NATL INST. OF STAND & TECH

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NBS TECHNICAL NOTE 1189

U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards

100

. U5753

No. 118

J

1984

A Thermodynamic

Surface for the Critical

Region of Ethylene
NATIONAL BUREAU OF STANDARDS

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OF SiailDAKDS

A Thermodynamic Surface for the l^

Critical Region of Ethylene ,-^

. 015162

J.M.H. Levelt Sengers\ G.A. Olchowy^, B. Kamgar-ParsP, and J.V. Sengers^'^ fx^^ )) 9.

1

.

Thermophysics Division ^ i ^

Center for Chemical Engineering

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

2. Institute for Physical Science and Technology

University of Maryland

College Park, MD 20742

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Veau 0*

c,^

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director

Issued May 1 984
National Bureau of Standards Technical Note 11 89

Natl. Bur. Stand. (U.S.), Tech. Note 1 189, 95 pages (May 1984)

CODEN: NBTNAE

U.S. Government Printing Office

Washington: 1984

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402
Table of Contents

ABSTRACT 1

1 . Introduction 2

2. Fundamental Equation 3

3. The Equation of State 5

4. Critical Parameters 6

5. Coexistence Properties 7

6. Speed of Sound 7

7. Enthalpy 7

8. Other Formulations 8

9. The Effect of Pressure and Temperature Errors on Density 9 10. The Effect of Impurity on Density 10

11. Tables of Thermodynamic Properties 11 12. References 11 APPENDIX A Revised and Extended Scaling Equations for the

Thermodynamic Properties of Fluids 14 APPENDIX B Comparison with Experiment 20

APPENDIX C Tables of Thermodynamic Properties 33

APPENDIX D Listing of Computer Program for Table Generation 58

APPENDIX E Units and Conversion Factors 72 FIGURES 73

111

A Thermodynamic Surface for the Critical Region of Ethylene

by

J.M.H. Levelt Sengers^, G.A. Olchowy'^, B. Kamgar-Parsi^,

and J.V. Sengers^''^

a. Thermophysics Division

Center for Chemical Engineering

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

b. Institute for Physical Science and Technology

University of Maryland

College Park, MD 20742

Tables are presented of thermodynamic properties of ethylene in the range 279-300 K in

3 temperature, 5.75 - 10.5 mol/dm in density, which range includes the critical point. The

tables presented here are based on the critical -point scaling laws and incorporate the

critical anomalies as presently known from renormalization-group theory. The tables complement the formulation of the equation of state of fluid ethylene by McCarty and Jacobsen

(NBS Tech. Note 1045, 1981) which does not claim accuracy near the critical point. The

predictions of the present formulation are compared with four sets of recent PVT data, and

with speed-of-sound and enthalpy data. Tables are presented of pressure, energy, enthalpy,

entropy, specific heats and speed of sound as function of temperature along finely-spaced

isochores. The computer program required for table generation is included. Even if the

surface were perfect, the reliability of densities calculated at experimental pressures and

temperatures of limited accuracy declines rapidly as the critical point is approached.

Contour plots in P-T space are presented of regions to be avoided in custody transfer for

given uncertainties in pressure , temperature and sample composition.

Key words: critical region; custody transfer; density; enthalpy; ethylene;

equation of state; impurity; scaling laws, specific heat;

speed of sound; supercritical extraction; thermodynamic

properties.

This work was part of a Joint Industry - Government project under the sponsorship of

Celanese Chemical Company, Cities Service Company, Continental Oil Company, Gulf Research

and Development, Mobil Chemical Company, Monsanto Polymers and Petrochemicals Company,

Phillips Chemical Company, Union Carbide Corp. and the National Bureau of Standards.
1 . Introduction

A fonnulation is presented of the thermodynamic behavior of ethylene in a region

3 around the critical point extending from 5.75 to 10.5 mol/dm in density and from 279 to 300 K in temperature. A correct formulation of this near-critical region is more urgent

for ethylene than for most other fluids, because in the climatic conditions of the United

States the fluid transported in pipes can assume states located in this region. The present

formulation will also be useful as a characterization of ethylene as a supercritical solvent.

It is well recognized that most engineering equations of state are deficient in representing

near-critical states [1-4]. Our formulation of the thermodynamic behavior of ethylene

derives from a thermodynamic potential which obeys the critical -point scaling laws; it

contains a first correction to scaling and also a revision to scaling designed to accommodate the lack of symmetry of the gas-liquid phase transition. The adjustable parameters in

the potential were obtained by a fit to the PVT data of Hastings et al . [5] and to the

speed-of-sound data of Gammon [6]. The advantage of our formulation is that the critical

anomalies that are common to all fluids are properly incorporated. For instance, the

flatness of the critical isotherm, which is hard to describe by analytic equations of

state, is built into our potential. Its strength is particularly striking when it comes to presenting the specific heat at constant volume, Cw, and the speed of sound, C . The weak

divergence of C^ cannot be described by analytic free energy surfaces. This divergence,

however, causes the speed of sound to approach the value zero at the critical point, a feature properly incorporated in our potential. The excellent speed-of-sound data of

Gammon therefore form a crucial test for the adequacy of our thermodynamic surface. We

stress that, by the use of so-called parametric variables, we have closed-form expressions

for all thermodynamic properties.

We will describe how our potential is constructed, and proceed to compare it with

experimental PVT data from four sources; with vapor pressures and coexisting densities from

two sources and with recent enthalpy data. Comparisons are also made with the predictions

of the global equation of state of ethylene recently published by McCarty and Jacobsen [7].

From these comparisons it will be evident that our potential will serve as a useful and

necessary supplement in a region where the global equation is deficient. In appendices, we present the equations defining our potential and a comparison of all data points mentioned

above with the predictions of our surface. A table of the thermodynamic properties pressure,

energy, entropy, enthalpy, specific heats Cp and C^ and speed of sound C , is presented

along finely-spaced isochores with temperature as an entry. Tables of saturation properties

are also given. The computer programs for generation of these tables are included. They

contain an inversion routine which permits transformation from pressure to density as an independent variable.

For the convenience of the user concerned with custody transfer, we conclude the main

body of the paper with a discussion of the uncertainties introduced in the density calculated from our surface due to limited precision in the measurement of pressure and temperature, and due to the presence of impurity. Contour plots indicating regions in P-T space

to be avoided if a certain precision in density is desired, are included in this paper.

2
Our work has been part of a joint industry-U.S. Government project to determine the thermodynamic properties of ethylene.

2. Fundamental Equation

At a critical point, thermodynamic behavior is anomalous. The critical point is

characterized by the facts that the compressibility K^ = -(l/V){3V/9P)j and the specific

heat Cp diverge and the coexisting densities p„.Pw become equal. We write, asymptotically

near the critical point,

K| = r|AT*r^ ,

Ap* = B|aT*I^ . (1)

Here asterisks denote reduced properties, while AT* = (T-T )/T and Ap* e (Po-Py)/2p--

For classical equations of state of the type of van der Waal s' equation, the critical

exponent y equals 1, 6 equals 1/2. In real fluids, y equals about 1.24 and 6 is of the

order 1/3. The critical -point scaling laws are constructed so that they yield the correct

critical exponents; although one can define as many critical exponents as one sees fit,

only two of them are independent. Their values are given by theory and they are the same for all fluids [3,4].

Our fundamental equation incorporates the scaling laws. The thermodynamic potential

used in our work is that Introduced by Ley-Koo and Green [8]. It is the dependent variable

P

c P*/T* as a function of y = y*/T* and T = -1/T*. Here P is the pressure, y is the

chemical potential and T the absolute temperature. Asterisks denote reduced properties:

P* = P/Pp. T* = T/T and y* = yp /P , where P is the critical pressure, T the critical

temperature and p the critical density. In terms of this potential, we have

(3P/9f)~ = U ,

(3P/3y)^ = p , (2)

where U is the reduced energy density U = U*/V* and p the reduced mass density, while the

other thermodynamic functions: Helmholtz free energy density A = A*/V*, enthalpy density

H = H*/V* and entropy density S = S*/V* follow from

A = p y - P , H = P - U T , S = H - p y . (3)

Since all variables are Intensive, the coexistent phases collapse onto a single curve, which, in the y,T plane, can be parametrized by the analytic relation

Co(f) = y^ + J: Mj(Af)^",

where AT = (T-T )/T. In scaling, the physical variables y, T are transformed to a new

3
coordinate system, one axis of which is the curve y-CT), while the other intersects the

first at the critical point. The two scalinq variables are linear combinations of u-v and

AT:

"y = V'(T) - UqCT) = Ap/a,

u^ = AT + c Ay, (4)

where a is a constant related to the scale of y. The term cAy breaks the liquid-vapor

symmetry.

The potential P is decomposed into two parts, one part, P , that is regular in the

scaling variables and one, aP, that contains the critical anomalies with correct power-law

dependence. We have assumed for P : reg

Preg = ^o^^) + Ay + P^^ Ay aT ,

~P.(T) = 1 + z P. (Af)J . (5) ° j=l ^

aP, in scaled form, is given by

The first term represents asymptotic scalinq, the second a correction to scaling. The

critical exponents 6 and 6 are those characterizing the shape of the coexistence curve and

the shape of the critical isotherm, respectively. The leading term contains one more adjustable constant k , while the function g is universal, i.e., the same for all fluids.

the correction term contains a new independent critical exponent A-,, also given by theory,

and a new free constant k-, . The function g, is the same for all fluids.

All thermodynamic functions can be given in algebraically closed form by the device of

transformation to parametric variables [9]

Ay = au = r^*^ a o (1-e^),

p u^ = r (1-b^e^). (7)

The variable r measures "distance from the critical point", while e is measured along a

2 contour of constant r and reaches the values +1 on the phase boundary; b is a constant

predicted to be universal. The critical anomalies are all imbedded in the r-dependence

while the dependence of the thermodynamic functions on e is always in the form of simple

polynomials or their ratios. All relevant equations are given in Appendix A. Note that the

functions are listed separately for the one- and two-phase regions.

The constants defining our potential were obtained as follows. The critical exponent

values 3,(S,A-, are those predicted by theory [10]. The critical parameters, the four
parameters in the scaling function: a, k^, k, , c and the three "background" parameters P.,

P^, and P^^ were determined by a fit to the PVT data of Hastings et al . [5]* while we imposed

the condition that the slope of the vapor pressure curve at the critical point be that of

the vapor pressure data of Level t Sengers and Hastings [11], that the critical point lie on the vapor pressure curve and that the diameter of the coexistence curve be that measured by

Douslin and Harrison [12]. This implies that the values of T and P are constrained to be on the vapor pressure curve and cannot be fitted independently. The constant b , which is

expected to be universal, was set equal to that found for steam [4], consistent with the

theoretical value to within the latter's uncertainty. This value of b (Table I) is, how- ever, different from that used in [5]. As a consequence, all adjustable parameters except

the critical constants p , P and T , differ from those reported in [5], Two background

parameters v.2>v-^ were determined by a fit to the speed-of-sound data of Gammon [6]. The

other two, ij and y-, , are related to the zeros for energy, entropy and enthalpy. They were

3 fixed by equating the energy and enthalpy at 288.15 K and 7 mol/dm to those derived from

their PVT data [12] by Harrison and Douslin [13]. The parameters characterizing our potential are listed in Table I. The range of validity of the potential is indicated in Fig. 1.

3. The Equation of State

We compare the predictions of our potential for the equation of state of ethylene with

experiment. The experimental data are those of Hastings et al . [5] for a 99.993% pure

sample, to which the potential was fitted, those of Douslin and Harrison [12], Trappeniers

et al . [14] and Thomas and Zander [15,16]. Older data have been adequately reviewed in the

lUPAC formulation of Angus et al , [17], and in the reviews of Date et al . [18] and Vashchenko

et al. [19].

The potential represents the data of Hastings et al . with a reduced chi-square of 3.6

5 -3 3 if the uncertainties are estimated as 5 x 10" MPa in pressure, 3x10 mol/dm in density

and 5 x 10" K in temperature. It is to be kept in mind that our data were fitted to about

twice these close tolerances even though the deviation plots of Fig. 2 show occasionally

large density deviations. The percentage differences in density, TOO(pexp.''^calc.^''*^exp.

between the data, pg^n-' ^"^^ ^^"^ surface, P^g-],- > assuming the pressures to be the same, and, alternatively, the percentage differences in pressure lOOtPg^ "^calc.^^^exp.' ^^^""^^"^

the densities to be the same, are shown for the various isotherms in Figs. 2 and 3. At 298.15 K the surface represents our own data to well within 0.1% in density. The agreement

between the data sets of [5], [12] and [14] is almost within the 0.1% tolerance originally

set as a goal for the U.S. Government - Industry joint project on properties of ethylene.

*The bulk of the experimental PVT data were taken near, but not necessarily exactly at, the

temperature values of 30°C, 25°C, 20°C, 16°C, 12.5°C and 10°C. In Ref. [5], the temperatures

were reported at these round values, and small adjustments in the experimental pressures had

been made accordingly. The fit presented here, however, is to the data as measured (except

for the four near-critical isochores that had been reported earlier [11]); these unadjusted

data are listed in Table Bl
The data set of Thomas and Zander [15,16] shows more scatter than the other three sets,

without, however, showing systematic departures from our formulation. The pressure deviations are similarly small at this temperature, with a tendency to grow in the highly com- pressed fluid, as is to be anticipated (Fig, 3). When the critical point is approached,

the density departures between the data sets, and their departures from the surface, increase

dramatically, while the pressure deviations remain more or less the same. At the temperatures from 0.7-3.7 K above the critical temperature, the density departures reach values

larger than 0.5% and on isotherms spanning the critical the largest departure is 15%. The

pressure deviations, however, remain as well-behaved as at 298.15 K if not better, the

departures being of the order of 0.02% in the range around critical (Fig. 3). This is a good illustration of the difference between "density" and "field" variables in the vicinity

of a critical point. ("Density" variables are different in coexisting phases while "field"

variables are the same.) Due to the strong divergences of the compressibility and expansion

coefficients, small systematic differences in temperature and pressure scales between the

various laboratories are amplified when the densities are compared. Furthermore, the

effect of impurity is largest at the critical point, and small differences in sample com- position can lead to large variations in density.

A study of the plots in Fig. 2 will convince the reader that most of the region covered

in this report should be avoided if an accuracy of 0.1% in density is desired in custody

transfer. Even if our surface were perfect, the finite precision of industrial pressure

and temperature measurement will result in large errors if the density is calculated from

the equation of state. Appendix B. Table BI, contains the deviations of the PVT data sets [5], [12], [14],

[15] and [16] from the present formulation.

4. Critical Parameters

The critical temperature and density of ethylene were measured by Moldover [20] by the

method of visual observation of the meniscus disappearance. His results are given in Table

II. The pressure given in his paper was a result of early vapor pressure measurements in

the apparatus of Hastings et al . Later, but prior to publications [11], [5], a small tem- perature calibration error was found in that work. The critical pressure reported by

Moldover should therefore be disregarded.

The critical parameters reported by Douslin and Harrison [12] and those determined by

us are also listed in Table II. These parameters are results of an analysis of PVT data.

As a general rule, such analyses give set of P , T values that are consistent with the

vapor pressure curve but do not determine the value of T sharply. A more accurate value

of T^ can be obtained by analyzing coexistence - curve data [12]. Coexistence curve data

resulting from PVT data, however, rapidly decline in accuracy as the critical point is approached. This is true for both the data of Douslin and Harrison, and those of Hastings

et al. It is therefore gratifying to see how well the critical temperatures and densities

obtained by PVT data analysis agree with the direct observation by Moldover.
5. Coexistence Properties

Vapor pressures from 279,15 to the critical temperature are compared in Fig. 4. The quantity aP equals P -Pr-air • ^^^^ sources are those of Hastings and Levelt Sengers [11] and those of Douslin

and Harrison [12]. These two data sets were shown to agree within combined error of 10" MPa at temperatures below 240 K [11]; the departures are systematic at higher temperatures, and reach a maximum of 7 x -4

10 MPa at the critical point. A satisfactory explanation for the difference has not been given. It is

larger than expected on the basis of the agreement of pressure scales (1 in 20,000) and temperature

scales (1 mK) and not quite of the form expected for a difference in purity [5]. Nevertheless, the

agreement between the data sets [11] and [12], better than 2 parts in 10 , is an order better than that

between these sets and the older data (cf. [12], p. 311). Table BII in Appendix B contains the deviations

of vapor pressure data sets [11] and [12] from our formulation.

Coexisting densities of Refs. [5] and [123 are compared with our formulation in Fig. 5 and in Table

Bin. The quantity Ap equals p„^„ -p^,i^ • The agreement between the two data sets and the formulation,

•3 exp . ca I c

.

to +0.02 mol/dm , is satisfactory in this region close to the top of the coexistence dome.

6. Speed of sound

As we mentioned before, we determined the parameters ijp,vo in our potential from a fit to Gammon's

speed-of-sound data [6], accepting his density and temperature values as independent variables. It should be stressed that the anomalous contribution to the speed of sound that drives it to zero at the

critical point has been completely predicted from the part of the potential that was determined by the

PVT data alone. A substantial loss of accuracy is to be expected when second derivatives are calculated

from the potential. We therefore consider the result of our procedure, a prediction of the speed of

sound that is generally well within 1% from experiment, as very satisfactory. A global view of the speed

of sound within the range of our correlation is shown in Fig. 6. Fig. 7 shows the percentage departures

of the speed of sound, 100(C^^^ -C^,n^ )/C„„„ , from our surface. It should be mentioned that we had to exp. ca I c . exp.

omit a few of Gammon's data points because our surface predicted them to be inside the two-phase region.

Also, we omitted the data points on the critical isotherm within j^ 10% from the critical density, these

points being heavily affected by dispersion.

The prediction of the speed of sound is about an order of magnitude less accurate than the precision

of the data as estimated from Gammon's assessment of uncertainties in density, temperature and speed of

sound. Permitting more than two of the model parameters to be freely adjustable did not improve the

precision of the fit by more than a factor of 2. Table BIV in Appendix B contains a listing of the departures of the experimental data from the

present formulation.

7. Enthalpy

Fan [21] recently obtained for ethylene values of the enthalpy and specific heat at constant pressure

in a range around the critical point. The data were obtained in a carefully designed flow calorimeter

with considerable precision. The calorimeter measures enthalpy changes along selected paths, isothermal or isobaric. The independent variables are pressure and temperature, A number of isobaric enthalpy

differences were obtained in the range of our formulation. We have calculated with our equation the

densities corresponding to Fan's temperatures and pressures, and then predicted the enthalpy differences

at isobaric conditions for the observed inlet and outlet temperatures. Experiment and prediction are compared in Table BV. The agreement is not good. The differences are of the order of 0.5 J/g or 14

J/mol , whereas our predicted enthalpies agree with those calculated by Harrison and Douslin on the level

7
of a few J/mol (cf. Section 8). Of course, a small offset in temperature or pressure scales between the

calorimetric experiment and the PVT experiments will have severe consequences for the density derived

from the measured pressures and temperatures; this, in turn, may affect the predicted enthalpy differences,

We have varied the pressures reported by Fan by amounts of the order of 0.1%, and the temperatures

by a few 0.01 K. Neither variation improved the agreement of prediction and experiment significantly.

We must, therefore, reluctantly conclude that the experimental enthalpy differences are not completely

consistent with the PVT data. The value of the latent heat reported by Fan, 102.8 J/g at 4.8212 MPa,

however, agrees closely with our value of 102.8 J/g and differs from that of Harrison and Douslin, 103.3

J/g by an amount corresponding to 25 mK in temperature.

8. Other Formulations

A recent comprehensive correlation of the properties of ethylene, in the form of an equation of

state based on the same data sets considered in this paper, is that of McCarty and Jacobsen [7]. It was preceded by several other correlations, such as the lUPAC formulation by Angus et al . [17], which formulation is based on a part-graphical, part-analytic representation of the PVT properties of ethylene

obtained prior to 1972; and the correlation obtained by graphical means by Harrison and Douslin [13] of

their own data. The dashed curves in Figs. 2 and 3 indicate the density and pressure departures of the

McCarty-Jacobsen formulation from our own; here Ap(%) = 100 (p^,, - P-g-.- )/pmj» ^^^ analogously for

aP(%). Since the Helmholtz function of McCarty and Jacobsen is analytic, it has difficulty representing

the flatness of near-critical isotherms, as was recognized by the authors. At 298.15 K the departures,

though systematic, are limited to a maximum of 0.3% in density, but as the temperature approaches the

critical the departures become more severe. At temperatures within 1 K from critical, where our formulation agrees with all data to well within 0.1% in pressure, the McCarty-Jacobsen formulation departs by

several tenths of a percent in pressure in a systematic fashion. These differences are magnified when

derived properties are considered. An example is shown in Fig. 8 for the enthalpy of ethylene, where the

departures of the McCarty-Jacobsen enthalpy from that predicted by our surface are shown along the 283.15

K, 288.15 K, and 298.15 K isotherms. Towards completion of this work, a new classical thermodynamic

surface was constructed by Jacobsen and Jahangiri. For comparison with our equation, we refer to that

work [22]. This new classical surface is considerably more accurate than that of [7].

The graphical method of Harrison and Douslin, if applied with care to excellent data, should be

expected to give better results that can be obtained with a fit to an empirical thermodynamic surface

that is seldom quite true to the data. A possible exception is the near-critical regime: the anomalous

curvature of isochores may be missed by graphical techniques and by the analytic surface alike, but is correctly incorporated in our potential. The intercomparison in Fig. 8, however, shows that the enthalpies calculated by Harrison and Douslin do not depart from our surface by more than a few J/mol anywhere,

while the departures of the analytical McCarty-Jacobsen surface peak at more than 20 J/mol at nearcritical temperatures and densities.

The departures from our surface of the derived properties according to the lUPAC formulation show

strong systematic trends. This formulation was based on older data and was never claimed to possess high

quality in the critical region.

First and second derivatives according to the^cCarty-Jacobsen formulation are compared with our own

in Figs. 9,10; here AH = H^.j-H , and similarly for U,S, where calc. refers to our surface. The first

derivatives U, H and S have somewhat different density dependence in the two formulations. Moreover,

appreciable departures build up around the critical density and near the critical temperature. The

departures of C,,, C., and the speed of sound are substantial; here aC (%) = 100 (C ,mi - C , )/C , r V "^ ' V V MJ VjCalc. v,calc.

8
and analogously for aC , aC , where calc. refers to our surface. They are about 1% at 298.15 K, 5 - 10% at 288.15 K and 20 - 40% at 283.15 K (0.8 K above critical). An analytic representation cannot describe

the divergence of C^ and the accompanying decline to zero of the (thermodynamic) speed of sound while the

divergence of Cp is not strong enough; so these large departures are not surprising. The authors themselves did not claim accuracy in the critical region. Since we have represented the speed-of-sound data

to about 1% in accuracy, we are confident that our model represents thermodynamic behavior, such as a weakly diverging Cw, accurately.

A formulation of the thermodynamic properties of ethylene in the critical region was recently published

by Nehzat et al . [23]. The formulation is a nonanalytic equation of state that incorporates some features

of scaled equations, such as a near-cubic coexistence curve and a critical isotherm of degree near 5. The

curvatures of the isochores, and the specific heat C^, however, do not exhibit the predicted weak divergence in the one-phase region. The equation has a higher-order anomaly at the critical isochore; it is

not integrable in closed form so that the thermodynamic functions H, G and S must be calculated by numerical integration. The equation of state contains 16 adjustable parameters and claims validity in a density

3 range of 4.5 to 11 mol/dm and 280.15 to 284.15 K. Additional constants in the thermodynamic functions were obtained by "matching" at each isotherm with the entropy and Gibbs function of Harrison and Douslin

3 along the isochore at 4.5 mol/dm . For comparison, our equation of state contains 10 constants (4 more

3 for determining the thermodynamic functions), while it is valid from 5.8 to 10.5 mol/dm and from 279-300

K. The equation of state of Nehzat et al . fits the PVT data of Douslin in the 4 K strip to close tolerance.

As far as derived properties are concerned, we compare their tabular values of Cy in the one- and

two-phase region with our surface in Figs. 11 and 12. In the two-phase region the two formulations agree

as to the values of C^ as demonstrated in Fig. 12. In the one-phase region, however, the Cw values

implied by the equation of Nehzat et al . differ appreciably from the behavior predicted from our surface

as illustrated in Fig. 11. In fact, along isotherms close to the critical temperature the Cw of Nehzat et

al . has an anomalous jump at the critical density. We do not believe that the Cw predictions of [23]

correspond with physical reality. In the absence of experimental C data for ethylene, we can only argue

that there is substantial evidence for many fluids that C diverges; furthermore, in the case of steam,

where C data are available, our scaled equation represents the data at the various isochores closely [4].

The only experimental data related to C for ethylene are those of Gaimion for the speed of sound [6].

Nehzat et al . predict this quantity on the coexistence curve. In Fig. 13, we compare their and our predictions for the speed of sound of liquid ethylene with the data of Gammon [6]. This comparison confirms

that the second derivatives are not accurately represented by the equation of Nehzat et al . [23].

9. The Effect of Pressure and Temperature Errors on Density

In custody transfer, the density of ethylene will be calculated from its measured pressure and temperature. Since these quantities are measured with limited accuracy, an error in density will result that is

given by

p or ^-(PK^)^, (8)

iL = .„p ,T = -K,

(f^)^

6T. (9)
In view of the strong divergence of the compressibility K-j. and the expansion coefficient ap, the density

error resulting from inaccuracy in the measurement of P or T is a maximum at the critical point. We show

the region in P-T space that should be avoided if an accuracy of 0.1% in density is desired and the

pressure is measured with an accuracy of 0.1, 0.05 and 0.02%, respectively, (Fig. 14); or the temperature

is measured to 0.02, 0.01 or 0.005 K, respectively, (Fig. 15).

10. The Effect of Impurity on Density

The pressure formulation of the equation of state of ethylene is based on the PVT data obtained for

99.993% pure ethylene, with ethane as the prime impurity. The formulation permits the calculation of the

density of an ethylene sample from its pressure and temperature. If impurities are present in the sample

of interest, the predicted density will differ from the actual one. It is of interest to know what effect

a given impurity has on density, and how the effect varies with the temperature and pressure.

Under simplifying assumptions, this question can be answered. We will assume that the impure fluid

is in corresponding states with the pure host, and that the impure system displays pseudo-critical con- stants that are shifted from those of the pure host by amounts linear in concentration:

Txc=T, (1 +ax),

P,, =P, (1 -bx),

^c ^ ^c (^ " ^^"^^^^ • ^^°^

Both assumptions are reasonable and readily justifiable in dilute mixtures not close to the critical

line; the only difficulty with the model is the actual assignment of the values of a and b, parameters

characteristic of the host-impurity interaction. They can be determined from the critical parameters of

the pure components in the case that the critical points are connected by a continuous critical line. For the sake of developing our estimate of the density error introduced by impurity, we will consider these

parameters a,b as known.

An equation for the impurity-induced density error was derived by one of us [5]. It was obtained by

applying the law of corresponding states to the pure host and the dilute mixture at the same pressure and

temperature. The following result was obtained for the change in density:

^ = x[(a-b) + bPK^ - aTap]

= x[(a-b) + bPK^ - a(PK^) (^ |^)] , (11)

where Kj is the compressibility, ex the expansion coefficient of the pure host at T, P. It is clear

that Eq. (11) permits calculation of the impurity-induced error in density at any point in P-T space

once the constants a, b are known. The relation (11) should not be applied too close to the critical

point since the coefficient of the term in x diverges. More seriously, an expansion in x has as little

justification as one in p, which is known to be invalid at the critical point.

A scrutiny of Eq. (11) immediately reveals that impurity-induced density errors will be largest near

the critical point. This is a consequence of the fact that both Kj and ap diverge strongly at this point.

The precise nature of this density error will, of course, depend on the values of a and b. Since these

values form the least-known part of our model, we will consider only a few extreme cases.

(1) a = - 0.5, b = 0: a highly volatile impurity that depresses the critical

the critical temperature of the mixture strongly without affecting the critical pressure,

10
(2) a = + 0.5, b = 0: a highly nonvolatile impurity that increases the critical temperature of

the mixture strongly without affecting the critical pressure.

The cases (1) and (2) have opposite effects on the density. The impurity-induced density error is given

by

^=10.5 X [1 - CP K^) (If^)] (5)

where the + sign refers to case 1, the sign to case 2. In Fig. 16, we show the region in P-T space that

should be avoided in custody transfer if an accuracy in density of 0.1% is desired and if various amounts

of an impurity very different in volatility from ethylene are present.

11. Tables of Thermodynamic Properties

In Appendix C we present the thermodynamic properties of ethylene in the critical region. It was

not possible to organize this table along isobars, as in [6]. The extremely rapid variation of the

"density"-! ike properties p, U, H, S with P and T would preclude interpolation in such a table. We have

therefore tabulated the properties along isochores, or at constant density, using temperature as the

second entry (Table CI). In addition, we present tables of saturation properties first with temperature,

then with pressure as an entry (Tables CII, CIII).

The computer program required for the generation of thermodynamic properties of ethylene is listed

in Appendix D. Appendix E contains units and conversion factors.

Acknowledgements

R.D. KcCarty, B.E. Gammon and Yu-Chun Fan provided us with results of their work prior to publication. Constructive observations by R.T. Jacobsen and M. Jahangiri at various stages of this work led to

a number of improvements. We have benefitted from the assistance of J.S. Gallagher in an earlier stage of

this project. Computer time for this project was provided by the Computer Science Center of the

University of Maryland.

12. References

[1] Sengers, J.V. and Levelt Sengers, J.M.H., "The critical region", Chem. and Eng. News 46^, 104, 1968.

[2] Levelt Sengers, J.M.H., "Scaling predictions for thermodynamic anomalies near the gas-liquid critical

point", Ind. Eng. Fund. 9, 470, 1970.

[3] Levelt Sengers, O.M.H., Morrison, G. and Chang, R.F., "Critical behavior in fluids and fluid mixtures".

Fluid Phase Equilibria 14^, 19, 1983.

[4] Levelt Sengers, J.M.H., Kamgar-Parsi , B. and Sengers, J.V., "Thermodynamic properties of steam in the

critical region", J. Phys. Chem. Ref. Data, 12^, 1, 1983.

[5] Hastings, J.R., Levelt Sengers, J.M.H. and Balfour, F.W., "The critical-region equation of state of

ethylene and the effect of small impurities", J. Chem. Thermodynamics 12^, 1009, 1980.

[6] Gammon, B.E., "Velocity of sound in ethylene", presented at the Advisory Committee Meeting of the

Joint Industry-Government Ethylene Project, Boulder, Colorado (Dec. 6, 1978).

11
[7] McCarty, R.D. and Oacobsen, R.T., "An equation of state for fluid ethylene", NBS Tech. Note 1045,

(Nat'l Bur. Stand., Washington, DC, 1981).

[8] Ley-Koo, M. and Green, M.S., "Consequences of the renormalization group for the thermodynamics of

fluids near the critical point", Phys. Rev. A 23, 2650, 1981.

[9] Schofield, P., "Parametric representation of the equation of state near a critical point", Phys. Rev. Letters 22^, 606, 1969.

[10] Le Guillou, J.C. and Zinn-Justin, J., "Critical exponents from field theory", Phys. Rev. B 21_, 3976,

1980.

[11] Hastings, O.R., and Levelt Sengers, O.M.H., "Vapor pressure, critical pressure, and critical isochore

of ethylene", in Proceedings 7th Symposium on Thermophysical Properties , Cezairliyan, A., ed.,

(American Society of Mechanical Engineers, New York, 1977) p. 794.

[12] Douslin, D.R., and Harrison, R.H., "Pressure, volume, temperature relations of ethylene", J. Chem.

Thermodynamics 8, 301 (1976).

[13] Harrison, R.H. and Douslin, D.R., "Derived thermodynamic properties of ethylene", J. Chem. Eng. Data

22^, 24 1977.

[14] Trappeniers, N.J., Wassenaar, J., and Wolkers, G.J., "Isotherms and thermodynamic properties of

ethylene at temperatures between and 150 C and at densities up to 500 amagat", Physica 82A, 305

(1976).

[15] Thomas, W. , Zander, M., Quietzsch, G., and Hartmann, H., "Dichte des Aethylens fuer Temperaturen

von -30 C bis 80 C bei Drucken bis zu 100 bar," Herausgeber Hoechst AG, Frankfurt/M-Hoechst (1976).

[16] Thomas, W., and Zander, M., "Pressure-density-temperature measurements of ethylene". Int. J. Thermophysics 1, 383 (1980).

[17] Angus, S., Armstrong, B., de Reuck, K.M., Featherstone, W., and Gibson, M.R., International Thermodynamic Tables of the Fluid State , Ethylene , 1972 , International Union of Pure and Applied Chemistry,

Division of Physical Chemistry, Commission on Thermophysic and Thermochemistry, Thermodynamic Tables

Project, Butterworths, London (1974).

[18] Date, K., Watanabe, J., and Uematsu, M., "Evaluation of P-V-T properties data, the most probable

values of the compressibility factor of gaseous ethane and ethene". Review of Phys. Chem. Japan 43^, 92 (1973).

[19] Vashchenko, D.M. , Voinov Yu, F., Voityuk, B.V., Dregulyas, E.K., Kolomiets, Ya., A., Labinov, S.D.,

Morozov, A. A., Neduzhii, I. A., (Principal Author), Provotar, V.P., A. Yu. Soldatenko, Storozhenko,

E.I. , and Khmara, Yu. I. , Thermodynamic and transport properties of ethylene and propylene (translated from the Russian as published by the State Committee of Standards of the Soviet Ministry,

U.S.S.R., State Officer of Standards and Reference Data, Series: Monograph No. 8, 1979), Office of

Standard Reference Data, National Bureau of Standards U.S. Department of Commerce, Washington, D.C.

[20] Moldover, M.R., "Visual observation of the critical temperature and density: CO, and CpH,", J. Chem.

Phys. 6]_, 1766 (1979). ^ ^ ^

[21] Fan, Yu-Chun, "Accurate Calorimetric Determination in the Critical Region of Ethylene", Ph.D. Thesis,

Dept. of Chem. Engineering, University of Michigan, Ann Arbor, Michigan, 1982.

[22] Jacobsen, R.T. and Jahangiri, M., to be published.

[23] Nehzat, M.S., Hall, K.R. and Eubank, P.T., "Thermophysical Properties of Ethylene in the Critical

Region", J. Chem. Eng. Data 28, 205 (1983).

[24] Waxman, M. and Davis, H.A., Adv. in Chem. Series 182 , K.C. Chao and R.L. Robinson, Jr., editors, ACS

Washington, p. 285 (1979).

12
Table I. Parameters in the Thermodynamic

Potential for Ethylene

Critical Exponents

6 = 0.325

6 = 4.82

Ai = 0.50

Critical Parameters T^ = 282.3452 K

p^ = 7.634 mol/dm3

P^ = 5.0403 MPa (derived)

Parameters in Scaling Function

Pressure background

parameters

Caloric background

parameters

a^ = 19.3214

ko = 1.12289

ki = 0.54617

c = -0.007811

b2 = 1.3757

Pi = 5.3350

P2 =-18.1475

Pii= -0.166687 (derived)

Po = -36.4889

vi = -27.3955

V2 = -12.2091

P3 = -11.8802

Table II. Critical Parameters of Ethylene

Author Data Source T^^.K P^, MPa p ,mol/dm

Moldover [20] visual observation of 282.344+0.004

meniscus disappearance

7.650+0.021

Douslin [12] PVT [12] 282.35 5.0420 7.635+0.006

This work PVT [5] 282.3452 5.0403 7.634

13
APPENDIX A: Revised and Extended Scaling Equations for the Thermodynamic

Properties of Fluids.

A.l Reduced thermodynamic quantities

T= .!£ 5 = H. ^i p =

P . !c

1 -p* Pfj. p > TP ' c c

s - p r, _ u 1 c _ s "^c p-^ ' "-v*p- ' ^-v*p- ' ^c c c

1 Jl Is. u JL Is. " A ( lE - VT • P^ > " - VT * P^ ' ^T -

I 95

(A.l)

T

^ C T C T

^v V P , ^P V P

c c

(T is temperature, y is chemical potential, P is pressure, p is density,

U is energy, S is entropy, A is Helmholtz free energy, H is enthalpy,

V is volume, (L. is heat capacity at constant V, C is heat capacity at

constant P)

.

A. 2 Thermodynamic relations

dP = Udf + pdp

dA = -Udf + ydp

(A. 2)

dH = -fdU + pdy

dS = -fdU - ydp

14
with

A = py - P

H = P - TO (A.3)

S=H-py=-TU-A

A.3 Fundamental equations

with

AT = T + 1 (A.4a)

Ay = V - y^(T) (A. 4b)

P = PqCT) + Ay + PjjAyAT + AP (A. 5)

~ 3 . MAT) = u * I y.(AT)^ CA.6a)

^ j=l J

2 ^ ^ . P^(T) = 1 + r P.fAT)^ (A. 6b)

j=l

A. 4 Derived thermodynamic quantities

p = l.P AT W^ CA.7)

'' V^AT

~ ^o ^1%

dT ^T 11 \9^T/^~ (A. 8)

^T (-.-2)^ (A. 9)

V^^^ /at

TD
31

£0 ^, L,_i.lh_4\ S 3^aP

Xj 3Ay3AT

(A. 10)

C d^P

V o ^ T dT^ dT^

2- ~ ?

a^AP 1 / 3^A?

3Ay3AT Xt \3Avj3AT

(A. 11)

r = c + ^p S l?['-'(S)J CA.12)

A. 5 Ci'itical exponents

a = a , a, = a - Aj^

B^ = 3 . gj = S * Aj (A. 13)

with

^0 = ^ ' ^1 = ^ - ^1

2 - a = 3(6+1) Y = 6(6-1) (A. 14)

A. 6 Parametric equations for singular terms

Ay = r^*ae(l-0^)

AT = r(l-b^9^) - cAu

CA.15)

(A. 16)

16
AP = E r "lak.p (0) CA.17)

i=0 ^ ^

(lilf = Jo [''%' * cr^-ialc.s.Ce)] (A.18)

3AP\ , J r^-Oiak.s.O) (A. 19)

'Ay

/ 3AP

\8Af 1 1

[l-^\ = .E r-^i-^u.(e) +2cr^i-\v (0) +cV'*iak.w (6) (A.20)

VsAyV^- 1=0 L ^ ^ 11 1 1 J

^-^ = .Z„ r^i"^k.v.(0) + cr"°iak.w. C0) CA.21)

)AuAT 1=0 L 1 i*-

'' 1 i'^ 3AviAT -J

' 2 ~\ 1 ^) = .1 r"°iak.w.C0) (A.22)

,3AT^/,~ i=0

^ /Ay

A. 7 ATJxiliary functions

Pi (6) = Poi + P2i9^ * V4i^^ CA.23)

s^(0) = s^^ + 52^0^ , 5^(0) = 252^6 (A. 24)

q(0) = 1 + {b^(266-l)-3}0^ - b^ (266-3)0^ (A. 25)

u^Ce) = [1 - b^Cl-2B^)0^]/q(0) (A.26)

Vi(0) = [6^(1-30^)6 - B6Cl-0^)0]/q(0) (A. 27)

17
w^iej = ui-o^3(i-3e-)s.(e) - B6(i-e-)6s|(e)]/q(e) (a.28)

with

B6-3S.-b^a.Yi

Poi

2b'*(2-a.)(l-a.)a.

66-3Bj.-b^a^ (266-1)

1*21 2b^(l-a.)a.

P4i

= . 266-3

2a.

1

^oi

= C2-a.)p .

^2i

66-36^

2b ^a^

A. 8 Two-phase properties

Variables :

e = ±1

Ay =

AT = r(l - b^)

(A. 29)

(A. 30)

(A. 31)

Vapor pressure:

P = P (T) + E r 1 ak.p. (1) (A. 32) vap o'- "' i=o 11

18
Coexisting Densities:

P^Py

1 + P„ AT + .Z„ c r "^ak.s. (1) 11 1=0 i i

'

P,-P.

V^= E r^ik.

2 i=o 1 (A. 33)

Helmholtz free energy:

A = p y^(T) - Pp(T) I r i ak.p. (1)

i=0 1^1 * (A. 34)

Energy:

dP dy (T) ' 1 . = _£ _ o_5__ + _i_ E (2-a )r^-°i ak p (1)

dT dT 1-b^ i=0 ^ ^

^ (A. 35)

Entropy:

~ - fdP dy

s = -p a (T) + p m - T -# - L

p ^

dT dT

1 ~ 1 + .Z r^""i ak.p.Cl) - ^ I (2-a )r^"°i ak.p CD CA.36) a=u 1 A j,^-' 1=0

Specific Heat C : y

C d^P d^iJ / 1 \2 ^ -a, ^ = -— -P-t:^* -4 .^ (2-a)(l-a)r ^ak p (1) (A.37)

r dT^ dT^ Vl-bV ^=°

19
Appendix B. Comparison with Experiment

In Table B I, the experimental PVT data are compared with the formulation (a) as pressure differences under the assumption that the temperatures and densities

are exact and (b) as density differences under the assumption that the temperatures

and pressures are exact. In Table B II, saturation pressures from two sources are compared with the formulation and in Table B III the saturation densities. In Table B IV, the speed-of-sound data [6] are compared with the theoretical predictions,

and in Table B V the enthalpy data. The legend for the various data sources is as follows

A Hastings et al . [5] 99.993% pure sample.

B Hastings et al . [5] 99.999% pure sample.

1 Douslin and Harrison [12].

2 Trappeniers et al . [14].

3 Thomas and Zander [15,16].

GAM Gammon [6].

20
TABLE BI. Comparison of the experimental PVT data

with the formulation.

EXP. ID TEMPERATURE PRESSURE DENSITY

MPA M0L/DM3

EXP CALC DIFF XDIFF EXP CALC DIFF ZDIFF

A 298 1386 8.32147 8.32105 .00042 .005 10.542 10.543 -.000 -.00

A 298 1386 8.32149 8.32105 .00044 .005 10.542 10.543 -.000 -.00

A 293 1388 7.32940 7.32704 .00236 .032 10.545 10.548 -.003 -.03

A 289 1390 6.54643 6.54307 .00336 .051 10.547 10.552 -.006 -.05

A 283 6392 5.49244 5.48964 .00280 .051 10.550 10.557 -.008 -.07

A 283. 6392 5.49234 5.48964 .00270 .049 10.550 10.557 -.007 -.07

A 282. 3333 5.24755 5.24556 .00199 .038 10.550 10.557 -.006 -.06

A 281. 1393 5.02650 5.02529 .00121 .024 10.551 10.555 -.005 -.04

A 280. 6394 4.93481 4.93404 .00077 .016 10.551 10.554 -.003 -.03

A 280. 3394 4.88010 4.87961 .00049 .010 10.551 10.553 -.002 -.02

A 280. 0394 4.82562 4.82543 .00019 .004 10.551 10.552 -.001 -.01

A 279. 7394 4.77146 4.77154 -.00008 -.002 10.551 10.551 .000 .00

A 298. 1386 7.89536 7.90041 -.00505 -.064 10.024 10.017 .007 .07

A 298 1386 7.89545 7.90041 -.00496 -.063 10.024 10.017 .007 .07

A 285 6391 5.68452 5.68402 .00050 .009 10.030 10.032 -.002 -.02

A 283. 6392 5.34404 5.34389 .00015 .003 10.031 10.032 -.001 -.01

A 282 3333 5.12547 5.12580 -.00033 -.006 10.031 10.029 .002 .02

A 281. 1393 4.92924 4.93023 -.00099 -.020 10.032 10.024 .009 .08

A 280 8393 4.88062 4.88185 -.00123 -.025 10.032 10.020 .012 .12

A 280 7393 4.86455 4.86581 -.00126 -.026 10.032 10.020 .013 .13

A 298 1386 7.46041 7.46406 -.00365 -.049 9.285 9.278 .007 .08

A 298. 1386 7.46049 7.46406 -.00357 -.048 9.285 9.278 .007 .08

A 293 1388 6.67996 6.68064 -.00068 -.010 9.288 9.286 .002 .02

A 289 1390 6.06498 6.06419 .00079 .013 9.289 9.293 -.003 -.04

A 285 6391 5.53737 5.53628 .00109 .020 9.291 9.299 -.008 -.09

A 283 6392 5.24276 5.24217 .00059 .011 9.292 9.299 -.007 -.08

A 282 3333 5.05492 5.05501 -.00009 -.002 9 . 292 9.290 .002 .02

A 281 8393 4.98547 4.98586 -.00039 -.008 9*. 293 9.279 .013 .14

A 281 7893 4.97849 4.97894 -.00045 -.009 9.293 9.277 .016 .17

A 298 1386 7.29300 7.29536 -.00236 -.032 8.911 8.905 .006 .06

A 298 1386 7.29308 7.29536 -.00228 -.031 8.911 8.905 .006 .06

A 293 1388 6.56382 6.56372 .00010 .001 8.913 8.913 -.000 -.00

A 289 1390 5.98874 5.98747 .00127 .021 8.914 8.921 -.007 -.08

A 285 6391 5.49490 5.49353 .00137 .025 8.916 8.930 -.014 -.16

A 283 6392 5.21907 5.21834 .00073 .014 8.917 8.932 -.015 -.17

A 282 3333 5.04370 5.04370 -.00000 -.000 8.917 8.917 .000 .00

A 282 1893 5.02483 5.02489 -.00006 -.001 8.917 8.913 .004 .05

A 282 0893 5.01180 5.01191 -.00011 -.002 8.917 8.907 .010 .11

A 282 0993 5.01308 5.01321 -.00013 -.003 8.917 8.906 .011 .12

A 282 0893 5.01180 5.01191 -.00011 -.002 8.917 8.907 .010 .11

A 282 0943 5.01245 5.01256 -.00011 -.002 8.917 8.908 .010 .11

A 282 0893 5.01182 5.01191 -.00009 -.002 8.917 8.909 .008 .09

A 282 0949 5.01251 5.01264 -.00013 -.003 8.917 8.906 .011 .13

A 282 .0946 5.01245 5.01260 -.00015 -.003 8.917 8.904 .013 .15

A 282 0942 5.01246 5.01255 -.00009 -.002 8.917 8.910 .008 .08

A 282 0936 5.01233 5.01247 -.00014 -.003 8.917 8.905 .012 .14

A 282 .0891 5.01176 5.01189 -.00013 -.003 8.917 8.906 .011 .13

A 282 0877 5.01156 5.01171 -.00015 -.003 8.917 8.904 .013 .15

A 298 1386 7.23223 7.23416 -.00193 -.027 8.758 8.753 .005 .06

A 298 .1386 7.23231 7.23416 -.00185 -.026 8.758 8.753 .005 .05

A 283 6392 5.21245 5.21172 .00073 .014 8.764 8.782 -.018 -.21

A 282 2193 5.02695 5.02703 -.00008 -.002 8.764 8.755 .009 .10

A 282 ,3333 5.04151 5.04152 -.00001 -.000 8.764 8.764 .000 .01

A 282 1893 5.02316 5.02323 -.00007 -.001 8.764 8.755 .009 .11

A 282 .1893 5.02316 5.02323 -.00007 -.001 8.764 8.755 .009 .11

A 282 .3960 5.04961 5.04952 .00009 .002 8.764 8.771 -.007 -.08

A 282 .1708 5.02097 5.02090 .00007 .001 8.764 8.774 -.010 -.11

A 282 .1915 5.02346 5.02351 -.00005 -.001 8.764 8.758 .006 .07

A 282 .1909 5.02335 5.02343 -.00008 -.002 8.764 8.753 .011 .12

21
EXP. ID TEMPERATURE

K

PRESSURE

MPA

riENSITY

M0L/DM3

EXP CALC DIFF %riIFF EXP CALC DIFF XniFF

A 282. 1911 5,,02344 5

,

.02346 -.00002 -.000

A 282..1916 5 i,02346 5,.02352 -.00006 -.001

A 303. 1500 7,,47231 7,,47406 -.00125 -.017

A 293. 1500 6..88256 6,.88293 -.00037 -.005

A 298. 1500 A,.88257 6.,88293 -.00036 -.005

A 293. 1500 A-.29461 A,,29429 .00032 .005

A 289. 1500 5 ^.82681 5,,82615 .00066 .011

A 285. 6500 5 i.42011 5

1

.41960 .00051 .010

A 285.,6500 5 i.42003 5 i,41960 ,00043 .008

A 284.,6500 5

1

.30458 5

.

.30419 .00039 .007

A 284,.6500 5 <.30469 u *.30419 .00050 .009

A 283..6500 5

.

.18952 5

.

.18925 .00027 .005

A 283..1500 «J 4.13217 5 <,13200 .00017 .003

A 283,,1500 5,.13210 5

.

,13200 .00010 .002

A 282,.6500 5 <.07503 5 i,07494 .00009 .002

A 282,,6500 5 i,07495 5

.

,07494 .00001 .000

A 282,,6500 5 ,07496 5 <,07494 .00002 .000

A 232,,5000 5 (,05789 5 •,05737 .00002 .000

A 303,.1500 7,,45336 7.,45446 -.00110 -.015

A 298,.1500 6,,86344 6.,86373 -.00029 -.004

A 298..1500 6,,86837 6.,86373 -.00036 -.005

A 293,.1500 6..28553 6..28525 .00028 .005

A 289,.1500 5 4.82149 5..82094 .00055 .007

A 285,,6500 5

.

.41783 5

.

,41742 .00041 .003

A 284,.6500 5 •.30310 er ,30279 .00031 .006

A 283,,6500 5

.

,18875 5 .,18855 .00020 .004

A 233,.1500 5.,13169 5

.

,13161 .00008 .002

A 282,.6500 5

.

,07481 5

.

,07482 -.00001 -.000

A 303,,1500 7,.43832 7,.43939 -.00107 -.014

A 298,,1500 6..85749 6..35782 -.00033 -.005

A 293,.1500 6i,85754 6,.85782 -.00028 -.004

A 293,,1500 6.,27857 6,.27328 .00029 .005

A 289,.1500 5

,

.8174<^ 5

.

.81oV3 .00056 .010

A 285,.6500 5

,

,41617 *"» ,41574 .00043 .008

A 284,.6500 ,j

,

,30193 5,,30171 .00027 .005

A 283,.6500 5

,

.13817 f .18801 .00016 .003

A 283,,1500 5

,

,13139 5

.

.13131 .00008 .002

A 282,,6500 5

,

.07473 S •.07473 .00000 .000

A 303,.1500 7,.40673 7,.40746 -.00073 -.010

A 293,.1500 6,,83445 6..83468 -.00023 -.003

A 293,.1500 6,.26383 A,. 26354 .00029 .005

A 239,.1500 U 1,80890 ,80344 .00046 .008

A 285,.6500 u <.41252 5 1.41219 .00033 .006

A 234,.6500 5 ,. 29966 5 .29941 .00025 .005

A 283,.6500 u .18698 5 .18686 .00012 .002

A 233 . 1500 f> .13070 5 .13067 .00003 .001

A 282 .6500 5 .07449 c- .07453 -.00004 -.001

A 293,.1336 A .53431 6 . 53356 .00075 .011

A 298

,

.1386 6 .58443 6 .53356 .00037 .013

A 293 .1308 6 .10011 6 .09990 .00021 .003

A 239,.1390 S .71065 5 .71073 -.00013 .002

A 285,.6391 vJ ,. 36r25 5

.

.36758 -. 00033 - . 006

A 233,.6392 rr .16339 5 .16922 -.00033 -.006

A 282,.3333 Jl .03721 5 .03751 -.00030 -.006

A 282,.2193 .02516 5

.

.02580 -.00064 -.013

8.764 8.762 .002 .03 8.764 8.756 .008 .09 7.672 7.669 .003 .04 7.674 7.673 .001 .02 7.674 7.673 .001 .02 7.676 7.678 -.002 -.02 7.677 7.684 -.006 -.08

7.678 7.690 -.012 -.15

7.678 7.689 -.010 -.13

7.679 7.693 -.014 -.18

7.679 7.697 -.018 -.23

7.679 7.699 -.019 -.25

7.679 7.702 -.022 -.29

7.679 7.693 -.013 -.18

7.680 7.719 -.039 -.51

7.680 7.685 -.005 -.07

7.680 7.689 -.010 -.13

7.680 7.698 -.019 -.24

7.622 7.619 .003 .04 7.624 7.623 .001 .01 7.624 7.622 .001 .02 7.625 7.627 -.002 -.02

7.627 7.632 -.005 -.07

7.628 7.638 -.010 -.13

7.628 7.640 -.011 -.15

7.629 7.643 -.015 -.19

7.629 7.640 -.011 -.14

7.629 7.625 .004 .05 7.583 7.580 .003 .04 7.585 7.583 .001 .02 7.585 7.584 .001 .01 7.586 7.588 -.002 -.02

7.588 7.593 -.005 -.07

7.589 7.599 -.010 -.13

7.589 7.599 -.010 -.13

7.590 7.601 -.012 -.15

7.590 7.600 -.011 -.14

7.590 7.590 -.000 -.00

7.499 7.497 .002 .03

7.501 7.500 .001 .01 7.503 7.505 -.002 -.02

7.504 7.509 -.005 -.06

7.506 7.513 -.008 -.10

7.506 7.515 -.009 -.12

7.506 7.515 -.009 -.12

7.506 7.510 -.004 -.05

7.507 7.433 .019 . 25

6.530 6.532 -.003 -.04

6,580 6.583 -.003 -.05

6.531 6.582 -.001 -.02

6.533 6.581 .001 .02 6.534 6.573 .006 .09 6.534 6.572 .012 .19 6.585 6.543 .041 .63 6.5G5 6.473 .106 1.61

22
Table BI. (Continued)

•,ID TEhr ^RATUI- E PRESSURE DENSITY

K MPA M0L/Df13 EXP CALC niFF %riiFP EXP CALC BIFF /.ZtlF

A 282 1893 5 02136 5 .02270 - .00004 -.017 6.585 6.443 .142 2.16

A 282 0893 5 01081 c- 01150 - .00069 -.014 6.585 6.322 .263 3.99

A 293 1386 6 38668 6 38502 .00166 .026 5.899 5.904 -.005 -.09

A 29S 1336 6 38663 6 ,38502 .00161 .025 5.899 5.904 -.005 -.09

A 282 3333 5 02445 U .02465 - .00020 -.004 5.903 5.898 .005 .09

A 282 0393 4 99780 4 99800 - .00020 -.004 5.903 5.897 .006 .11

A 231 6893 4 96445 4 96603 - .00158 -.032 5.904 5.842 .062 1.04

B 298 1336 8 39404 8 .39185 .00219 .026 10.617 10.619 -.002 -.02

B 293 1386 8 .39409 8 .39105 .00224 .027 10.617 10.620 -.002 -.02

B 280 0394 4 84374 4 .84224 .00150 .031 10.626 10.633 -.006 -.06

B 279 5394 4 75176 4 .75086 .00090 .019 10.627 10.631 -.004 -.04

B 298 1386 7 22930 7 .23118 - .00188 -.026 8.750 8.745 .005 .06

B 298 1386 7 22931 7 .23113 - .00187 -.026 8.750 8.745 .005 .06

B 282 3693 5 04648 5 .04602 .00046 .009 8.757 8.794 -.037 -.42

B 202 3333 5 04177 5 04143 .00034 .007 8.757 8.786 -.030 -.34

B 282 2143 yj 02663 5 02633 .00030 .006 8.757 8.791 -.034 -.39

B 282 1393 5 02345 5 02317 .00028 .006 8.757 8.791 -.034 -.39

E 282 1893 5 02348 5 .02317 .00031 .006 8.757 8.794 -.038 -.43

B 282 1893 5 02345 »j 02317 .00028 .006 8.757 8.791 -.034 -.39

B 303 1500 7 44551 7 44692 - .00141 -.019 7.602 7.599 .004 .05

B 293 1500 6 86299 6 86327 - .00028 -.004 7.604 7.603 .001 .01

B 298 1500 6 86292 6 86327 - .00035 -.005 7.604 7.603 .001 .02

B 293 1500 6 28229 6 .28176 .00053 .008 7.606 7.609 -.003 -.04

B 289 1500 5 81975 5 .81893 .00082 .014 7.607 7.615 -.008 -.10

B 285 6500 5 41734 5 ,41653 .00076 .014 7.609 7.626 -.018 -.23

B 284 6500 5 30307 5 .30225 .00082 .016 7.609 7.639 -.030 -.39

B 283 6500 5 18886 5 18828 .00058 .011 7.609 7.651 -.042 -.55

B 283 1500 5 13189 5 .13146 .00043 .008 7.609 7.666 -.056 -.74

B 298 1336 6 56543 6 56455 .00088 .013 6.511 6.514 -.003 -.05

B 298 1386 6 56551 6 56455 ,00096 .015 6.511 6.515 -.003 -.05

B 293 13BB 6 08762 6 08714 .00040 .008 6.513 6.515 -.003 -.04

B 289 1390 5 70295 c.- 70280 .00015 .003 6.514 6.515 -.001 -.02

B 285 6391 5 36362 5 36356 .00006 .001 6.515 6.516 -.001 -.02

B 283 6392 5 16741 w) 16734 .00007 .001 6.516 6.518 -.002 -.04

B 282 3333 5 03714 5 03699 .00015 .003 6.516 6.534 -.018 -.28

B 282 239,5 5 02761 c- 02745 .00016 .003 6.516 6.540 -.024 -.37

B 282 1393 u 02242 fi 02236 .00006 .001 6.516 6.526 -.010 -.16

h 298 1386 6 38518 6 38351 .00167 .026 5.894 5.900 -.005 -.09

B 293 1336 6 38512 6 38351 .00161 .025 5.894 5.899 -.005 -.09

B 293 1388 5 96215 J 96127 .00083 .015 5.896 5.899 -.004 -.07

B 239 1390 5 62038 61934 .00054 .010 5.897 5.900 -.004 -.06

B 285 6391 5 31734 5 31702 .00032 .006 5.893 5.901 -.003 -.06

B 283 6392 5 14149 u 14121 .00023 .006 5.893 5.903 -.005 -.08

B 282 3333 5 02474 5 02447 .00027 .005 5.898 5.906 -.007 -.13

B 202 2393 5 01624 5 01598 .00026 .005 5.899 5.906 -.008 -.13

B 282 1393 J 00720 5 00692 .00028 .006 5.899 5.907 -.008 -.14

B 281 9393 4 98901 4 98876 .00025 .005 5.899 5.907 -.009 -.15

B 281 3393 4 97992 4 97964 .00028 .006 5.899 5.909 -.011 -.18

B 281 7393 4 97071 4 97049 .00022 .004 5.899 5.907 -.009 -.15

B 281 6093 4 9,'.579 4 96591 - .00012 -.002 5.899 5.894 .005 .09

B 281 6393 4 96035 4 96132 - .00097 -.020 5.099 5.853 .040 .68

23
TABLE BI. (Continued)

EXP. in TEMPERATURE PRESSURE DENSITY

K MPA M0L/DM3

EXP CALC DIFF %IiIFF EXP CALC DIFF ZDIFF 282.3500 5.04197 5.04084 .00113 .022 7.635 8.563 -.928 -12.15

282.3600 5.04288 5.04197 .00091 .018 7.635 8.499 -.864 -11.32

282.3700 5.04403 5.04311 .00092 .018 7.635 8.483 -.848 -11.11

I 282.3800 5.04518 5.04424 .00094 .019 7.635 8.467 -.832 -10.90

L 282.3900 5.04626 5.04537 ,00089 .018 7.635 8.433 -.798 -10.46

282.4000 5.04744 5.04650 .00094 .019 7.635 8.425 -.790 -10.34

L 282.4100 5.04858 5.04763 .00095 .019 7.635 B.406 -.771 -10.10

282.4200 5.04978 5.04876 .00102 .020 7.635 8.403 -.768 -10.06

282.4300 5.05083 5.04990 .00093 .018 7.635 8.360 -.725 -9.50

282.4500 5.05324 5.05216 .00108 .021 7.635 8.359 -.724 -9.49

I 282.5500 5.06452 5.06349 .00103 .020 7.635 8.159 -.524 -6.87

L 282.65O0 5.07586 5.07483 .00103 .020 7.635 8.019 -.384 -5.02

I 282.7500 5.08723 5.08618 .00105 .021 7.635 7.930 -.295 -3.86

I 282.8500 5.09858 5.09754 .00104 .020 7.635 7.865 -.230 -3.01

L 282.9500 5.10994 5.10890 .00104 .020 7.635 7.821 -.186 -2.44

L 283.0500 5.12136 5.12028 .00108 .021 7.635 7.798 -.163 -2.13

L 283.1500 5.13277 5.13165 .00112 .022 7.635 7.778 -.143 -1.87

283.3500 5.15567 5.15443 .00124 .024 7.635 7.757 -.122 -1.59

284.1500 5.24722 5.24574 .00148 .028 7.635 7.706 -.071 -.93

L 285.1500 5.36197 5.36030 .00167 .031 7.635 7.682 -.047 -,62

286.1500 5.47701 5.47522 .00179 .033 7.635 7.670 -.035 -.46

287.1500 5.59247 5.59047 .00200 .036 7.635 7.664 -.029 -.39

L 288.1500 5.70808 5.70600 .00208 .036 7.635 7.659 -.024 -.32

L 293.1500 6.28886 6.28697 .00189 .030 7.635 7.646 -.011 -.14

L 298.3 500 6.87365 6.87194 .00171 .025 7.635 7.641 -.006 -.08

I 303.1500 7.46149 7.45959 .00190 .025 7.635 7.640 -.005 -.06

L 303.1500 6.84890 6.84568 .00322 .047 6.000 6.008 -.008 -.14

I 303.1500 7.03963 7.03704 .00259 .037 6.500 6.507 -.007 -.11

L 303.1500 7.22319 7.22142 .00177 .025 7.000 7.005 -.005 -.07

L 303.1500 7.40872 7.40769 .00103 .014 7.500 7.503 -.003 -.04

I 303.1500 7.60625 7.60600 .00025 .003 8.000 8.001 -.001 -.01

I 303.1500 7.82674 7.82818 -.00144 -.018 8.500 8.497 .003 .04

I 303.1500 8.08490 8.08845 -.00355 -.044 9.000 8.994 .006 .07

I 303.1500 8.39804 8.40388 -.00584 -.069 9.500 9.492 .008 .09

I 303.1500 8.79026 8.79482 -.00456 -.052 10.000 9.995 .005 .05

I 303.1500 9.28873 9.28491 .00382 .041 10.500 10.503 -.003 -.03

I 298.1500 6.42028 6.41712 .00316 .049 6.000 6.010 -.010 -.17

I 298.1500 6.56526 6.56251 .00275 .042 6.500 6.510 -.010 -.15

L 298.1500 6.70124 6.69887 .00237 .035 7.000 7.009 -.009 -.13

I 298.1500 6.83652 6.83436 .00216 .032 7.500 7.508 -.008 -.10

I 298.1500 6.98029 6.97806 .00223 .032 8.000 8.007 -.007 -.09

I 298.1500 7.14174 7.14057 .00117 .016 8.500 8.503 -.003 -.04

I 298.1500 7.33468 7.33480 -.00012 -.002 9.000 9.000 .000 .00

I 298.1500 7.57508 7.57669 -.00161 -.021 9.500 9.497 .003 .03

I 298.1500 7.88281 7.88568 -.00287 -.036 10.000 9,996 .004 .04

I 290.1500 8.29048 8.28482 .00566 .068 10.500 10.506 -.006 -.06

I 293.1500 5.98672 5.98523 .00149 .025 6.000 6.007 -.007 -.12

I 293.1500 6.08774 6.08581 .00193 .032 6.500 6.510 -.010 -.16

I 293.1500 6.17782 6.17598 .00184 .030 7.000 7.011 -.011 -.15

I 293.1500 6.26526 6.26302 .00224 .036 7.500 7.513 -.013 -.17

I 293.1500 6.35743 6.35471 .00272 .043 8.000 8.014 -.014 -.17

I 293.1500 6.46250 6.46012 .00238 .037 8.500 8.510 -.010 -.12

I 293.1500 6.59227 6.59055 .00172 .026 9.000 9.006 -.006 -.06

I 293.1500 6.76196 6.76051 .00145 .021 9.500 9.504 -.004 -.04

I 293.1500 6.99048 6.98849 .00199 .028 10.000 10.004 -.004 -.04

I 293.1500 7.30284 7.29694 .00590 .081 10.500 10.508 -.008 -.08

24
Table BI. (Continued)

EXP. ID TEMPERATURE

K

PRESSURE IiENSITY MPA M0L/IIM3 EXP CALC niFF XDIFF EXP CALC niFF /CD IFF

1 288. 1500 5.54964 5,54851 .00113 ,020

1 288. 1500 5.60692 5,60585 ,00107 ,019

1 288. 1500 5.65366 5.65247 ,00119 .021

1 288. 1500 5.69652 5.69461 .00191 .033

1 288. 1500 5.74088 5.73834 .00254 .044

1 288. 1500 5.79342 5.79053 .00289 .050

1 288. 1500 5.86313 5.86034 .00279 .048

1 288. 1500 5.96313 5.96052 .00261 .044

1 288. 1500 6.11098 6.10843 .00255 .042

1 288. 1500 6.33296 6.32614 .00682 .108

1 288. 1500 5.67503 5.67373 .00130 .023

1 288. 1500 5.63106 5.63009 .00097 .017

1 284. 1500 5.57352 5.56745 .00607 .109

1 284. 1500 5.42568 5.42329 .00239 .044

1 284. 1500 5.34153 5.33931 .00222 .042

1 284. 1500 5.29548 5.29321 .00227 .043

1 284. 1500 5.27042 5,26832 .00210 .040

1 284, 1500 5.25551 5.25371 .00180 .034

1 284. 1500 5.24964 5.24814 .00150 .029

1 284. 1500 5.24427 5.24298 .00129 .025

1 284, 1500 5.23885 5.23777 .00108 .021

1 284 1500 5.23306 5.23207 .00099 .019

1 284 1500 5.22627 5.22539 .00088 .017

1 284 1500 5.21797 5.21715 .00082 .016

1 284 1500 5.19400 5.19304 .00096 .018

1 284 1500 5.15364 5.15266 .00098 .019

1 283. 1500 5.10345 5.10259 .00086 .017

1 283, 1500 5.11928 5.11850 .00078 .015

1 283 1500 5.12707 5.12620 .00087 .017

1 283, 1500 5.13169 5.13062 .00107 .021

1 283, 1500 5.13594 5.13469 .00125 .024

1 283 1500 5.14271 5.14122 .00149 .029

1 283, 1500 5.15732 5 . 15b56 .00176 .034

1 283, 1500 5.18994 5.18820 .00174 .033

1 283 1500 5.25792 5.25591 .00201 .038

1 283 1500 5.38690 5.38124 .00566 .105

1 283 1500 5.13368 5.13255 .00113 ,022

1 283 1500 5.12950 5.12861 .00089 .017

1 283 1500 5.12379 5.12301 .00078 .015

1 283 3500 5.18470 5.18289 .00181 .035

1 283 3500 5.16820 5.16646 .00174 .034

1 283 3500 5,15981 5.15838 .00143 .028

1 283 3500 5.15692 5.15560 .00132 .026

1 283 .3500 5.15419 5.15308 .00111 .022

1 283 3500 5.15144 5.15047 .00097 .019

1 283 3500 5.14829 5.14743 .00086 .017

1 283 3500 5.14440 5.14356 .00084 .016

1 283 3500 5.13908 5.13832 .00076 .015

1 283 3500 5.12159 5.12076 .00083 .016

1 283 .3500 5.08842 5.08745 .00097 .019

1 282 .5500 5.06449 5.06351 .00098 .019

1 282 .5500 5.06446 5.06344 .00102 .020

1 282 ,6500 5.08928 5.08779 .00149 .029

1 282 .6500 5.07993 5.07866 .00127 .025

1 282 .6500 5.07695 5.07580 .00115 .023

1 282 ,6500 5.07616 5.07511 ,00105 .021

6.000 6.009 -.009 -.15

6.500 6,511 -.011 -.16

7.000 7.014 -.014 -.20

7.500 7.523 -.023 -.30

8.000 8.027 -.027 -.34

8.500 8.524 -.024 -.28

9.000 9.017 -.017 -.19

9.500 9.511 -.011 -.11

10.000 10.007 -.007 -.07

10.500 10.513 -.013 -.12

7.250 7.266 -.016 -.21

6.750 6.760 -.010 -.15

10.500 10.516 -.016 -.16

10.000 10.011 -.011 -.11

9.500 9.518 -.018 -.19

9.000 9.033 -.033 -.37

8.500 8.555 -.055 -.65

8.000 8.074 -.074 -.92

7.750 7.820 -.070 -.90

7.500 7.563 -.063 -.84

7.250 7.301 -.051 -.70

7.000 7.041 -.041 -.59

6.750 6 . 780 -.030 -.45

6.500 6.522 -.022 -.34

6.000 6.016 -.016 -.26

5.500 5.510 -.010 -.17

6.000 6.020 -.020 -.33

6.500 6.537 -.037 -.57

7.000 7.083 -.083 -1.19

7 . 500 7.640 -.140 -1.86

8.000 8.125 -.125 -1.56

8.500 8.576 -.0/6 -.90

9.000 9.040 -.040 -.44

9.500 9.518 -.018 -.19

10.000 10.011 -.011 -.11

10.500 10.517 -.017 -.16

7.750 7 . 888 -.138 -1.78

7.250 7.357 -.107 -1.47

6.750 6.804 -.054 -.80

9.000 9.037 -.037 -.41

8.500 8.575 -.075 -.88

8.000 8.112 -.112 -1.40

7.750 7.874 -.124 -1.59

7.500 7.611 -.111 -1.48

7.250 7.340 -.090 -1.25

7.000 7.065 -.065 -.93

6.750 6.798 -.048 -.71

6 . 500 6.532 -.032 -.49

6.000 6.018 -.018 -.29

5.500 5.511 -.011 -.20

7.650 8.150 -.500 -6.53

7.600 8.140 -.540 -7.10

9.000 9.047 -.047 -.52

8.500 8.615 -.115 -1.35

8.000 8.270 -.270 -3..67 7.750 8.101 -.351 -4.53

25
Table BI. (Continued)

EXP. ID TEMPERATURE PRESSURE

MPA

DENSITY

M01./I.IM3

EXP CALC DIFF %IiIFF EXP CALC tUFF l^iDIFF

1 282.6500 5.07590 5.07487 .00103 .020 7.650 8.030 -.380 -4 97

1 282.6500 5.07575 5.07475 .00100 .020 7.600 7.985 -.385 -5 07

1 282.6500 5.07556 5.07452 .00104 .021 7.500 7.923 -.423 — 5 63

1 282.6500 5.07481 5.07386 .00095 .019 7.250 7.625 -.375 -5 17

1 282.6500 5.07383 5.07292 .00091 .018 7.000 7.240 -.240 -3 43

1 282.6500 5.07221 5.07136 .00085 .017 6.750 6.870 -.120 -1 //

1 282.6500 5.06950 5.06869 .00081 .016 6.500 6.563 -.063 - 96

1 282.6500 5.05791 5.05694 .00097 .019 6.000 6.028 -.028 - 46

1 282.8500 5.10045 5.09928 .00117 .023 8.000 8.183 -.183 -2 .28

1 282.8500 5.09920 5.09804 .00116 .023 7.750 7.985 -.235 -3 ,03

1 282.8500 5.09867 5.09760 .00107 .021 7.650 7.883 -.233 -3 .05

1 282.8500 5.09845 5.09739 .00106 .021 7.600 7.838 -.238 -3 .13

1 282.8500 5.09804 5.09696 .00108 .021 7.500 7.749 -.249 -3 .32

1 282.8500 5.09675 5.09579 .00096 .019 7.250 7.453 -.203 — ':> .80

1 282.8500 5.09507 5.09428 .00079 .016 7.000 7.121 -.121 -1 . 73

1 282.1500 5.20165 5.19681 .00484 .093 10.500 10.517 -.017 - .16

1 282.1500 5.09211 5.09070 .00141 .028 10.000 lO.OOV -.009 - .09

1 282.1500 5.04078 5.03976 .00102 .020 9.500 9.516 -.016 - .17

1 282.1500 5.02694 5.02591 .00103 .021 9.200 9.231 -.031 - .34

1 282.1500 5.02425 5.02313 .00112 .022 9.100 9.144 -.044 - .48

1 282.1500 5.02198 5.02105 .00093 .018 9.000 9.048 -.048 - .54

1 282.1500 5.01959 5.01856 .00103 .021 8.802 8.902 -.100 -1 .14

1 282.1500 5.01843 5.01757 .00086 .017 6.400

1 282.1500 5.01741 5.01655 .00086 .017 6.300 6.382 -.082 -1 .30

1 282.1500 5.01606 5.01514 .00092 .018 6.200 6.262 -.062 -1 .00

1 282.1500 5.01181 5.01091 .00090 .018 6.000 6.035 -.035 - .59

1 282.1500 5.00892 5.00794 .00098 .020 5.900 5.931 -.031 - .52

1 282.1500 5.00530 5.00431 .00099 .020 5.800 5.825 -.025 - ,44

1 282.1500 4.98973 4.98863 .00110 .022 5.500 5.517 -.017 - ,31

1 282.2500 5.03540 5.03429 .00111 .022 9.000 9.051 -.051 - ,56

1 282.2500 5.03228 5.03127 .00101 .020 8.800 8.882 -.082 - .93

1 282.2500 5.03142 5.03039 .00103 .020 8.700 8.814 -.114 -1 ,31

1 282.2500 5.03089 5.02V82 .00107 .021 8.600 8.761 -.161 -1 .88

1 282.2500 5.03035 5.02956 .00079 .016 6.750

1 282.2500 5.02995 5.02904 .00091 .018 6.600

1 282.2500 5.02939 5.02843 .00096 .019 6.500 6.687 -.187 _'7 .88

1 282.2500 5.02842 5.02755 .00087 .017 6.400 6.499 -.099 -1 ,55

1 282.2500 5.02118 5.02016 .00102 .020 6.000 6.037 -.037 - ,62

1 282.2500 4.99803 4.99692 .00111 .022 5.500 5.517 -.017 - ,30

1 282.3500 5.23803 5.23354 .00449 .086 10.500 10.515 -.015 - .14

1 282.3500 5.12506 5.12355 .00151 .030 10.000 10.010 -.010 - .10

1 282.3500 5.07067 5.06918 .00149 .029 9.500 9.521 -.021 - ,22

1 282.3500 5.04902 5.04759 .00143 .028 9.000 9.058 -.058 - .64

1 282.3500 5.04295 5.04166 .00129 .026 8.500 8.697 -.197 -2 ,32

1 282.3500 5.04200 5.04087 .00113 .023 8.000 8.568 -.568 -7 ,10

1 282.3500 5.04200 5.04084 .00116 .023 7.750 8.568 -.818 -10 ,55

1 282.3500 5.04194 5.04084 .00110 .022 7.500 8.557 -1.057 -14 ,10

1 282.3500 5.04186 5.04082 .00104 .021 7.250 8.542 -1.292 -17 ,82

1 282.3500 5.04178 5.04067 .00111 .022 7.000 8.526 -1.526 -21 ,80

1 282.3500 5.03966 5.03854 .00112 .022 6.500 6.657 -.157 -2 .42

1 282.3500 5.03051 5.02938 .00113 .022 6.000 6.039 -.039 - .64

1 282.3500 5.00613 5.00520 .00093 .019 5.500 5.513 -.013 - ,25

1 282.4000 5.04746 5.04650 .00096 .019 7.650 8.430 - . 780 -10 .19

1 282.4000 5.04741 5.04649 .00092 .018 7.600 8.417 -.817 -10 .75

1 282.4500 5.05343 5.05245 .00098 .019 8.000 8.405 -.405 -5 .07

1 282,4500 5.05322 5.05224 .00098 .019 7.750 8.354 -.604 -7 ,80

26
Table BI. (Continued)

EXP. ID TEMPERATURE PRESSURE DENSITY

MPA H0L/riM3 EXP CALC niFF %LiIPF EXP CALC UlFF %DiFF

282 .4500 5 .05309 5.05217 .00092 .018 7 .650 8 317 -.667 -8.72

282 .4500 5 .05309 5.05214 .00095 .019 7 .600 8 317 -.717 -9.44

282 .4500 5 05303 5.05208 .00095 .019 7 .500 8 299 -.799 -10.65

282 4500 5 05283 5.05187 .00096 .019 7 250 8 225 -.975 -13.45

282 4500 5 05235 5.05146 .00089 .018 7 .000 7 901 -.901 -12.87

281 1500 5 01853 5.01448 .00405 .081 10 500 10 516 -.016 -.16

281 1500 4 92924 4.92831 .00093 .019 10 000 10 008 -.008 -.08

281 1500 4 91885 4.91817 .00068 .014 9 899 9 906 -.007 -.07

281 1500 4 91325 4.91263 .00062 .013 9 833 9 841 -.008 -.08

281 1500 4 91168 4.91113 .00055 .011 9 813 9 821 -.007 -.07

281 1500 4 91022 4.90969 .00053 .011 9 794 9 801 -.007 -.08

281 1500 4 90938 4.90876 .00062 .013 9 .780 9 789 -.009 -.09

281 1500 4 90885 4.90831 .00054 .011 9 .774 9 782 -.008 -.08

281 1500 4 90837 4.90788 .00049 .010 9 767 9 7 75 -.007 -.07

281 6500 4 97260 4.97177 .00083 .017 9 592 9 606 -.014 -.15

281 6500 4 96918 4.96838 .00080 .016 9 530 9 546 -.016 -.16

281 ,6500 4 96762 4.96693 .00069 .014 9 500 9 515 -.015 -.15

281 6500 4 96606 4.96529 .00077 .016 9 463 9 481 -.018 -.19

281 6500 4 96472 4.96406 .00066 .013 9 432 9 449 -.017 -.18

281 6500 4 96393 4.96317 .00076 .015 9 408 9 429 -.021 — '> :> 281 6500 4 96300 4.96233 .00067 .013 5 900

281 6500 4 96067 4.95970 .00097 .020 5 800 5 aj,4 -.034 -.58

281 6500 4 95740 4.95631 .00109 .022 5 700 5 730 -.030 -.52

280 1500 4 83757 4.83472 .00285 .059 10 500 10 514 -.014 -.13

280 1500 4 81814 4.81631 .00183 .038 10 400 10 411 -.011 -.10

280 1500 4 81214 4.81065 .00149 .031 10 366 10 375 -.009 -.09

280 1500 4 80596 4.80505 .00091 .019 10 329 10 335 -.006 -.06

280 1500 4 80263 4.80183 .00080 .017 10 .307 10 313 -.006 -.05

n 283 6500 5 14322 5.14253 .00069 .013 5 .904 ^ 916 -.012 -.20

2 285 6500 5 31888 5.31860 .00028 .005 5 904 5 907 -.003 -.05

o 289 1500 5 62216 5.62196 .00020 .004 5 904 5 906 -.001 -.02

r> 293 1500 5 96416 5.96417 -.00001 - . 000 i=- 904 5 904 .000 .00

o 298 1500 6 38814 6.38761 .00053 .008 5 904 5 906 -.002 -.03

'} 283 6500 5 16045 5.15960 .00085 .017 6 254 6 276 -.022 -.35

'p 285 6500 5 34820 5.34745 .00075 .014 6 254 6 264 -.010 -.17

1) 289 1500 5 67198 5.67157 .00041 .007 6 254 6 257 - . 003 -.05

n 293 1500 6 03833 6.03806 .00027 .004 6 254 6 255 -.001 -.02

O 298 1500 6 49362 6.49257 .00105 .016 6 254 6 258 -.004 -.06

n 283 6500 5 16362 5.16340 .00022 .004 6 357 6 363 -.006 -.10

o 285 6500 5 35447 5.35460 -.00013 -.002 6 357 6 355 .002 .03

n 289 1500 5 68487 5.68477 .00010 .002 6 357 6 358 -.001 -.01

2 293 1500 6 05796 6.05841 -.00045 -.007 6 357 6 355 .002 .04

o 298 1500 6 52247 6.52218 .00029 .005 6 357 6 358 -.001 -.02

2 283 .6500 5 .17651 5.17571 .00080 .015 6 815 6 855 -.040 -.58

2 285 6500 5 38111 5.38112 -.00001 -.000 6 815 6 815 .000 .00

r* 289 1500 5 73825 5.73774 .00051 .009 6 815 6 820 -.005 -.07

n 293 1500 6 14315 6.14340 -.00025 -.004 6 fil5 6 814 .001 .02

o 298 1500 6 64913 6.64900 .00013 .002 6 815 6 816 -.000 -.01

2 283 6500 5 17738 5.17668 .00070 . 1 ,5 6 863 6 899 -.036 — • 52

n 285 6500 5 38421 5.38352 .00069 .013 6 863 6 877 -.014 -.20

n 289 1500 5 74278 5.74291 -.00013 -.002 6 863 6. 862 .001 .02

n 293 1500 6 15210 6.15195 .00015 .002 6 863 6. 864 -.001 -.01

9 298 1500 6 66181 6.66204 -.00023 -.003 6 863 6 862 .001 .01

o 283 6500 5 18517 5.18372 .00145 .028 7 284 7. 385 -.101 -1.39

O 285 6500 5 40368 5.40273 .00095 .018 7 284 7. 306 -.022 -.30

27
Table BI. (Continued)

EXP. in TEMPERATURE PRESSURE

MPA

DENSITY

M0L/DM3

EXP CALC DIFF XIIIFF EXP CALC DIFF XDIFF

2 289 .1500 5.78719 5.78619 .00100 .017 7.284 7.294 -.010 -.14

2 293 .1500 6.22585 6.22530 .00055 .009 7.284 7.287 -.003 -.04

2 298 ,1500 6.77549 6.77535 .00014 .002 7.284 7,284 -.000 -.01

2 283 .6500 5.18330 5.18655 -.00325 -.063 7.484 7,255 .229 3,06

2 285 6500 5.41285 5.41128 ,00157 .029 7.484 7,521 -.037 -.49

2 289 1500 5.80755 5.80640 .00115 .020 7.484 7.496 -.011 -.15

2 293 .1500 6.26115 6.26025 .00090 .014 7.484 7.489 -.005 -.07

2 298 1500 6.82979 6.83002 -.00023 -.003 7.484 7.483 .001 .01

2 283 ,6500 5.19154 5.18979 .00175 .034 7.718 7.839 -.121 -1.57

2 285 ,6500 5.42238 5.42132 .00106 .020 7.718 7.742 -.024 -.31

2 289 ,1500 5.83135 5.83039 .00096 .016 7.718 7.727 -.009 -.12

2 293 ,1500 6.30224 6.30193 .00031 .005 7.718 7.720 -.002 -.02

2 298 ,1500 6.89369 6.89543 -.00174 -.025 7.718 7.712 .006 .08

2 283 ,6500 5.19785 5.19576 .00209 .040 8.102 8.214 -.112 -1.38

'y 285 ,6500 5.44163 5.43920 .00243 .045 8.102 8.149 -.047 -.58

2 289 .1500 5.87440 5.87253 .00187 .032 8.102 8.118 -.016 -.20

2 293 ,1500 6.37711 6.37473 .00238 .037 8.102 8.114 -.012 -.15

2 298 ,1500 7.00764 7.00923 -.00159 -.023 8.102 8.097 .005 .06

2 283 ,6500 5.21258 5.21123 .00135 .026 8.713 8.749 -.036 -.42

2 285 6500 5.47945 5.47747 .00198 .036 8.713 8.738 -.025 -.28

2 289 1500 5 . 95566 5.95499 .00067 .011 8.713 8.717 -.004 -.05

2 293 1500 6.51140 6.51178 -.00038 -.006 8.713 8.711 .001 .02

9 298 1500 7.21383 7.21847 -.00464 -.064 8.713 8.701 .012 .14

*:) 283 6500 5.21950 5.21655 .00295 .056 8.846 8.910 -.064 -.73

2 285 6500 5.49165 5.48863 .00302 .055 8.846 8.879 -.033 -.38

2 289. 1500 5.97733 5.97699 .00034 .006 8.846 8.848 -.002 -.02

2 293. 1500 6.54496 6.54687 -.00191 -.029 8.846 8.839 .007 .08

2 298. 1500 7.26451 7.27067 -.00616 -.085 8.846 8.831 .015 .17

9 283. 6500 5.24750 5.24662 .00088 .017 9.326 9.336 -.010 -.11

2 285. 6500 5.54389 5.54281 .00108 .020 9.326 9.334 -.008 -.08

2 289 1500 6.07423 6.07457 -.00034 -.006 9.326 9.325 .001 .02

2 293. 1500 6.69265 6.69588 -.00323 -.048 9.326 9.317 .009 .10

2 298. 1500 7.47712 7.48608 -.00896 -.120 9.326 9.308 .018 .19

2 283. 6500 5.28952 5.28946 .00006 .001 9.708 9.709 -.000 -.00

2 285. 6500 5.61008 5.60834 .00174 .031 9.708 9.717 -.008 -.09

2 289. 1500 6.17898 6.17981 -.00083 -.014 9.708 9.705 .003 .03

2 293. 1500 6.84089 6.84716 -.00627 -.092 9.708 9.694 .014 .15

o 298. 1500 7.68440 7.69590 -.01150 -.150 9.708 9.689 .019 .20

2 283. 6500 5.50719 5.50544 .00175 .032 10.587 10.591 -.005 -.04

2 285. 6500 5.89065 5.88784 .00281 .048 10.587 10.593 -.006 -.06

2 289. 1500 6.56807 6.56873 -.00066 -.010 10,587 10.586 .001 .01

9 293. 1500 7.35645 7.36051 -.00406 -.055 10.587 10.581 .005 .05

2 298 1500 8.35838 8.36512 -.00674 -.081 10.587 10.580 .007 .07

3 283 1700 5.10770 5.10700 .00070 .014 6.060 6.077 -.017 -.28

3 287 3700 5.48740 5.48663 .00077 .014 6.060 6.067 -.007 -.11

3 293 3400 6.01530 6.01477 .00053 .009 6.060 6.062 - . 002 -.04

3 298 1900 6.43890 6.43758 .00132 .021 6.056 6.060 -.004 -.07

3 285. 5400 5.42540 5.42385 .00155 .029 8.063 8.095 -.032 -.40

3 291. 9000 6.21100 6.21050 .00050 .008 8.063 8.066 -.003 -.04

3 292. 7500 6.31690 6.31689 .00001 .000 8,063 8.063 -.000 -.00

3 293. 1500 7.20000 7.20233 -.00233 -.032 10.362 10.358 .004 .03

3 293. 6900 7.30330 7.30549 -.00219 -.030 10,362 10.359 .003 .03

3 298. 1400 7.99060 8.02350 -.03290 -.412 10,190 10.147 .043 .42

3 298. 1400 6.99690 6.99876 -.00186 -.027 8.072 8.066 .006 .07

3 298 1400 6.69610 6.69971 -.00361 -.054 7.007 6.994 .013 .19

28
Table BII. Comparison of experimental saturation

pressures with the present formulation,

EXP TEMPERATURE PRESSURE DfcNSITY

ID. K MPA M0L/riM3 EXP CALC BIFF y.lilFF 279.1500 4.69367 4.69366 .00001 .0002

280.1500 4.79973 4.79939 .00034 .007

281.1500 4.90813 4.90753 .00006 .012

281.6500 4.96331 4.96256 .00075 .015

282.1500 5.01915 5.01831 .00084 .017

282.2000 5.02481 5.02393 .00088 .018

282.2500 5.03046 5.02956 .00090 .018

282.3000 5.03612 5.03519 .00093 .018

A 279.4394 4.72372 4.72402 -.00030 -.006 10.552

A 2B0.63V4 4.85179 4.85200 -.00021 -.004 10.032

A 280.5894 4.84640 4.84660 -.00020 -.004 10.032

A 280.5844 4.84596 4.84606 -.00010 -.002 10.032

A 281.7393 4.97264 4.97246 .00013 .004 9.293

A 281.6893 4.96707 4.96692 .00015 .003 9.293

A 281.7393 4.97271 4.97246 .00025 .005 9.293

A 282.0693 5.00943 5.00933 .00015 .003 8.917

A 282.0733 5.00997 5.00985 .00012 .002 8.917

A 282.0493 5.00729 5.00702 .00027 .005 8.917

A 282.1632 5.02002 5.01994 .00008 .002 8.764

A 282.1380 5.01718 5.01696 .00022 .004 8.764

A 281.1500 4.90746 4.90753 -.00007 -.001 7.680

A 282.0500 5.00720 5.00710 .00010 .002 7.680

A 281.7500 4.97377 4.97365 .00012 .002 7.680

A 281.4500 4.94055 4.94047 .00008 .002 7.630

A 281.7500 4.97373 4.97365 .00008 .002 7.630

A 282.3440 5.04018 5.04016 .00002 .000 7 . 680

A 282.3440 5.0401.9 5.04016 .00003 .001 7.630

A 282.3440 5,04024 5.04016 .00008 .002 7.630

A 281.7500 4.97366 4.97365 .00001 .000 7.629

A 282.3440 5.04007 5.04016 -.00009 -.002 7.629

A 281.7500 4.97366 4.97365 .00001 .000 7.590

A 281.7500 4.97365 4.97365 -.00000 -.000 7.590

A 282.3440 5.04016 5.04016 .00000 .000 7.590

A 282.3440 5.04011 5.04016 -.00005 -.001 7.507

A 280.6394 4.35177 4.85200 -.00023 -.005 6.585

A 281.6893 4.96654 4.96692 -.00038 -.008 6.585

A 281.6893 4.96655 4.96692 -.00037 -.007 6.585

A 281.1393 4.90608 4.90636 -.00028 -.006 6.585

A 281.4393 4.93896 4.93929 -.00033 -.007 6.585

A 281.4393 4.93780 4.93929 -.00149 - . 030 5.904

A 281.4393 4.93779 4.93929 -.00150 -.030 5.904

A 280.6394 4.85132 4.85200 -.00068 -.014 5.904

A 279.4394 4.72339 4.72402 -.00063 -.013 5.904

B 282.1393 5.01753 5.01711 .00042 .008 8.757

If 282.0893 5.01192 5,01150 .00042 .008 8.757

B 282.0393 5.00628 5.00590 .00038 .008 8.757

B 281.1500 4.90747 4.90753 -.00006 -.001 7.610

B 281.4500 4.94046 4.94047 -.00001 -.000 7.610

B 281.7500 4.97369 4.97365 .00004 .001 7.610

B 282.0500 5.00718 5.00710 .00003 .002 7.610

B 282.0500 5.00724 5.00710 .00014 .003 7.610

B 282.1500 5.01841 5.01S31 .00010 .002 7.610

B 282.2500 5.02967 5.02956 .00011 .002 7.610

B 282.3440 5.04045 5.04016 .00029 .006 7.610

B 282.3440 5.04044 5.04016 .00028 .005 7.610

B 281.7500 4.97377 4.97365 .00012 .002 7.610

B 281.7500 4.97369 4.97365 .00004 .001 7.610

B 281.6893 4.96693 4.96692 .00001 .000 6.516

B 281.4393 4.93935 4.93929 .00006 .001 6.516

B 282.1893 5.02242 5.02236 .00006 .001 6.516

B 282.1393 5.01690 5.01711 -.00021 -.004 6.516

B 282.0893 5.01135 5.01150 -.00015 -.003 6.516

B 282.0393 5.00573 5.00590 -.00017 -.003 6.516

B 281.7393 4.97239 4.97246 -.00007 -.001 6.516

B 281.4393 4.93925 4.93929 -.00004 -.001 6.516

B 281.4393 4.93873 4.93929 -.00056 -.011 5.399

B 281.1393 4.90599 4.90636 -.00037 -.007 5.899

29
Table Bill. Comparison of experimental coexisting

densities with the present formulation

EXP TEMPERATURE DENSITY

ID. K M0L/DM3

EXP CALC DIFF '/.lilF 279.150 10.674 10.692 -.018 -.17

279.150 4.724 4.711 .013 .28

280.150 10.290 10.290 .000 .00

280.150 5.071 5.073 -.002 -.05

281.150 9.767 9.762 .005 .05

281.150 5.546 5.559 -.013 -.24

281.650 9.387 9.390 -.003 -.04

281,650 5.911 5.910 .001 .02

282.150 8.780 8.770 .010 .12

282.150 6.489 6.509 -.020 -.30

A 279.523 10.552 10.551 .001 .01

A 280.697 10.032 10.024 .008 .08

A 281.781 9.293 9.267 .026 .28

A 282.084 8.917 8.887 .030 .34

A 282.165 8.764 8.739 .025 .29

A 281.630 5.904 5.893 .011 .18

B 281.660 5.899 5.919 -.020 -.34

B 282.165 8.757 8.739 .018 .20

B 279.317 10.627 10.630 -.003 -.03

30
Table BIV. Comparison of the experimental speed

of sound data with the present formulation,

EXP. ID DENSITY TEHPERATURE

M0L/DM3 K

298.15

293.15

288.15

284.15

282.35

281.65

298.15

293.15

288.15

284.15

282.35

298.15

293.15

288.15

284.15

282.35

298.15

293.15

288.15

284.15

298.15

293.15

288.15

284.15

298.15

293.15

288.15

284.15

298.15

293.15

288.15

284.15

282.35

298.15

293.15

288.15

284.15

282.35

298.15

293.15

288.15

284.15

282.35

281.65

281.15

298.15

293.15

288.15

284.15

282.35

281.65

281. 15 280.15

SOUND yELOCITY

GAM 5 * 500

GAM 5. 549

GAM 5

«

580

GAM 5. 603

GAM 5 * 613

GAM 5

.

616

GAM 6. 000

GAM 6. 057

GAM 6. 099

GAM 6. 125 GAM 6 136 GAM 6 500

GAM 6 570

GAM 6 619 GAM 6 648

GAM 6 660

GAM 7 000

GAM 7 082

GAM 7 139 GAM 7 .171 GAM 7 500

GAM 7 .594 GAM 7 659

GAM 7 .695 GAM 8 .000 GAM 8 .104 GAM 8 ,179 GAM 8 .219 GAM 8 .500 GAM 8 .611 GAM 8 ,698 GAM 8 742 GAM 8 757 GAM 9 000

GAM 9 111 GAM 9 214 GAM 9 263

GAM 9 281 GAM 9 500

GAM 9 603

GAM 9 725 GAM 9 .783 GAM 9 802

GAM 9 ,809 GAM 9 814

GAM 10 000

GAM 10 088

GAM 10 227 GAM 10 298 GAM 10 321 GAM 10 328

GAM 10 334

GAM 10 344

M/S

EXP CALC DIFF %DIFF

241 910 241.055 .855 .35

232. 932 232.661 .271 .12 222 i 628 222.961 -.333 -.15

212. 166 212.958 -.792 -.37

205. 512 206.612 -1.100 -.54

201. 862 203.264 -1.402 -.69

241. 573 240.766 .807 .33 231 574 231.315 .259 .11 219 513 219.808 -.295 -.13

205 844 206.628 -.784 -.38

194 091 195.808 -1.717 -.88

242 772 242.006 .766 .32 231 740 231.462 .278 .12 217 774 217.942 -.168 -.08

200 183 200.702 -.519 -.26

174 ,989 179.834 -4.845 -2.77

245 ,751 245.075 .676 .28 233 ,763 233.505 .258 .11 217 894 217.962 -.068 -.03

196 ,298 196.498 -.200 -.10

250 ,886 250.338 .548 . 22 238 ,059 237.944 .115 .05 220 , 575 220.651 -.076 -.03

196 .030 195.816 .214 .11 258 .502 258.204 .298 .12 245 .187 245.313 -.126 -.05

226 .697 226.881 -.184 -.08

200 .896 200.342 .554 .28 269 .043 269.075 -.032 -.01

255 .621 256.097 -.476 -.19

236 .918 237.450 -.532 — 22 211 682 211.236 .446 .21 185 ,537 182.228 3.309 1.78

282 854 283.285 -.431 -.15

269 788 270.527 -.739 -.27

251 935 252.829 -.894 -.35

228 793 228.735 .058 .03 210 086 208.576 1.510 .72 300 682 301.021 -.339 -.11

287 875 288.593 -.718 -.25

271 ,836 272.975 -1.139 -.42

251 ,845 252.209 -.364 -.14

238 ,193 237.495 .698 .29 231 ,047 229.618 1.429 .62 224 ,901 222.440 2.461 1.09

3'^2 343 322.283 .060 .02 309 818 310.092 -.274 -.09

296 382 297.219 -.837 -.28

279 924 280.329 -.405 -.14

269 661 269.404 .257 .10 264 938 264.150 .788 .30 261 152 260.014 1.138 .44 252 477 249.908 2.56.9 1.02

31
Table BV. Comparison of the isobaric enthalpy differences

[21] with the present formulation.

T4„ T Inlet H(exp) H(eqn) AH(exp) AH(eqn) Diff % Diff

(o.) fop^ Pressure (J/g) (J/g) (J/g) (J/g) (J/g)

6.934 9.372 5.1755 25.367 25.591

6.928 9.709 5.1749 31.816 32.014

6.931 10.041 5.1749 41.557 41.447

6.934 10.192 5.1748 49.713 48.937

6.933 10.290 5.1748 58.592 57.456

6.934 10.356 5.1748 68.191 67.115

6.936 10.431 5.1747 82.142 80.619

6.931 10.492 5.1749 89.603 88.760

6.932 10.537 5.1749 93.449 93.372

6.932 10.648 5.1749 101.400 101.519

6.931 10.823 5.1747 109.668 109.967

6.930 11.080 5.1747 118.258 118.257

6.449 6.423 .026 0.4

9.741 9.433 .308 3.2

8.156 7.490 .666 8.2

8.879 8.519 .360 4.0

9.599 9.659 -.060 -0.63

13.951 13.504 .447 3.2

7.461 8.141 -.680 -9.1

3.846 4.612 -.766 -19.9

7.951 8.147 -.196 -2.5

8.268 8.448 -.180 -2.8

8.590 8.290 .300 3.55

32
APPENDIX C

Tables of Thermodynamic Properties

33
Tab! e CI. The thermodynamic properties of ethylene in the

critical reg ion as a function of temperature al ong isoc hores

5. 75 M0L/DM3 ISOCHORE

MfERATURE PRESSURE ISOTHERM

DERIV. ISOCHORE

DERIV. INTERNAL

ENERGY

ENTHALPY ENTROPY CV CP SOUND

VELOCITY

K MPA hPA.DM3/hOL MPA/K J/MOL J/MOL J/MOL.

K

J/MOL.

K

M/S

279.500 4.73040 .0000 .1054 22225.4 23048.1 167.139 169.9

280.000 4.78338 .0000 .1066 22311.0 23142.9 167.445 172.8

280.500 4.83695 .0000 .1078 22398.3 23239.5 167.757 176.6

281.000 4.89114 .0000 .1090 22488.0 23338.6 168.076 182.2

281.500 4.94477 .0306 .0891 22573.8 23433.7 168.381 62.6 2267.7 198.9

282.000 4.98903 .0409 .0880 22604.3 23472.0 168.490 59.7 1677.1 202 ,

2

282.500 5.03284 .0504 .0873 22633.7 23508.9 168.594 57.8 1349.1 204,8

283.000 5.07632 .0596 .0867 22662.2 23545.0 168.694 56.3 1135.7 207.0

283.500 5.11954 .0686 .0862 22690.0 23580.3 168.793 55 .

1

984.3 208.9

284.000 5.16253 .0774 .0858 22717.3 23615.1 168.889 54.1 870.6 210.7

284.500 5.20533 .0862 .0854 22744.2 23649.4 168.983 53.3 781.9 212.3

285.000 5.24797 .0949 .0851 22770.6 23683.3 169.076 52.6 710.6 213.8

285.500 5.29046 .1036 .0848 22796.8 23716.8 169.168 52,0 652.0 215.2

286.000 5.33281 .1122 .0846 22822.6 23750.1 169.258 51.4 602.9 216.6

286.500 5.37505 .1209 .0844 22848.2 23783.0 169.348 50.9 561,1 217.9

287.000 5.41717 .1295 .0841 22873.5 23815.7 169.436 50.5 525.2 219.1

287.500 5.45920 .1381 .0840 22898.7 23848.1 169.524 50.1 493.9 220.3

288.000 5.50113 .1467 .0838 22923.6 23880.4 169.610 49.7 466.4 221.5

288.500 5.54297 .1553 .0836 22948.4 23912.4 169.696 49,4 442,1 222,6

289.000 5.58474 .1639 .0834 22973.0 23944.3 169.782 49.1 420.4 223,7

289.500 5.62642 .1726 .0833 22997.5 23976.0 169.866 48.8 400,9 224.8

290.000 5.66804 .1812 .0832 23021.9 24007.6 169.950 48.6 383.3 225 .

8

291.000 5.75107 .1985 .0829 23070.2 24070.4 170.117 48.1 352.9 227,8

292.000 5.83385 .2158 .0827 23118.1 24132.6 170.281 47.7 327.4 229.8

293.000 5.91641 .2331 .0825 23165.6 24194.5 170.443 47.3 305.8 231.7

294.000 5.99877 .2505 .0823 23212.8 24256.0 170.604 47.0 287,2 233.5

295.000 6.08094 .2680 .0821 23259.6 24317.2 170.763 46.8 271,1 235,3

296.000 6.16294 .2855 .0819 23306.3 24378.1 170.921 46.5 256.9 237.1

297.000 6.24476 .3030 .0818 23352.7 24438.7 171.078 46.3 244.4 238,8

298.000 6.32644 .3206 .0816 23398.9 24499.1 171.233 46.1 233.3 240,5

299.000 6.40797 .3382 .0815 23444.9 24559.3 171.387 45.9 223,3 242.1

300.000 6.48936 .3559 .0813 23490.7 24619.3 171.540 45.8 214,4 243.8

34
Table CI. (Continued)

6.00 H0L/DH3 ISOCHORE

MPERATURE PRESSURE ISOTHERM

DERiy.

ISOCHORE

LiERiy. INTERNAL ENERGY

ENTHALPY ENTROPY cy CP SOUND

VELOCITY

K HPA MPA.DM3/M0L MPA/K J/hOL J/MOL J/MOL.

K

J/MOL.

K

M/S

279.500 4.73040 .0000 .1054 22046.3 22834.7 166.376 165.2

280.000 4.78338 .0000 .1066 22129.5 22926.7 166.673 167.9

280.500 4.83695 .0000 .1078 22214.4 23020.5 166.976 171.6

281.000 4.89114 .0000 .1090 22301.4 23116.6 167.286 177.0

281.500 4.94598 .0000 .1103 22391.9 23216.2 167.608 185.7

282.000 4.99700 .0237 .0929 22455.7 23288.5 167.834 64.1 2916.6 196.1

282.500 5.04318 .0331 .0919 22486.9 23327.4 167.945 60.8 2062.1 200.0

283.000 5.08893 .0420 .0911 22516.7 23364.8 168.050 58.7 1613.3 202.9

283.500 5.13436 .0507 .0906 22545.6 23401.3 168.152 57.0 1331.5 205.4

284.000 5.17953 .0593 .0901 22573.8 23437.1 168.252 55.8 1136.6 207.5

284.500 5.22450 .0678 .0897 22601.4 23472.2 168.349 54.7 993.3 209.5

285.000 5.26929 .0763 .0894 22628.5 23506.8 168.444 53.8 883.3 211.2

285.500 5.31392 .0848 .0891 22655.3 23540.9 168.538 53.1 796.0 212.9

286.000 5.35842 .0933 .0889 22681.7 23574.7 168.630 52.4 725.1 214.4

286.500 5.40280 .1018 .0886 22707.7 23608.2 168.721 51.8 666.2 215.9

287.000 5.44706 .1103 .0884 22733.5 23641.4 168.811 51.3 616.7 217.3

287.500 5.49123 .1188 .0882 22759.1 23674.3 168.900 50.9 574.3 218.7

288.000 5.53531 .1273 .0881 22784.4 23706.9 168.988 50.4 537.7 219.9

288.500 5.57930 .1359 .0879 22809.5 23739.4 169.075 50.1 505.8 221.2

289.000 5.62321 .1444 .0877 22834.5 23771.7 169.162 49.7 477.7 222.4

289.500 5.66705 .1530 .0876 22859.2 23803.7 169.247 49.4 452.7 223.6

290.000 5.71082 .1616 .0875 22883.9 23835.7 169.332 49.1 430.4 224.7

291.000 5.79817 .1789 .0872 22932.7 23899.1 169.500 48.6 392.4 226.9

292.000 5.88529 .1963 .0870 22981.1 23962.0 169.666 48.1 361.0 229.1

293.000 5.97220 .2138 .0868 23029.0 24024.4 169.830 47.8 334.7 231.1

294.000 6.05893 .2313 .0866 23076.6 24086.4 169.992 47.4 312.4 233.1

295.000 6.14548 .2489 .0865 23123.9 24148.1 170.153 47.1 293.3 235.0

296.000 6.23188 .2666 .0863 23170.9 24209.5 170.312 46.9 276.6 236.9

297.000 6.31812 .2844 .0862 23217.6 24270.6 170.470 46.6 262.0 238.7

298.000 6.40422 .3022 .0860 23264.1 24331.5 170.626 46.4 249.1 240.5

299.000 6.49019 .3201 .0859 23310.4 24392.1 170.781 46.2 237.7 242.3

300.000 6.57603 .3381 .0858 23356.5 24452.5 170.935 46.0 227.4 244.0

35
Table CI. (Continued)

6,'. M0L/DM3 ISOCHORE

MPERATURE PRESSURE ISOTHERM

IiERiy.

ISOCHORE

DERIV.

INTERNAL

ENERGY

ENTHALPY ENTROPY cy CP SOUNli

VELOCITY

K MPA MPA.IIM3/M0L MPA/K J/MOL J/MOL J/MOL.

K

J/MOL.

K

M/S

279.500 4.73040 .0000 .1054 21881.5 22638.3 165.673 160.8

280.000 4.78338 .0000 .1066 21962.5 22727.8 165.963 163.5

280.500 4.83695 .0000 .1078 22045.1 22819.0 166.258 167.0

281.000 4.89114 .0000 .1090 22129.8 22912.4 166.559 172.2

281.500 4.94598 .0000 .1103 22217.8 23009.1 166.872 180.6

282.000 5.00126 .0111 .0979 22309.7 23110.0 167.199 70.7 6299.8 187.8

282.500 5.04976 .0203 .0963 22343.3 23151.3 167.317 64,5 3375.0 194.5

283.000 5.09768 .0287 .0954 22374.7 23190.3 167.428 61.2 2359.0 198.6

283.500 5.14523 .0370 .0948 22404.7 23227.9 167.534 59.0 1823,4 201.8

284.000 5.19251 .0452 .0943 22433.8 23264.6 167.637 57.4 1489,3 204.4

284.500 5.23957 .0534 ,0939 22462.1 23300.5 167.737 56,1 1260,2 206,7

285.000 5.28645 .0616 .0936 22489.9 23335.7 167.834 55.0 1093.2 208,8

285.500 5.33317 .0698 .0933 22517.2 23370.5 167.930 54.1 965.8 210.7

286.000 5.37977 .0781 .0931 22544.0 23404.8 168.024 53.3 865.6 212.5

286.500 5.42624 .0864 .0928 22570.5 23438.7 168.116 52.7 784.6 214.2

287.000 5.47262 .0947 .0927 22596.7 23472.3 168.208 52.1 717.8 215.8

287.500 5.51890 .1031 .0925 22622.6 23505.6 168.298 51.5 661.9 217.3

288.000 5.56509 .1116 .0923 22648.3 23538.7 168.387 51.1 614.3 218.7

288.500 5.61121 .1200 .0922 22673.7 23571.5 168.475 50.6 573.3 220 .

1

289.000 5.65726 .1285 .0920 22698.9 23604.1 168.563 50.3 537.7 221.4

289.500 5.70324 .1371 .0919 22724.0 23636.5 168.649 49.9 506.5 222 .

7

290.000 5.74916 .1457 .0918 22748.8 23668.7 168.735 49.6 478.9 223.9

291.000 5.84083 .1630 .0916 22798.1 23732.7 168.905 49.0 432.3 226.4

292.000 5.93230 .1804 .0914 22846.9 23796.1 169.072 48.5 394.6 228.6

293.000 6.02359 .1979 .0912 22895.2 23859.0 169.237 48.1 363.3 230.9

294.000 6.11472 .2156 .0911 22943.1 23921.5 169.400 47.7 337,1 233.0

295.000 6.20570 .2334 .0909 22990.7 23983.6 169.562 47.4 314,8 235.0

296.000 6.29654 .2513 .0908 23038.0 24045.4 169.722 47.1 295,6 237.0

297.000 6.38725 .2693 .0907 23084.9 24106.9 169.880 46.9 278,9 239.0

298.000 6.47785 .2874 .0905 23131.7 24168.2 170.038 46.6 264,2 240,9

299.000 6.56833 .3056 .0904 23178.3 24229.2 170.193 46,4 251,2 242.8

300.000 6.65871 .3239 .0903 23224.6 24290.0 170.348 46,3 239.7 244.6

36
Table CI. (Continued)

6.50 M0L/DM3 ISOCHORE

HPERATURE PRESSURE ISOTHERM

DERIV,

ISOCHORE

DERIV. INTERNAL ENERGY

ENTHALPY ENTROPY cy CP SOUND

VELOCITY

K MPA MPA,Iih3/M0L MPA/K J/MOL J/MOL J/MOL,

K

J/MOL,

K

M/S

279,500 4.73040 .0000 ,1054 21729,3 22457.1 165.025 156.8

280.000 4.78338 .0000 ,1066 21808,3 22544.2 165.307 159,4

280.500 4.83695 .0000 ,1078 21888,8 22633.0 165,594 162,8

281.000 4.89114 .0000 ,1090 21971,4 22723.9 165,889 167,7

281.500 4.94598 .0000 ,1103 22057,1 22818,0 166,193 175.8

282.000 5.00150 .0000 ,1118 22148,7 22918,2 166,519 194.0

282.500 5.05365 ,0114 ,1005 22203,3 22980,8 166.712 68,8 5967.6 188.1

283.000 5.10360 ,0192 ,0994 22236,4 23021,5 166.829 63.9 3508.8 194.0

283.500 5.15315 ,0269 ,0988 22267.5 23060,3 166.939 60.9 2493.6 198,1

284.000 5.20242 ,0346 ,0983 22297,5 23097,8 167.044 58,9 1934.0 201,4

284.500 5.25147 ,0424 ,0979 22326,5 23134,4 167,146 57,3 1578.9 204,2

285.000 5.30036 ,0503 ,0976 22354.8 23170,3 167,246 56,0 1333.6 206,6

285.500 5.34912 ,0583 ,0974 22382.6 23205,5 167,343 55,0 1154.2 208,8

286.000 5.39775 ,0663 ,0972 22409.8 23240,3 167,439 54,1 1017.4 210,8

286.500 5.44628 ,0745 ,0970 22436.7 23274,6 167,532 53,4 909.7 212,7

287.000 5.49472 ,0827 ,0968 22463.2 23308.5 167,625 52.7 822.8 214,5

287.500 5.54308 ,0909 ,0967 22489.4 23342.2 167,716 52,1 751.2 216,2

288.000 5.59137 ,0993 ,0965 22515,3 23375.5 167.806 51,6 691.3 217,8

288.500 5.63960 ,1077 ,0964 22541.0 23408,6 167,895 51,1 640.5 219,3

289.000 5.68777 ,1161 ,0963 22566,4 23441,5 167,983 50.7 596.8 220,8

289.500 5.73588 ,1246 ,0962 22591,7 23474,1 168,071 50,3 558 9 222 * 2 290.000 5.78395 ,1332 ,0961 22616,7 23506,6 168.157 50.0 525.7 223,5

291.000 5.87994 .1505 ,0959 22666,4 23571,0 168.328 49.3 470.3 226,1

292.000 5.97578 ,1680 ,0958 22715.4 23634.8 168,496 48.8 426.1 228.6

293.000 6.07147 ,1857 ,0956 22764.0 23698.1 168.662 48.4 389.9 231.0

294.000 6.16704 ,2035 ,0955 22812.2 23761.0 168,827 48.0 359.8 233.3

295.000 6.26249 ,2215 ,0954 22860.0 23823.5 168,989 47.6 334.5 235.5

296.000 6.35783 ,2397 ,0953 22907.5 23885.6 169,150 47,3 312.8 237.6

297.000 6.45308 .2580 ,0952 22954.7 23947.5 169,309 47,1 294.1 239,7

298.000 6,54824 ,2764 ,0951 23001.6 24009,0 169.467 46.8 277.7 241,7

299.000 6.64332 ,2949 ,0950 23048.3 24070,4 169.623 46.6 263.3 243,7

300.000 6,73831 ,3135 ,0950 23094.9 24131,5 169.778 46.4 250.6 245.6

37
Table CI. (Continued)

6.75 M0L/DM3 ISOCHORE

:mperature PRESSURE ISOTHERM

DERIV. ISOCHOREDERIV. INTERNAL

ENERGY

ENTHALPY ENTROPY cy CP SOUND

VELOCITY

K MPA MPA.riM3/M0L MPA/K J/hOL J/MOL J/MOL,J/MOL.

M/S

279.500 4.73040 .0000 .1054 21588.5 22289.3 164,424 153,1

280.000 4.78338 ,0000 .1066 21665.6 22374.2 164,700 155,6

280.500 4.83695 ,0000 .1078 21744.2 22460.8 164,980 158,9

281.000 4.89114 ,0000 .1090 21824.7 22549.3 165,267 163.6

281.500 4.94598 ,0000 .1103 21908.3 22641.0 165,565 171,4

282.000 5.00150 ,0000 .1118 21997.6 22738,6 165,882 188,9

282.500 5.05576 ,0060 .1042 22067.4 22816,4 166,129 73,8 11381.1 180.9

283.000 5.10756 .0129 .1031 22102.1 22858.8 166,252 66.4 5185.4 189.5

283.500 5,15895 .0200 ,1025 22134.3 22898.6 166,365 62.6 3337.5 194.7

284.000 5,21009 ,0272 ,1021 22165.0 22936,9 166,473 60,1 2447.9 198.7

284.500 5.26105 ,0346 ,1018 22194.6 22974.0 166,578 58.3 1926.5 201.9

285.000 5.31187 ,0422 .1015 22223.4 23010,3 166,679 56.9 1585,0 204.7

285.500 5.36258 .0499 .1013 22251,5 23045.9 166,777 55.7 1344,8 207.3

286.000 5.41320 .0577 .1012 22279 ,23081,0 166,874 54,7 1167,0 209,5

286.500 5.46374 .0657 .1010 22306,2 23115.7 166,969 53.9 1030,3 211.7

287.000 5.51421 .0738 .1009 22333.0 23149,9 167,062 53.1 922.1 213.6

287.500 5.56463 .0820 .1008 22359.4 23183,8 167,154 52.5 834,5 215.5

288.000 5.61499 .0902 .1007 22385.5 23217,3 167.244 51.9 762,1 217.2

288.500 5.66531 .0986 .1006 22411.3 23250.6 167.334 51.4 701,5 218.9

289.000 5.71559 ,1070 .1005 22436.9 23283.7 167.423 51.0 649,9 220.5

289.500 5.76583 ,1155 .1005 22462.3 23316,5 167,511 50.6 605,5 222.0

290.000 5.81604 ,1241 .1004 22487.5 23349.1 167,598 50.2 566,9 223.5

291.000 5,91637 ,1415 .1003 22537,4 23413.9 167,769 49.6 503,4 226.4

292.000 6,01660 ,1592 .1002 22586.7 23478.0 167,938 49.0 453,1 229.0

293.000 6,11673 ,1770 .1001 22635.4 23541,6 168,105 48.5 412,5 231,6

294,000 6,21679 ,1951 ,1000 22683.8 23604,8 168,270 48.1 379.0 234,0

295.000 6,31677 ,2134 .1000 22731.7 23667.5 168,432 47.8 350.9 236,4

296.000 6,41669 ,2318 .0999 22779.3 23730.0 168.594 47.5 327,1 238,6

297.000 6.51655 ,2504 .0998 22826.7 23792.1 168.753 47.2 306,6 240.8

298.000 6.61636 ,2692 .0998 22873.7 23853.9 168,911 46.9 288,8 243.0

299.000 6.71611 ,2881 .0997 22920.6 23915.5 169,068 46.7 273.2 245.1

300.000 6.81582 .3072 .0997 22967.2 23976,9 169,224 46.5 259.5 247,1

38
Table CI. (Continued)

7.00 M0L/DM3 ISOCHORE

MPERATURE PRESSURE ISOTHERM

DERIV. ISOCHOREDERIV. INTERNAL ENERGY

ENTHALPY ENTROPY CV CP SOUND

VELOCITY

K MPA MPA,DM3/M0L MPA/K J/MOL J/MOL J/MOL.

K

J/MOL.

K

M/S

279,500 4.73040 ,0000 .1054 21457.7 22133.4 163.867 149.7

280.000 4.78338 .0000 .1066 21533.1 22216.4 164.136 152.0

280.500 4.83695 .0000 .1078 21609.8 22300.8 164.410 155.2

281.000 4.89114 .0000 .1090 21688.5 22387,2 164.691 159.8

281.500 4.94598 .0000 .1103 21770.1 22476,7 164.981 167.3

282.000 5.00150 .0000 .1118 21857.3 22571,8 165.290 184.2

282.500 5.05684 .0030 .1074 21935.9 22658.3 165.569 79.2 22577,5 173,4

283.000 5.11026 .0090 .1064 21972.3 22702.3 165.697 68.5 7334,6 185,3

283.500 5.16334 .0155 .1059 22005.3 22742.9 165.814 63.9 4259,9 191,7

284.000 5.21623 ,0223 .1057 22036.5 22781.7 165.924 61.1 2962,5 196,4

284.500 5.26900 .0294 .1054 22066.5 22819.2 166.029 59.0 2255.0 200,1

285.000 5.32168 .0367 .1053 22095.6 22855.8 166.132 57.4 1812.9 203,3

285.500 5.37430 .0443 .1052 22124.0 22891.7 166.231 56.1 1512.1 206,2

286.000 5.42686 .0520 .1051 22151.7 22927.0 166.328 55.1 1294.9 208,7

286.500 5.47937 .0598 .1050 22179.1 22961.8 166.424 54.2 1131.3 211,1

287.000 5.53186 .0679 ,1049 22205.9 22996.2 166.517 53.4 1003.8 213,2

287.500 5,58431 .0760 ,1049 22232.5 23030.2 166.610 52.7 901,9 215,3

288.000 5.63674 .0843 .1048 22258.7 23063.9 166.701 52.1 818.7 217,2

288.500 5,68915 .0926 ,1048 22284.6 23097.4 166.791 51.6 749,6 219,0

289.000 5,74154 .1011 ,1048 22310.3 23130,5 166.880 51.1 691,3 220,7

289.500 5.79392 .1097 ,1047 22335.8 23163,5 166.968 50.7 641,6 222,4

290.000 5.84629 .1184 ,1047 22361.1 23196,2 167.055 50.3 598,6 224.0

291.000 5.95098 .1359 ,1047 22411.0 23261,2 167.227 49.7 528.4 227.0

292.000 6.05565 ,1538 ,1046 22460.4 23325,5 167.397 49.1 473.4 229.9

293.000 6.16028 .1720 ,1046 22509.3 23389,3 167.564 48.6 429.2 232.6

294.000 6.26490 .1904 ,1046 22557.7 23452.7 167.729 48.2 393.0 235.2

295.000 6.36949 .2090 ,1046 22605.7 23515.6 167.892 47.8 362.9 237.7

296.000 6.47407 .2279 ,1046 22653.4 23578.3 168.053 47.5 337.4 240.1

297.000 6.57864 .2469 ,1046 22700.8 23640.6 168.213 47.2 315.6 242.5

298.000 6.68319 .2661 ,1045 22747.9 23702.6 168.371 47.0 296.8 244.7

299.000 6,78773 .2855 ,1045 22794.8 23764.5 168.528 46.8 280.3 246.9

300.000 6,89225 .3050 .1045 22841.5 23826.1 168.684 46.6 265.8 249.1

39
Table CI. (Continued)

7.25 M0L/DM3 ISOCHORE

MPERATURE PRESSURE ISOTHERM

DERIV. ISOCHOREDERIV.

INTERNAL

ENERGY

ENTHALPY ENTROPY CV CP SOUND

VELOCITY

K MPA MPA.DM3/M0L MPA/K J/MOL J/MOL J/MOL.

K

J/MOL .

K

M/S

279.500 4.73040 .0000 .1054 21335.9 21988.3 163.348 146.5

280.000 4.78338 .0000 .1066 21409.7 22069.4 163.611 148.7

280.500 4.83695 .0000 .1078 21484.8 22151.9 163.879 151.8

281.000 4.89114 .0000 .1090 21561.7 22236.3 164.154 156.3

281.500 4.94598 .0000 .1103 21641.5 22323.7 164.437 163.5

282.000 5.00150 .0000 .1118 21726.6 22416.5 164.739 179.8

282.500 5.05738 .0016 .1101 21809.4 22507.0 165.033 83.9 41809.0 166.5

283.000 5.11221 .0069 .1094 21847.0 22552.2 165.166 69.9 9471.3 181.9

283.500 5.16685 .0129 .1092 21880.5 22593,2 165.284 64.7 5043.1 189.5

284.000 5.22141 .0195 .1091 21912.0 22632.2 165.395 61.5 3363.4 194.8

284.500 5.27593 .0264 .1090 21942.2 22669.9 165.501 59.3 2.496.6 199.0

285.000 5.33043 .0336 .1090 21971.4 22706.7 165.604 57.6 1973.5 202.6

285.500 5.38492 .0411 .1090 21999.9 22742.7 165.704 56.3 1626.1 205.7

286.000 5.43940 .0488 .1090 22027.8 22778.0 165.801 55.2 1379.7 208.5

286.500 5.49388 .0567 .1090 22055.1 22812.9 165.897 54.3 1196.6 211.0

287.000 5.54837 ,0647 .1090 22082.1 22847.3 165.991 53.5 1055.6 213.4

287.500 5.60287 .0729 .1090 22108.6 22881.4 166.083 52.8 944.0 215.6

288.000 5.65737 .0813 .1090 22134.9 22915.2 166.174 52.2 853.5 217.7

288.500 5.71189 .0898 .1090 22160.8 22948.6 166.264 51.6 778.7 219.6

289.000 5.76641 ,0984 .1091 22186.5 22981.9 166.353 51.2 716.1 221.5

289.500 5.82095 .1071 .1091 22212.0 23014.9 166.441 50.7 662.9 223.3

290.000 5.87550 .1159 .1091 22237.2 23047.6 166.529 50.3 617.2 225.0

291.000 5.98463 .1338 .1092 22287.2 23112.7 166.701 49.7 542.7 228.3

292.000 6.09381 .1521 .1092 22336.6 23177.1 166.870 49.1 484.8 231.4

293.000 6.20303 .1706 .1092 22385.4 23241.0 167.037 48.6 438.5 234.2

294.000 6.31230 .1895 .1093 22433.8 23304.5 167.202 48.2 400.8 237.0

295.000 6.42161 .2086 .1093 22481.8 23367.6 167.365 47.8 369.4 239.7

296.000 6.53096 .2279 .1094 22529.5 23430.3 167.526 47.5 343.0 242.2

297.000 6.64035 .2475 .1094 22576.9 23492.8 167.686 47.2 320.5 244.7

298.000 6.74977 .2673 .1094 22624.0 23555.0 167.844 47.0 301.1 247.1

299.000 6.85923 .2872 .1095 22670.8 23616.9 168.001 46.8 284.1 249.4

300.000 6.96871 .3073 .1095 22717.5 23678.7 168.157 46.6 269.2 251.6

40
Table CI. (Continued)

7.50 M0L/DM3 ISOCHORE

MF-ERATURE PRESSURE ISOTHERM ISOCHORE

DERiy. DERIV. INTERNAL ENERGY

ENTHALPY ENTROPY CV CP SOUND

VELOCITY

K MPA MPA.DM3/M0L MPA/K J/MOL J/MOL J/MOL.

J/MOL.M/S

279.500 4.73040 .0000 1054 21222.2 21852.9 162.863 143.5

280.000 4.78338 .0000 1066 21294.5 21932.3 163.122 145.7

280.500 4.83695 .0000 1078 21368.0 22012.9 163.384 148.7

281.000 4.89114 .0000 1090 21443.4 22095.5 163.652 153.0

281.500 4.94598 .0000 1103 21521.4 22180.9 163.930 160.0

282.000 5.00150 .0000 1118 21604.6 22271.5 164.225 175.7

282.500 5.05769 .0011 1122 21688.3 22362.6 164.522 86.2 60195.4 161,9

283.000 5.11379 .0060 1122 21726.4 22408.2 164.656 70.3 10666.2 179.9

283,500 5.16992 .0119 1123 21760.0 22449.3 164.775 64.7 5408.3 188.2

284.000 5.22611 .0184 1124 21791.5 22488.3 164.886 61.5 3528.7 194.1

284.500 5.28236 .0254 1126 21821.6 22525.9 164.992 59.2 2586.8 198.7

285.000 5.33867 .0326 1127 21850.8 22562.6 165.094 57.5 2028.4 202.6

285.500 5.39503 .0402 1128 21879.2 22598.5 165.194 56.2 1661.9 205.9

286.000 5.45145 .0480 1129 21907.0 22633.8 165.291 55.1 1404.4 209.0

286.500 5.50792 .0560 1130 21934.3 22668.7 165.387 54.1 1214.3 211.7

287.000 5.56444 .0643 1131 21961.1 22703.0 165.480 53.3 1068.7 214.3

287.500 5.62101 .0727 1132 21987.6 22737.1 165.572 52.6 953.8 216.6

288.000 5.67762 .0812 1133 22013.8 22770.8 165.663 52.0 861.0 218.9

288.500 5.73428 .0899 1134 22039.7 22804.2 165.753 51.5 784.7 221.0

289.000 5.79098 .0987 1134 22065.3 22837.4 165.842 51.0 720.8 223.0

289.500 5.84772 .1077 1135 22090.7 22870.4 165.930 50.6 666.7 224.9 . 290.000 5.90450 .1167 1136 22115.9 22903.2 166.017 50.2 620.2 226.7

291.000 6.01817 .1351 1137 22165.8 22968.2 166.188 49.5 544.8 230.2

292.000 6.13198 .1540 1139 22215.0 23032.6 166.357 49.0 486.2 233.4

293.000 6.24592 .1731 1140 22263.7 23096.5 166.524 48.5 439.6 236.5

294.000 6.35998 .1925 1141 22312.0 23160.0 166.689 48.1 401.5 239.4

295.000 6.47414 .2123 1142 22359.9 23223.2 166.851 47.7 370.0 242.2

296.000 6.58839 .2322 1143 22407.5 23286.0 167.012 47.4 343.5 244.9

297.000 6.70275 .2524 1144 22454.8 23348.5 167.172 47.2 320.9 247.5

298.000 6.81719 .2729 1145 22501.8 23410.8 167.330 46.9 301.4 250.0

299.000 6.93170 .2935 1146 22548.6 23472.8 167.486 46.7 284.4 252.4

300.000 7.04630 .3143 .1146 22595.2 23534.7 167.642 46.5 269.5 254.8

41
Table CI. (Continued)

7.75 M0L/riM3 ISOCHORE

MPERATURE PRESSURE ISOTHERM ISOCHORE

DERIV. DERjy.

INTERNAL

ENERGY

ENTHALPY ENTROPY CV CP SOUND

VELOCITY

K MPA MPA.DM3/M0L MPA/K J/MOL J/MOL J/MOL,

J/MOL.

M/S

279,500 4.73040 .0000 1054 21115.9 21726.3 162,410 140.7

280.000 4.78338 .0000 1066 21186.7 21803.9 162,663 142.8

280.500 4.83695 ,0000 1078 21258.8 21882.9 162.921 145.7

281.000 4,89114 ,0000 1090 21332.6 21963,7 163,183 149.9

281.500 4.94598 ,0000 1103 21409.1 22047.3 163.455 156.7

282.000 5.00150 ,0000 1118 21490.6 22135.9 163.744 171.9

282.500 5,05794 ,0011 1142 21572.5 22225,1 164,035 85.0 57363,7 160.5

283.000 5,11528 ,0062 1150 21610,1 22270.1 164,168 69.5 10192,5 179,4

283.500 5.17291 ,0123 1155 21643,3 22310,8 164,285 64.1 5189,0 188,3

284.000 5.23075 .0190 1159 21674,6 22349.5 164,395 60.9 3396,6 194,4

284.500 5.28876 .0262 1162 21704.4 22386,9 164,500 58.7 2496,5 199.3

285.000 5.34692 .0338 1164 21733.4 22423,3 164,602 57.1 1961,9 203,5

285.500 5,40521 .0416 1167 21761.6 22459.0 164,701 55.7 1610.6 207,1

286,000 5,46361 ,0497 1169 21789,1 22494.1 164,797 54,7 1363,3 210,3

286.500 5.52213 ,0581 1171 21816,2 22528.8 164,892 53,8 1180,6 213.2

287.000 5.58074 .0666 1173 21842,9 22563.0 164,985 53,0 1040,4 215.9

287.500 5.63944 .0753 1175 21869,2 22596.9 165.077 52,3 929,7 218.4

288.000 5.69823 .0842 1177 21895,3 22630.5 165.167 51,7 840,2 220,8

288.500 5.75710 .0932 1178 21921,0 22663,8 165.256 51,2 766,5 223,0

289.000 5.81605 ,1024 1180 21946,5 22696,9 165.344 50,7 704,8 225 ,

289.500 5.87506 .1117 1181 21971,7 22729,8 165,432 50,3 652,4 227,1

290.000 5.93415 ,1211 1182 21996,8 22762,5 165,518 50,0 607,5 229,1

291.000 6.05251 ,1402 1185 22046,4 22827,4 165,689 49,3 534,4 232,7

292.000 6.17111 .1598 1187 22095.5 22891,7 165,857 48,8 477,6 236,2

293.000 6.28992 ,1796 1189 22144.0 22955.6 166,023 48,3 432.3 239 ,

294.000 6.40892 ,1998 1191 22192,

23019.0 166,187 47,9 395.3 242.5

295.000 6.52811 .2203 1193 22239.8 23082.2 166,349 47,6 364.7 245.4

296.000 6.64746 .2411 1194 22287.2 23145.0 166,510 47,3 338.8 248,2

297,000 6.76696 .2621 ,1196 22334.4 23207,5 166,669 47,0 316.8 250.9

298,000 6.88661 .2833 ,1197 22381.3 23269.9 166,826 46,8 297,7 253,5

299.000 7.00638 .3047 ,1198 22427.9 23332.0 166,983 46,6 281,2 256,1

300.000 7.12628 .3264 1200 22474.4 23393.9 167,138 46.4 266.6 258,6

42
Table CI. (Continued)

8.00 H0L/DM3 ISOCHORE

MPERATURE PRESSURE ISOTHERM ISOCHORE

IiERIV. DERIV. INTERNAL ENERGY

ENTHALPY ENTROPY cy CP SOUND

VELOCITY

K MPA MPA.riM3/M0L MPA/K J/MOL J/MOL J/MOL.

J/MOL.

M/S

279.500 4.73040 .0000 1054 21016.2 21607.5 161.985 138.0

280.000 4.78338 .0000 1066 21085.7 21683.6 162.234 140.1

280.500 4.83695 .0000 1078 21156.4 21761.1 162.486 142.9

281.000 4.89114 .0000 1090 21228.8 21840.2 162.744 147.0

281.500 4.94598 .0000 1103 21303.8 21922.0 163.010 153.5

282.000 5.00150 .0000 1118 21383.6 22008.8 163.294 168.3

282.500 5.05827 .0017 1165 21461.5 22093.8 163.570 80.8 36291.8 162.8

283.000 5.11696 .0075 1180 21497.8 22137.4 163.698 67.7 8299.2 180.8

283.500 5.17619 .0142 1188 21530.3 22177.3 163.813 62.8 4470.0 189.7

284.000 5.23578 .0215 1195 21561.0 22215.4 163.921 59.9 3008.7 196.1

284.500 5.29564 .0292 1200 21590.4 22252.3 164.024 57.9 2250.3 201.2

285.000 5.35575 .0372 1204 21618.9 22288.4 164.124 56.3 . 1790.3 205.5

285.500 5.41605 .0456 1208 21646.7 22323.7 164.222 55.1 1483.3 209.2

286.000 5.47654 .0542 1211 21674.0 22358.5 164.317 54.0 1264.7 212.6

286.500 5.53719 .0630 1215 21700.8 22392.9 164.411 53.2 1101.7 215.6

287.000 5.59799 .0720 1217 21727.2 22426.9 164.503 52.5 975,7 218.5

287.500 5.65893 .0812 1220 21753.3 22460.6 164.594 51.8 875.6 221.1

288.000 5.71999 .0905 1222 21779.0 22494.0 164.683 51.3 794.3 223.6

288.500 5.78118 .1000 1225 21804.5 22527 .

164.772 50.8 726.9 225.9

289.000 5.84247 .1096 1227 21829.8 22560.1 164.859 50.3 670.4 228.1

289.500 5.90386 .1194 1229 21854.9 22592.9 164.946 49.9 622.2 230.2

290.000 5.96536 .1293 1231 21879.8 22625.4 165.032 49.6 580.6 232.3

291.000 6.08862 .1493 1234 21929.0 22690.1 165.202 49.0 512.9 236.1

292.000 6.21221 .1698 ,1237 21977.7 22754.3 165.369 48.5 459.9 239.7

293.000 6.33610 .1906 ,1240 22026.0 22818.0 165.534 48.0 417.5 243.1

294.000 6.46027 .2118 ,1243 22073.8 22881.3 165.697 47.7 382.8 246.3

295.000 6.58470 .2332 ,1245 22121.3 22944.4 165.858 47.3 353.9 249.3

296.000 6.70935 .2549 ,1248 22168.5 23007.2 166.018 47.1 329.5 252.2

297.000 6.83422 .2768 ,1250 22215.4 23069.7 166.176 46.8 308.6 255.1

298.000 6.95928 .2990 ,1252 22262.23132.0 166.333 46.6 290.5 257.8

299.000 7.08453 .3214 ,1253 22308.6 23194.2 166.489 46.4 274.8 260.4

300.000 7.20995 .3439 1255 22354.9 23256.2 166.643 46.2 260.9 263.0

43
Table CI. (Continued)

8.25 M0L/DM3 ISOCHORE

MPERATURE PRESSURE ISOTHERM ISOCHORE

DERIV. DERIV. INTERNAL

ENERGY

ENTHALPY ENTROPY CV CP SOUND

VELOCITY

K MPA MPA.DM3/M0L MPA/K J/MOL J/MOL J/MOL.

J/MOL.

M/S

279.500 4.73040 .0000 .1054 20922.6 21495.9 161.586 135.6

280.000 4.78338 .0000 ,1066 20990.8 21570.6 161.830 137.6

280.500 4.83695 .0000 ,1078 21060.3 21646.6 162.078 140.3

281.000 4.89114 .0000 ,1090 21131.3 21724.2 162.331 144.2

281.500 4.94598 .0000 ,1103 21204.9 21804.4 162.592 150.6

282.000 5.00150 .0000 ,1118 21283.1 21889.4 162.870 164.9

282.500 5.05886 .0033 ,1195 21354.4 21967.6 163.123 74.7 18061.6 168.5

283.000 5.11915 .0104 1214 21388.9 22009.4 163.245 65.1 5965.2 184.2

283.500 5.18018 .0181 ,1226 21420.4 22048.3 163.356 61.0 3523.6 192.8

284.000 5.24168 .0262 ,1234 21450.2 22085.6 163.461 58.5 2484.6 199.2

284.500 5.30357 .0347 1241 21479.0 22121.8 163.562 56.7 1913.1 204.3

285.000 5.36577 .0435 1247 21506.9 22157.3 163.660 55.

1553.3 208.7

285.500 5.42825 .0525 1252 21534.3 22192.3 163.756 54.1 1306.7 212.5

286.000 5.49096 .0618 ,1257 21561.1 22226.7 163.850 53.2 1127.5 216,0

286.500 5.55389 .0712 1261 21587.5 22260.7 163.942 52.4 991.8 219,1

287.000 5.61702 .0809 1264 21613.6 22294.4 164.033 51.8 885.5 222.0

287.500 5.68033 .0907 ,1268 21639.3 22327.8 164.123 51.2 800.1 224.8

288.000 5.74380 .1006 ,1271 21664.8 22361.0 164.211 50.7 730.0 227.3

288,500 5.80743 .1107 1274 21690.0 22393.9 164.299 50,2 671,6 229.7

289.000 5.87120 .1210 1277 21715.0 22426.7 164.385 49.8 622.1 232.0

289.500 5.93511 .1313 ,1279 21739.8 22459.2 164.471 49,5 579.7 234.2

290.000 5.99914 .1418 1282 21764.5 22491.6 164.556 49.1 543.0 236.3

291.000 6.12756 .1630 ,1286 21813.3 22556.0 164.724 48.6 482.6 240.3

292.000 6.25641 .1846 ,1290 21861.6 22620.0 164.890 48.1 435.1 244.0

293.000 6.38564 .2066 1294 21909.5 22683.5 165.054 47.7 396.8 247.5

294.000 6.51523 .2288 1298 21957.0 22746.7 165.216 47.3 365.2 250.9

295.000 6.64515 .2514 1301 22004.2 22809.6 165.376 47.0 338.8 254.0

296.000 6.77536 .2742 1304 22051.1 22872.3 165.535 46.8 316.3 257.1

297.000 6.90585 .2972 1306 22097.7 22934.8 165.692 46.6 297,1 260.0

298.000 7.03659 .3204 1309 22144.2 22997.1 165.848 46.4 280,3 262.8

299.000 7.16756 .3439 ,1311 22190.4 23059.2 166.003 46.2 265.7 265.6

300.000 7.29876 .3676 ,1313 22236.5 23121.2 166.157 46.0 252.8 268.2

44
Table CI. (Continued)

8.50 M0L/DM3 ISOCHORE

:mperature PRESSURE ISOTHERM

DERI*^. ISOCHORE

DERIV. INTERNAL ENERGY

ENTHALPY ENTROPY CV CP SOUND

VELOCITY

K MPA MPA.DM3/M0L MPA/K J/MOL J/MOL J/MOL.

K

J/MOL.

K

H/S

279.500 4.73040 .0000 .1054 20834.4 21391.0 161.210 133.2

280.000 4.78338 .0000 .1066 20901.5 21464.3 161.450 135.2

280.500 4.83695 .0000 .1078 20969.7 21538.8 161.694 137.8

281.000 4.89114 .0000 .1090 21039.6 21615.0 161.942 141.6

281.500 4.94598 .0000 .1103 21111.8 21693.7 162.199 147.9

282.000 5.00150 .0000 .1118 21188.6 21777.0 162.472 161.8

282.500 5.06009 .0070 .1234 21250.3 21845.6 162.690 68.5 8563.9 176.7

283.000 5.12236 .0157 .1255 21282.7 21885.3 162.805 62.1 3983.0 189.6

283.500 5.18545 .0247 .1268 21312.9 21922.9 162.912 58.9 2615.3 197.6

284.000 5.24913 ,0339 .1278 21341.8 21959.3 163.013 56.8 1950.4 203.8

284.500 5.31325 .0434 .1287 21369.8 21994.9 163.112 55.3 1556,7 208.8

285.000 5.37776 .0531 .1294 21397.1 22029.8 163.208 54.0 1296.5 213.2

285.500 5.44261 .0631 .1300 21423.9 22064.2 163.302 53.1 1111.8 217.0

286.000 5.50774 .0732 .1305 21450.2 22098.2 163.394 52.2 974.0 220.5

286.500 5.57314 .0835 .1310 21476.1 22131.8 163.484 51.6 867.4 223.7

287.000 5.63877 .0939 .1315 21501.8 22165.1 163.574 51.0 782.4 226.7

287.500 5.70462 .1045 .1319 21527.1 22198.2 163.662 50.4 713.2 229.5

288.000 5.77068 .1152 .1323 21552.2 22231.1 163.749 50.0 655.7 232.1

288.500 5.83692 .1260 .1327 21577.1 22263.8 163.836 49.6 607.2 234.6

289.000 5.90334 .1370 .1330 21601.8 22296.3 163.921 49.2 565.7 236.9

289.500 5.96992 .1480 .1333 21626.3 22328.6 164.006 48.9 529.9 239.2

290.000 6.03665 .1592 .1336 21650.6 22360.8 164.090 48.6 498.7 241.4

291.000 6.17054 .1818 .1342 21699.0 22424.9 164.256 48.1 446.8 245.5

292.000 6.30496 .2048 .1347 21746.8 22488.6 164.420 47.6 405.5 249.3

293.000 6.43985 .2281 .1351 21794.2 22551.9 164.582 47.3 371.9 252.9

294.000 6.57516 .2516 .1355 21841.3 22614.9 164.743 47.0 344.0 256.3

295.000 6.71087 .2754 .1359 21888.2 22677.7 164.902 46.7 320.4 259.6

296.000 6.84693 .2995 .1362 21934.7 22740.3 165.060 46.5 300.3 262.7

297.000 6.98333 .3238 .1366 21981.1 22802.7 165.216 46.3 283.0 265.7

298.000 7.12004 .3483 .1369 22027.3 22864.9 165.371 46.1 267.9 268.6

299.000 7.25703 .3730 .1371 22073.3 22927.0 165.525 45.9 254.6 271.5

300.000 7.39429 .3979 .1374 22119.1 22989.0 165.678 45.8 242.8 274.2

45
Table CI. (Continued)

8.75 M0L/DM3 ISOCHORE

MPERATURE PRESSURE ISOTHERM

DERIV. ISOCHOREIiERIV. INTERNALENERGY

ENTHALPY ENTROPY CV CP SOUND

VELOCITY

K MPA MPA.DM3/M0L MPA/K J/MOL J/MOL J/MOL.

K

J/MOL.

K

H/S

279 . 500 4.73040 .0000 .1054 20751.3 21292.0 160.856 131.0

280.000 4.78338 .0000 .1066 20817.3 21364.0 161.092 133.0

280.500 4.83695 .0000 .1078 20884.4 21437.2 161.331 135.5

281.000 4.89114 .0000 .1090 20953.0 21512.0 161.576 139.2

281.500 4.94598 .0000 .1103 21024.0 21589.3 161.828 145.3

282.000 5.00150 .0000 .1118 21099.4 21671.0 162.096 158.8

282.500 5.06266 .0142 .1282 21147.9 21726.5 162.268 63.1 4324.0 186.5

283.000 5.12732 .0247 .1303 21178.3 21764.3 162.375 59.0 2598.0 196.9

283.500 5.19284 .0351 .1317 21207.2 21800.7 162.477 56.6 1884.2 204.1

284.000 5.25898 .0457 .1328 21235.1 21836.1 162.576 55.0 1487.1 209.9

284.500 5.32563 .0564 .1337 21262.3 21870.9 162.671 53.7 1232.5 214.8

285.000 5.39271 .0672 .1345 21288.8 21905.2 162.764 52.7 1055.0 219.1

285.500 5.46016 .0782 .1353 21315.0 21939.0 162.856 51.9 924.0 222.9

286.000 5.52795 .0893 .1359 21340.7 21972.5 162.946 51.2 823.2 226.4

286.500 5.59603 .1006 .1365 21366.2 22005.7 163.035 50.6 743.2 229.6

287.000 5.66439 .1120 .1370 21391.3 22038.7 163.123 50.1 678.2 232.6

287.500 5.73300 .1235 .1375 21416.2 22071.4 163.209 49.6 624.3 235.4

288.000 5.80184 .1351 .1379 21440.9 22104.0 163.295 49.2 578.9 238.0

288.500 5.87090 .1468 .1383 21465.4 22136.4 163.380 48.8 540.1 240.5

289.000 5.94016 .1586 .1387 21489.8 22168.6 163.465 48.5 506.6 242.9

289.500 6.00960 .1704 .1391 21513.9 22200.8 163.548 48.2 477.3 245.2

290.000 6.07922 .1824 .1394 21538.0 22232.8 163.631 48.0 451.6 247.4

291.000 6.21896 .2066 .1401 21585.7 22296.5 163.795 47.5 408.3 251.6

292.000 6.35931 .2311 .1406 21633.0 22359.8 163.958 47.1 373.5 255.5

293.000 6.50020 .2559 .1411 21680.0 22422.9 164.118 46.8 344.7 259.2

294.000 6.64158 .2809 .1416 21726.7 22485.7 164.277 46.5 320.7 262.7

295.000 6.78342 .3062 .1421 21773.1 22548.3 164.435 46.3 300.2 266.0

296.000 6.92568 .3317 .1425 21819.3 22610.8 164.591 46.1 282.6 269.2

297.000 7.06832 .3574 .1428 21865.3 22673.1 164.747 45.9 267.4 272.3

298.000 7.21132 .3832 .1432 21911.2 22735.3 164.901 45.8 253.9 275.3

299.000 7.35466 .4093 .1435 21956.9 22797.4 165.054 45.6 242.1 278.2

300.000 7.49830 .4355 .1438 22002.4 22859,4 165.206 45.5 231.5 281.0

46
Table CI. (Continued)

9.00 M0L/riM3 ISOCHORE

MPERATURE PRESSURE ISOTHERM

DERiy.

ISOCHORE

DERIV. INTERNAL ENERGY

ENTHALPY ENTROPY cy CP SOUND

VELOCITY

K hPA MPA.DM3/M0L MPA/K J/MOL J/MOL J/MOL.

K

J/MOL.

K

M/S

279.500 4.73040 ,0000 .1054 20672.9 21198,5 160.522 129.0

280.000 4.78338 .0000 .1066 20737.8 21269,3 160.754 130,8

280.500 4.83695 .0000 .1078 20803.8 21341,2 160,989 133,3

281.000 4.89114 .0000 .1090 20871.3 21414,8 161,230 136,9

281.500 4.94598 .0000 .1103 20941.1 21490,7 161,478 142,8

282.000 5.00150 .0000 .1118 21015.2 21570.9 161,741 155,9

282.500 5.06764 .0267 .1340 21046.5 21609.6 161,852 58,7 2408.0 197.4

283.000 5.13514 .0388 .1359 21075.1 21645.7 161,953 56,1 1717.0 205.9

283.500 5.20346 .0508 .1373 21102.7 21680.9 162.051 54,4 1352.4 212.3

284.000 5.27242 ,0628 .1385 21129.6 21715.4 162.145 53,1 1123.2 217.6

284.500 5.34190 .0748 .1394 21155.9 21749.4 162.238 52,1 964.7 222.3

285.000 5.41185 .0869 .1403 21181.7 21783,0 162.328 51,3 848.0 226.4

285.500 5.48219 .0991 .1411 21207.2 21816,3 162.418 50,6 758.3 230.1

286.000 5.55290 .1114 .1417 21232.3 21849,3 162.506 50,0 687.1 233.5

286.500 5.62393 .1237 .1424 21257.2 21882,1 162.593 49.5 629,1 236.7

287.000 5.69526 .1361 .1429 21281.9 21914,7 162.679 49,1 581.0 239.6

287.500 5.76687 .1486 .1435 21306.3 21947,1 162.764 48.7 540.3 242.4

288.000 5.83873 ,1612 .1440 21330.6 21979,3 162.848 48.4 505.5 245.1

288.500 5.91083 .1739 .1444 21354.7 22011,5 162.932 48.1 475.3 247.6

289.000 5.98315 ,1866 .1449 21378.7 22043,5 163.015 47.8 449.0 250.0

289.500 6.05569 .1994 .1453 21402.5 22075,3 163.097 47.5 425.7 252.3

290.000 6.12842 .2123 .1456 21426.2 22107,1 163.179 47.3 405.0 254.5

291.000 6.27442 .2383 .1464 21473.3 22170,5 163.341 46.9 369.9 258.7

292.000 6.42112 ,2645 .1470 21520.1 22233,6 163.502 46.6 341.1 262.7

293.000 6.56841 ,2910 .1476 21566.6 22296,4 163.660 46.3 317.1 266.4

294.000 6.71624 ,3176 .1481 21612.7 22359,0 163.818 46.1 296.8 270.0

295.000 6.86459 ,3445 .1486 21658.7 22421.5 163.974 45.9 279.3 273.4

296,000 7.01341 ,3715 .1490 21704,5 22483.8 164.129 45.7 264.2 276.7

297.000 7.16267 .3987 .1495 21750,2 22546.0 164.283 45.6 251.0 279.8

298.000 7.31232 .4261 .1498 21795,7 22608.1 164.436 45.4 239.3 282.8

299.000 7.46235 .4537 .1502 21841.0 22670.2 164.588 45.3 228.9 285.8

300.000 7.61273 .4814 .1505 21886,3 22732.2 164.739 45.2 219.6 288.6

47
Table CI. (Continued)

9,25 M0L/DM3 ISOCHORE

MPERATURE PRESSURE ISOTHERM

DERIV,

ISOCHORE

DERiy.

INTERNAL

ENERGY

ENTHALPY ENTROPY CV CP SOUND

VELOCITY

K MPA MPA,DM3/M0L MPA/K J/MOL J/MOL J/MOL.

K

J/MOL.

K

M/S

279.500 4,73040 ,0000 .1054 20598.6 21110.0 160.205 127.0

280.000 4,78338 ,0000 .1066 20662.6 21179.7 160.434 128.8

280.500 4,83695 ,0000 .1078 20727.6 21250.5 160.666 131.3

281.000 4,89114 ,0000 .1090 20794.0 21322.8 160.902 134.8

281.500 4.94598 ,0000 .1103 20862.7 21397.4 161.147 140.5

282.000 5,00679 ,0315 .1383 20917.2 21458.4 161.340 57.8 2058.9 200.0

282.500 5,07656 .0460 .1406 20945.3 21494,1 161.440 55.1 1475.0 209.4

283.000 5.14731 .0598 .1423 20972.4 21528.9 161.536 53.5 1174,0 216.3

283.500 5,21883 ,0733 ,1437 20998.9 21563,1 161.629 52.2 984,9 222 . 284.000 5,29096 ,0868 .1448 21024.7 21596.7 161,720 51.3 853.5 226.9

284.500 5,36362 .1002 .1458 21050.2 21630.0 161.810 50.5 756.2 231.2

285,000 5,43675 .1136 .1467 21075.3 21663.0 161.898 49.9 680.9 235.1

285.500 5,51029 ,1270 .1475 21100.1 21695.8 161,985 49.3 620.7 238.7

286,000 5,58421 ,1405 ,1482 21124.6 21728.3 162,071 48.9 571.4 242.0

286.500 5,65848 ,1540 .1488 21149.0 21760.7 162.156 48.5 530.2 245.0

287.000 5,73306 ,1676 .1495 21173.1 21792.9 162.240 48.1 495.3 248.0

287.500 5,80793 ,1812 .1500 21197.1 21825.0 162.323 47.8 465.2 250.7

288.000 5,88307 ,1948 .1505 21220.9 21856.9 162.406 47.5 439.1 253.3

288,500 5,95846 ,2085 .1510 21244.6 21888.8 162.488 47.3 416.1 255.8

289.000 6,03410 ,2223 .1515 21268.2 21920.5 162.570 47.0 395.8 258.2

289.500 6.10996 .2361 .1519 21291.6 21952.2 162.651 46.8 377,6 260.5

290.000 6,18603 .2500 .1523 21315.0 21983.8 162.732 46.6 361,3 262.7

291,000 6.33876 .2779 .1531 21361.5 22046.7 162.892 46.3 333.3 267.0

292.000 6,49223 .3059 .1538 21407.6 22109.5 163.050 46.0 309.9 270.9

293.000 6.64635 .3342 .1544 21453.6 22172.1 163.207 45.8 290.2 274.7

294.000 6.80108 .3626 .1550 21499.3 22234.5 163.363 45.6 273.3 278.3

295.000 6.95636 .3912 . 1555 21544.8 22296.8 163.517 45.5 258,7 281.7

296.000 7,11215 .4199 .1560 21590.2 22359.1 163.671 45.3 245,9 285.0

297,000 7,26841 .4488 .1565 21635.4 22421 .

2

163.824 45.2 234,6 288.2

298.000 7,42512 .4778 .1569 21680.6 22483.3 163.975 45.1 224,6 291.3

299.000 7.58223 .5069 .1573 21725.6 22545.3 164.126 45.0 215.6 294.2

300,000 7,73984 .5363 .1577 21770.6 22607.4 164.277 44.9 207.5 297.1

48
Table CI. (Continued)

9.50 M0L/DM3 ISOCHORE MPERATURE PRESSURE ISOTHERM

UERiy. ISOCHORE

DEftlU. INTERNAL ENERGY ENTHALPY ENTROPY CV CP SOUND VELOCITY

K MPA MPA.riM3/M0L MPA/K J/MOL J/MOL J/MOL.

J/MOL .K (l/S 279.500 4.73040 .0000 .1054 20528.3 21026.2 159.905 125 2 280.000 4.78338 .0000 .1066 20591.3 21094.8 160.131 126 9 280.500 4.83695 .0000 .1078 20655.3 21164.5 160.359 129 3 281.000 4.89114 .0000 .1090 20720.8 21235.6 160.592 132 7 281.500 4.94598 .0000 .1103 20788.4 21309.0 160.833 138 3 282.000 5.01779 .0581 .1461 20817.4 21345.6 160.936 53 8 1203 215.2

282.500 5.09135 .0739 .1480 20843.9 21379.8 161.029 52 2 980 5 222.3

283.000 5.16574 .0892 .1495 20869.7 21413.5 161.121 51 1 837 2 228.1

283.500 5.24083 .1042 .1508 20895.1 21446.7 161.210 50 3 735 6 233.1

284.000 5.31650 .1191 .1519 20920.0 21479.7 161.298 49 6 659 •t 237.5

284.500 5.39269 .1339 .1529 20944.7 21512.3 161.385 49 599 2 241.5

285.000 5.46934 .1486 .1537 20969.1 21544.8 161.471 48 5 550 6 245.2

285.500 5.54640 .1633 .1545 20993.2 21577.1 161.555 48 1 510 5 248.5

286.000 5.62384 .1781 .1552 21017.2 21609.2 161.639 47 7 476 7 251.7

286.500 5.70163 .1928 .1559 21041.0 21641.2 161.722 47 4 447 7 254.7

287.000 5.77975 .2075 .1565 21064.6 21673.0 161.805 47 1 422 6 257.5

287.500 5.85816 .2223 .1571 21088.1 21704.8 161.887 46 9 400 7 260.2

288.000 5.93686 .2371 .1577 21111.5 21736.4 161.968 46 7 381 3 262.8

288.500 6.01582 .2519 .1582 21134.8 21768.0 162.049 46 5 364 265.2

289.000 6.09503 .2667 .1587 21158.0 21799.6 162.129 46 3 348 5 267.6

289.500 6.17447 .2816 .1591 21181.1 21831.0 162.209 46 1 334 5 269.9

290.000 6.25414 .2965 .1595 21204.1 21862.4 162.288 46 321 8 272.0

291.000 6.41409 .3264 .1604 21249.9 21925.1 162.446 45 7 299 7 276.2

292.000 6.57482 .3564 .1611 21295.5 21987.6 162.602 45 5 281 ,0 280.2

293.000 6.73624 .3866 .1618 21340.9 22050.0 162.757 45 3 265 .0 283.9

294.000 6.89830 .4169 .1624 21386.1 22112.2 162.912 45 1 251 .1 287.5

295.000 7.06095 .4473 .1629 21431.2 22174.4 163.065 45 239 .0 291.0

296.000 7.22415 .4778 .1635 21476.1 22236.6 163.217 44 9 228 .3 294.3

297.000 7.38785 .5084 .1639 21521.0 22298.6 163.368 44 8 218 .8 297.5

298.000 7.55202 .5392 .1644 21565.7 22360.7 163.518 44 7 210 .2 300.6

299.000 7.71663 .5700 .1648 21610.4 22422.7 163.668 44 7 202 .6 303.6

300.000 7.88166 .6010 .1652 21655.1 22484.7 163.817 44 6 195 .6 306.5

49
Table CI. (Continued)

9,75 H0L/DM3 ISOCHORE

MPERATURE PRESSURE ISOTHERH

DERI*^. ISOCHORE

DERIV. INTERNAL ENERGY ENTHALPY ENTROPY CV CP SOUND

VELOCITY

K MPA HPA.DH3/H0L HPA/K J/MOL J/HOL J/HOL.

K

J/HOL .K H/S

279.500 4.73040 .0000 .1054 20461.6 20946.7 159,621 123.4

280.000 4.78338 .0000 .1066 20523.7 21014.3 159.843 125.

1

280.500 4.83695 .0000 .1078 20586.8 21082.9 160,068 127.4

281.000 4.89114 .0000 .1090 20651,3 21152.9 160.298 130.8

281.500 4.95987 .0770 .1526 20690,9 21199.6 160,439 52.1 947.9 223,5

282.000 5.03667 .0948 .1545 20716.6 21233.2 160.530 50.8 798,2 230.4

282.500 5.11434 .1119 ,1561 20741.8 21266.3 160,619 49.9 697.2 236.1

283.000 5.19274 .1286 ,1574 20766.

S

21299.1 160.707 49.2 623.1 241.0

283.500 5.27176 .1450 .1586 20790.9 21331.6 160.793 48.6 566.0 245.4

284.000 5.35132 .1613 .1596 20815,1 21363.9 160,878 48.1 520.2 249.4

284.500 5.43138 .1774 ,1606 20839,0 21396.1 160.962 47.6 482,6 253.1

285.000 5.51188 .1935 ,1614 20862,7 21428.1 161.046 47.3 451.1 256.5

285.500 5.59278 .2095 .1622 20886,3 21459.9 161.128 47.0 424,1 259.7

286.000 5.67406 .2254 .1629 20909.7 21491.7 161.210 46.7 400.9 262.7

286.500 5.75569 .2414 ,1636 20933,0 21523.3 161.291 46.4 380.5 265.6

287.000 5.83764 .2573 ,1642 20956.1 21554.9 161.372 46.2 362.6 268.3

287.500 5,91989 .2733 ,1648 20979,2 21586.4 161.452 46.0 346.6 270.9

288.000 6.00243 .2892 .1653 21002,1 21617.8 161.532 45.8 332.2 273,4

288.500 6.08523 .3051 .1659 21025,0 21649.1 161.612 45.7 319.3 275,7

289.000 6.16829 .3211 .1664 21047,8 21680.5 161.691 45.5 307.6 278,1

289.500 6.25159 .3370 .166^ 21070,6 21711.7 161.769 45,4 296.9 280.3

290.000 6.33511 .3530 .1673 21093,2 21743.0 161.847 45.3 287.1 282.4

291.000 6.50281 .3850 .1681 21138.4 21805.4 162.003 45,1 269.7 286.6

292.000 6.67129 .4171 .1689 21183.4 21367.6 162,157 44,9 254.9 290.5

293.000 6.84050 .4492 .1695 21228.3 21929,8 162.311 44,8 242.0 294.2

294.000 7.01037 .4815 .1702 21273.0 21992.0 162.463 44.7 230.7 297.8

295.000 7.18086 .5138 .1708 21317.6 22054,1 162.614 44.6 220.7 301.2

296.000 7.35192 ,5462 .1713 21362.1 22116.2 162.765 44.5 211.8 304.5

297.000 7.52351 .5786 .1718 21406.6 22178.2 162.915 44.4 203.9 307.7

298.000 7.69559 ,6112 .1723 21451.0 22240.2 163.064 44,4 196.7 310.8

299.000 7.86811 .6438 .1728 21495.3 22302.3 163.213 44.3 190.1 313.8

300.000 8,04109 .6765 .1732 21539.6 22364.3 163.361 44.3 184.2 316.7

50
Table CI. (Continued)

10.00 M0L/DM3 ISOCHORE

TEMPERATURE PRESSURE

MPA

ISOTHERM ISOCHORE

riERIV. DERiy.

MPA.DM3/M0L MPA/K

279 500 4.73040

280 000 4.78338

280 500 4.83695

281 000 4.90425

281 500 4.98477

282 000 5.06615

282 500 5.14825

283 000 5.23098

283 500 5.31427

284 000 5.39806

284 500 5.48232

285 000 5.56699

285 500 5.65206

286 000 5.73748

286 500 5.82325

287 .000 5.90933

287 500 5.99572

288 .000 6.08238

288 500 6.16931

289 000 6.25650

289 500 6.34393

290 000 6.43158

291 000 6.60754

292 .000 6.78430

293 .000 6.96180

294 .000 7.13998

295 .000 7.31879

296 .000 7.49819

297 .000 7.67812

298 .000 7.85857

299 .000 8.03950

300 .000 8.22087

.0000

.0000

.0000

.1047

.1243

.1431

.1614

.1793

.1971

.2146

.2321

.2494

.2667

.2839

.3011

.3182

.3353

.3524

.3695

.3865

.4036

.4207

.4548

.4890

.5231

.5574

.5916

.6259

.6603

.6947

.7291

.7636

.1054

.1066

.1078

.1601

.1619

.1635

.1649

.1660

.1671

.1681

.1689

.1698

.1705

.1712

.1719

.1725

.1731

.1736

.1741

.1746

.1751

.1755

.1764

.1771

.1778

.1785

.1791

.1797

.1802

.1807

.1812

.1816

INTERNAL ENERGY

J/MOL

20398.2

20459.4

20521.7

20565.3

20590.2

20614.6

20638.7

20662.6

20686.2

20709.6

20732.9

20756.0

20779.0

20801 .9 20824.7

20847.4

20870.0

20892.5

20915.0

20937.5

20959.9

20982.2

21026.8

21071.2

21115.5

21159.7

21203.9

21248.0

21292 .

1

21336.1

21380.1

21424.0

ENTHALPY ENTROPY cy CP

J/MOL

20871.2

20937.8

21005.4

21055.7

21088.7

21121.2

21153.6

21185.7

21217.6

21249.4

21281.1

21312.7

21344.2

21375.6

21407.0

21438.3

21469.6

21500.8

21532.0

21563.1

21594.2

21625.4

21687.5

21749.6

21811.7

21873.7

21935.8

21997.8

22059.9

221 21.9

22184.0

22246.1

J/MOL.

K

159.351

159.570

159.792

159.947

160.036

160.123

160.208

160.292

160.376

160.458

160.540

160.621

160.702

160.782

160.862

160.941

161.019

161.098

161.176

161.254

161.331

161.408

161.561

161.714

161.865

162.016

162.166

162.315

162.464

J/MOL.

K

SOUND

VELOCITY

M/S

162

162

,612

,759

162.906

121.7

123.4

125.7

50.2

49.3

48.5

47.9

47.4

47.0

46.7

46.4

46.1

45.9

45.7

45.5

45.3

45.2

45.0

44.9

44.8

44.7

44.6

44.5

44.4

44.3

44.2

44.1

44.1

44.0

44.0

44.0

44.0

738.0 234.1

643.5 240.5

575.6 245.9

523.8 250.7

482.5 255.0

448.7 258.9

420.4 262.5

396.3 265.9

375.4 269.0

357.1 272.0

340.9 274.9

326.6 277.6

313.6 280.2

302.0 282.6

291.4 285.0

281.7 287.4

272.8 289.6

264.6 291.8

257.1 293.9

243.5 297.9

231.8 301.7

221.4 305.4

212.3 308.9

204.1 312.3

196.7 315.6

190.1 318.7

184.1 321.8

178.6 324.8

173.5 327.8

51
Table CI. (Continued)

10.25 hOL/DM3 ISOCHORE

TEKPERATURE PRESSURE ISOTHERM ISOCHORE

DERIV. DERIV.

MPA MPA.DM3/M0L MPA/K

INTERNAL

ENERGY

J/MOL

ENTHALPY ENTROPY

J/MOL J/MOL.

K

CV CP

J/MOL.

K

SOUND

VELOCITY

M/S

279.500

280.000

280.500

281.000

281.500

282.000

282.500

283.000

283.500

284.000

284.500

285.000

285.500

286.000

286.500

287.000

287.500

288.000

288.500

289.000

289.500

290.000

291.000

292.000

293.000

294.000

295.000

296.000

297.000

298.000

299.000

300.000

4.73040

4.78338

4.85286

4.93755

5.02305

5.10926

5.19608

5.28346

5.37134

5,45968

5.54845

5.63761

5.72715

5.81703

5.90723

5.99775

6.08855

6.17964

6.27098

6.36257

6.45441

6.54646

6.73123

6.91679

7.10309

7.29008

7.47770

7.66592

7.85469

8.04397

8.23374

8.42397

.0000

.0000

.1428

.1639

.1842

.2041

.2235

.2427

.2616

.2804

.2991

.3177

.3362

.3546

.3729

.3912

.4095

.4278

.4460

.4642

.4823

.5005

.5368

.5730

.6093

.6455

.6818

.7180

.7543

.7906

.8269

.8633

.1054

.1066

.1685

.1702

.1717

.1730

.1742

.1753

.1762

.1771

.1779

.1787

.1794

.1801

.1807

.1813

.1819

.1824

.1829

.1834

.1839

.1843

.1852

.1859

.1867

.1873

.1879

.1885

.1890

.1895

.1900

.1904

20337.9

20398.3

20440.1

20464.2

20487.9

20511.3

20534.6

20557.7

20580.6

20603.4

20626.0

20648.6

20671.1

20693.5

20715.8

20738.1

20760.3

20782.5

20804.6

20826.7

20848.8

20870.8

20914.8

20958.7

21002.5

21046.2

21089.9

21133.6

21177.3

21221.0

21264.6

21308.3

20799.4

20865.0

20913.6

20945.9

20977.9

21009.8

21041.5

21073.1

21104.6

21136.0

21167.4

21198.6

21229.8

21261.0

21292.2

21323.3

21354.3

21385.4

21416.4

21447.5

21478.5

21509.5

21571.5

21633.5

21695.5

21757.5

21819.5

21881.5

21943.6

22005.7

22067.9

22130.1

159.094

159.310

159.459

159.545

159.629

159.712

159.795

159.876

159.957

160.038

160.117

160.197

160.275

160.354

160.432

160.509

160.587

160.664

160.741

160.817

160.893

160.969

161.121

161.271

161.421

161.570

161.719

161.867

162.014

162.161

162.307

162.453

120.1

121.8

48.4

47.7

47.2

46.7

46.3

46.0

45.7

45.5

45.2

45.1

44.9

44.7

44.6

44.5

44.4

44.3

44.2

44.1

44.1

44.0

43.9

43.8

43.8

43.7

43.7

43.7

43.7

43.7

43.7

43.7

579.1 246.7

520.6 252,5

476.1 257,5

440.6 262.0

411.5 266.1

387,0 269.8

366,0 273.3

347.8 276.6

331.9 279,7

317.8 282,6

305.1 285.4

293.7 288.1

283.4 290.6

274.1 293.1

265.5 295.5

257.6 297.8

250.3 300.0

243.5 302.1

237.3 304.2

231.4 306.3

220.9 310.2

211.5 313.9

203.3 317.5

195.8 321.0

189.2 324.3

183.1 327.5

177.6 330.7

172.5 333.7

167,9 336.7

163.6 339.6

82
Table CI. (Continued)

10.50 M0L/DM3 ISOCHORE

:mperature pressure ISOTHERM

DERIV. ISOCHORE

DERIV. INTERNAL ENERGY

ENTHALPY ENTROPY CV CP SOUND

VELOCITY

K MPA MPA.Dh3/M0L MPA/K J/MOL J/MOL J/MOL.J/MOL .K M/S

279.500 4.73040 .0000 .1054 20280.5 20731.0 158.849 118.6

280.000 4.80802 .1928 .1778 20314.9 20772.8 158.972 46.8 463.1 260.9

280.500 4.89731 .2151 .1794 20338.2 20804.6 159.055 46.2 426.7 266.0

281.000 4.98734 .2368 .1808 20361.2 20836.2 159.137 45.8 397.5 270.6

281.500 5.07803 .2580 .1820 20384.0 20867,6 159.218 45.5 373.3 274.7

282.000 5.16932 .2788 .1831 20406.7 20899,0 159.299 45.2 352.8 278.6

282.500 5.26114 .2993 .1841 20429.2 20930,3 159.379 44.9 335.2 282.1

283.000 5.35345 .3196 .1851 20451.6 20961.5 159.458 44.7 319.8 285.5

283.500 5.44622 .3398 .1860 20473.9 20992.6 159.537 44.5 306.3 288.6

284.000 5.53941 .3597 .1868 20496.2 21023.7 159.615 44.4 294.2 291.6

284.500 5.63300 .3796 .1875 20518.3 21054.8 159.693 44.2 283.3 294.4

285.000 5.72695 .3993 .1883 20540.4 21085.8 159.771 44.1 273.5 297.1

285.500 5.82125 .4190 .1889 20562.4 21116.8 159.848 44.0 264.6 299.7

286.000 5.91588 .4386 .1896 20584.4 21147.8 159.925 43.9 256.5 302.2

286.500 6.01083 .4581 .1902 20606.3 21178.8 160.001 43.8 249.0 304.6

287.000 6.10606 .4775 .1908 20628.2 21209.7 160.078 43.7 242.1 307.0

287.500 6.20158 .4969 .1913 20650.0 21240.7 160.154 43.7 235.7 309.2

288.000 6.29736 .5163 .1918 20671.9 21271.6 160.229 43.6 229.8 311.4

288.500 6.39340 .5356 .1923 20693.7 21302.6 160.305 43.6 224.3 313.5

289.000 6.48967 .5549 .1928 20715.4 21333.5 160.380 43.5 219.1 315.6

289.500 6.58619 .5742 .1932 20737.2 21364.4 160.456 43.5 214.3 317.6

290.000 6.68292 .5934 .1937 20758.9 21395.4 160.531 43.4 209.7 319.6

291.000 6.87702 .6318 .1945 20802.3 21457.3 160.680 43.4 201.4 323.4

292.000 7.07191 .6702 .1953 20845.7 21519.2 160.829 43.3 194.0 327.0

293.000 7.26754 .7085 .1960 20889.0 21581.1 160.977 43.3 187.4 330.5

294.000 7,46384 .7468 .1966 20932.3 21643.2 161.124 43.3 181.4 333.9

295.000 7.66078 .7850 .1972 20975.6 21705.2 161.271 43.3 175.9 337.2

296.000 7.85830 .8233 .1978 21018.9 21767.3 161.418 43.3 170.9 340.3

297.000 8.05638 .8615 .1983 21062.2 21829.5 161.564 43.3 166.3 343.4

298.000 8.25498 .8997 .1988 21105.5 21891.7 161.710 43.3 162.1 346.4

299.000 8.45407 .9379 .1993 21148.9 21954.0 161.855 43.3 158.2 349.4

300.000 8.65362 .9762 .1998 21192.2 22016.4 162.000 43.4 154.6 352.2

53
Table CI la. Saturation properties of ethylene

as a function of temperature

COEXISTING PHASE PROPERTIES* LICHJID

:mperature PRESSURE DENSITY LATENT

HEAT

INTERNAL

ENERGY

ENTHALPY ENTROPY cy CP VELOCITY

OP SOUND

K MPA M0L/DM3 J/MOL J/MOL J/hOL J/MOL.

J/MOL.M/S

27V. 700 4.75152 10.481 3216.9 20308,5 20761.9 158.952 47.3 502.2 255.9

279.800 4.76211 10.440 3168.9 20329,8 20785.9 159.035 47.6 519.9 253.6

279.900 4.77273 10.398 3120.0 20351,4 20810.4 159.119 47.8 539 .

251,3

280.000 4.78338 10.356 3069,9 20373.4 20835.3 159.204 48.1 560,0 249.0

280.100 4.79404 10.312 3018.8 20395.8 20860.7 159.291 48.4 583,0 246.6

280.200 4.80473 10.267 2966.4 20418.7 20886.7 159.380 48.8 608,2 244.2

280.300 4.81545 10.221 2912.7 20442.1 20913.2 159.471 49.1 636,0 241.7

280.400 4.82619 10.174 2857.5 20465.9 20940.3 159,564 49.5 666,9 239.2

280.500 4.83695 10.125 2800.8 20490.4 20968.1 159,659 49.8 701,5 236.7

280.600 4.84774 10.074 2742.4 20515.5 20996.7 159,757 50.3 740,2 234.1

280.700 4.85855 10.022 2682.1 20541.2 21026.0 159,858 50,7 784,1 231.4

280.800 4.86939 9.969 2619.7 20567.7 21056.2 159,961 51.1 834.1 228.7

280.900 4.88026 9.913 2555.0 20595.1 21087,4 160,069 51.6 891.6 225.9

281.000 4.89114 9.854 2487.8 20623.3 21119,7 160.180 52 .

958.3 223.0

281.100 4.90206 9.793 2417.7 20652.7 21153.2 160,295 52.8 1036.8 220,0

281.200 4.91300 9.730 2344.3 20683.2 21188.1 160,415 53.4 1130.3 216.9

281.300 4.92397 9.662 2267.1 20715.1 21224,7 160.541 54.1 1243.3 213.7

281.400 4.93496 9.591 2185.5 20748.6 21263,1 160,674 54,9 1382.8 210,3

281.500 4.94598 9.515 2098.6 20784.0 21303,8 160.814 55,8 1558.7 206,8

281.600 4.95703 9,434 2005.5 20821.7 21347.1 160,964 56,8 1787.1 203,0

281.700 4.96810 9,345 1904.7 20862.2 21393,8 161.125 58,0 2094,6 199,0

281.800 4.97921 9,248 1794.0 20906.3 21444,8 161.302 59,5 2528,8 194.7

281.900 4.99034 9.138 1670.2 20955.3 21501,4 161.499 61,3 3183,9 189.9

282.000 5.00150 9.012 1528.0 21011.1 21566,1 161.724 63.6 4273,4 184,4

282,100 5.01270 8.861 1357.2 21077.6 21643.3 161.993 66.8 6396.2 178,0

282.200 5,02393 8.662 1134.4 21163.6 21743.6 162.344 72.2 12021.7 169,5

282.300 5,03519 8.330 766.1 21305.2 21909,6 162.928 85.6 50818.0 154,5

282.345 5.04030 7.634 0,0 21610,1 22270.3 164.203 O.'O

54
Table Cllb. Saturation properties of ethylene

as a function of temperature

COEXISTING PHASE PROPERTIES. VAPOR

:mperature PRESSURE DENSITY LATENT

HEAT INTERNAL ENERGY

ENTHALPY ENTROPY CV CP VELOCITY

OF SOUND

K MPA M0L/DM3 J/hOL J/MOL J/MOL J/MOL.

J/MOL.

M/S

281.400 4.93496 5.720 2185.4 22585.8 23448.5 168.440 62.7 2253.7 199.0

281.500 4.94598 5.792 2098.6 22548.4 23402.4 168.269 63.6 2545.1 197.7

281.600 4.95703 5.869 2005.5 22508.0 23352.7 168.086 64.7 2921.0 196.2

281.700 4.96810 5.953 1904.7 22464.0 23298.5 167.887 65.9 3423.2 194.5

281.800 4.97921 6.046 1794.0 22415.2 23238.8 167.668 67.4 4125.8 192.4

281.900 4.99034 6.151 1670.2 22360.3 23171.6 167.424 69.2 5173.2 190.0

282.000 5.00150 6.273 1528.0 22296.7 23094.0 167.142 71.5 6887.8 186.9

282.100 5.01270 6.420 1357.2 22219.7 23000.5 166.804 74.7 10155.8 182.7

282.200 5.02393 6.614 1134.4 22118.4 22878.0 166.364 80.0 18527.2 176.2

282.300 5.03519 6.940 766.1 21950.2 22675.7 165.641 93.0 72255.4 162.1

282.345 5.04030 7.634 0.0 21610.2 22270.4 164.203 0.0

55
Table Cllla. Saturation properties of ethylene as a funtion of pressure

COEXISTING PHASE PROPERTIESr LIQUID

:mperature PRESSURE DENSITY LATENT

HEAT INTERNAL

ENERGY

ENTHALPY ENTROPY cy CP VELOCITY

OF SOUND

K MPA M0L/DM3 J/MOL J/MOL J/MOL J/MOL.

J/MOL.

M/S

279.686 4.75000 10.487 3223.7 20305.5 20758.4 158.941 47.3 499.8 256.2

279.780 4.76000 10.443 3178.6 20325.5 20781.1 159.018 47.5 516.2 254.0

279.874 4.77000 10.409 3132.7 20345.8 20804.0 159.097 47.8 534.0 251.9

279.968 4.78000 10.369 3085.9 20366.4 20827.4 159.177 48.0 553.2 249.7

280.062 4.79000 10.329 3038.3 20387.3 20851.0 159.258 48.3 574.0 247.5

280.156 4.80000 10.287 2989.7 20408.5 20875.1 159.340 48.6 596 .

245.3

280.249 4.81000 10.245 2940.2 20430.1 20899.6 159.424 48.9 621.5 243.0

280.342 4.82000 10.201 2889.5 20452.1 20924.6 159.510 49.3 648.7 240 .

280.435 4.83000 10.156 2837.6 20474.5 20950.1 159.597 49.6 678.7 238.3

280.528 4.84000 10.111 2784.5 20497.4 20976.1 159.687 50.0 712.0 236.0

280.621 4.85000 10.064 2729.9 20520.8 21002.7 159.778 50.3 748.9 233.5

280.713 4.86000 10.015 2673.9 20544.7 21030.0 159.871 50.7 790.4 231.0

280.806 4.87000 9.965 2616.1 20569.2 21057.9 159.967 51.2 837.1 228.5

280.898 4.88000 9.914 2556.6 20594.4 21086.6 160.066 51.6 890.1 225.9

280.989 4.89000 9.861 2495.0 20620.3 21116.2 160.168 52.1 950.8 223.3

281.081 4.90000 9.805 2431.1 20647.0 21146.8 160.273 52.6 1021.0 220.5

281.173 4.91000 9.747 2364.7 20674.7 21178,4 160.382 53.2 1102.9 217.7

281.264 4.92000 9.687 2295.4 20703.4 21211.3 160.495 53.9 1199.9 214.8

281.355 4.93000 9.624 2222.8 20733.3 21245.5 160.613 54.5 1316.1 211.8

281.446 4.94000 9.557 2146.4 20764.5 21281.4 160.737 55.3 1458.0 208 .

281.536 4.95000 9.486 2065.5 20797.4 21319.2 160.867 56.2 1634.7 205.4

281.627 4.96000 9.411 1979.3 20832.2 21359.3 161.006 57.1 1860.5 202.0

281.717 4.97000 9.329 1886.5 20869.5 21402.2 161.155 58.3 2158.1 198.3

281.807 4.98000 9.240 1785.6 20909.7 21448.6 161.315 59.6 2566.6 194.3

281.897 4.99000 9.142 1674.2 20953.7 21499.6 161.492 61.2 3159.1 190.0

281.987 5.00000 9.031 1548.5 21003.1 21556.8 161.691 63.2 4087.2 185.2

282.076 5.01000 8.900 1401.8 21060.3 21623.2 161.923 65.9 5722.8 179.7

282.165 5.02000 8.739 1220.9 21130.2 21704.7 162.208 69.9 9256.3 172.8

282.254 5.03000 8.514 969.4 21227.0 21817.8 162.604 77.3 21237.6 163.0

282.343 5.04000 7.909 301.1 21486.9 22124.2 163.686 127.5 1.8003-I-6 128.3

282.345 5.04030 7.634 0. 21610.1 22270.3 164.203 0.

56
Table Clllb. Saturation properties of ethylene as a function of pressure

COEXISTING PHASE PROPERTIES^ VAPOR

:mperature PRESSURE DENSITY LATENT

HEAT INTERNAL ENERGY

ENTHALPY ENTROPY cy CP VELOCITY

OF SOUND

K MPA M0L/DM3 J/MOL J/MOL J/MOL J/MOL.

J/MOL.

M/S

281.446 4.94000 5.752 2146.4 22569.0 23427.8 168.363 63.1 2378.5 198.4

281.536 4.95000 5.819 2065.5 22534.1 23384.7 168.204 64.0 2670.5 197.2

281.627 4.96000 5.891 1979.3 22496.6 23338.6 168.034 65.0 3041.2 195.8

281.717 4.97000 5.968 1886.5 22456.0 23288.7 167.851 66.1 3526.4 194.2

281.807 4.98000 6.053 1785.6 22411.6 23234.2 167.652 67.5 4186.7 192.3

281.897 4.99000 6.148 1674.2 22362.1 23173.8 167.431 69.1 5133.8 190.1

281.987 5.00000 6.255 1548.5 22305.9 23105.2 167.183 71.1 6596.8 187.3

282.076 5.01000 6.381 1401.8 22239.9 23025.0 166.892 73.8 9127.7 183,8

282.165 5.02000 6.538 1220.9 22157.8 22925.6 166.535 77.8 14453.0 1 78 .

282.254 5.03000 6.759 969.4 22043.1 22787.2 166.039 84.9 31738.1 170.5

282.343 5.04000 7.360 301.1 21740.5 22425.3 164.752 133.1 2.1474+6 132.4

282.345 5.04030 7.634 0. 21610.2 22270.4 164.203 0.0

57
APPENDIX D

Listing of Computer Program for Table Generation

58
c

C MAIN PROGRAM TO GENERATE ISOCHORE TABLES AS IN REPORT

C IMPLICIT REAL*8(A-H»0-Z)

REAL ANAMESrQNAMES

C COMMON /COEFS/ A(20) »Q(20) . JAA( 20 ) » ANAMES( 20) »QNAMES( 20)

COMMON /CRITS/ TC» XMLUGTr RHOC»PC»PCON»UCONf SCON.DPCON

COMMON /THERM/ IPHASEf riPIili»DpriT»UfH.ENTROPfCPf CW » CS.COMP

C DATA TMINrTMAX»riMIN»riMAX/279.4D0»303.15D0f5.7D0»10.6D0/

DATA XMLUGT/28.0541D0/

C CALL CONGEN

C TC=0(4)+A(8)

RH0L=Q(5)-iA(3)

PC=aC6)+Q(3)

PCON=PC/TC

UC0N=1.D3*PC

SCON=UCON/TC

DPCDN=PC0N/RH0C/RH0C

C

1 WRITE(6»101>

101 FORMATC <ENTER DENSITY (M0L/DM3)> ') READ(5.100,END=999) DENS

100 FORMAT ( ) C IF(DENS.LE.DMAX. AND. DENS. GE.DMIN) GO TO 11 URITE(6»102)

102 FORMAT (' <**THE DENSITY INPUT IS OUTSIDE RANGE OF '» l'EOUATION"S VALIDITY**:')

GO TO 1 C

11 IDFIND=0

C WRITE(6»130)

130 FORMATC ENTER START TEMP. » STOP TEMP.f S INCREMENT')

READ(5rl00)- Tl.T2fTINC

IF(Tl.LT.TMIN) T1=TMIN

IF<T2.6T.TMAX) T2=TMAX

C URITE(6rllO) DENS

110 FORMAT( 'I'f5(/)»T20»F5.2»' M0L/DM3 ISOCHORE' »/)

URITE(&flll)

111 FORMAT( ' ' fT2» 'TEMPERATURE»T15r 'PRESSURE ' f T25> ' ISOTHERM'

r

1T35. 'ISOCHORE' »T45» 'INTERNAL' »T55, 'ENTHALPY' »T65» 'ENTROPY'?

2T76 » ' CV ' » T86 »' CP ' » T94 »

' SOUND '

)

WRITE(&.113)

113 FORMATC ' fT26f 'DERIV. ' rT36. ' DERI V. '» T46» 'ENERGY ' .T93»

I'VELOCITY')

URITE(6f 112)

112 FORMATC 'r/»T6f' K 'fT16f' MPA '.T23»' MPA.DM3/M0L ' f T35f

1' MPA/K ',T45»' J/MOL '»T55f' J/MOL 'fT64»' J/MOL.K ' » T78»

2' J/MOL.K '.T93.' M/S '»/) C XNUM=(T2-T1>/TINC

INUM=IFIX(XNUM)

C

DO 200 I=1fINUM

TEMK=T1+TINC*(I-1)

C CALL THERMO ( I DF IND » TEMK » DENS r PRESS r R » THETA

)

C IFdPHASE.GT.l. > GO TO 12 WR I TE ( 6 » 120 ) TEMK , PRESS » DPDD » DPDT r U , H f ENTROP . CV » CP » CS

120 FORMATC ' rT4 »F7.3f T13»F9.5»T26f F6. 4 » T35f F6.4f T43f F9. 1

»

1 T53»F9.1.T64»F8.3.T75»F5.1rT83fF7.1.T94fF5.1)

GO TO 13

12 URITE<6»120) TEMK>PRESS»DPDDf DPDT>U»Hf ENTROPf CV

13 CONTINUE

C 400 CONTINUE

200 CONTINUE

URITE(6f 121)

121 FORMAT( '1' »19(/))

60 TO 1 C 999 STOP

END

59
c

C THIS PROGRAM CALCULATES THE COEXISTENCE PROPERTIES

C INDEPENDENT VARIABLE IS TEMPERATURE

C IMPLICIT REAL*8 (A-H»0-Z) REAL TITLE REAL ANAMESfQNAMES

COMMON/CDEFS/A ( 20 ) » Q ( 20 ) » JAA < 20 ) » ANAMES < 20 ) » ONAMES ( 20

)

COMMON/SATUR/I WAP f HEAT fRHOL»RHOG

COMMON/THERM/ IPHASE » DPDD . DPDT » U > H » S r CP » CW » CS » COMP

COMMON/CRI TS/TC » XMLUGT » RHOC f PC » PCON f UCON » SCON » DPCON

DATA DMIN»DMAX/5.5D0.10.5D0/

DATA XMLWGT f TMIN/28 .0541D0 »279. 7D0/

C CALL CONGEN

Q<3>=A(8)*Q(7)

TC=Q(4>-fA<8)

fiHQC^G ( 5 ) +A ( 3

)

PC=CU6)+a(3)

PCON=PC/TC

UC0N=1.D3*PC

SCON=UCON/TC

DPCON=PCON/RHOC/RHOC

C WRITE(6.333)

333 FORMATC <ENTER SELECTION PARAMETER. ... 1=LI0»-1=VAP>'

READ(5»1) IVAP IP(IVAP.EO.-l). TITLE='VAPOR ' IF<IVAP.EQ.l) TITLE='LIQUID'

IFdVAP.EQ.-l) TMIN=281.4

201 FORMAT (1H1////»4X» 'COEXISTING PHASE PROPERTIES* ' » A6//4Xf ' TEMPERAT

lURE' .2X. 'PRESSURE DENSITY LATENT INTERNAL ENTHALPY' »3Xf

2 'ENTROPY CV CP VELOCITY' /39X» 'HEAT ENERGY' »38X»

3' OF SOUND '//8X»' K MPA M0L/DM3 J/MOL J/MOL 'r 4 3Xf'.- J/MOL J/MOL. K J/MOL. K M/S '/)

IFIN=0

C WRITE(6»334)

334 FORMATC <ENTER START TEMP.fSTOP TEMP.. 8 INCREMENTS')

READ(5>1) Tl.T2rTINC

IF(Tl.LT-TMIN) T1=TMIN

URITE(6.201) TITLE T=T1-TINC

100 T=T+TINC

IF(T.GT.T2) IFIN=1

IF(T.GE.TC) IFIN=2

IF(T.GE.TC) T=TC-1.D-14

D=RHOC

CALL THERMO (0»T»D>P»R.THETA)

IF(IFIN.Ea.2) HEAT=0.D0

IF(IFIN.EQ.2) WRITE(6f202) TrPC.RHOCfHEAT.UrH»S»HEAT

202 F0RMAT(lX/F13.3.F11.5.F10.3.F10.1»F9.1fF10.1»F11.3rl7X»F9.1////)

IF<T.LT.TC .AND. CP.LT. 99999. 99) WRITE(A»203)

1 T»P.D.HEATfU.H.S»CV.CP»CS

203 F0RMAT(F13.3,F11.5»F10.3»F10.1»F9.1fF10.1»F11.3fF8.1»F9.1»F9.1)

IICP=0

IF<T.LT.TC .AND. CP.GT .99999. 99. AND. IFIN.NE. 2) IICP=1

IF(IICP.EQ.l) ICP=DL0G10<CP)

IF(IICP.EO.l) CP=CP/10.D0**ICP

IFdICP.EQ.l) URITE(6»204) Tf P»Df HEAT»U»H»S»CV»CP» ICP.CS

204 FORMAT (F13.3.F11.5»F10.3fF10.1.F9.1»F10.1»F10.3»F8.1.F9.4.'+'» II

1 >F8.1>

IFUFIN.EO.O) GO TO 100

C URITE(6»210)

210 FORMATC ' .20</))

STOP

C

1 FORMAT ( ) END

60
SUBRCIUI INE THERMO (inriNrtfTrrwfrRl.THl ) c

C 1. NOT ON THE SATURATION CURWE (ISAT=0) : C GIVEN THE TEMFEKAIURE T(K) ANH HENSITY li<KG/M3)f THIS ROUTINE

C CALCULATES PRESSURE P(MPA) AND ITS DERiyATiyES W.R.T D AT

C CONSTANT T IipniKMPA/ ( M0L/DM3 ) ) ANH W.R.T T AT CONSTANT D

C riPriT(MPA/K)T ENERGY U AND ENTHALPY H(J/MOL)» ENTROPY AND

C SPECIFIC HEATS CP AND CV(J/MOL.K)f VELOCITY OF SOUNn CS(M/S)»

C AND COMPRLSSIEtlLITY COMPd/MPA).

C IF THE ENTRY POINT IS IN THE 2-PHASE REGION (IPHASE=2) IT

C RETURNS CP=COMP=CS=0.

C IF IDFIND=1 IT CALCULATES ONLY P AND DPDD.

C 2. ON THE SATURATION CURVE (ISAT.NE.O) : C GIVEN THC TEMPERATURE Tf IT CALCULATES THE DENSITY Df LATENT HEAT

C ANIi ALL THE ABOVE PROPERTIES ON THE VAPOR SIDE (ISAT=-l)f OR THE

C LIQUID SliiC (JSAT = 1), C IMPLICIT DOUBLE PRECISIOW (A-HfO-7)

COMMON/TH£ f<M/IFHASE t KPntt » DPUT » U » H . ENTROP » CP » CV » CS

»

COMP

COhMON/S ATUR/ iSAT , HEAT f DLIQ » DVAP

COMMON/CDEFS/A ( 20 ) » Q ( 20

)

COMMON/CR I TS/TC r XMLWGT r RHOC » PC t PCON . UCON » SCON » DPCON

DIMfTNSION S<2) »XK(2) .SD(2)

EQUIVALENCE (PW1»A(5) )»(PU2fA(4) > , <PU3.A<2) )»

1 (AMC.A(13) ). <AM1.A( 14) ). <AM2»A(15) ) r <AM3f A(16) )

»

2 < POO . Q ( 1 1 ) ) . ( P20 . Q ( 1 2 ) > . < P40 f Q ( 1 3 ) > » 3 <P01.Q(18) )r (P21.0(19) ) F <P41.Q(20) )r 4 (AAf A< 10) ) f (XK0»A(7) ) f (XKl »A( 12) >

.

<PUllfQ<9) )

f

5 ( ALPHA. Q(10) )f <ALHIfO<15) > r (BESQ»A(9)

)

DATA XMLUGT/28.0541D0/

C XK<1)=XK0

XK<2)=XK1

TEE=(T-TC)/TC

TIJ = -TC/T

DTU=1.D0+TU

IF(ISAT.NE.O) GO TO 10 RHa=D/RHOC

CALL CONVER ( RHO . TEE » AMU . THl . R 1 r RHO 1 » S f RHODI . ERR > GO TO 12

10 TH1=1,D0

IF< ISAT.EQ.-l) ^H1=-0.99999999999999999D0

IFdSAT.EG. 1) TH1= .99999999999999999D0

Rl=nTU/(l.D0-BESQ)

CALL SS(Rl.THlfS.SD)

RH0=TH1*<XK0*R1**A(6)+XK1*R1**Q(16) )+A( 1 )*( S( 1)+S<2 )

)

RHD=1.D0+PU11*DTU+RH0

D=KHO*RHOC

AMU=0.D0

12 TT1=TH1*TH1

TT2=TT1*TT1

PUO= 1 . DO + DTU* < PUl +DTW* ( PU2 + DTU*PU3 )

)

PWMU=AMU*RHODI

POTH=POO+P20*TT1+P40*TT2

P1TH=P01+P21*TT1+P41*TT2

DPW0=XK0«P0TH«R1** ( 2 . -ALPHA

)

DPU1=XK1«P1TH*R1**<2.-ALHI)

DPU=AA*<DPW0+DPW1)

PU=PU0+PUMU+DPU

IF(IDFIND.EO.l) GO TO 11 DP0DT = PU1 +DTU* ( 2 . D0)ltPW2+3 . D0*PU3*DTU )_ DMODT = AM1+DTUI*(2.DO«AM2 + 3.DO«AM3*DTW)

UU=DP0DT-RH0*DM0DT+PW1 1*AMU+S ( 1 ) +S ( 2

)

HW=PU-TW*UU

AMU=AMU+AMC+DTU* ( AMl+DTU* ( AM2+DTU*AM3 )

)

SU=HU-RHO*AMU

61
D2F0riT = 2 . D0*FU2+6 . riO*PU3*DTU

ri2M0riT = 2 . IiO*AM2 + 6 . D0*AM3*DTU

11 ir(DAEiS(THl).GE.l.-DO) GO TO 13

IPHASE=1

CALL AUX ( Rl f THl r D2PIIT2 » D2PDMT t D2PEiH2 r AA f XK » SD » CVCOEX

)

riPDIi = EipC0N*ri*T/D2PD«2

IFdDFIND.EQ.l) GO TO 15

riPDTCD=riPOriT+PUl l * ( AMU-RH0/D2PDM2 ) +S ( 1 ) +S ( 2 ) -D2PDMT*RH0/ri2PnM2

DPWDTU=PW-TW*DPDTCn

CVITW2 = ri2P0riT-RH0*ri2M0riT+ri2PriT2-(PUlH-D2PtiMT)**2/Ii2PIiM2

Cyw=CyiTU2*TU*TW

Cpy=CVU + ri2PriM2#riPUDTU*DPUDTU/<RH0*RH0)

coMP=i.iio/(ri*ripDri)

CS= 1 . ti3*liSQRT ( CPU/CyU*IlpriD ) /DSQRT ( XMLWGT

)

IFdSAT.EO.O) GO TO 14 KH01 = 1 .Ii0+PW11*DTU + A(l )*(S( 1 )+S(2) ) RH02=XK0*R1*«A(6)+XK1*K1»*0<16)

IiLIH=RH0C*(RH01-»-RH02)

nWP^RHaC* ( RHOl -RH02 ) riPDT2 = PU-TU* < UU+RHO*riMODT

)

HEAT= 1 . ri3*T* < PC0N*DPLiT2 ) * ( 1 . DO/DVAP- 1 . DO/DLIQ

)

GO TO 14

13 IPHASE=2

riPDEi=0. IF(IDFINIi.EO.l) GO TO 15

ripIiTCD = UU+RHO*IiMODT

DPWIiTU=PU-TW*DPriTCD

Cy I 0= ( 2-ALPHA ) *

(

1 . -ALPHA ) *R1 «* ( -ALPHA ) «XKO*POTH

CVI1=(2.-ALHI )*<1.-ALHI )*R1*«(-ALHI )*XK1*P1TH

CyiTU2=ri2P0riT-RH0*D2M0riT+AA*<l./(l.-EiESQ) )**2* (CVIO+CVI 1

)

CyU=CyiTU2*TU*TU,

CPU=0.

^OMP=0.

cs=o.

14 DPriT = PCON*DPUriTU

SCONli = SCON/ri

U=UU*UCON/D

H=HW*SCONri*T

ENTROP = SU*SCONri

cy=cvw*scoNri

cp=cpw*scoNri

15 P=PU*PCON*T

RE TURN

END

62
i

SUBROUTINE CONNER ( RHO» TEE » AHU , THl rRl fRHOlS r SI » RHODI »ERR0R1

)

C THIS ROUTINE TRANSFORMS TEMPERATURE AND DENSITY TO THE

C PARAMETRIC VARIABLES R AND THETA ACCORDING TO THE REVISED

C AND EXTENDED SCALING EQUATIONS.

IMPLICIT REAL*8 (A-H»0-Z)

COMMON /COEFS/ A(20)»Q<20)

DIMENSION S1<2)»SD<2)

EQUIVALENCE(BETA,A<6)).(DELTA»A(ll))F(XKlfA<12>)f (CC.Ad))

1 . ( ALHI » Q ( 1 5 ) ) . ( ALPHA »Q(10))»(BESQ.A(9))»(P11.Q(9))

2 r(DELI»Q(14))»(PlUFQ(18))»(P2UFQ(19) ) » <P4Wr Q(20)

)

3» (AA.A(IO) )f (XK0.A(7) )» (S00fA(17) ) , (S20fA<18) )f (BETAIfQ(16) ) TSTAR = TEE+l.DO

DTSTIN = l.DO - (l.DO/TSTAR)

R1=DTSTIN

IF ( DTSTIN. LT.O.) Rl=DTSTIN/( 1 .-BESQ)

TH1=0.

IF<DTSTIN.LT.O.) TH1=1.

CALL SS(RIfTHIfSIfSD)

RHODI = l.DO + P11*DTSTIN

RHODIT = RHODI + CC*S1<1) + CC«S1<2)

DRHO = RHO - RHODIT

AMU = O.DO

IF(DTSTIN.GT.O.DO) GO TO 1 RHOICO = XK0*R1**BETA + XK1*R1**BETAI

TUOFAZ = RHOICO

IF (DABS(DRHO) .GT. TUOFAZ) GO TO 1 RHOIS = DSIGN(RHOICOfDRHO) + CC*S1(1)

THl = DSIGN(I.DOfDRHO)

ERRORl = l.DO

GO TO 999

1 CONTINUE

IF < DRHO. NE. O.DO) GO TO 2 THl = O.DO

Rl = DTSTIN

RHOIS = CC*S1(1)

2 CONTINUE

C RULE FOR FIRST PASS

Yl = DTSTIN

DENl = RHO - RHODIT

CALL RTHETA(R1fTH1»DEN1fY1)

TT=TH1*TH1

AMU = AA* R1**(BETA*DELTA)#TH1#(1.D0-TT)

Yl = DTSTIN + CC*AMU

CALL SS(RIfTHIfSIfSD)

RHOUEG = XK1*<R1##BETAI)*TH1 + CC*S1<2)

RHOIS = DENl + CC*Sl(l) + RHOUEG

ERRORl = RHO - RHODI - RHOIS

IF< DABS<ERR0R1) .LT.l.D-5 ) GO TO 999

C RULE FOR SECOND PASS

DEN12 = RHO - RHODI - CC*S1(1) + RHOUEG

IF (DEN12.EQ.DEN1) DEN12 = DENl - l.D-OA

CALL RTHETA(R1»TH1fDEN12fY1)

TT = TH1*TH1

AMU = AA* R1**(BETA*DELTA)*TH1*(1.D0-TT)

Yl = DTSTIN + CC*AMU

CALL SS(R1»TH1fS1fSD)

RHOUEG = XK1*R1#*BETAI*TH1 + CC*S1(2)

RH01S2 = DEN12 + CC*S1(1) + RHOUEG

ERR0R2 = RHO - RHODI - RH01S2

IF( DABS(ERR0R2).GT.1.D-5 ) GO TO 998

ERRORl = ERR0R2

RHOIS = RH01S2

GO TO 999

63
yya LuNTiNut

C RULE FOR NTH PASS

DEN2 = riEN12 DO 44 ISIG = 1»10

SLOPE = (ERR0R2-ERR0Rl)/<riEN2 -DENl)

HOLD = DEN2

DEN2 = DENl - (ERRORl/SLOPE)

CALL RTHETA(R1»TH1»DEN2»Y1)

TT = TH1#TH1

AMU = AA* R1**(BETA*DELTA)*TH1*<1.D0-TT)

Yl = DTSTIN + CC*AMU

CALL SS<R1»TH1»S1»SD)

RHOUEG = XK1*R1#*BETAI*TH1 + CC*S1(2)

RHOIS = DEN2 + CC*S1(1) + RHOUEG

ERRORl = ERR0R2

ERR0R2 = RHO - RHODI - RHOIS

IF< DABS<ERR0R2) .LT.l.D-6 ) GO TO 999

DENl = HOLD

44 CONTINUE

IF(DABS(ERR0R2).GT.l.D-6) WRITE <6f66) ERR0R2»RH0r DTSTINf DEN2»CC

66 FORMATdXf 'CONVER DOES NOT CONyERGE 'r5E12.6)

999 CONTINUE

RETURN

END

EOF AT LINE 87

«

BLOCKDATA

DOUBLE PRECISION AfQ

COMMON /C0EFS/A(20) »Q(20) » JAA(20) rANAMES(20) f QNAMES(20)

C THIS SUBROUTINE SUPPLIES THE PARAMETERS USED IN THE EQUATION

C OF STATE. DATA A/-.0078HD0»0.D0,0.D0.-18.1475D0»5.3350D0» .32?ID0»1. t2289

IDO. 0. DO » 1. 3757D0 f 19. 3214D0» 4. 82D0».54617D0» -36. 48891D0r -27,39553400

2»-12.2091D0»-11.8802D0f4*0.D0/

DATA Q/- . 008369D0 . - . 001 2 18D0 r . DO » 282

.

3452D0t 7 . A34D0 » 5 . 0403D0

1 » . 1 13090D0 » - . 777D0 » 12*0 . DO/ DATA ANAMES/6HC »6HC0T3 .6HDELR0C»6HC0T2 .6HDPDT »6HBETA

1»6HK0 f6HDELTC »6HB*B »AHA .6HDELTA »6HK1 »6HMUC

2.6HMU1 »6HMU2 »6HMU3 . 6HS00 »6HS20 »6HS01 »6HS21 / DATA QNAMES/2*6H .6HDELPC »6HTC ,6HRH0C t6HPC

l»6HDPCDTC»6HSL0PDIf6HPll »6HALPHA ,6HP00 »6HP20 r6HP40

2»6HDELTAI»6HALPHAIf6HBETA I t 6HGAMMAI f 6HP01 »6HP21 .6HP41 / END

EOF AT LINE 17

*

64
SUBROUTINE CONGEN

C THIS SUBROUTINE CALCULATES ALL QUANTITIES NOT DEPENDENT ON R OR THETA

IHPLICIT DOUBLE PRECISION (A-H»0-Z)

COMMON /COEFS/ A(20).Q(20)

DATA DELPP ? DELPM . DELPPH . DELPMH/1 . D-6 » -1 . D-6 » 1 . OOOOOIDO t . 999999D0/

EQUIVALENCE ( DELI .Q( 14) ) » (DRHOC » A< 3) ) . ( BETA» A( 6) ) » (DELTA» A( 11 )

)

1 » ( C0TEE2 . A ( 4 ) ) » ( DPDT f A < 5 ) ) » ( BESQ » A ( 9 )

2»(CC.A(l))»(AA»A<10))f <TCK.Q(4)) . <RHOC >Q(5) )

(PCfQ(6) ) . (XKO. A(7)

)

3»(ALHI»Q<15))f(BETIiiQ(16))F(GAMIfQ(17))»(P01»Q(18))f (P21fQ(19))

4»(ALPHAfQ(10))»<POO»Q(ll))»<P20rQ(12))»(P40»Q(13))»(P41»Q(20))

5»<S00»A(17)

)

t (S20»A(18)) »<S01»A(19) ) » ( S21 » A< 20)

)

ALPHA = 2. DO - A<6)*(A(11) + l.DO ) GAMMA = BETA*<DELTA - l.DO) DELI = 0.50D0

ALHI = ALPHA - DELI

BETI = BETA + DELI GAMI = GAMMA - DELI

ERR = 2.D0)KBETA*DELTA - l.DO

POO = (BETA*(DELTA-3.D0)-BESQ*ALPHA#GAMMA)/(2.D0«

1 BESQ*BESQ* ( 2 . DO-ALPHA ) * ( 1 . DO-ALPHA ) *ALPHA

)

P20=-( BETA* (DELTA-3.)-BESQ*ALPHA*ERR)/(2.*BESQ«<l.-ALPHA)«( ALPHA))

P40=(ERR-2. )/2. /ALPHA

500 = (2.-ALPHA)*P00

520 = -BETA*(DELTA-3.)/2./BESQ/ALPHA

DA=Q(1)

DB=Q(2)

RA = DA/ (l.DO - BESQ)

RB = DB/(1.D0 - BESQ)

SUO = S00+S20

DRO=SUO* ( RA** < 1

. -ALPHA ) -RB** ( I. -ALPHA )

)

POl = (BETA*(DELTA-3.D0)-3.D0*DELI-A(9)*ALHI«GAMI)

1 / ( 2 . DO*A ( 9 ) *A ( 9 ) * < 2 . DO- ALH I ) * ( 1 . DO- ALHI ) * ALH I

)

P21 = -<(BETA*(DELTA-3.D0)-3.D0*DELI-A<9)*ALHI*ERR)/

1 <2.D0*A<9)*(1.D0-ALHI)*ALHI))

P41 = (.5*ERR - l.)/ALHI

501 = (2.-ALHI)*P01

521 = -(BETA*DELTA-3.*BETI)/2./BESQ/ALHI

PTU = POl + P21 + P41

SUl = S01+S21

DR1=SU1*(RA**( 1 .-ALHI )-RB**( 1 .-ALHI )

)

GO TO 10 C ENTRY Q96EN

10 IF(XKO.LE.O.DO) XK0=0.0001D0

CC Q(6)=A(13)

CC Q(8)=A(14)

D1=CC«AA*XK0*DR0

D2=CC*AA*A(12)*DR1

Q(9) = (Q(8)«(1./<1.-DB)-1./(1.-DA) )+Dl+D2)/<DB-DA)

Q(7)=<A(5)+1.D0)*Q(6)/Q(4)

Q(3)=A(8)*Q<7)

RETURN

END

EOF AT LINE 53

65
SUBROUTINE AUX( Rl »TH1 » D2PDT2,D2PIiMT»D2PDM2r AA»XK»SD»CyCOEX)

C THIS ROUTINE CALCULATES SECOND DERiyATIVES OF THE SCALED

C EQUATION OF STATE

IMPLICIT REAL*8 (A-H»0-Z)

COMMON /COEFS/ A(20)jQ<20)

DIMENSION XK(2)fS<2)» SD(2) »U< 2 ) » Y( 2) »Z(2 ) .C0EX(2)

EQUIVALENCE (CC» A( 1 ) ) » ( BETA» A(6 ) > » ( BESQ» A( 9) ) » (DELTA* A( 11 )

)

If (ALPHA»Q<10))»<S00fA(17)),(S20fA(18)),(S01»A(19))f (S21jA<20) ) DELI = O.DO

S<

1

)=S00+S20*TH1*TH1

S(2)=S01+S21*TH1*TH1

SD<1) = 2.*TH1*S20

SD(2) = 2.*TH1*S21

UU = O.DO

YY = O.DO

ZZ = O.DO

GAMMA = BETA*<DELTA - l.DO)

TTl = TH1*TH1

TER = 2.D0*BETA*DELTA - l.DO

6 = (l.+(BES«*TER-3.)*TTl - BESQ«( TER-2 . ) *TT1*TT1

)

CVCOEX = O.DO

DO 30 I = 1»2 ALHI = ALPHA - DELI

BETI = BETA + DELI GAM I = GAMMA - DELI U<I)=(1.-ALHI)*(1.-3.*TT1)*S<I)-BETA*DELTA*(1.-TT1)*TH1*SD<I)

U(I) = (U(I) #<R1*«(-ALHI)))/G

W(I) = W(I)*XK(I)

UU = UU -I- U(I)

Y(i) = BETI*(1.D0-3.D0*TT1)*TH1 - BETA*DELTA*( 1 . DO-TTl )#TH1

Yd) = (Yd) #(R1#*(BETI - l.DO)))*XKd)/G

YY = YY + Yd)

Zd) = l.DO - BESQ«(1.D0 - (2 . DO*BETI ) )«TT1

Zd) = (Zd) *(Rl**(-GAMI)))*XKd)/G

ZZ = ZZ + Zd)

Al = (BETA*(DELTA-3.D0)-3.D0*DELI-BES0*ALHI*6AMI)

1 / ( 2 . D0*BESQ*BESQ* ( 2 . DO-ALHI ) * < 1 . DO-ALHI ) *ALHI

)

A2 = l+( (BETA*(DELTA-3.D0)-3.D0*DELI-BESQ«ALHI*TER)/

1 (2.D0*BESQ*(1.D0-ALHI)*ALHI)

)

A2 = - A2

A4 = l.D0+((TER-2.D0)/(2.D0*ALHI))

Fl = Al + A2 + A4

COEXd) = ((2. DO - ALHI)*(1.D0 - ALHI )*(R1**( -ALHI ) )«Fl*XKd ) > CVCTOEX = CVCOEX + COEXd)

DELI = 0.5D0

30 CONTINUE

+ (CC««2))KAA«UU

D2PDT2 = AA:«UU D2PDMT = YY + AA«CC*UW

D2PDM2 = ZZ/AA + 2.D0*CC«YY

RETURN

END

EOF AT LINE 51

66
SUBROUTINE DFINrKT .P, ti,DGUESS . DMINtDMAX)

C

C GIVEN THE TEMPERATURE T(K). PRESSURE P(MPA). AND AN INITIAL

C GUESS DENSITY DGUESS (KG/M3 ) » THIS ROUTINE FINDS THE

C CORRESPONDING DENSITY D<KG/M3) IN THE RANGE (DMINfDMAX).

C IF T IS BELOW THE CRITICAL ISOTHERM^ DGUESS MUST BE SET

C EQUAL TO THE CRITICAL DENSITY, OTHERWISE IT MAY YIELD

C ERRONEOUS RESULTS. IF THE ENTRY POINT IS IN THE 2-PHASE

C REGION CRITICAL DENSITY IS RETURNED FOR D. C IMPLICIT REAL#8(A-H»0-Z)

COMMON/THERM/IPHASE,DPDD

C D=DGUESS

DO 10 1=1,20

CALL THERMO(lTT,D,PPfR,THETA)

PDIF=PP-P

IF(IPHASE.EQ.2) GO TO 18 DELD=-PDIF/DPDD

D=D+DELD

IF(D.LT.DMIN) D=DMIN

IF(D.GT.DMAX) D=DMAX

IF<DABS(DELD/D).LT.l.D-6) GO TO 19 GO TO 10 18 IF<DABS(PDIF).LE.O.DO) GO TO 19 IF(PDIF.LT.O.DO) D=DMAX

IF<PDIF.GT.O.DO) n=DMIN

10 CONTINUE

WRITE(<i,21) T,P,PP,D

21 FORMATOX, 'DFIND DOES NOT CONUERGE" :

' r 4F12 . 4) 19 RETURN

END

EOF AT LINE 32

SUBROUTINE TFIND(P»T)

IMPLICIT DOUBLE PRECISION (A-H»0-Z)

COMMON/THERM/IPHASEjDPDD»DPDT»U»H,ENTROP»CP»CVrCSrCOMP

COMMON/SATUR/iyAP.HEATfRHOLfRHOG

C0MM0N/C0EFS/A(20) »Q(20)

COMM0N/CRITS/TC»XMLWGT.RHOC.PCTpC0N»UCONfSC0N»DPCON

T=TC-1.D0

n=RH0C

iSAyE=iyAP

IVAP=2

DO 10 1=1.20

CALL THERMQ(O.T»D.PP»RlrTHl)

DT=(PP-P)/DPDT

T=T-DT

IF(T.GT.TC) GO TO 12 IF(DABS(DT/T) .LT.l.D-8> GO TO 20 GO TO 10

12 T=TC-0.001D0

10 CONTINUE

WRITE<6»11) P.PPrT

11 FORMATdX/lX'TFIND DOES NOT CONVERGE :'f3F12.6/)

20 IVAP=ISAVE

RETURN

END

67
MAIN PROGRAM TO GENERATE TABLES

IMPLICIT REAL*S('A-HfO-Z)

REAL ANAMES^QNAMES

IN DIFF-ERENT UNITS

COMMON /COEFS/ A<20) y 0(20) , JAA<20) » ANAMES(20) » QNAMES(20)

COMMON /UNITS/ ITf IDr IPy IHf NTyNDy Np!.NHyFTy FD s-FPy FH

COMMON /CR I TS/ TC y XMLUGT y RHOC y PC y PCON y UCON y SCON y DPCON

COMMON /THERM/ IPHASE y DPDD y DPDT y U y H y ENTROP y CP y CV y CS y COMP

C

C

1 01

00

c

DATA TMIN y TMAX y DMIN y riMAX/279 ABO y 303 . 1 5D0 y 5 . 7110 y 1 . 6T)0/

DATA XMLUGT/23,0541D0/

CALL CONGEN

TC=Q(4)fA<8)

RH0C=:a(5)+A(3)

PC=Q(6)+a(3)

PC0N=:PC/TC

UC0N=1,D3*PC

SCON=UCON/TC

DPCON^:PCON/RHOC/RHOC

CALL UNIT

WRITE<6yl01)

FORMATC <ENTER DENSITY (M0L/DM3)> ')

READ < 5 y 1 00 y END-=--999 ) DENS IN

FORMAT < ) DENS--::DENSIN*FD

IF ( DENS LE » DMAX . AND DENS GE . DMI N

)

WRITE(6yl02)

GO TO 11

L02 FORMAT (' <*)KTHE DENSITY INPUT

1 'EQUATION' 'S VALIDITY**;:-' ) GO TO 1

11 IDFIND-=0

IS OUTSIDE RANGE OF

WRITE(Ayl30)

130 FORMAT (' ENTER START TEMP.

READ(5yl00) TTl y TT2y TTINC

T1=TTT(TT1)

T2=TTT(TT2)

IF(T1,LT»TMIN) T1=TMIN

IF(T2.GT.TMAX) T2=TMAX

TT1=TTI(T1)

TT2-TTI(T2)

y STOP TEMP»y X INCREMENT')

URITE(6yllO) DENSIN

110 FORMAT ISOCHORE'y/) ( 'l'y5(/)yT20yF5.2y

URITE(6ylll)

111 FORMAT (

' ' yT2y 'TEMPERATURE' yT15y 'PRESSURE ' y T25y ISOTHERM'

y

lT35y 'ISOCHORE' yT45y 'INTERNAL' yT55y

2T7A 9'CV'

T86 y

' CP ' y T94 y' SOUND '

)

URITE<6yll3)

ENTHALPY ' y TA5 y

' ENTROPY '

y
113 FORMAT (' 'fT26f 'DERI V. ' yT36y 'DERiy* 'fT46y 'ENERGY' »T93f

I'VELOCITY* .M/S')

C

XNUM=(TT2-TT1)/TTINC

INUM=IFIX(XNUM)

C

DO 200 I=:lfINUM

TEMK=TT1+TTINC*( I-l

)

C

TEMKK=TTT(TEMK)

CALL THERMO ( I DP I ND » TEMKK » DENS » PRESS f R t THETA

)

DPDD=DPDD*FP/FD

DPDT=DPDT*FP*FT

PRESS=PRESS*FP

U=U*FH

H==H*FH

ENTROP=ENTROP*FH*FT

Cy=CV*FH*FT

CP=CP*FH*FT

C

i IFdPHASE.GT.l, ) GO TO 12

URI TE ( 6 ? 1 20 ) TEMK y PRESS y DPDD y DPDT y U y H ? ENTROP y C V y CP y CS

120 FORMAT( ' '

y T4 y F7 . 3y T13y F9 5y T26 y F6 . 4 y T35 y F6 . 4 y T-43y F9 , 1 y 1 T53yF9.1yTA4yF3.3yT75yF5.1yTS3yF7»lyT94yF5,l)

GO TO 13

12 UR I TE ( 6 y 1 20 ) TEMK y PRESS y DPDD y DPDT y U y H y ENTROP y C

V

13 CONTINUE

C

400 CONTINUE

200 CONTINUE

WRITE(6yl21)

121 FORMATCl' yl9(/) ) GO TO 1 C

999 STOP

END

L

69
FUNCTION TTT(T)

FUNCTION TO CONVERT INPUT TEMPERATURES IN EXTERNAL UNITS TO DEG K

DOUBLE PRECISION Ty TTTyFT^FD* FP^FH

COMMON /UNITS/ IT» ID.. IP» IHyNTy NDy NP^ NHs-FTi-Friy FPi-FH

GO TO (Iy2y3y4) ylT

1 TTT=T

FT=1.D0

RETURN

2 TTT=T+273. 151.10 FT^--1.D0

RETURN

3 TTT=T/l,ei:iO

FT=.5555555555S56D0

RETURN

4 TTT-= ( T i459 . 67D0 ) /I , SDO

FT=.55t

RETURN

END

FUNCTION TTI(T)

FUNCTION TO CONVERT INTERNAL TEMPERATURES IN DEG K TO EXTERNAL UNIT

D U B L E P R E C I S 1 N I" y T" T I y F T y F' D «

I- F^' y F- H

COMMON /UNITS/ IT y ID y IP y IH y NT y ND y NP y NFIv FT y FD ? FP y FH

GO TO (5y6y7yS)yIT

5 TTI=T*1.D0

RETURN

6 TTI=T-273.15D0

TTI=:TTI*1,D0

RETURN

7 TTI--=T*1»SD0

RETURN ^._

8 TTI-:=T*1 , 8D0-459 . 67D0

RETURN

END

7Q
10

11

12

13

1-4 15

SUBROUTINE UNIT

IMPLICIT DOUBLE PRECISION (A-HyO-Z)

COMMON /UNI TS/ I T y I D y I P y I II y NT y ND y NP y NH y FT y FD

DIMENSION FFD ( 4 ) y FFP ( 4 ) y FFII (6) y NNT ( 4 ) y NNP ( 4

)

DIMENSION NND(4)yNNH(A)

FPyFH

DATA

DATA

DATA

DATA

DATA

DATA

DATA

DATA

16HY

FFD/0 0356454 1 DO y 35 » 6454 1 DO y 1 . DO

FFP/ 1 . DO y 1 . DO y 9 . 86923266 7D0 y 1

FFH/2* » 0356454 1 DO y 1 . DO y 8 . 51379D

NNT/lHKylHCylHRylHF/

NND/6HKG/M3 y6HG/CM3 y6HM0L/L y6HLB/FT3/

NNP/3HMPA y 3HBAR y 3IIATM y 3IIPSI/

NNH/6HKJ/KG y6H J/G y6HJ/M0L y6ilCAL/G

y .5709853D0/

5»037738D0/

-3 9 »23S8459D0y .01532476D0/

WRITE(6yll)

URITE(6yl2)

READ(5ylO)

NT-=NNT(IT)

URITE(6yll)

URITE(6yl3)

READ(5ylO)

ND=NND(ID)

FD::=FFD(ID)

WRITE(6yll)

URITE(6yl4)

READ(5ylO)

NP=NNP(IP)

Fp=:FFP(IP)

WRITE(6yll)

WRITE(6yl5)

READ(5ylO)

NH"NNH(IH)

FH--=FFiKIH)

RETURN

FORMAT ()

FORMAT (

FORMAT (

FORMAT ( FORMAT (

FORMAT (

IRIES/MOLy

END

A 1 y A2 y A3 y A4 y A5 y A6 y A7 y A8/6HTEMPER • 61

y 6HPRESSU y 6HRE y 6HENERG Y y 6H

AlyA2

y6HCAL/M y6HBTU/LB/

lATURE y6HDENSITy

/

IT

A3yA4

ID

A5

IP

A7yA8

IH

ENTER UNITS

CHOOSE FROM

CHOOSE FROM

CHOOSE FROM

CHOOSE FROM

6-BTU/LB')

CHOSEN FOR ?A6)

l::^a;iEG Ky 2^==DE0 Cy 3^^DEG Ry 4:^:^DEG F')

1^^^KG/M3y 2:=G/CM3y 3^^=M0L/Ly 4::::LB/FT3 ' ) l^:^MPAy 2==BARy 3^^:^ATMy 4^^PSIA')

1=KJ/K0y 2^J/Gy 3^:=J/M0Ly 4^=CALnRIES/G y ^CALi

71
Appendix E. Units and Conversion Factors

Units used in the Tables

Pressure - MPa

Temperature - K Density - mol/dm^

Energy, Enthalpy - J/mol

Entropy - J/(mol -K)

Specific heat - J/(mol'K)

Speed of sound - m/s

Molecular weight

Gas constant*

of ethylene M = 28.0541

R = 8.31434 J/mol

Reduction Factors

Pressure

MPa to Multiply table value by

Pabar

atmosphere

psi, Ibf/in^

106

10

9.869233

145.037738

Density

mol/dm^ to Multiply table value by

kg/m^

lbm/ft3

28.0541

1.7513585

Energy, Enthalpy

J/mol to Multiply table value by

kJ/kg

BTU/lbm

0.0356454

0.01532476

Entropy, Specific heats

J/(mol.K) to Multiply table value by

kJ/(kg.K)

BTU/(lbm-R)

0.0356454

0.00851375

Temperature

K to Transform table value by

°C (T,°C) = (T,K) - 273.15

°F {T.°F) = 1[(T,K) - 273.15] + 32

R (T.R) = 1

(T,K)

Speed of sound

m/s to Multiply table value by

ft/s 3.28083

*The actual value of the gas constant is not required for the programs

in this Tech. Note. The value given here is that used in reducina the

original Burnett PVT data [5,24] and in NBS Tech. Note 1045 [7].

72
FIGURES

73

(0 Q.

0)

3

(A

Vi

0)

Density, mol/dm'

280 290

Temperature, K

300

Fig. 1 Range of validity of the present formulation. Left: in

temperature - density space. Right: in pressure - temperature

space.

75
2-

-I -2

-3

20

10

-10

DENSITY DEVIATIONS

~1 r T T

284-287

K

"/ y \

\

^ Q-v-^T;^7^^77a-^;-

\

_Li_j L 1

5.5 6.5 7.5 8.5 9.5 10.5

-20.

"^

\ ^^

^ r~ 279-284K

-^p-g—+-n—»-

1 I I 1

5.5 6.5 7.5 8.5 9.5 10.5

20

10

Q. 0.

-10-

-20

--MJ xHLSB-B

^DH +TWW

HLSB-A *TZ

1 ' r~

279-284 K J

. re

-4B*-

5.5 6.5 75 8.5 95 10.5

DENSITY (mol/dm^)

Fig. 2a Departures of the experimental densities of Douslin and Harrison {<),

Hastings et al . (a, sample A and X, sample B), Trappeniers et al . ( + ) and

Thomas and Zander (*) from our formulation (baseline) if compared at the

same temperature and pressure. The dashed curve represents the departures

of the McCarty-Jacobsen formulation from our own.

76
DENSITY DEVIATIONS

<

0.4

0.2

•0.2

0.4

-T \

f T 298.15 K * // \

^y

4 + \

-—^^.^j;^^.^..^!] ^-M—^—^^^—aJ i L J L 5.5 6.5 7.5 8.5 9.5 105

<

0.4

0.2

0.2

-0.4

293. I5K

- / \

/ \

1—^—

r

+/ \

7

\ + + / ^

'

\ /

/

J L 5.5 6.5 7.5 8.5 9.5 10.5

<]

1.2

0.6

•06

-1.2

—

/

1 r- "T—

r

\

287-290K -- MJ XHLSB-B

< DH +TWW

D HLSB-A *TZ

\

-rT--»'J'&4f—ViJD q^ ^ ^ " /

\ A-

<*-7^^-

^ .

5.5 6.5 7.5 8.5 95 10.5

DENSITY (mol/dm^)

Fig. 2b As in Fig. 2a.

77
0.4

0.3

0.2

? 0.1

PRESSURE DEVIATIONS

"n—

r

T T

284- 287 K

\

^-/

<l -0.1

-0.2

-0.3

-0.4

^ <^^^ ^<^<^

\ < A

\.+ .^

MJ

< DH

HLSB-A

X HLSB-B

+ TWW

* TZ

_U ^ \ \ L 1

0.2

0.1

5.5 6.5 7.5 8.5 9.5 10.5

CL

-01

-0.2

\

' v~

279-284 K J

/'"^ + .—

.

o.o'^^3M^ ^ai/

*^

/

'^

Pc

_l L 5.5 6.5 7.5 8.5 9.5 10.5

DENSITY (mol/dm^)

Fig. 3a Departures of the experimental pressures of Douslin and Harrison ('^),

Hastings et al . (a, sample A and X, sample B), Trappeniers et al . (+)

and Thomas and Zander (*) from our formulation (base line) if compared

at the same temperature and density. The dashed curve represents the

departures of the McCarty-Jacobsen formulation from our own.

78
PRESSURE DEVIATIONS

Q_

0.4|-

0.2

0.0

0.2

0.4

298.I5K

J^?^.bA-*,1-+.fej:^^

\+ . \

\

/

\_^/

J L 5.5 6.5 7.5 8.5 9.5 10.5

a.

0.3

0.2

0.1

0.0

0.1

-0.2

-0.3,

"T r 293.1 5K

/

/

< . /

^ \

+

-

fc \.^

J L 5.5 6.5 7.5 8.5 9.5 105

0.3

0.2|-

Q_

0.1

0.0

-0.1

-0.2

-0.3

T 1 '

\

^ r 287- 290

K

/

/

_:,J!U-+1b^lJ^

\

M -I D — MJ

< DH

HLSB-A

X HLSB-B

+ TWW

*TZ

1 A.

N A

5.5 6.5 7.5 8.5 9.5

DENSITY (mol/dm3)

Fig. 3b As in Fig. 3a.

79

105
0.002

VAPOR PRESSURE DEVIATIONS

0.001 -

cE

Q_

0000

-0.001 -

-0.002

1 A DH

1

1

1

1

1 '

- n A

- X B

A

A

^

A

A

S >€ Sx

D 4 5

5^

^

D Q

>*S<

D D

X

'1

1 1

1

Q

1

1

1

1

1 1 . 279 280 28! 282

TEMPERATURE (K)

Fig. 4 Departures of the experimental vapor pressures of Douslin and Harrison

(A ) and Hastings et al . (q , sample A and X, sample B) from the present

formulation.

283

80
DEVIATIONS OF COEXISTING DENSITIES

E

T3

O

E.

<1

0.04

003

002

001

000

•0.01

0.02

0.03

-004

_

1 -

1 1 1

1

1 ' — __ DH

-X

• HLSB-A

HLSB-B

f i —

l_ 4.

r

- t X —

Jt i i

-

- Tc

1 —

1 1 1 1 1 1 i 1 - 279 280 281 282

TEMPERATURE (K)

283

Fig. 5 Departures of experimental coexisting densities of Douslin and

Harrison {^) and Hastings et al . (, sample A and», sample B)

from the present formulation. Upward-pointing line segments denote

vapor densities; downward-pointing ones denote liquid densities.

81
SPEED OF SOUND

350

280.1 5 K

7.5 8.5

DENSITY (mol/dm3)

10.5

Fig. 6 The speed of sound as measured by Gammon compared with the present

formulation.

82
SPEED OF SOUND

DEVIATIONS OF GAMMON'S DATA

IQ5

DENSITY (mol/dm3)

Fig. 7 Departures of Gammon's spee formulation.

d of sound data, in %, from the present

83
20

10

~"T

1 T a D.H. —M.J.

T

\—

r

Q?V°

u u

^

-10

303.15 K

20

10

p

-20,

20

J I LL

1—^—

r

288.I5K

-i -10

r20 i__^ L 1 J L 5.5 6.5 7.5 8.5 9.5 105 ""5.5 6.5 7.5 8.5 9.5 10.5

O

E

10-

1 r 1

\

\—

298.15 K

X -10

-20,

20

10

a D n n °

J \ \A^

Tj—q^m-^

30

20 h

10

^—I—

r

/ /

-10

J -20

-30

T

1

1 1 1—

•-^ 283.I5K-

\\

-CT—n^•^jn n

Pc

J_Lj I L

T

293.1 5 K

OV-^:>-D u u

5.5 6.5 75 8.5 9.5 105 ""^55 6.5 75 85 9.5 10.5

30

20

10

y" \

1

\ r282.35KH

\

-lOK

-2Q

Pc

J L

n D D

-10-

-20

-30

J:^—o-^ :^Ct]

J \ L J L 5.5 6.5 7.5 8.5 9.5 10.5 55 6.5 75 8.5 9.5 10.5

DENSITY (mol/dm^)

Fig. 8 Comparison of the enthalpies of ethylene according to different

formulations. The base line is the present formulation, which was anchored to the Douslin and Harrison data at 7 mol/dm^, 288.15 K. The squares are from the Douslin-Harrison calculation and the dashed

curves from the McCarty-Jacobsen formulation.

84
CO

< -0.06

6.5 7.5 8.5 - DENSITY (mol/dm^)

Fig. 9 The difference between the prediction of the McCarty and Jacobsen

surface for several first-derivative thermodynamic properties and

the present formulation.

85
298.15

293.15

288.15

283.15

10.5

10.5

(A o

10

-10

-20,

ItriM i<

JJ L 5.5 6.5 7.5 8.5 9.5

DENSITY (mol/dm^)

10.5

Fig. 10 Percentage differences between the McCarty-Jacobsen and the present

formulation for second-derivative values.

86
o

E

140

NEHZAT et a I PRESENT FORMULATION

140

120

100

1 1 1 1 1 \—

r 283.35 K

140

>O 1201-

"1 1

1 1 1 1 1 r 282.45 K 282.35 K

DENSITY (mol/dm^)

Fig. 11 Comparison of the specific heat C^ predicted by Nehzat et al . [23] with our formulation in the

one-phase region above the critical temperature.

87
o

E

240

200

160

120

80

40

"^D

T—I

1 1 r 282.25 K

'SD.

-^Dy \

J U I I I L

D NEHZAT et a I — PRESENT FORMULATION

240

200

160

1-"^D.

6 7 8 9 10

240

120-

80-

40

n—I—I—1—I—I

\—I

281.35 K

'"^.

J L

1 --.

J I I I I L. 10

o

2001-

160

120

80

40

T r 1—I—I

\—

r

280.45 K

n*

a-r

•DI

I J I I U I I 1 1 L 6 7 8 9 10 DENSITY (mol/dm^)

Fig. 12 Comparison of the specific heat Cw predicted by Nehzat et al . [23] with our formulation in

the two-phase region below the critical temperature.

88
240

o

o

en

Q

UJ

LlI Q.

210 1

80 -

150 -

120

1 1 1 1 1 1 1

D r-i ^^^

° ° °

a ^^v

—

- "^ —

" ^ GAMMON °\ —

D NEHZAT et al

°

" PRESENT FORMULATION

D

1 1 1 1 1 ill

279 280 281 282

TEMPERATURE (K)

283

Fig. 13 Comparison of the formulation of Nehzat et al . [23] and of our formulation with the

experimental speed of sound data of Gammon for the saturated vapor below the critical

temperature. The dashed part of the curve indicates our formulation when extrapolated

outside its range of validity.

89
P,MPa

280 290 300 310 320 330

T, K

Fig. 14 The regions of P-T space that should be avoided in custody transfer if

the pressure is measured to, respectively* 0.1%, 0.05% or 0.02% and an accuracy of 0.1% is desired in density.

90
Fig. 15 The regions of P-T space that should be avoided in custody transfer if the temperature is measured to, respectively,

0.02 K, 0.01 K and 0.005 K and an accuracy of 0.1% is desired

in density.

91
285 290 295 300

T, K

305 310

Fig. 16 The regions of P-T space that should be avoided in custody transfer if respectively 0.005%, 0.01% or 0.02% (in mole fraction) of an impurity very different in volatility from ethylene is present and an accuracy of 0.1% is desired in density

tr U.S. GOVERNMENT PRINTING OFFICE: 1984-420-997/126

92
NBS-n4A IREV. 2>8CI U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. NBS TN 1189

2. Performing Organ. Report No, 3. Publication Date May 1984

4. TITLE AND SUBTITLE

A Thermodynamic Surface for the Critical Region of Ethylene

5. AUTHOR(S)

J.M.H. Levelt Sengers, G.A. Olchowy, B. Kamgar-Parsi , and J.V. Sengers

6. PERFORMING ORGANIZATION {(fyo/nt or other thon NBS. see in struct /on sj

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

I. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State. ZIP)

See footnote on page 1,

10. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-I8S, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

Tables are presented of thennodynamlc properties of ethylene in the range 279-300 K in

3 temperature, 5.75 - 10.5 mol/dm in density, which range Includes the critical point. The tables presented here are based on the critical-point scaling laws and incorporate the critical anomalies as presently known from renormalization-group theory. The tables comple- ment the formulation of the equation of state of fluid ethylene by McCarty and Jacobsen

(NBS Tech. Note 1045, 1981) which does not claim accuracy near the critical point. The predictions of the present formulation are compared with four sets of recent PVT data, and with speed-of- sound and enthalpy data. Tables are presented of pressure, energy, enthalpy,

entropy, specific heats and speed of sound as function of temperature along finely-spaced

isochores. The computer program required for table generation is included. Even if the surface were perfect, the reliability of densities calculated at experimental pressures and temperatures of limited accuracy declines rapidly as the critical point is approached. Contour plots in P-T space are presented of regions to be avoided in custody transfer for given uncertainties in pressure , temperature and sample composition.

12. KEY WORDS (S/x to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

critical region; custody transfer; density; enthalpy; ethylene; equation of state;

impurity; scaling laws; specific heat; speed of sound; supercritical extraction;

thermodynamic properties

13. AVAILABILITY ^^ Unlimited

I I For Official Distribution, Do Not Release to NTIS

S^ Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C

20402. [^ Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

95

15. Price

USCOMM-DC e043>P80



NBS TECHNICAL NOTE 1189

A Thermodynamic Surface for the Critical Region of Ethylene

May 1984

Erratum

Equation (A. 28), top p. 18, should read:

Wi (e) = [(1 - a.) (1 - 30^) s.(e)- 36 (1 - 9^) 6 s\ (6)] / q(e)

\

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