10774 

1279 361.283 364.473 10.661 6.5186 0.10772 

1280 361.284 364.677 10.658 6.5174 0.10735 

1281 361.348 362.951 20.129 6.5828 0.11019 

1282 361.351 363.015 20.049 6.5820 0.11125 

1283 361.355 363.330 20.011 6.5801 0.11026 

1284 361.348 363.499 20.042 6.5794 0.11002 

1285 361.353 363.908 20.091 6.5775 0.11017 

1286 361.352 364.024 20.106 6.5770 0.11053 

1287 361.354 364.354 20.102 6.5752 0.11038 

1288 361.354 364.466 20.097 6.5746 0.11034 

1289 361.346 364.779 20.090 6.5729 0.11019 

1290 361.350 364.937 20.084 6.5721 0.11032 

1291 361.450 363.390 30.070 6.6352 0.11302 

1292 361.452 363.452 29.987 6.6345 0.11354 

1293 361.449 363.700 29.917 6.6328 0.11306 

1294 361.454 363.548 29.768 6.6328 0.11356 

1295 361.456 363.777 29.582 6.6307 0.11304 

1296 361.460 363.817 29.442 6.6297 0.11346 

1297 361.459 364.088 29.346 6.6278 0.11291 

1298 361.458 364.196 29.267 6.6268 0.11274 

1299 361.458 364.587 29.247 6.6248 0.11276 

1300 361.459 364.818 29.274 6.6237 0.11288 

1301 361.436 363.380 0.157 6.4574 0.10501 

1302 361.439 363.387 0.157 6.4574 0.10476 

1303 361.438 363.583 0.158 6.4562 0.10428 

1304 361.441 363.678 0.159 6.4557 0.10462 

1305 361.441 363.915 0.160 6.4543 0.10435 

1306 361.440 364.090 0.163 6.4533 0.10438 

1307 361.443 364.543 0.170 6.4506 0.10425 
60

Point ID T0 Te Pe ρe λe 

 (K) (K) (MPa) (mol·L-1) (W·m-1K-1) 

1308 361.447 364.752 0.176 6.4494 0.10424 

1309 361.446 365.092 0.181 6.4474 0.10425 

1310 361.447 365.256 0.184 6.4465 0.10443 

1311 380.665 382.692 9.643 6.4099 0.10472 

1312 380.657 382.696 9.650 6.4099 0.10582 

1313 380.639 382.697 9.610 6.4096 0.10497 

1314 380.622 382.743 9.529 6.4088 0.10583 

1315 380.615 382.932 9.460 6.4073 0.10529 

1316 380.599 383.028 9.408 6.4064 0.10488 

1317 380.590 383.298 9.365 6.4046 0.10530 

1318 380.588 383.399 9.328 6.4037 0.10490 

1319 380.573 383.821 9.349 6.4015 0.10469 

1320 380.572 384.046 9.411 6.4007 0.10489 

1321 380.522 382.414 0.196 6.3442 0.10185 

1322 380.513 382.526 0.199 6.3436 0.10202 

1323 380.501 382.805 0.201 6.3419 0.10226 

1324 380.490 382.894 0.203 6.3414 0.10240 

1325 380.480 383.183 0.205 6.3396 0.10163 

1326 380.473 383.293 0.206 6.3390 0.10204 

1327 380.468 383.421 0.206 6.3382 0.10217 

1328 380.462 383.393 0.201 6.3384 0.10254 

1329 380.465 383.715 0.196 6.3364 0.10173 

1330 380.459 383.810 0.194 6.3358 0.10210 

1331 380.508 382.124 5.413 6.3838 0.10396 

1332 380.503 382.261 5.436 6.3832 0.10353 

1333 380.487 382.624 5.491 6.3814 0.10334 

1334 380.482 382.733 5.528 6.3811 0.10400 

1335 380.464 383.014 5.560 6.3797 0.10361 

1336 380.457 383.159 5.585 6.3790 0.10413 

1337 380.455 383.452 5.604 6.3774 0.10369 

1338 380.449 383.582 5.623 6.3768 0.10403 

1339 380.448 383.924 5.642 6.3750 0.10351 

1340 380.444 383.932 5.653 6.3750 0.10455 

1341 380.602 382.512 10.907 6.4195 0.10513 

1342 380.613 382.583 10.922 6.4192 0.10562 

1343 380.623 382.875 10.936 6.4176 0.10558 

1344 380.632 382.912 10.939 6.4174 0.10575 

1345 380.640 383.045 10.898 6.4164 0.10565 

1346 380.644 383.083 10.813 6.4156 0.10592 

1347 380.647 383.324 10.746 6.4138 0.10513 

1348 380.652 383.412 10.697 6.4130 0.10593 

1349 380.651 383.760 10.673 6.4109 0.10511 

1350 380.659 384.014 10.705 6.4097 0.10535 

1351 380.709 382.381 20.288 6.4808 0.10893 

1352 380.709 382.425 20.250 6.4803 0.10829 

1353 380.711 382.806 20.267 6.4784 0.10805 

1354 380.722 383.014 20.334 6.4777 0.10848 

1355 380.726 383.338 20.390 6.4764 0.10838 

1356 380.734 383.491 20.432 6.4758 0.10827 

1357 380.736 383.791 20.464 6.4744 0.10822 
61

Point ID T0 Te Pe ρe λe 

 (K) (K) (MPa) (mol·L-1) (W·m-1K-1) 

1358 380.743 383.935 20.489 6.4738 0.10854 

1359 380.747 384.280 20.512 6.4721 0.10813 

1360 380.746 384.409 20.529 6.4715 0.10832 

1361 380.848 382.552 30.559 6.5413 0.11151 

1362 380.855 382.660 30.593 6.5409 0.11162 

1363 380.858 382.923 30.617 6.5397 0.11148 

1364 380.860 383.031 30.636 6.5393 0.11180 

1365 380.865 383.323 30.652 6.5379 0.11130 

1366 380.862 383.401 30.666 6.5376 0.11160 

1367 380.864 383.710 30.679 6.5361 0.11138 

1368 380.867 383.788 30.687 6.5358 0.11167 

1369 380.873 383.889 30.650 6.5351 0.11143 

1370 380.873 383.929 30.561 6.5343 0.11143 

1371 401.017 402.715 3.090 6.2449 0.10029 

1372 401.014 402.816 3.090 6.2443 0.10045 

1373 401.000 402.833 3.041 6.2438 0.10058 

1374 400.991 402.821 2.970 6.2433 0.10100 

1375 400.976 403.020 2.916 6.2417 0.10051 

1376 400.960 403.102 2.863 6.2408 0.10072 

1377 400.948 403.362 2.832 6.2389 0.10039 

1378 400.928 403.670 2.794 6.2368 0.10066 

1379 400.908 404.297 2.797 6.2330 0.09997 

1380 400.888 404.504 2.844 6.2322 0.10039 

1381 400.820 402.798 0.179 6.2204 0.09941 

1382 400.836 402.846 0.177 6.2201 0.09950 

1383 400.848 402.951 0.169 6.2194 0.09950 

1384 400.860 402.957 0.158 6.2192 0.09995 

1385 400.873 403.261 0.154 6.2173 0.09895 

1386 400.889 403.341 0.151 6.2168 0.09976 

1387 400.900 403.638 0.151 6.2150 0.09929 

1388 400.916 403.776 0.150 6.2141 0.09975 

1389 400.929 404.087 0.150 6.2122 0.09909 

1390 400.938 404.367 0.156 6.2105 0.09943 

1391 401.352 403.247 10.524 6.2998 0.10286 

1392 401.356 403.120 10.470 6.3002 0.10369 

1393 401.353 403.390 10.422 6.2983 0.10296 

1394 401.357 403.440 10.382 6.2977 0.10306 

1395 401.360 403.688 10.345 6.2960 0.10275 

1396 401.363 403.773 10.312 6.2953 0.10283 

1397 401.363 404.046 10.292 6.2936 0.10293 

1398 401.370 404.197 10.287 6.2927 0.10271 

1399 401.370 404.581 10.308 6.2906 0.10268 

1400 401.370 404.828 10.351 6.2896 0.10274 

1401 401.377 403.240 20.307 6.3700 0.10625 

1402 401.378 403.329 20.314 6.3695 0.10682 

1403 401.372 403.399 20.285 6.3690 0.10694 

1404 401.376 403.430 20.230 6.3684 0.10702 

1405 401.376 403.643 20.177 6.3669 0.10611 

1406 401.380 403.704 20.139 6.3663 0.10703 

1407 401.378 403.991 20.101 6.3645 0.10600 
62

Point ID T0 Te Pe ρe λe 

 (K) (K) (MPa) (mol·L-1) (W·m-1K-1) 

1408 401.381 404.062 20.072 6.3640 0.10633 

1409 401.380 404.347 20.052 6.3623 0.10598 

1410 401.380 404.543 20.055 6.3613 0.10615 

1411 401.379 403.213 30.722 6.4383 0.10983 

1412 401.378 403.232 30.726 6.4382 0.10978 

1413 401.374 403.266 30.677 6.4377 0.10979 

1414 401.377 403.314 30.615 6.4371 0.11014 

1415 401.382 403.525 30.561 6.4357 0.10964 

1416 401.383 403.630 30.528 6.4349 0.11049 

1417 401.386 403.863 30.483 6.4335 0.10973 

1418 401.387 403.994 30.450 6.4326 0.10996 

1419 401.385 404.272 30.433 6.4311 0.10928 

1420 401.387 404.428 30.431 6.4303 0.10958 

1421 420.018 421.347 6.327 6.1610 0.10022 

1422 420.016 421.349 6.284 6.1606 0.10071 

1423 420.011 421.585 6.248 6.1589 0.09945 

1424 419.988 421.626 6.216 6.1583 0.10004 

1425 419.970 421.878 6.194 6.1566 0.09891 

1426 419.949 422.054 6.213 6.1558 0.09962 

1427 419.931 422.387 6.251 6.1541 0.09920 

1428 419.902 422.523 6.280 6.1536 0.09973 

1429 419.880 422.833 6.300 6.1519 0.09941 

1430 419.852 422.987 6.314 6.1511 0.09950 

1431 419.799 421.886 0.106 6.1013 0.09656 

1432 419.803 422.032 0.109 6.1005 0.09754 

1433 419.821 422.336 0.112 6.0986 0.09676 

1434 419.834 422.443 0.114 6.0979 0.09721 

1435 419.841 422.799 0.116 6.0957 0.09679 

1436 419.864 422.807 0.117 6.0957 0.09755 

1437 419.877 422.950 0.116 6.0948 0.09660 

1438 419.888 423.047 0.115 6.0941 0.09730 

1439 419.900 423.317 0.114 6.0924 0.09663 

1440 419.910 423.464 0.114 6.0915 0.09749 

1441 419.966 421.912 5.235 6.1480 0.09875 

1442 419.975 422.005 5.196 6.1471 0.10009 

1443 419.969 422.267 5.159 6.1452 0.09864 

1444 419.972 422.389 5.142 6.1443 0.09911 

1445 419.979 422.786 5.171 6.1422 0.09841 

1446 419.977 423.033 5.230 6.1413 0.09893 

1447 419.983 423.404 5.276 6.1394 0.09863 

1448 419.986 423.537 5.308 6.1389 0.09903 

1449 419.983 423.885 5.336 6.1371 0.09859 

1450 419.988 424.051 5.355 6.1363 0.09929 

1451 420.057 422.071 10.316 6.1906 0.10064 

1452 420.054 422.185 10.351 6.1902 0.10074 

1453 420.055 422.463 10.374 6.1888 0.10062 

1454 420.057 422.598 10.391 6.1882 0.10112 

1455 420.057 422.881 10.406 6.1867 0.10074 

1456 420.060 423.035 10.422 6.1859 0.10098 

1457 420.059 423.336 10.435 6.1843 0.10054 
63

Point ID T0 Te Pe ρe λe 

 (K) (K) (MPa) (mol·L-1) (W·m-1K-1) 

1458 420.061 423.455 10.450 6.1838 0.10072 

1459 420.065 423.586 10.436 6.1829 0.10105 

1460 420.070 423.644 10.362 6.1819 0.10123 

1461 420.140 421.820 20.331 6.2708 0.10456 

1462 420.138 421.932 20.310 6.2700 0.10398 

1463 420.143 422.290 20.334 6.2683 0.10410 

1464 420.144 422.450 20.379 6.2678 0.10452 

1465 420.144 422.834 20.418 6.2660 0.10407 

1466 420.144 422.940 20.448 6.2656 0.10491 

1467 420.147 423.262 20.465 6.2640 0.10442 

1468 420.150 423.429 20.482 6.2633 0.10494 

1469 420.143 423.736 20.492 6.2617 0.10428 

1470 420.145 423.851 20.503 6.2612 0.10464 

1471 420.190 422.138 28.922 6.3307 0.10685 

1472 420.190 422.235 28.792 6.3293 0.10740 

1473 420.194 422.521 28.662 6.3269 0.10688 

1474 420.194 422.640 28.533 6.3254 0.10747 

1475 420.193 422.885 28.401 6.3233 0.10676 

1476 420.189 422.949 28.268 6.3220 0.10756 

1477 420.192 423.042 28.073 6.3202 0.10734 

1478 420.196 423.156 27.867 6.3182 0.10713 

1479 420.199 423.379 27.680 6.3157 0.10697 

1480 420.203 423.503 27.502 6.3138 0.10721 

2001 441.923 443.655 0.151 5.9631 0.09391 

2002 441.896 443.686 0.151 5.9629 0.09434 

2003 441.867 443.911 0.151 5.9615 0.09375 

2004 441.838 443.792 0.150 5.9622 0.09504 

2005 441.806 443.930 0.148 5.9613 0.09457 

2006 441.778 443.964 0.147 5.9611 0.09526 

2007 441.748 444.214 0.146 5.9594 0.09436 

2008 441.716 444.245 0.145 5.9592 0.09401 

2009 441.691 444.507 0.144 5.9575 0.09407 

2010 441.665 444.637 0.144 5.9567 0.09482 

2011 441.702 443.014 4.889 6.0166 0.09610 

2012 441.722 443.087 4.858 6.0158 0.09630 

2013 441.749 443.355 4.822 6.0138 0.09641 

2014 441.768 443.861 4.797 6.0105 0.09724 

2015 441.779 444.192 4.788 6.0083 0.09620 

2016 441.802 444.409 4.805 6.0072 0.09613 

2017 441.807 444.737 4.820 6.0053 0.09597 

2018 441.816 444.915 4.831 6.0043 0.09633 

2019 441.822 445.259 4.837 6.0022 0.09602 

2020 441.828 445.373 4.837 6.0015 0.09616 

2021 441.877 443.827 9.742 6.0589 0.09814 

2022 441.877 443.955 9.732 6.0580 0.09816 

2023 441.883 444.222 9.713 6.0563 0.09787 

2024 441.889 444.345 9.688 6.0553 0.09888 

2025 441.889 444.635 9.661 6.0534 0.09791 

2026 441.895 444.772 9.632 6.0523 0.09855 

2027 441.895 445.065 9.603 6.0503 0.09803 
64

Point ID T0 Te Pe ρe λe 

 (K) (K) (MPa) (mol·L-1) (W·m-1K-1) 

2028 441.898 445.231 9.572 6.0490 0.09835 

2029 441.897 445.547 9.543 6.0469 0.09791 

2030 441.901 445.700 9.510 6.0456 0.09808 

2031 441.969 443.852 20.822 6.1562 0.10243 

2032 441.969 443.965 20.742 6.1549 0.10264 

2033 441.975 444.232 20.654 6.1527 0.10212 

2034 441.974 444.341 20.565 6.1514 0.10301 

2035 441.967 444.617 20.472 6.1491 0.10224 

2036 441.963 444.713 20.379 6.1479 0.10271 

2037 441.965 445.001 20.286 6.1455 0.10223 

2038 441.963 445.126 20.194 6.1441 0.10247 

2039 441.960 445.449 20.105 6.1416 0.10232 

2040 441.960 445.599 20.016 6.1400 0.10239 

2041 442.013 443.916 30.198 6.2293 0.10585 

2042 442.012 443.978 30.027 6.2277 0.10624 

2043 442.016 444.249 29.866 6.2251 0.10569 

2044 442.016 444.354 29.705 6.2234 0.10564 

2045 442.017 444.629 29.547 6.2208 0.10524 

2046 442.026 444.745 29.386 6.2190 0.10529 

2047 442.031 444.972 29.220 6.2166 0.10549 

2048 442.038 445.019 29.028 6.2149 0.10616 

2049 442.048 445.166 28.793 6.2123 0.10509 

2050 442.057 445.341 28.576 6.2098 0.10570 

2051 460.687 462.668 0.106 5.8375 0.09146 

2052 460.693 462.888 0.121 5.8363 0.09213 

2053 460.693 463.282 0.164 5.8342 0.09139 

2054 460.692 463.462 0.200 5.8334 0.09274 

2055 460.701 463.754 0.229 5.8318 0.09149 

2056 460.692 463.899 0.247 5.8311 0.09216 

2057 460.692 464.254 0.264 5.8289 0.09142 

2058 460.697 464.399 0.277 5.8281 0.09157 

2059 460.692 464.715 0.289 5.8261 0.09159 

2060 460.696 464.889 0.300 5.8251 0.09253 

2061 460.722 462.640 5.095 5.8966 0.09431 

2062 460.729 462.700 5.042 5.8956 0.09459 

2063 460.730 462.962 4.993 5.8934 0.09418 

2064 460.733 463.054 4.955 5.8924 0.09417 

2065 460.733 463.383 4.939 5.8902 0.09394 

2066 460.735 463.615 4.966 5.8890 0.09398 

2067 460.735 464.038 4.988 5.8866 0.09368 

2068 460.734 464.193 5.001 5.8857 0.09480 

2069 460.732 464.551 5.008 5.8836 0.09384 

2070 460.734 464.719 5.009 5.8825 0.09428 

2071 460.736 462.918 9.945 5.9476 0.09550 

2072 460.727 463.036 9.923 5.9466 0.09574 

2073 460.726 463.293 9.899 5.9448 0.09636 

2074 460.726 463.360 9.875 5.9442 0.09758 

2075 460.724 463.393 9.809 5.9433 0.09618 

2076 460.731 463.419 9.696 5.9419 0.09633 

2077 460.731 463.721 9.605 5.9392 0.09634 
65

Point ID T0 Te Pe ρe λe 

 (K) (K) (MPa) (mol·L-1) (W·m-1K-1) 

2078 460.736 463.783 9.529 5.9380 0.09719 

2079 460.737 464.065 9.461 5.9356 0.09607 

2080 460.744 464.236 9.407 5.9340 0.09669 

2081 460.740 462.703 19.945 6.0462 0.10010 

2082 460.739 462.827 19.884 6.0449 0.10001 

2083 460.738 463.069 19.814 6.0430 0.09998 

2084 460.737 463.141 19.741 6.0419 0.10106 

2085 460.737 463.416 19.663 6.0397 0.09979 

2086 460.735 463.545 19.584 6.0383 0.10010 

2087 460.732 463.803 19.499 6.0361 0.10054 

2088 460.724 463.928 19.418 6.0346 0.10030 

2089 460.721 464.224 19.333 6.0322 0.09982 

2090 460.714 464.297 19.250 6.0310 0.10077 

2091 460.671 462.559 30.896 6.1404 0.10436 

2092 460.671 462.625 30.769 6.1390 0.10580 

2093 460.662 462.897 30.639 6.1366 0.10430 

2094 460.659 462.958 30.509 6.1353 0.10480 

2095 460.658 463.211 30.379 6.1329 0.10417 

2096 460.655 463.317 30.244 6.1313 0.10447 

2097 460.652 463.556 30.102 6.1289 0.10399 

2098 460.655 463.595 29.939 6.1274 0.10456 

2099 460.652 463.782 29.751 6.1249 0.10421 

2100 460.652 463.920 29.580 6.1228 0.10431 

2161 479.267 481.560 0.246 5.7107 0.08982 

2162 479.266 481.665 0.251 5.7101 0.09046 

2163 479.264 481.934 0.253 5.7082 0.08984 

2164 479.262 482.045 0.256 5.7075 0.09020 

2165 479.259 482.327 0.257 5.7055 0.09016 

2166 479.261 482.293 0.256 5.7058 0.09041 

2167 479.261 482.518 0.247 5.7041 0.08965 

2168 479.260 482.657 0.243 5.7031 0.08990 

2169 479.260 482.924 0.247 5.7013 0.08947 

2170 479.266 483.041 0.248 5.7005 0.09057 

2171 479.280 481.568 5.531 5.7812 0.09164 

2172 479.289 481.657 5.527 5.7806 0.09330 

2173 479.287 481.936 5.522 5.7787 0.09203 

2175 479.298 482.214 5.498 5.7766 0.09240 

2176 479.305 482.249 5.446 5.7757 0.09304 

2177 479.308 482.505 5.403 5.7735 0.09209 

2178 479.315 482.665 5.373 5.7721 0.09283 

2179 479.317 482.928 5.344 5.7700 0.09234 

2180 479.328 483.147 5.318 5.7683 0.09238 

2181 479.339 481.593 10.427 5.8402 0.09411 

2182 479.334 481.676 10.402 5.8394 0.09478 

2183 479.336 481.964 10.376 5.8373 0.09386 

2184 479.336 482.035 10.350 5.8366 0.09481 

2185 479.340 482.211 10.319 5.8351 0.09492 

2186 479.334 482.261 10.255 5.8341 0.09476 

2187 479.339 482.520 10.183 5.8317 0.09454 

2188 479.351 482.625 10.124 5.8303 0.09477 
66

Point ID T0 Te Pe ρe λe 

 (K) (K) (MPa) (mol·L-1) (W·m-1K-1) 

2189 479.353 482.925 10.073 5.8279 0.09402 

2190 479.353 483.031 10.023 5.8267 0.09497 

2191 479.403 481.552 20.315 5.9461 0.09820 

2192 479.409 481.624 20.242 5.9450 0.10000 

2193 479.399 481.901 20.168 5.9427 0.09867 

2194 479.407 482.010 20.095 5.9414 0.09926 

2195 479.403 482.282 20.023 5.9391 0.09878 

2196 479.408 482.377 19.949 5.9379 0.09882 

2197 479.413 482.639 19.875 5.9357 0.09838 

2198 479.413 482.653 19.774 5.9346 0.09905 

2199 479.407 482.904 19.649 5.9319 0.09818 

2200 479.416 483.002 19.538 5.9303 0.09894 

2201 479.458 481.566 30.462 6.0404 0.10241 

2202 479.454 481.624 30.311 6.0388 0.10355 

2203 479.452 481.874 30.160 6.0362 0.10299 

2204 479.452 481.988 30.012 6.0343 0.10449 

2205 479.453 482.261 29.860 6.0316 0.10228 

2206 479.453 482.360 29.714 6.0298 0.10333 

2207 479.452 482.612 29.561 6.0271 0.10268 

2208 479.453 482.568 29.377 6.0257 0.10369 

2209 479.452 482.859 29.179 6.0224 0.10217 

2210 479.456 482.955 28.998 6.0203 0.10205 

2211 479.455 481.770 5.631 5.7812 0.09238 

2212 479.450 481.848 5.634 5.7807 0.09312 

2213 479.455 482.152 5.636 5.7788 0.09194 

2214 479.461 482.276 5.631 5.7779 0.09279 

2215 479.462 482.575 5.624 5.7759 0.09216 

2216 479.466 482.713 5.618 5.7749 0.09297 

2217 479.465 483.003 5.611 5.7729 0.09199 

2218 479.467 483.121 5.602 5.7721 0.09322 

2219 479.476 483.476 5.592 5.7697 0.09198 

2220 479.480 483.619 5.582 5.7686 0.09290 

2221 503.337 505.292 0.600 5.5473 0.08754 

2223 503.349 505.683 0.568 5.5439 0.08694 

2224 503.348 505.836 0.585 5.5430 0.08769 

2225 503.350 506.203 0.606 5.5407 0.08714 

2227 503.335 506.653 0.638 5.5380 0.08710 

2228 503.323 506.788 0.648 5.5371 0.08755 

2229 503.309 507.080 0.654 5.5351 0.08668 

2230 503.302 507.128 0.657 5.5348 0.08750 

2231 503.239 505.272 5.440 5.6239 0.08982 

2232 503.246 505.381 5.428 5.6230 0.09063 

2233 503.250 505.663 5.417 5.6209 0.08971 

2234 503.264 505.761 5.406 5.6201 0.09005 

2235 503.276 506.100 5.398 5.6177 0.08946 

2237 503.291 506.146 5.320 5.6162 0.08965 

2239 503.319 506.496 5.210 5.6122 0.08977 

2240 503.334 506.649 5.175 5.6106 0.09002 

2241 503.314 505.422 10.815 5.6982 0.09279 

2242 503.297 505.568 10.787 5.6969 0.09268 
67

Point ID T0 Te Pe ρe λe 

 (K) (K) (MPa) (mol·L-1) (W·m-1K-1) 

2243 503.285 505.786 10.757 5.6951 0.09161 

2244 503.274 505.895 10.725 5.6940 0.09251 

2245 503.266 506.034 10.695 5.6928 0.09206 

2246 503.258 506.099 10.663 5.6919 0.09264 

2247 503.252 506.415 10.633 5.6896 0.09207 

2248 503.251 506.548 10.604 5.6883 0.09300 

2249 503.248 506.843 10.575 5.6861 0.09234 

2250 503.255 506.991 10.546 5.6848 0.09264 

2251 503.305 505.055 15.249 5.7565 0.09408 

2252 503.311 505.242 15.219 5.7551 0.09493 

2253 503.312 505.544 15.191 5.7530 0.09416 

2254 503.306 505.689 15.159 5.7517 0.09472 

2255 503.295 505.950 15.122 5.7497 0.09423 

2256 503.284 506.061 15.083 5.7486 0.09488 

2257 503.276 506.342 15.040 5.7464 0.09428 

2258 503.266 506.470 14.994 5.7451 0.09466 

2259 503.250 506.688 14.948 5.7432 0.09415 

2260 503.244 506.881 14.899 5.7414 0.09487 

2261 503.030 504.977 21.321 5.8270 0.09670 

2262 503.021 505.041 21.330 5.8268 0.09749 

2263 503.023 505.315 21.338 5.8253 0.09693 

2264 503.023 505.334 21.345 5.8253 0.09878 

2265 503.029 505.429 21.321 5.8245 0.09730 

2266 503.026 505.510 21.262 5.8234 0.09744 

2267 503.029 505.765 21.220 5.8215 0.09681 

2269 503.036 506.071 21.159 5.8191 0.09678 

2270 503.036 506.201 21.135 5.8182 0.09722 

2272 502.988 504.718 30.822 5.9257 0.10159 

2273 502.993 504.954 30.785 5.9242 0.10101 

2274 502.993 505.058 30.756 5.9234 0.10089 

2275 503.000 505.329 30.746 5.9219 0.10062 

2276 502.997 505.568 30.787 5.9211 0.10073 

2277 502.990 505.947 30.827 5.9195 0.10076 

2278 502.985 506.088 30.852 5.9190 0.10129 

2279 502.978 506.368 30.865 5.9177 0.10062 

2280 502.975 506.483 30.873 5.9172 0.10087