NBSIR 74-398

NAT'L INST. OF STAND & TECH

PROVISIONAL VALUES FOR THE

THERMODYNAMIC FUNCTIONS OF ETHANE

Robert D. Goodwin 320- 3 IT?

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

3'10 -3 o-o o

June 1, 1974

Prepared for

The American Gas Association

Wilson Boulevard

tfon, Virginia 22209

/OO

• ULSb

0<L

!?7f

NBSIR 74-398

PROVISIONAL VALUES FOR THE

THERMODYNAMIC FUNCTIONS OF ETHANE

Robert D. Goodwin

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

June 1, 1974

Prepared for

The American Gas Association

1515 Wilson Boulevard

Arlington, Virginia 22209

U S DEPARTMENT OF COMMERCE. Frederick B Dent. Secretary

NATIONAL BUREAU OF STANDARDS Richard W Roberts Director

TABLE OF CONTENTS

Page

PREFACE vii

1. INTRODUCTION 1

2. PHYSICAL PROPERTIES AND THEIR REPRESENTATION . . 2

2.1 Fixed-Point Constants 2

2.2 Melting Line and Vapor Pressures 3

2.3 The Orthobaric Densities. 5 2.4 The Virial Equation 9

2. 5 The Equation of State 11

2.6 The Ideal Gas Functions 13

2.7 The Heats of Vaporization 14

2.8 Specific Heats for Saturated Liquid 15

2.9 Specific Heats Cp (T) along Isobar P^ 15

3. COMPUTATIONAL METHODS 16

3. 1 The Homogeneous Domain 16

3.2 The Vapor -Liquid Transition. 17

3.3 Compressed Liquid States 17

4. TESTS AND COMPARISONS 18

4.1 The P-p-T Compressibility Data 18

4.2 Calculated P(p) Critical Isotherm 19

4.3 Heats of Vaporization and Closure Computation. . . .- . 19

4.4 Heat Capacity for Saturated Liquid. 20

4.5 Specific Heats, C (p, T) 20

ir 4.6 Comparison of Enthalpies 20

4.7 Speed of Sound for Saturated Liquid 20

iii
TABLE OF CONTENTS (Continued)

Page

5. TABLES OF PHYSICAL AND THERMODYNAMIC

PROPERTIES 21

5. 1 Calculated P-p-T Isochores and Isotherms 21

5.2 The Joule -Thomson Inver sion Locus 21

5.3 Thermophysical Properties of the Saturated Liquid . . 21

5.4 Thermophysical Properties along Selected Isobars. . . 21

6. COMMENTS AND RECOMMENDATIONS 21

7 . ACKNOWLEDGMENTS 23

8. BIBLIOGRAPHY 24

APPENDIX A. Symbols and Units 31

APPENDIX B. Fixed-Point Values 32

APPENDIX C. Exposition of the Equation of State 33

APPENDIX D. Manuscript, "The Vapor Pressures of Ethane" . 35

APPENDIX E. Manuscript, "Ethane Virial Coefficients and

Saturated Vapor Densities" 58

APPENDIX F. Manuscript, "The Orthobaric Densities of

Ethane, Methane, Oxygen, and Fluorine ... 79

APPENDIX G. Manuscript, "Liquid-vapor Saturation

(orthobaric) Temperatures of Ethane

and Methane" Ill

APPENDIX H. Computer Programs for Equation of State .... 123

APPENDIX I. Computer Programs for Thermofunctions .... 142

LIST OF FIGURES

Figure 1. The locus of recent P-p-T data 159

Figure 2. Generalized locus of isochore inflection points .... 160

Figure 3. Generalized behavior of the critical isotherm .... 160

Figure 4. Generalized behavior of the locus 0(p) 1 6

Figure 5. Generalized behavior of the function $(p, T) 1 62

IV
TABLE OF CONTENTS (Continued)

Page

Figure 6. Generalized behavior of the function iji(p, T) 162

Figure 7. Behavior of coefficients B(/») , C(^>) for methane .... 163

Figure 8. Presumed behavior of C(p) for hydrogen 164

Figure 9. Generalized density-temperature phase diagram. . . 165

Figure 10. Comparisons for saturated liquid ethane 166

Figure 11. Speeds of sound for saturated liquid ethane 1 6

LIST OF TABLES

Table 1. Experimental and calculated vapor pressures ..... 168

Table 2. Comparison with vapor pressures of Regnier 5 Table 3. Experimental and calculated saturated liquid

densities 170

Table 4. Vapor densities via vapor -pre s sure and virial

equations 171

Table 5. Experimental and calculated saturated vapor

densities 172

Table 6. Experimental and calculated liquid saturation

temperatures 173

Table 7. Experimental and calculated vapor saturation

temperatures 174

Table 8. Experimental and calculated second virial

coefficients 175

Table 9. Experimental and calculated third virial

coefficients 177

Table 10. Summary of P-p-T data 10

Table 11. Coefficients of the equation of state 178

Table 12. Experimental and calculated P-p-T data 179

Table 13. Experimental and calculated ideal gas functions .... 200

Table 14. Interpolated ideal gas functions 201

Table 15. Experimental and calculated heats of vaporization. . . 202

v
TABLE OF CONTENTS (Continued)

Page

Table 16. Experimental and calculated specific heats for

saturated liquid . .... 203

Table 17. Experimental and calculated specific heats C (T)

on isobar Pp 204

Table 18. Calculated P(p) critical isotherm 205

Table 19. Loop closure computations for staurated liquid .... 207

Table 20. Experimental and calculated specific heats Cp(p,T). . 208

Table 21. Comparison of enthalpies for saturated liquid,

J/mol 213

Table 22. Comparison of enthalpies, J/mol 214

Table 23. Calculated P(T) isochores 215

Table 24. Calculated P(p) isotherms . 237

Table 25. The Joule -Thomson inversion locus 262

Table 26. Thermophysical properties of the saturated liquid . . 263

Table 27. Thermophysical properties along isobars 266
PREFACE

The Cryogenics Division of the National Bureau of Standards,

with support from the American Gas Association, is engaged in a program to provide input data and computational methods for physical and

thermodynamic properties of the constituents of liquefied natural gas

mixtures (LNG). These thermophysical properties are the basis of all

LNG technology. All operations such as liquefaction, separation,

storage, pumping, transport, custodial transfer, and regasification

will benefit from accurate data. As the commercial value of LNG

depends on its heat of combustion, the densities of LNG mixtures and

other requisite properties are important data.

The compositions of LNG mixtures vary widely, depending on

the source and selective vaporization during handling. To predict

properties of mixtures, it is essential to know accurately the properties

of the pure components and of selected binary mixtures, so that the

excess property (over the mole- fraction average of the components)

can be examined.

The equation of state of pure components is an essential tool

in work on mixtures because from this single formulation there can be

obtained not only the density but also thermodynamic properties such as

the enthalpy and specific heats at any desired temperature and pressure

for which the component exists as a fluid.

A major contribution from this laboratory for computations on LNG and its components is the development of a simple, rational

equation of state which originates on the liquid-vapor coexistence

boundary, and gives a qualitatively correct behavior for derived specific

heats, especially about the critical point. A form of this equation was

used in our recently completed, comprehensive project on the major

Vll
component of LNG, namely methane, "The Thermophysical Properties

of Methane from 90 to 500 K at Pressures to 700 bar. " NBS Technical

Note 653, April, 1974.

In addition to the above publication, this laboratory has provided

accurate experimental data on the compressibilities, vapor pressures,

saturated liquid densities, specific heats, sound velocities, dielectric

constants, refractive indices, and viscosities of compressed and liquid

methane at temperatures down to 90 K.

A similar comprehensive project on ethane now is under way. The

present report makes use of available physical properties data to obtain

tables of thermodynamic functions, and provides the first of such tables

available for liquid ethane below its normal boiling point temperature

(184. 5 K). In this work we use a simplified and more highly constrained

version of the equation of state formerly used for methane. Auxiliary

functions also are improved to accommodate the enormous range of ethane

vapor pressures and saturated vapor densities. The use of these new

analytical descriptions of PVT data for ethane does not in any way invalidate the methods used to compute the thermodynamic properties of

methane in NBS TN 653. The equation of state used for methane in TN

653 had nine least- square s coefficients, and thereby gives a better representation of some of the experimental PVT data than does the present,

more highly constrained equation with only five such coefficients. For

ethane, the present equation of state is valuable because the available

PVT data are less precise (over the entire P(p,T) surface ) than tho se used for methane in TN 653. Further work on the equation of state has

been carried out to obtain the simplest possible form, amenable to corresponding states computations on mixtures. This work, "Equation of

State for Thermodynamic Properties of Fluids, " was submitted to the

NBS Journal of Research in October, 1974.

viii
PROVISIONAL VALUES FOR THE

THERMODYNAMIC FUNCTIONS OF ETHANE*

Robert D. Goodwin

Thermophysical properties are tabulated at integral

temperatures over the entire range of fluid states from 90

to 600 K along isobars to 700 bar. A new, rational equation

of state is employed for the first time. Thermodynamic

functions in the compressed liquid at T<T are obtained by

c use of specific heats C (T) along a high-pressure isobar.

P

Keywords: Densities; enthalpies, entropies; equation of

state; internal energies; isobars; isochores; isotherms;

Joule- Thomson inversion; latent heats of vaporization;

melting line; orthobaric densities; specific heats; speeds

of sound; vapor pressures.

1. INTRODUCTION

The economic importance of methane and ethane, as the major

components of liquefied natural gas (LNG), is well known. Our objective is to produce basic thermodynamic information, needed for the

prediction of properties of the constituents of liquefied natural gas mixtures. For the wide range of compositions encountered, it will be neces

sary to utilize accurate thermodynamic properties ofthepure components

We recently have published the properties of methane [25]. The

present work on ethane provides background on available physical properties data, and may serve engineering needs for thermodynamic

properties until such time as new physical data permit a revision of

the table s .

* This work was carried out at the National Bureau of Standards under

sponsorship of The American Gas Association.

1
All of the analytical formulations of physical properties data

in this report are new as compared with [25]. The major contribution

of present work is development of a rational equation of state. As in [25],

our description of the P(p, T) surface originates on a given liquid-vapor

coexistence boundary (vapor-pressure and orthobaric densities equations).

It yields a maximum in the specific heats C (p, T) at the critical point,

and has only five arbitrary coefficients to be found by least squares

from experimental P-p-T data. We give constants of this equation of

state both for methane and for ethane because uniform methods of

computation will be helpful with mixtures.

Some recent thermal data have been especially valuable for

our computation of the thermodynamic network. These are the ideal

gas functions of Chao et al. [8], and the low temperature specific heats

C (T) of Furtado along isobars [20].

Symbols and units of this report, listed in Appendix A, are the

same as for methane [25]. For equation of state (5) the gas constant is

R = (0.0831434) • (d ) bar/K, consistent with use of the dimensionless

density, p h d/d^_.

2. PHYSICAL PROPERTIES AND THEIR REPRESENTATION

2 . 1 Fixed- Point Constants

These values are listed in Appendix B. For methane, they are

taken from [25].

The triple-point temperature and pressure for ethane are from

our analysis of ethane vapor pressures [26]. The liquid density is a short extrapolation of the saturated liquid densities of Miller [48]. The

vapor density is given by intersection of our present virial equation of

state with our vapor-pressure locus [27].

The critical-point temperature and density for ethane were adjusted by examination of the critical isotherm from the present equa2
tion of state. Our value of T = 305.37 K agrees with the recent experic mental observation of Strumpf et al[68-a], namely T

c = 305.368 ± 0.005 K.

Our critical density, = 6. 74 mol/4 may be compared with 6. 83 ±

0. 07 mol/4 from [68-a], with 6. 79 ± 0. 02 mol/4 from [49], and with

6.87 mol/4 from [14]. Critical densities reviewed in [ 14, 17, 70]

range from 6.75 ± 0.07 to as high as 7.32 mol

/

-t , a s pr e ad of 8/o

.

Our critical pressure of 48. 755 bar at T = 305. 37 K may be compared with other authors by use of the slope of the vapor pressure

curve at the critical point, namely dP^/dT = 1. 04 bar/K. Most recently, for example, Douslin and Harrison [14] give = 48. 718 bar at

T = 305. 33 K.

c The reader should note that our "critical density" is essential for

the present equation of state to give a critical isotherm with no negative

slopes, (SP/d p)rp 2: 0. Our procedure is an altogether new method for

x c finding this characteristic constant, but may depend heavily on the analytical form of the equation of state used [29a]. It follows that our "critical density, " dc , should be regarded as a fitting parameter, and not necessarily as the best value for this characteristic constant.

2. 2 Melting Line and Vapor Pressures

For the melting line of ethane we have found only the rough data

of Clusius and Weigand to 42 bar [ 11] . In the Simon equation [25],

P = P + aT(T/T ) g -?

t I t we assumed e = 2, finding A = (1. 01325)- (2840. 0) bar from their data by

averaging P/ ! (T/T ) £

-l

The vapor pressure equation (2) for ethane is an extension [ 26]

of our early form [23],

2 3 4 . , 3/2 . . 4n(P/P ) = a- x + b- x + c- x + d- x + e- x- (1-x)

f (2)

where the argument is x = (1 -T /T)/(l -T /T ), and the coefficients are t t c

3
Coefficients for Vapor Pressure Equation (2)

Methane Ethane

10.7954 9166

8. 3589 9001

-3. 1149 0770

-0.6496 9799

6. 0734 9549

Table 1 for ethane compares the data.

After the present report was completed, we received the vapor

pressures of Regnier [58] from 80 to 135 K. His results for the liquid

were described in mm Hg by

log 10 (P) = 7. 75-881 /T.

The following Table 2 compares results from our present vapor pressure

equation (2) with his calculated pressures. If we use the ideal gas law to

obtain the vapor density, and obtain dP/dT from the above equation, the

Clapeyron equation gives the heat of vaporization independent of temperaa = 4. 7774 8580

b = 1. 7606 5363

c = -0.5678 8894

d = 0.0

e = 1.3278 623 1

ture. The Clapeyron equation is -

' Qvap =T- (dP/dT)- (v

g

- v

t ). From the above vapor pressure equation, P = exp[a - b/T], one obtains - (dP/dT) = b* P/T 2

At low pressures, v^ is negligible relative to Vg, hence via the ideal gas

law - , (Vg - vt ) = R-T/P.

Introducing the last two expressions into the first yields

Q-wan = b*R = 16.87 kJ/mol. V ct p

The smoothed experimental value of previous workers at 100 K is

17.3 ± 0.2 kJ/mol (Table 15). Regnier's duplicate pressure gages

agreed to 1% or better, but he makes no estimate of absolute accuracy.

4
Table 2. Comparison with vapor pressures of Regnier

-3

(U nits of bar* 1 0 ) T , K This Report Regnier [ 58]

89.899 0.0101 0.0119

90 0.0104 0.0122

95 0.0363 0.0399

100 0.1110 0.1161

105 0.3025 0.3051

110 0.7463 0.7342

115 1.689 1.637

120 3.546 3.414

125 6.967 6.713

130 12. 92 12. 53

135 22. 77 22. 33

The Orthobaric Densities

For the saturated liquid and vapor densities, o(T), we have

developed analytical expressions which are constrained to any given

boundaries, namely the triple and critical points [28], In eqs (3 -a) and

(3-b) the basic behavior is given by Y(p, T) = const. , and polynomials

on the right side are selected to describe small deviations.

a) For the saturated liquid, define the variables

x(T) = (T -T) / (T -T ), c c t y(p) = (p-p )/(P -P ), c t c

0

Y(p,T) = (y-x)/(x -x),

when the equation is

2/3 Y = a + b* x + c • x, (3 - a)

5
with the following coefficients

e =

a =

b =

c =

Methane

0. 36

0. 8595 3758

0. 0243 6448

-0. 0268 5285

Ethane

0. 33

0. 72 19 0944

0.2965 7790

-0. 3003 6548

Table 3 compares data with (3-a).

b) For the saturated vapor, define the variables--

x(T) = (T / T -1) / (T / T -1),

c c t y ( p) = 4n(p / p) /j?.n(p c /p t

), Y(p,T) = (y-x)/(x G -x),

when the equation is--

Y = A

i A.-x l/3

, (3-b)

i = 2

with the following coefficients --

Methane Ethane

e = 0.41 0.39

A 1 - 0.4171 4211 0.2158 7515

A2 = -0.5194 9762 -0.0852 2342

a3 = 1. 2077 7553 -0.6152 3457

A4

= -1.4613 0509 0.2545 2490

A5 = 0.5765 8540 0. 1517 7230
The data of Table 4 are obtained from the virial and vapor pressure

equations [27], The heading PLANK/KAMB refers to [52]. The data

of Table 5 for ethane are compared with (3-b).

c) For the equation of state, we use the liquid-vapor, equilibrium (saturation) temperature T(T (p) as a function of density. Densities

are obtained from the following expressions for T rT (p) by iteration,

using eqs (3 -a) and (3-b) only to find the initial density. We shall

describe T^p) in two parts, according as p>p^. This simplifies the

design of constraints to the boundaries (vapor and liquid triple points).

At the critical point the two parts are continuous because the derivatives of all orders n, d

I1 T rT /dpn

, from each are zero. For each range

the dependent variable is

Y(T_(p)) = (T /T ct -1)/(T IT -1),

c c t and we use the following function,

U(c ) = - y (1/x-l/x ),. where

x = |ct- 1 I, x

fc = l a

t " 1 1 >

cr - d/d , CT

. = d

t / d

c t t c

,

and d^_ refers to vapor or liquid at the triple point according as ~ $ 1. For the liquid range at n> 1 the equation is --

5 f,n(Y) = U(o) + B.- (a

1

) . (3-c)

i = l

For the vapor range at a < 1 we need a modification for extremely low densities approaching the triple point. The form is selected for

7
qualitative consistency with the ideal gas law and the basic vapor pressure equation. Define--

W(o) = Tn( 14-e /ct ) /Tn( 14-e /cr ), when the equation is --

ln(Y) = U(a ) + A -TnrW(a )] + A • (a o 1 1/3 1/3.

" CT t

>

A , 2/3 2/3 +

+ A

2

-(a -a

t

)

f £

i=3

A

i- 2 i

(3-d)

The coefficents for (3-c) and (3-d) are —

Coefficients for Saturation Temperatures, Eqs. (3-c, d)

Methane Ethane

Y 1/2 1/2

e 1/4 1/4

Ao 0.9034 9557 0.8681 0517

A i 0.0 0.0151 6978

A 2 0.0 -0.7296 0432

A

3

-0.3834 4338 1.0096 5493

A

4

-3.9210 8638 -8.7340 2710

a5 6. 2600 3837 21. 1071 2823

a6 -9.3296 0083 -31.4499 4087

A? 5.6060 2816 17.8637 0397

B 1 11.4317 7230 23.7245 1840

b 2 -3.8765 9480 -14.8860 5161

B

3 0.5378 8326 5.4317 7443

B4 0.0 -1.0715 0566

B

5

0.0 0.0913 5183

8
I

For ethane the liquid saturation temperatures appear in Table 6,

and the vapor temperatures in Table 7. Densities of the freezing liquid

are obtained by use of the equation of state in present work.

2. 4 The Virial Equation

For the virial equation of state,

Pv/RT = 1 + B(T) • ct + C(T)-

a

2

+---

? (4)

the second and third coefficients B(T), C(T) are dimensionless. We

reduce temperature and density of the critical point, x = T/T , a =

c d/d^. Following initial research on the representation of these coefficients [27], we now have adopted McGlashan's formula for B (T),

B(T) = B + B /x + B

3

/x

2 + B

4

/x

4 * 5

(4-a)

B = 0. 552 671, B

3 = -0. 592 947,

B_ = -1. 106 244, B = -0. 041 944.

2 4

These constants were obtained with our values for p , T . Date from c c McGlashan were increased by 0. 5 percent in absolute value to improve

consistency with the data of Michels and of Douslin near 300 K.

Table 8 compares data and calculated values.

For C(T) our new representation from [27] is,

C(T) = C /x +

1 C2

/x

' + C

3

/x- ]• ( 1 -T /T),

o

(4-b)

T0

= 217. 8 K, C

2

=

0. 83253,

C = 0.24423, C

3 = 0. 53488,

using critical constants of the present report. Table 9 compares data

and calculated values.

9
Table

10.

Summary

of

P-p-T

Data

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>

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CO CM vO lO o CM r-H CM 00

• • • • • o T—

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r-H r-H CM r-H

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4->3

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o r-H CM CM 00 vO LO sO CO

1

1 o o CO 00

CO r—

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l> LT) CM CO CM CM r-H

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1

1 LO

f—

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0-

LO "st

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£

o

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4-> £ £

a5 4—1 H-> d CD CD cr

CD Jha)

#H

r-H

r-H 0) £

• I- s

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U £ o

• r-1 CD

• r-1

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t—

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CM 00 O' +

10
2 . 5 The Equation of State

Data reproduced in the present report are summarized by Table

10. The locus of recent data is shown by Figure 1. From the data of

A. K. Pal we selected only twelve isochores at the highest densities,

runs Nos. 13 through 24 of Table 12, because they were found to be

self-consistent. An increase of all densities by 0. 5 percent than made

these PVT data compatible with data of other authors (Table 10) via

our equation of state. We finally used adjusted data of A. K. Pal

kindly provided by Professor R. Kobayashi, J. R. Ely, et al of the

Chemical Engineering Department, Rice University. We omitted the

data of Reamer et al because those of Douslin and Harrison are believed to be more accurate.

For background on this equation of state, the reader may refer

to our work on methane [25]. We consider density to be a parameter

in the description of P(T) isochores, Figure 2. (In Figure 3 we show

the well-known zero slope and curvature of the critical isotherm. ) For any density we obtain the liquid-vapor coexistence temperature

from our function for T CT (p), eqs (3-c, 3-d). Placing this in the vapor

pressure equation gives the coexistence pressure. The equation of

state thus is defined as a function of density on the coexistence boundary.

By subtraction we shift the origin to this boundary. Define the

variables - -

x(T) = T/T , c X (p) = T (p )/T

ct a c

Y (P , p,T)= (Z-l).x/p,

when the equation of state is--

Y (P) * (Z - 1

)

• x /p , o a a

(Y-Y ) = B(p)*$ (p , T) + C(p). Y (P , T)

<3 (5)

li
where B(p), C(p) are polynomial coefficients to be found by least squares,

and the temperature-dependent functions are

$(p , T) = x

1 / 2 -^n[T/T

a

(p)], (5 -a)

Y(p , T) = [ 1 - 0) -Tn(l+l/ci))] /x - [ 1 -uj jTn(l+l/u>^ jj/x^ . (5-b)

Each of these functions is zero on the coexistence boundary at

T = T a (p). The second gives nonanalytic behavior for C (p, T) about

the critical point by use of the variables,

uu(p,T) h 5 . [T/0(p)-l], a) a

(p) = 6 - [T

CT (p)/0(p)-l],

where 6 is an adjustable constant and 0 (p) is our locus of temperatures

inside the coexistence envelope, Figure 4,

Q(P) = T^(P )• exp* _cy. | cr _ 1 1 3

/(a - l ) 3

! e (5-c)

In the above, = d^/d

c for liquid at the triple point. Figures 5 and 6

show behavior of the functions $(p, T) and Y (p, T).

The coefficients of (5) are--

B(p ) = B + B «p + B «p

2 /(1+b.p 2

), (5-d)

o 1 c

C(p) = (a - 1)» (a -C )• (C + C • p ) , (5-e)

o 1 4

and the constants are--

12
Constants for Equation of State (5)

Methane Ethane

O' = 2 2

b = 1 1

6 = 1/2 1/2

Bo

= 1.5082 12989 1.8481 67996

V 0.6544 90304 1,5697 04511

B 2

= 4. 1320 82291 5.5601 86452

Co" 1. 90 1.90

C 1 = -0.7654 09076 -1.0428 42462

n ro

ii -0.0590 88717 +0.2249 78299

Behavior of B(p) and C(p) for ethane is given by Table 11. For

methane the behavior is shown by Figure 7. Figure 8 shows the presumed behavior of C(p) for hydrogen, discussed in Appendix C. Deviations of experimental data for ethane appear in Table 12. Appendix

C explains the rationale of this equation of state.

2. 6 The Ideal Gas Functions

For use in our computations we have represented the internal

energies of Chao et al. [8], by the following empirical power series--

9

(E°-E°)/RT = 3.0 + Zv (T/100)

(l+3)/3

,

< 6)

l=f

13
with coefficients

A

o

= 21.705 718 A

5 = 906.218 4427

A 1 = 65.498 641 a6

= -459. 230 2545

A2

= -362.011 5914 a7 = 143.030 0226

A

3 = 853.340 8616 A

8

= -25.074 95605

A4 =-1123.601 6220 A

9

= 1.897 54004

The specific heats are obtained by differentiation,

C°(T) = dE° /dT

,

v and the entropies by integration of C°,

AS° = C

v .dT/T

The dimensionless integration constant for S /R is the value A tabuo lated above. The concise computations are given by computer subroutine IDEAL, below. Table 13 gives the comparisons, and Table 14

gives values interpolated by means of (6).

We have compared the results of Chao et al [8] with those obtained earlier by Ziegler et al [77], At temperature, 200 K, (values

in Joules, moles, kelvins)-

o o H -H

o C

Ziegler et al [77] 7281.4 210.72 42.45

Chao et al [8], 7257.6 210.50 42.26

o o We see a difference of 24 Joules in (H - H ), or 0. 3 percent. We o

r have not further compared these independent calculations.

2. 7 The Heats of Vaporization

The data of Table 15 are represented as follows,

6

i/3

Q

vap 2>.

• X

, kJ/mol, (7)

i=l

14
where the argument is x(T) = (T -T)/(T -T ) c c t

T = 89. 899 K T = 305. 37 K

t c A

i 12. 102 730 A

4

= -71. 854 695

A

2

11.165 588 a

5 = 82. 166 239

A, = 16. 539 265 A. =-32. 610 514

3 6

Comparisons are given in Table 15.

2. 8 Specific Heats for Saturated Liquid

Data shown in Table 16 have been represented in J/mol/K with a minimum of arbitrary constants as follows by use of the argument,

x = T/T , (T = 305. 37 K) - c c

C (T) = a+ b-x + c«x/(l-x)

£

, J/mol/K, (8)

CT with these constants,

e = 0. 5 b = -16.5876

a = 67. 3153 c = 16. 3526

The form of (8) permits integration,

AS

a

= J

C

a 'dx/x,

giving results in closed form. Comparisons are given in Table 16.

2. 9 Specific Heats C (T) along Isobar P

P ®

In our computations of the thermodynamic functions we have entered the compressed liquid region at T<340 K by use of specific heats

C (T) kindly provided by Andre Furtado, as obtained with the flow

calorimeter at the University of Michigan [20].

Data shown in Table 17 for the isobar at P, = 137. 895 bar are

b

represented by use of the argument,

x(T) = (T-T )/ (T -T ),

t m t

15
as follows in J/mol/K,

C (T) =k.[C -exp(Y)] , J/mol/K, (9)

p

m

where

Y " A

1 + A2

* x2 /n-x ) + A

3 -x

2 + A

4 -x

3

+ A

5 -x

4

,

with constants T^_ = 89.899 K, and--

Tm

354. 0 K II

<M < -0. 154 423

C m = 62.60 A3 = -0. 141 489

k 00 rr—

1

335 C ii -0.506 438

A

1 3. 263 00 00 CM a

5 = 0. 276 992

The data were estimated by the author to be accurate to 0. 7% on

average, with a few values uncertain by several percent.

3. COMPUTATIONAL METHODS

The numerical values for E and H in this report are on the same

o absolute basis as those of Tester [701, obtained by use of E =

L J o

(4. 1868)- (4827. 2) J/mol.

3. 1 The Homogeneous Domain

With reference to Figure 9, we start our computations with ideal

gas values at zero density, and then integrate along isotherms by use

of the equation of state in the following relations,

AE = ' [P-T. (5P/8T)]-dp /p

2

, (10)

AC

v

= -T. 1 (8

2

p/dT 2).dp/p

2

, (11)

AS = R* -Ln [P / (pRT)] 4- [R -(dP/d T) /p] . dp /p . 12 )

Equation

states at P =

(12) is for use with initial entropies in hypothetical gas

1 atm. For the compressed liquid at T<T, and p>p

b c

16
(the cross-hatched region of Figure 9) we start with values of S(T, P^)

on isobar P, , and then use

b

AS =

- J (3P/3T).dp/p

2

. (12 -a)

In each (p, T) state, reached by above integrations, we compute

H = E + P. v , (13)

Cp = C

v

+ T. (dP/dT)

2

/(SP/3p)/p

2

, (14)

W

2

= C • (dP/Sp ) /C . P v

(15)

3. 2 The Vapor-Liquid Transition

As discussed below, we have used this computation only as a check against experimental heats of vaporization, and for closedloop checks terminating on the saturated liquid.

We traverse the vapor-to-liquid "dome" of Figure 9 by use of the

Clapeyron equation, and Av = (v -v ), f e

AH = T. (dP/dT). Av, (16)

AE = AH - P. Av, (17)

AS = AH/T, (18)

where (dP/dT) is slope of the vapor pressure curve.

3. 3 Compressed Liquid States

Computations along isotherms which pass close to the critical

point, Figure 9, cannot be expected to be accurate, as discussed in

[25]. For ethane there is an additional problem for use of the

Clapeyron equation to enter compressed liquid states. At low temperatures the vapor pressures become so small that they have yet to

be measured accurately, and the saturated vapor densities obtained

17
here are correspondingly uncertain. We therefore have used the following procedure to compute around the critical point into the crosshatched region of Figure 9: We use the isobar of specific heats C (T) at P = 137. 895 bar

P b

from [20]. We then select = 340 K, obtaining (by integration along

T. )

H(T PJ = 25 737 -97 J/mol, S(T , PJ = 176.4384 J/mol/K.

b

:

By use of our description (9) for C (T, P ) we then integrate down to

P b

any T<T

b

AH

T,

C -dT,

P

We finally integrate along isotherm T as described among eqs (10)

through (18). On the saturated liquid boundary we compute the specific heat C rj.(T) of liquid along the coexistence path from the following

relation [61],

C

CT (T) = C

v

(P ’ T) T -( ap /5 T).(dp^/dT)/p^ , (19)

where (dp^/dT) is the slope of saturated liquid density vs. T.

4. TESTS AND COMPARISONS

4. 1 The P-p-T Compressibility Data

Deviations of experimental densities and pressures from the

smooth P(p, T) surface of the equation of state (5) are given in Table

12, using author identifications from Table 10. The data of Michels

[47] and Douslin [ 14] are highly precise, and the deviations generally

are systematic, as might be expected from an equation of state with

as little freedom as (5). Any inaccuracies in the liquid-vapor boundary will be propagated along calculated isochores because the equation

18
of state originates on this boundary. At high densities in the compressed liquid, the derivative BP/Bp becomes extremely large, hence pressure deviations should be ignored.

4. 2 Calculated P(p) Critical Isotherm

Table 18 gives a high-resolution examination of the P(p) critical

isotherm from equation of state (5). This was obtained by adjusting

the assigned critical point (p , T^) to eliminate negative slopes BP/3p

in the neighborhood of p . The selected critical point is within the

range of values found by previous workers.

4. 3 Heats of Vaporization and Closure Computation

The last column of Page 1 of Table 26 gives experimental heats of

vaporization from eq (7) for comparison with values in column Q, VAP

computed by the Clapeyron equation. The differences are plotted in

Figure 10 as (Q -Q ). xptl calc

Table 19 gives loop-closure computations for the saturated liquid.

Values for enthalpy in Column H_ and for entropy in Column S are obtained by computing around the critical point, whereas values in

Columns HC and SC are via the Clapeyron equation (see Sections 3. 2,

3. 3). The enthalpy differences are plotted in Figure 10 as (H . -H^ ) in which refers to computation around the C. P. by

calc Furt Furt

use of C (T) data of Furtado [201.

P

Heats of vaporization via the Clapeyron equation at low temperatures are uncertain by several percent (up to about 500 J/mol) due to

uncertainty in the vapor-pressure equation and the vapor densities.

In Table 16, moreover, we see that experimental heats of vaporization may differ by over 2 percent at 100 K, (about 350 J/mol). The

apparently large deviations seen in Figure 10 therefore do not exceed

known uncertainties. The heats of vaporization have not been used for

present computations.

19
4. 4 Heat Capacity for Saturated Liquid

The last column of the second page of Table 26 gives experimental

heat capacities for the saturated liquid from eq (8) for comparison with

values in column CS computed as described above in Section 3. 3. As

seen in eq (19), this is a difficult computation from which to obtain

high accuracy. We also have computed C a(T) = T* (dS^/dT), but prefer

to omit this further complication of present work.

4. 5 Specific Heats, C

^

(p, T)

Table 20 compares specific heats of [20] at constant pressure

with values calculated by present methods. Except near the sharp

maxima in Cp in the critical region, the differences generally do not

exceed combined uncertainties of a few percent.

4. 6 Comparison of Enthalpies

Table 21 compares our saturated liquid enthalpies (obtained by

computation around the critical point) with results of Tester [70]. From

low-temperature specific heat data on the solid, and the heat of fusion,

he obtained the third-law entropy of liquid at the triple point. He then

used experimental C a

(T) data, liquid densities and dP/dT from the

vapor-pressure equation to obtain AH(T) on the liquid coexistence path.

Table 22 compares enthalpies of three authors for the homogeneous domain at a few, selected (P, T) points. To make use of the values

of Eubank et al. , we have added H°(T) obtained from Tester. This comparison shows that our results from the present very simple equation of

state are consistent with the work of other authors.

4. 7 Speed of Sound for Saturated Liquid

Figure 11 compares the speed of sound W for saturated liquid

from Table 26 of present work with the experimental data of Poole and

Aziz [53], Positive curvature of our calculated results below the boiling point (184. 55 K) suggests that derivatives of our P(p, T) surface are

20
not sufficiently accurate in the compressed liquid. Below 105 K the

calculated dependence of the saturated liquid densities on the temperature in Table 6 also has a positive curvature, which probably is qualitatively incorrect.

5. TABLES OF PHYSICAL AND THERMODYNAMIC

PROPERTIES

5. 1 Calculated P- p -T Isochores and Isotherms

A selection of calculated isochores and isotherms is given by

Tables 23 and 24. They are useful to examine behavior of the surface

generated by the equation of state, and to supplement the isobars of

Table 27 in obtaining P-p-T values and their derivatives.

5. 2 The Joule-Thomson Inversion Locus

Table 25 gives our calculated P-p-T locus for the J. T. inversion,

(ST /^P)h = These results are obtained from the equation of state

under the condition, T* OP/ST) = p*(dP/dp).

5. 3 Thermophysical Properties of the Saturated Liquid

Table 26 gives physical and thermodynamic properties for the

saturated liquid. Column headings are interpreted on the first page

of this table.

5. 4 Thermophysical Properties Along Selected Isobars

Table 27 gives physical and thermodynamic properties on isobars,

as computed by methods of Section 3. Explanations for the table are

given on the first page. This table is extrapolated beyond the range of

P-p-T data used for adjusting the equation of state (P ~ 350 bar).

6. COMMENTS AND RECOMMENDATIONS

Uncertainty of the saturated liquid densities (Table 3) is estimated

to be 0. 1 percent from 90 to 140 K. Greatest uncertainty, approaching

0. 5 percent, exists in mid-range (160 to 250 K) where no experimental

data were found. Whereas several sets of precise data exist approach21
ing the critical temperature, we have not been able to represent them

with a function of simple form to better than 0. 2 to 0. 3 percent [28].

Saturated vapor densities at very low temperatures are uncertain

by several percent because they have been estimated by use of the

vapor-pressure equation which is uncertain by at least 2 percent at

these temperatures [26], and the virial equation of state. The latter

is extrapolated below the range of data for the virial coefficients where,

however, we approach ideal gas behavior [27].

Our calculated densities (Table 27) over the homogeneous domain

(

n

<0 , or T>T ) are uncertain by an estimated 0. 2 percent, except for r c c the critical region (p r /3<p<2* p c at 0. 9* T C <T<1. 2- T c ) where deviations

from experimental data may exceed one percent, Table 12. For the

compressed liquid at low temperatures, densities probably are uncertain by about 0. 2 percent (adjusted P-p-T data of A. K. Pal [54]).

Uncertainty of enthalpy differences is most difficult to estimate.

Along isotherm T^ of Figure 9, we compute Cp(p, T) at point (T^, P^)

within one percent of the experimental value from [20]. For the homogeneous domain, having an adequate density of P-p-T data, therefore,

the uncertainty of enthalpy differences probably is comparable with

that estimated for methane [25], namely about 2 percent. For compressed liquid, as seen in Section 4 above, however, the uncertainty

may be several-fold greater.

The purpose of this report has been, in part, to find the inadequacies in physical properties data needed for thermal computations.

Some recommendations can be made, based on the inaccuracies shown

in Section 4 above. The possible methods for preparing a thermodynamic network are so numerous and varied, however, that the reader

may wish to draw his own conclusions. We make only the following

simple observations and recommendations:

22
1) The melting line is poorly defined. Accurate P-p-T data for

the freezing liquid would provide a boundary for the equation of state.

The triple-point temperatures which have been published are highly

discordant. Extrapolation of the P(T) melting line to zero pressure

might yield a reliable value. This is needed especially for the vapor

pressure equation.

2 ) More accurate P-n-T data (better than 0. 1% in density) are

needed for the low-temperature compressed liquid. From such data

accurate saturated liquid densities may be obtained by intersection

with an accurate vapor-pressure line.

3) Accurate densities for the saturated liquid are needed in midrange where few if any experimental data exist.

4) Accurate vapor pressure measurements apparently exist

only from 200 K (2 atm) upwards. These could be extended down to

150 K (0. 1 atm) by use of the "air dead-weight gage. " Their use might

give a vapor pressure equation with more reliable derivatives, dP/dT,

over the entire range.

5) Sound velocity measurements over a wide range, as well as additional specific heat measurements, e. g. C v (p, T), would provide

further tests of the thermodynamic computations.

7. ACKNOWLEDGMENTS

We are indebted to The American Gas Association for generous support of this work, to Robert D. McCarty for the essential lea st - square s program, and to Dwain E. Diller and Lloyd A. Weber for discussions and

valuable suggestions. Importance of the nonanalytic behavior of C (p,T)

about the critical point, in formulating an equation of state, was emphasized for us by Anneke Levelt Sengers, for which we are most grateful.

The PVT compressibility data of Douslin and Harrison, of A.K. Pal as revised at Rice University, and the specific heat data of A. Furtado,

have all been essential ingredients making possible the present provisional computations of thermodynamic functions.

23
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[68] K. E. Starling, Fluid thermodynamic properties for light petro - leum systems, Gulf Publishing Co. , Houston, Texas (1973).

[68a] H. J. Strumpf, A. F. Collings and C. J. Pings, Viscosity of

Xenon and Ethane in the Critical Region, J. Chem Phys. 60(8),

3109 (1974).

[69] A. S. Teja and J. S. Rowlinson, The prediction of the thermodynamic properties of fluids and fluid mixtures - -IV. Critical and

azeotropic states, Chem. Eng. Sci. 2_8, 529 (1973).

[70] H. E. Tester, Ethane, in Thermodynamic Functions of Gases,

V ol 3, F. Din, Editor, (Butterworths Scientific Publications,

London, 1961).

[71] A. W. Tickner and F. P. Lossing, The measurement of low vapor

pressures by means of a mass spectrometer, J. Phys. Colloid

Chem. 5_5 , 733 (1951).

[72] J. R. Tomlinson (Gulf Research and Development Co. , Pittsburgh,

Pa. ), Liquid densities of ethane, propane and ethane-propane

mixtures, Tech. Pub. TP-1, Natural Gas Processors Assoc.,

(808 Home Federal Bldg. , Tulsa, Okla. 74103, Feb. 1971).

[73] R. Wiebe, K. H. Hubbard and M. J. Brevoort, The heat capacity

of saturated liquid ethane from the boiling point to the critical

temperature and heat of fusion of the solid, J. Am. Chem. Soc.

52_, 61 1 (1930).

[74] G. M. Wilson, R. G. Clark and F. L. Hyman, Thermodynamic

properties of cryogenic fluids, Ind. Eng. Chem. 6_0(6), 58 (1968).

[75] R. K. Witt and J. D. Kemp, The heat capacity of ethane from 15° K

to the boiling point. The heat of fusion and the heat of vaporization,

J. Am. Chem. Soc. _5_9 , 273 (1937).

[76] W. T. Ziegler, The vapor pressures of some hydrocarbons in the

liquid and solid state at low temperatures, NBS Tech. Note 4,

(May, 1959).

[77] W. T. Ziegler, B. S. Kirk, J. C. Mullins and A. R. Berquist,

Calculation of the vapor pressure and heats of vaporization and

sublimation of liquids and solids below one atmosphere pressure.

VII Ethane, Tech. Report No. 2, Proj. A-764, Eng. Expt. Sta.,

Georgia Inst. Tech., Atlanta, Georgia, (Dec. , 1964).

30
APPENDIX A. Symbols and Units

Subscripts c and t refer to critical and liquid triple points.

Subscripts g and & refer to saturated vapor and liquid.

Subscript a refers to liquid-vapor coexistence (usually the liquid).

Superscript o refers to ideal gas states.

a, b, y, e, non-linear constants in the equation of state

B(p),C(p), density-dependent coefficients in the equation of state

C

v

(p,T),

C (p, T),

P

c

a

( T ),

d.

molal heat capacity at constant volume, J/ (mol* K)

molal heat capacitu at constant pressure, J/ (mol* K)

molal heat capacity for saturated liquid, J/(mol*K)

density, mol/ £

E(p,T), the internal energy, J / mol

H(p, T), the enthalpy, J / mol

J. the joule, 1 N-m,

1,

-3 -3

the liter, 10 m , mol, 30. 07 grams of ethane (C^ = 12 scale)

P,

5 2

pressure in bars, 1 bar = 10 N/m

(1 atm = 1. 01325 bar)

PCT (p), the vapor pressure, bar

§(p, T), function in the equation of state

ilr(p, T), function in the equation of state

Q , vap

R,

AH , the heat of vaporization

vap

the gas constant, 8. 31434 (J/mol)/K, 0. 0831434

(bar - jj/mol) /K

P. d/d^_, density reduced at the liquid triple point

CT» d/d , density reduced at the critical point

c S(P, T), the entropy, (J/mol)/K

T, temperature, K, (IPTS-68.) [59]

T>),

0(p).

liquid-vapor coexistence temperature, K

defined locus of temperatures, Fig. 4

31
APPENDIX A. (Continued)

U (ct), defined function for eq (3-c)

v, 1/d, molal volume, £/mol

oi(p, T), 6* [T / 9-1], for the equation of state

W(ct), defined function for eq (3-d)

W(p, T), the speed of sound, meter s / s econd

x(T), T/T , for the equation of state

c Y, variously defined functions

z, Pv/RT, the "compressibility factor

APPENDIX B. Fixed-Point Values

Triple Point

Density Mol/'t

Vapor

Liquid

Temperature, K

Pressure, bar

Critical Point

Density, mol/'t

Temperature, K

Pressure, bar

Methane

-2

1 . 567 865 • 10

28. 1470

90.680

0 . 1174 35675

10.0

190. 555

45.988

Ethane

1.35114* 10

21.680

89.899

1 . 009 906- 10

6.74

305.37

48.755

32
APPENDIX C. Exposition of the Equation of State

Equation (5) may be written explicitly-

P = P (P) + pR*[T -T (p)J

CT O'

+ P 2 RT . [B(p). §(p, T) + C(p).¥(p,T)]. (5-1)

c

'

This has only two temperature -dependent terms (in addition to pRT),

which is the minimum number needed to describe the sigmoid shape of

isochores [ 6 1 ] in the range p^<o<2* p^, Figure 2. Each of these terms

is zero on the coexistence boundary at T = T (p). a The first term, §(p, T), is shown by Figure 5. It is linear

2 . 2

(3 $/3 T = 0) on the coexistence boundary. It gives a critical isochore

which is linear at the critical point because C(p) = 0 along this isochore.

The second term, Y(p, T), is shown by Figure 6. It starts with

2 . 2

infinite curvature (3 Y/3T ) on the locus of temperatures, 0(p), inside

the coexistence envelope of Figure 4. Sufficiently far away from the

2

critical point it behaves like 1/T , found in the well-known BeattieBridgeman equation.

2 2

The sign of the curvature (3 P/BT ) of isochores at the coexistence boundary is determined uniquely by the sign of C(p). Figure 7

shows the behavior of B(p) and of C(p) for methane. The root in C(p)

at p/p =1.9 was found by least squares both for methane and for

ethane. It then was introduced as the non-linear constant, C , in the

o equation of state. This constraint is valuable. In its absence we quite

often have failed to obtain any such root from P-p-T data by least

squares. Figure 8 shows the presumed behavior of C(p) for hydrogen

(a double root near p/p = 1. 9), needed to give the observed positive

curvature of isochores in the compressed liquid at the lowest temperatures [13, 21],

33
APPENDIX C. (Continued)

The critical isotherm from eq. (5) necessarily has zero slope,

dP/dp = 0, at the critical point, Figure 3. This follows from our

definitions of T rr (p), 0(p), $(p, T) and Y(p, T). The second derivative,

2 , 2

3 P/dp , also is zero because the vapor pressure here is expressed

as a function of T rj (p). Our detailed examinations of this isotherm

show however, that small changes in the assigned critical point (q , T ) c c give rise to irregularities nearby at p § p . Adjusting the critical

density to p =6. 74 mol /

H

yields a well-behaved critical isotherm

c having no negative slopes, i. e. dP/dp^O.

Specific heats along the critical isotherm of Figure 4 are comput2 2

ed by integrating the curvatures of isochores, (d P/dT ), in eq. (11),

starting at p = 0. Curvatures from the term C(p)‘ Y(p, T) in the equation of state at first increase sharply (with negative sign) as p-*p , bec come zero at p = p , then strongly positive at first for p>p , finally

c c diminishing at still higher densities. This behavior is seen along the

critical isotherm in Table 24. It gives a maximum in C (p, T) at the v

critical point via eq0 (11).

34
APPENDIX D.

Cryogenics Drmion - NSS Institute tor Ink Standards LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3PAGE

1 SUBJECT The Vapor Pressures of Ethane

NAME /- J R . D . Goodwin

DATE Julv 7 , 1773

This is the first of several reports planned on the physical properties of ethane.

Our ultimate purpose is to compute tables of thermodynamic functions over the entire

range of fluid states. We first will discover regions where data are inadequate or

lacking by attempting to compute provisional tables based on existing data.

Accurate vapor pre s sure s, and a proper analytical representation of these data, are essential for computing heats of vaporization via the Clapeyron equation.

In this note we give a limited bibliography. Not all of these references were

available at this writing. We compare several sets of data by use of our newtonanalytic vapor pressure equation. We make a choice of the best for least squares, and

we give deviations from this selected equation.

At the triple point near 90 K the vapor pressure of ethane is about 0.00001 atm

(10 LL-atm). Experimental methods therefore differ for the range below one atm

( 184 . 5K) and for the range of higher pressures to 48 atm at T = 305 K.

Data to about I960 are reviewed by Tester [19], who selected the representation of Barkelew et al. [3] for the entire range from triple- to critical point.

Below one atm the data to 1964 are reviewed by Ziegler et al. , who give their

own, high quality set of data computed for thermodynamic consistency with all related or derived data, in a work for the National Standard Reference Data Program [23],

More recently we have the measurements of Carruth, obtained by the gas saturation

flow technique, employing a flame ionization detector for analysis of the gas mixture [4]. See also J. J. Chen et al. (Rice University), paper G-l, 1972 Cryogenic

Engineering Conference, on the same technique.

For high pressures the only new data of which we presently are aware are those

of Pope (Table 25) [ 13], and those attributed to Dr. A. K. Pal by Pope [13] in Table 31.

For these latter data there is no description of experimental method.

After this note was written we received the new precise measurements of

Douslin and Harrison [24], and therefore have recomputed our results including these

data. Douslin and Harrison note especially the new, precise measurements of

Miniovich and Sorina [25], which were not available to us at this writing.

sp ii34? a 35
APPENDIX D. (Continued)

Cryogenics Division - N®S Institute for Bosk Stamfords LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3

PAGE 2

SUBJECT The Vapor Pressures of Ethane

NAME R. D. Goodwin

DATE July 9, 1973

Our vapor pressure equation [6] uses the reduced argument,

x(T) = ( 1 -T /T)/ ( 1 -T /T ) , t t c where subscripts t and c refer to triple- and critical points,

2 3 4 £ In (P /P ) = a« x + b* x + c • x + d • x + e • x. ( 1 -x) ( 1

)

and the exponent is e = 1 . 3 for methane [1 5] and for oxygen [ 16] . Originally the term

4 i d-x was absent. It has been added here to improve representation of the ethane data.

The following discoveries are found with the original equation of four terms.

Optimum exponents in the range 1 . 1 < e ^ 1.9 are obtained merely by changing the

sets of data used for least squares. Hence we must rely on the more precise methane

and oxygen data to select e =1.5. Varying the critical-point temperature within

reasonable limits has no significant effect on the overall, rms relative pressure deviation s

.

By examining numerous results we have selected for least squares only the data

of Ziegler at P < 1 atm [ 23], and the data of Pope, Pal [13] and Douslin [24] at P > 1.9 atm.

Whereas the temperature scale of Ziegler may be thermodynamic (the report is not

clear), we nevertheless find that deviations (rms in relative P) are minimized by

converting both sets of data to T-1968 as if they had been on T-1948 [

1 ] . All T used

in the following are T-68.

The triple-point temperature was reviewed by Ziegler et al. Their selection

of 69.89 K becomes 89.899 on the 1968 scale. The critical-point temperature 305.42 K

of Pope has been changed to 305.33 K for consistency with the data of Douslin ( 24] . A

value T = 305.33 r 0.005 K is given by P. Sliwinski, Zeit. Phys. Chem. b_8, 91

c

( 19'; t) based on analysis of dielectric constants. This was kindly pointed out by

D. E. Diller. We obtain pressures at these end points from the vapor pressure

equation:

T , K (1968) P, atm

Triple point 89.899 9,61b. 10

Criticalpoint 305.33 48.07695

$P 1 134?

A

36
APPENDIX D. (Continued)

PACE 3

Cryogenics Division - NftS Institute for Bosk Standards LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-3

SUBJECT NAME The Vapor Pressures of Ethane

R. D. Goodwin

DATE July 9, 1973

The constants for eq (1) were obtained via the data of Ziegler, Pope, Pal and

Douslin. They include e = 1.6 as shown at the head of table 1.

a = 8.4549 8734 d =

b = 12.4880 3978 e =

c = -4. 1042 8155

-1.4138 6053

8.5265 2253

In the following tables we give the author^ ID, his temperature and as converted to T-68 , and the published and calculated pressures. Next is the deviation of

his temperature from our calculated value,

DT = T -T = _ (p -P 1/ldP/dTl xpt calc ' xpt calc m '

and finally his relative pressure deviation,

P, PC T = 100- (P -P )/P

xpt calc calc

At the bottom of each table we give the number of datum pairs, NP, and the rms of

relative pressure deviations in percent.

The source of data in each table is identified by the numerical code, ID, in the

first column--

Table No I.D. Author s Referen<

1 4 A. K. Pal [13]

7 Ziegler et al. [23]

9 G. A. Pope [13]

10 Douslin, Harrison [24]

2 1 Tickner, Lossing [20]

2 API Proj . 44 [2]

3 Carruth [4]

3 5 Loomis, Walters [11]

4 6 F. Porter [14]

8 Barkelew et al [3]

5 Calculated vapor pressures (this report)

6 Reduced v.p. functions (this report)

JP 11347 * 37
APPENDIX D . (Continued)

Cryogenics Division - NBS Institute tor Bask Standards LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-3

PAGE 4

SUBJECT The Vapor Pressures of Ethane

name D. Goodwin

July 9, 1973

As additional data may be found, we reserve comment on the deviations of

individual authors, and omit the labor of preparing deviation plots.

Calculated pressures, slopes and curvatures are given at uniform temperatures

by Table 5.

For comparison with functions in our original vapor pressure publication [6],

we give these functions in Table 6, as computed via eq (1) namely

x(T ) 5 (T-T /T ) /( 1 - T / T ),

t t c

Y (P ) s tn(P/P )/tn(P /P ). (2)

These variables range from zero to unity. The equation

Y = x (3)

represents the basic vapor pressure equation

£n(P) = a - b/T (4)

when this is constrained to the end-points (triple and critical). Hence (Y-x) is the

deviation of data from (4).

Finally, we give the computer programs used in this work as a means to check

for errors, and to facilitate resumption of this research.

Addendum. Following work shows that the second virial coefficient used by Ziegler

et al. to obtain vapor pressures is not consistent with our selection. At 200°K his

B(T) = - 455 cc /mol, whereas our B(T) = - 417.5. We therefore have recomputed our apor pressure constants using Ziegler's vapor pressure data from his Table IX for

"Curve B” of his Figure 1, for which B(T) = - 410 cc/mol at 200 K. The difference in

his vapor pressures at 90 K is (7.80-7.33)/7.33 = 6.4 percent, the new values being

the greater. Our new results for eq (1) are given in Table 7, (pages 20, 21) and tables

8 , q on pages 22, 23 of this report. We prefer these constants for future use.

SP 11147* 38
APPENDIX D. (Continued)

Cryogenics Division - NIS Institute for Bosk Standards LABORATORY NOTEPROJECT NO. 2750364FILE NO. 73-3

PAGE

5

SUBJECT NAME The Vapor Pressures of Ethane R. D. Goodwin

DATE July 9, 1973

Bibliography

[1] The International Practical Temperature Scale of 1968, Metrologia 5(2), 35 (1969).

[2] Amer. Petrol. Inst. Res. Proj. 44, Selected Values of Properties of Hydrocarbons and Related Compounds (loose-leaf), Table 20 k, (Part 1), p. 1,

Dec. 31 (1952).

[3] C. H. Barkelew, J. L. Valentine and C. O. Hurd, Thermodynamic properties

of ethane, Trans. Amer. Inst. Chem. Eng. 43, 25 (1947).

[4] F. G. Carruth, Determination of the vapor pressure of n-paraffins and extension

of a corresponding states correlation to low reduced temperatures, Thesis,

Dept. Chemical Engineering, Rice University, Houston, Texas, (Nov. 1970).

[5] N. M. Dykhno, M. V. Tsyrulnikova and M. V. Mochalova, Hyd rocarbon vapor

pressures at low temperatures, Zh. Fiz. Khim. 42 (9), 2310-1 (1968).

[6] R. D. Goodwin, Nonanalytic vapor pressure equation with data for nitrogen and

oxygen, J. Res. NBS 73A (5), 487 (1969).

[7] A. S. Holmes, W. G. Braun and M. R. Fenske, Bibliography of Vapor Pressure

Data for Hydrocarbons , Amer. Petrol. Inst., New York, Bibliog. No. 2, (1964).

[8] E. E. Hughes and S. G. Lias, Vapor Pressures of Organic Compounds in the

Range Below one Millimeter of Mercury, NBS Tech. Note 70, Washington, D. C.

(Oct., 1960).

[9] J. G. Hust, A compilation and historical review of temperature scale differences,

Cryogenics 9(6), 443 (Dec., 1969).

[10] G. Klipping and F. Schmidt, Dampfd r ucktabellen Tiefsiedender Case (V),

Kaltetechnik 18(11), (Nov. 1966).

[11] A. G. Loomis and J. E. Walters, The vapor pressure of ethane near the normal

boiling point, J. Amer. Chem. Soc. 48, 2051 (1926).

[12] R. E. Perry and G. Thodos, Vapor pressures of the light normal saturated

hydrocarbons, Ind. Eng. Chem. 44(7), 1649 (1952).

[13] G. A. Pope (quotes v.p. of Dr. A. K. Pal), Calculation of Argon, Methane, and

Ethane Virial Coefficients at Low Reduced Temperature Based on Data Obtained

by Isochor ically Coupled Burnett Experiments, Thesis, Dept. Chemical Engineering, Rice University, Houston, Texas (July, 1971).

[14] F. Porter, The vapor pressures and specific volumes of the saturated vapor of

ethane, J. Amer. Chem. Soc. 48, 2055 (1926).

[15] R. Prydz and R. D. Goodwin, Experimental melting and vapor pressures of

methane, J. Chem. Thermodynamics 4. 127 (1972).

[16] Rolf Prydz, An improved oxygen vapor pre s sure representation, Metrologia 8 ( 1 ),

1 (1972).

if 11342 A 39
APPENDIX D . (Continued)

Cryogenics Division - MBS Institute for Bosk Standards LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3

PAGE 6

SUBJECT The Vapor Pressures of Ethane

NAME R. D. Goodwin

DATE July 9, 1973

[17] C. T. Sciance, C. P. Colver and C. M. Sliepcevich, Bring your Cj-C, up to date, Hydrocarbon Process. 46(9), 173 (1967).

[18] N. E. Sondak, and G. Thodos, Vapor pressures, the saturated aliphatic hydrocarbons, A.I.Ch.E. Journal 2, 347 (1956).

[19] H. E. Tester, ETHANE, in Thermodynamic Functions of Gases, F. Din, Editor,

Butte rworths , London (1961).

[20] A. W. Tickner and F. P. Lossing, The measurement of low vapor pressures by

means of a mass spectrometer, J. Phys . Colloid Chem. 55, 733 (1951).

[21] G. M. Wilson, R. G. Clark and F. L. Hyman, Thermodynamic properties of

cryogenic fluids, Ind. Eng. Chem. 60(6), 58 (1968).

[22] W. T. Ziegler, The Vapor Pressures of Some Hydrocarbons in the liquid and

solid state at low temperatures, NBS Tech. Note 4, (May, 1959).

[23] W. T. Ziegler, B. S. Kirk, J. C. Mullins and A. R. Berquist, Calculation of

the Vapor Pressure and Heats of Vaporization and Sublimation of Liquids and

Solids below One Atmosphere Pressure. VII Ethane, Tech. Rpt. No. 2 Proj.

A-764, Eng. Expt. Sta., Georgia Inst. Tech.; Atlanta, Georgia, Dec., 1964.

[24] D.R. Douslin and R. H. Harrison, Pressure-Volume-Temperature Relations

of Ethane (manuscript for the Journal of Chemical Thermodynamics), 1973.

[25] V. M. Miniovich and G. A. Sorina, Russian J. Phys. Chem. 4^5, 306 (1971).

st ii34? a 40
APPENDIX D . (Continued)

Cryogenics Division - NSS bwtitute lor hac Standords LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3

PAGE 7

suuect The Vapor Pressures of Ethane

Table 1 . Data of Pal (4), Ziegler (7), Pope (9), and Douslin ( 10)

.

NAME R. I0. Goodwin

DATE July 9, 1973

ETHANE VAPOR PRESSURES, E = 1.60

TTRP = 89.899, TCRT = 305.330

PTRP, MUATM = 9.61600, PORT, ATM = 48.07695

8 . 454 987341+ 12.488039775 -4.104281551

-1 . 41 3 86 j 5 3 3 8.526522526 O.OOOUGCCOG

ID T . XPT L T-68 P, ATM CALCC DEL T P» PCT

7 94. 000 94. 013 0. 00 00274 0. C0G0 274 -0. 00 1 0 .02

7 98. CCC 98. 012 0.0000693 0. 00C0694 0. 00 2 -0.05

7 1J2.0CG 102. 00 8 0. 00 C1616 0. C0C1619 0 • GO 2 -0.05

7 106. uOC 1C o. 00 2 0.0003526 0. 0003522 -0 . 00 6 0 . 11

7 110. J00 109. 998 0. 0007207 0. 0GG7 205 -0. 00 2 0 .03

7 114. COO 113. 995 0.0013947 0. 0C13947 -C. 000 O.OC

7 11 3. C G 0 117. 991 0.0025697 G . G 025 698 0 . 00 0 . -0 . 00

7 122. 300 121. 988 0.0345303 C. CC45293 -a . GO 2 0.02

7 1 2 6 « j u u 125. 987 0. 0076737 0. 0076734 -0. 000 0.00

7 1 3 0 • C Q 0 129. 987 0.012538 0 .G1254G G.001 -0.01

7 1 3 4. j u 0 133. 988 G .G1983C 0 .019834 0 . 00 2 -0.02

7 138. dGO 137. 990 G .0 30447 0.0 30 460 0 . 004 -0.04

7 142. COO 141. 993 0 .0 45504 0 .045527 0. 005 -0.05

7 146. JOG 145. 996 0 .066355 0 .066389 0. 006 -0.05

7 150. OCC 150. 00D 0 .094606 0 .094657 0. 006 -G .05

7 15 4. C 0 0 154. 0C 4 0. 13213 G.1322G 0 . 00 7 -0.35

7 1 5 8 . J 0 0 158. uG 8 J. 181 39 0.18117 0.005 -0.04

7 162. COO 162. 012 0. 24392 0.24 39 7 0. 00 3 -0.02

7 16 6. j C 0 166. 015 0. 32333 C .32 33 0 -0 . 00 1 0.01

7 1 7 C • COG 170. 01

9

0. 422 3

C

D. 42214 -0 . 00 6 0 .04

7 1 7 4. C 0 0 174. 023 0.54409 G. 54371 -0.011 0 .C7

7 17 3. CO G 178. 026 0.69224 C. 69145 -0. 020 0 . 11

7 18 2. w 0 v 18 2. 026 0. 870 47 0 .66905 -0. 329 0.16

7 184. 520 164. 550 1. 0 0 3 OC 0.9980 3 -0 . 036 0.20

9 196.181 193. 216 1.9737 1.9758 0 .023 -0 . 11

4 214. 3D 2 214. 334 3.9209 3.9176 -0. 021 0 . 08

4 224. ID 2 224. 130 5.6367 5.6429 G. C31 -0.11

4 229. 755 229. 762 6.8569 . 6.8629 0 . 026 -0 . 09

4 234. 556 234. 581 8.0335 8.0 42 3 0 . 034 -0 . 11

9 234.092 234.715 8.0741 8.0772 0 . 312 -0 . 04

10 233. 150 238. 15 G 9.00 97 9.0 10 8 0 . 004 -G . G

1

9 23 3. 77 1 238. 792 9.1843 9.1935 0 . 032 -0 . 10

4 239. 644 239. 364 9.4959 9.5049 0.030 -0 .09

4 24C. 514 240. 534 9.696C 9.7032 0 . 024 -0 . 07

1C 243. 15 C 243. 150 10 .5063 1C.5C71 0.00 3 -0 . 01

4 243. 359 243. 377 10 .5761 10.579C 0. 009 -0.03

4 246. 314 246. 830 11 .7137 11.7183 0.014 -0 .04

4 247. 816 247. 831 12 .0502 12.0648 0.042 -0 .12

1C 2 48. 15 G 248. I5u 12.1756 12.1766 0. 30 3 -0 .Cl

4 249. 741 249. 755 12.7520 12.7512 -0.030 a . os

4 250.146 250. 160 12.8985 12.8991 3. 00 2 -0 .01

4 251. 567 251.600 13.4425 13.4356 -0.018 0.05

4 252. 544 252. 556 13.8065 13.800 6 -0. 015 0.04

li. 253. 15 Z 253. 150 14.031C 14. J 31

C

-0.000 0 . 00

4 25 4. 29 u 254. 3C 1 14.4396 14.4854 -0.011 0 . C 3 4 257. 543 257. 552 15 .8252 15.8264 0. 0C 3 -0 . 01

1C 25 3. 150 258. 15 J 16 .03 36 16.0 823 -0. CO 3 0 .01

IP 1134? « 41
APPENDIX D. (Continued)

Cryoganks Drmton - MBS InaMuta for Bosk Standards LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-3

PAGE a

SU,JECT The Vapor Pressures

Table 1 - -continued

of Ethane NAME R. D. Goodwin

DATE July 9

,

1973

ID T ,XPTL T-68 P A T M CALCO DEL T P.PCT ~

10 2 6 3. 15 C 263. 153 18 .3464 18.3433 -0. 007 0.32

4 253.380 263.386 18 .4543 18.4553 0. 002 -0.01

4 267. 536 267. 539 20 .5197 20.5113 -0. 016 0 . 04

If; 268.150 268. 15 u 20 .63 16 20.8274 -0.309 0.02

4 271. 749 271. 753 22 .7661 22.7618 -0.008 0.02

9 272. 949 272. 949 23.4515 23.4347 -0.030 0.07

10 27 3. 15273. 150 23.5549 23.5488 -0. Oil 0.03

4 275. 922 275. 921 25.1584 25,1648 3. 01

-0 . 03

4 276. 363 276. 362 25 .4558 25.4293 -0 . 044 0.10

4 276. 385 276. 384 25 .4491 25.4425 -0 . 011 0.03

4 276.514 276. 513 25.5472 25.520 3 -0 . 044 0 . 11

4 277. 813 277. 811 26.3185 26.3133 -0 . 00 8 0 • 02

lo 278. 150 278. 150 26.5309 26.5233 -0 . 012 0.03

4 2 8 u • - 4

280. 038 27 .7J 39 27.7158 0 . 019 -0 . 04

4 282. 247 282. 243 29.1537 29.1588 0. 00 6 -0.02

1C 283.150 283. 153 29.7763 29.7681 -0. 012 0.03

4 284,635 284. 633 30 .7664 30.7836 0. 02 5 -0.06

9 284. 345 284. 840 30 .9555 30.9296 -0 . 037 0.08

4 287. 653 287. 648 32 . 92 89 32.9340 . 0. 007 -0.02

10 28 8. 15 C 286. 15 C 33.3110 33.3030 -0. Oil 0.32

4 283.263 268. 257 33 .3899 33.3822 -0.010 0 . 02

4 290. 0 40 290. 034 34.6873 34.7148 0 . 036 -0.08

9 290.214 290. 208 34.8746 34.8474 -0 . 036 0.08

4 292.236 292. 229 36 .4440 36.4182 -0. 033 0.C7

H 293. 066 293. 091 37 .08 16 37.1044 0 . 028 -0.36

10 293. 15 C 293. 150 37.1583 37.1 51

-3. 008 0.02

9 293. 266 293, 259 37 .2672 37.2 39 4 -0.035 3.07

4 296. J47 296. 339 39 .7596 39.7842 0. 029 -0.06

1C 296. 153 296. 153 41 . 3494 41.345C -0. 005 0 . 31

4 299. o65 299. 657 42 .6543 42.6822 3. 031 -0.37

G 299.363 299. 855 42 .8863 42.860 6 -3 . C2 8 0.06

4 3 C 0. 20 5 303. 196 43 .16 51 43.170 3 j . C 0 6 -0 . 31

4 30 1. 251 3G1. 242 44 .10 8 5 44.1297 0 . 02 3 -0 . 05

1 l 3u 2. 15 0 302. 153 44 .98 05 44.9776 -0. 00 3 0.01

1 0 33 3. 15 0 30 3. 150 45 .9327 45.9295 -0 . 00 3 0.01

4 30 3.471 30 3. 46 2 46 . 20 32 46.230 Q 0 . 028 -C . 06

4 j j 3 4/7 303. 468 46 .2796 46,2358 -0 . G46 0 • 1C

G 304.012 304. 002 46.7736 46.7558 -3 . 018 0 . 04

4 3 3 4

1. 4 9 304. 039 *6.7696 46.7920 0.023 -0.05

1 0 3 C 4. 150 304. 150 46.904C 46.901G -0. 00 3 0.01

u 3u 4 , 36 j 30 4. 35 3 47 .0931 47.0 974 0 . 00 4 -0 . 01

4 3u 4, *4 6 304. 435 47 . 21 96 47.1 822 -0.038 0.08

4 3 0 4 . 5 1 9 304. 50 8 47.2025 47.2544 0. 35 2 -0 . 11

4 3 u 4. 734 3 0 4 , 723 47 .431 0 47.4677 0. 037 -0 . 08

4 3u 4, 796 304. 785 47.51 85 47.5294 3.011 -0.02

4 334. 524 304. 91 3 47 .6846 47.6572 -0 . 027 0 . 36

4 33 4. 963 3C4. 969 47 .71 31 47.7132 0 • 00 0 — 0 . 0 u 4 305. 121 305. 110 *7,8496 47.8547 0 . 00 5 -c . 01

4 335. 135 3C5. 124 47 .8251 47.3688 0. 34 3 -3 . G9

i306* 150 30 5. 15 0 47 .8992 47.8950 -0 . 03 4 0.01

4 305. 153 30 5. 142 47.8807 47.8869 a . 006 -0.01

1C 305. 253 305. 250 47 .9994 47.9959 - 0. 00 3 0.01

NP - 9 9 RMS PC T = 0.061

. 42

JP 1134? A
APPENDIX D. (Continued)

Cryogenics Division - NBS institute for Basic Standards LABORATORY NOTE

PftOJECT NO. 2750364FILE NO. 73-3

PAGE 7

SUBJECT The Vapor Pressures of Ethane NAME -p. K . D. Goodwin

T able 2. Data of Tickner ( 1 )

,

API (2), and Carruth ( 3)

.

DATE July 9, 1973

ID T ,XPTL T - 6 8 P, ATM CALCD DEL T P, PCT

1 91. 35 U 91. 361 G.Q0G0132 0. G0C0 141 Q. 26 5 -6. 86

1 94. <+5 0 94. 463 0. 0000263 U. GOTO 306 0. 58 2 -13. 98

1 98. 55G 98. 562 0.0000658 0. 0CC0 783 0 . 73 0 -15. 98

1 101. 35 C 1C1. 858 0. 00 0 13 16 0. 0 uol 57 1 0 . 79 7 -16. 23

1 105.350 105. 353 G. 00 C 26 32 0. 0 0 03 11

8

0. 825 -15. 60

1 110.550 110. 548 0. 0006579 C. GCG7914 0. 99 2 -16. 87

1 1 1 4. 65 G 114. 644 0.00 131 56 0 . 00 15 453 0 . 94 7 -14. 85

1 119.050 119. 040 0.0026316 C. 0029942 0 . 83 9 -12. 11

1 125. 650 125. 537 3.00 657 89 0 . C072450 0.717 -9. 19

1 130.650 130. 637 0.0 13158 0 .013539 0. 24 0 -2. 81

NP = 10, RMS PC T = 13.226

ID T » X PTL T-68 P , A T M CALCD DEL T P, PCT

2 130.270 130. 257 0 .0 131 56 0 .012947 -0 . 13 8 1

.

63

2 136.460 136. 449 0.026316 0 .02590 9 -0. 148 1 • 57

2 140.410 14 0. 4C 2 C .0 39474 0 .038925 -0. 141 1

.

41

2 143. 370 143. 364 0.052632 0 .051 945 -0. 139 1. 32

2 14 5. 76G 145. 756 0 .0 657 89 0.064946 -0. 14 2 1

.

30

2 147. 790 147. 78 8 0 .078947 0.073018 -0. 134 1. 19

2 151. 12 G 151. 121 0. 10526 0.10 415 -0. 127 1 • 07

2 153. o20 153. 824 0. 13158 0.13028 -0. 12 2 0 . 99

2 15 9. j 3 0 159. G39 0. 19737 C. 19591 -0. 099 0 . 74

2 162. 96

u

162. 973 0. 26316 0.26140 -0. 094 0 . 67

2 166. 17G 166. 185 0. 32895 C .3270 8 »0. 084 0 . 57

2 168. 500 168. 918 0. 39474 0.39284 -0. 074 0 . 48

2 173.410 173. 432 0.52632 0.52422 -0.064 0 . 40

2 177. 100 177. 125 0. 657 89 0 • 65 57 4 -0 . 356 0. 33

2 18 0. 250 180. 277 0.78947 0.78743 — 0 . j 4 6 u • 26

2 183. Cl

C

183.039 0. 921 0 5 0 .91908 -0 . 039 0 . 21

2 184. 520 18 4. 55 j 1. 00 j 31 0.998Q 3 -0 . 036 0 . 20

2 185. 480 185.510 1.0526 1.0509 -0 . 031 c

.

16

r>c 187.710 187. 74 1 1.1842 1.1821 -0. 034 0 . 18

2 189. 770 189. 8C

2

1.3156 1.3143 -0.023 0 . 11

2 193. 44

1

193. 473 1.5739 1.5777 -0.017 0 . 38

2 198. 15 C 198.185 1 .97 37 1.9729 -0.008 0 . 04

NP = 22, RMS PC T = 0.857

ID T , X PT L T - 6 6 P, A T M CALCD DEL T P, PCT

3 9 1. 340 91. 351 0. 00 C 0 1 5 2 0. COCO 141 -0 . 315 8. 14

3 93. 700 93. 712 G • 00 00 27 1 0. G0C0 25 5 -0. 237 5. 80

3 96. 240 96. 253 0. 00 00491 C . 0CC0466 -0 . 235 5. 42

3 1 0 & . 7 0 0 ICO. 710 0. 00 012 97 0. C0G1239 -0.222 4. 64

z 105. 600 105. 6G 3 C. 00 C3263 3. 0CC3268 0. 009 -G . 16

3 1 1 4. 240 114. 235 0.00 14461 0. 0014487 a . 012 -0 . 19

3 12 0. 380 120. 369 0. 00 363 66 0. 0036185 0.023 -0 . 33

3 129. 610 129. 797 C .0 12312 0 .012260 - 0 • 036 0 . 42

3 135. 77G 135. 759 0 .0 241 97 0 .024065 -0. 051 0 . 55

3 140. 551 140. 542 0 . 0 40211 0 .039472 -0 . 188 1

.

87

3 144. 140 144, 135 0 .0 562 89 0 .055 871 -0. 080 0 . 75

NP = 11, RMS!3 CT = 3.759

SP 11142* 43
APPENDIX D. (Continued)

Cryogenics Drmron - N®$ Intfitate ter Bosk Standards LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-3

PAGE ID

subject ^ „ The Vapor Pressures of Ethane

Table 3. Data (5) of Loomis, Walters [llj.

NAME

). Goodwin

DATE July 9, 197 3

ID T ,XPTL T-68 P » A TM CALCD DEL T P, PCT

5 135. 736 135. 725 0.0245CC 0 .023977 -0 . 20 3 2.18

5 143. 267 143. 261 0.052200 0 .051437 -0 . 156 1.48

5 147. 324 147. 321 0 .0 7590 0 0 .074840 -0 . 158 1.42

5 154. 546 154. 550 0. 1 4 J 0 t 0.13816 -0. 16 6 1 . 33

5 158.335 158. 393 Q. 18961 0.18657 -0 . 14 3 1.09

5 162. 629 162. 641 G. 257 3 0 0 .2552 e -0.110 0.79

r 165.529 165. 544 0. 31600 0.31300 -0 . 139 0.96

’ 5 167. 336 167. 853 0. 36930 0.36606 -0. 13 3 0.89

5 169. 175 169. 193 3 • 40 3 3 u 0.40000 -0 . 126 0 .82

c 171. 7G0 171. 721 3. 47430 0.47084 -0. 116 0 . 74

6 1 7 J . 6C 2 170. 622 0. 443 JC o .43890 -0 . 145 0.93

5 174. 062 174. 085 0. 549 8 C 0.54579 -0. 119 0.73

c. 175. 7 u 8 175. 732 J.6073C 0.60 338 - j. 10 8 0.65

5 177. 623 177. 649 0. 680 40 0.67631 -0. 10 3 0.61

r 178. 621 178. 647 0. 7210C 0.71696 -0 . 097 0.56

c 179. 750 179. 777 0. 76960 0.76525 -0. 099 3.57

5 181.506 181. 534 3.84990 C .64537 -0 . 096 0.54

5 182. +63 182. 492 3. 896 3C 0.89172 -0 . 093 0.51

5 183.773 183. 8b 7 0. 9634L o.95 860 -0.092 0.50

5 184.539 184. 569 1. 0 040b 0.99906 -0. 091 0.49

t; 135. 137 185. 167 1.0366 1.0 318 -0. J87 0.47

9 185.514 165. 94+ 1 . 08 3 0 1.0755 -0.078 0.42

5 186.609 166. 640 1.12Gb 1.1158 -0 . G84 G . 44

5 187. 30 2 187. 3 33 1.1619 1.1572 -0. 37 7 0.40

5 137.726 167. 757 1.1881 1.1831 -0. 08 1 0.42

5 18 3. 879 163. 4L 1 .22 89 1.2239 - 0 • j 8 0 G . 41

r 139. 114 169.146 1.2757 1.271 j -C . 072 0. 37

5 189. 658 189. 690 1 . 32 48 1.32C 2 -0 . 069 0 . 35

5 190. 731 190. 823 1.3865 1.3839 -G . 057 0 . 33

9 1 9 1 • + 3 C 191. 463 1.4334 1.4268 -0 . G64 0 . 32

9 192.266 192. 319 1.4953 1.490 8 -0.061 0 . 3b

c 192. 7 77 192. 810 1.5318 1.5273 -0 . C60 0 . 29

9 196. 244 196. 27 3 1.8086 1.8049 - 0 . 04 6 0.22

6 199. 90 9 199. 944 2.1417 2.1 384 — u . u 3 4 0.15

NP = 34, RMSPCT = 0.789

» 1 1M? A 44
APPENDIX D. (Continued)

Cryoganici Dtvnion - NSS Imtituta for link Standards LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3

PAGE ii

The Vapor Pressures of Ethane

Table 4. Data of Porter (6), and Barkelew (8).

NAME R. D. Goodwin

DATE July 9, 1973

ID T ,XPTL T-68 P, ATM CALCD DEL T P, PCT

6 184. 4 7

0

184. 500 0. 9994G C .99534 -0. 075 0 • 41

6 23 3.493 20 3. 524 2 .4960 2,5076 3.10 6 -0.46

6 205. 62C 205. 653 2.733C 2.7489 0.135 -0 .58

6 210.960 210. 992 3.4140 3.430 8 0.121 -0.49

6 216. 310 216. 341 4.2250 4.2338 0. 05 4 -0.21

6 221. 86 u 221. 910 5.2070 5.2104 0. 018 -0.06

6 225.100 225. 128 5 .8380 5.8456 0 . 037 -0 . 13

6 226. 180 226. 20 7 6,0730 6.0709 -0.010 0 .03

6 234.580 234.603 8.0440 8.0481 0. 016 -0.05

6 238. 900 238. 921 9.2290 9.2305 C. 005 -0.02

6 243.220 243. 238 10 .5360 10.535G -0. 00 3 0 . 01

6 248. 65G 243. 665 12.3540 12.3588 0 . 01 3 -0.04

6 253. 0 3

G

253.042 14.0430 13.9889 -0. 139 0 . 39

6 258.600 258. 8C9 16.4210 16.3679 -0. 122 0.32

6 263.260 263. 286 18.4481 18.4078 -0 . 085 0.22

6 263. 73

G

268. 732 21.1850 21.1317 -0. 10

1

0.25

6 273.090 273. 090 23.5440 23.5147 -0.051 0.12

6 278. b 40 278. 638 26 .8370 26.8276 -0. 015 0.04

6 283.580 283. 576 30 .13 60 30.0575 -0. 071 0 . 16

6 288. 260 268. 254 33.4680 33.380 0 -3 . 119 0.26

NP - 20. RMSPCT = 0.274

ID t.xftl T-68 P , A TM CALCD DEL T P, PCT

8 1 1 3 . j 0 w lu 9. 99 3 C . 00 076 0t 0. CGC72G5 -0. 319 5.49

6 1 2 a . 6 c c 119. 989 0 . 00 346 0 C 0. 00 34 29

5

-0.063 3 . 89

6 1 3 0 . J 0 0 129. 987 0.0127 2

G

0 .012540 -0. 121 1.44

8 14 0. j o 0 139. 992 0 .0 3785C 0 .037359 -0. 131 1.31

8 1 5 G . 00 G 150. JO j 0 .395600 0 • G 94 65 7 -0. 116 1.00

8 1 6 G • G C 0 160. 010 0. 2120C 0.21068 -0.084 0.63

8 170.000 170. C19 0. 4236G 0.42214 -0.053 0 . 35

8 ISO. 0 G 0 180. 027 3. 77780 C. 77 62 8 -0.034 C .20

8 190. JOC 190. 032 1 .33 0 0 1.3297 -0. 004 0 . 02

8 2 0 0 . «j 3 u 200. 035 2.1462 2.1472 0. 011 -0 . 35

8 2 1 u . u 0 C 210. 033 3 . 29 7

1

3.2998 0.020 -0.08

8 2 2 o . l 0 0 22 0. 03 C 4.8580 4.8639 0. 033 -0.12

6 23 3. JOC 230.025 6. 9120 6.9196 0. 032 -0.11

8 2 4 0 . * 0 0 240. 020 9.551C 9.5508 -0. GO 1 0 . 00

8 250. u00 250. 014 12 . 85 0c 12.8456 - U.C12 0 .03

8 2feu. JOG 26u. 00 8 16.910C 16.8973 -0.028 0.08

8 270. JOG 270. 001 21 .83 01 21.8066 0. C12 -0.03

8 280. «G0 279. 997 27 . 65 0 0 27.6895 3. 06 2 -0 . 14

8 290. CC0 289. 994 34.6500 34.6843 3. 04 5 -0 . 1G

NP = 19, RMSPCT = 1.383

V 11142 A 45
APPENDIX D. (Continued)

Cryoganics Division - NBS birtitate for Rowe Standards LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-3

PAGE 12

The Vapor Pressures of Ethane

Table 5. Calculated Ethane Vapo.r Pressures.

***** R. D. Goodwin

DATE July 9. 1973

ETHANE VAPOR PRESSURES

T i K P , A T M OP/DT 02P/DT2

89.399 C.GGG0096 G. 00 00 C26 0.Q0000C63

9 c . a o c C.GQJ0099 0.0000026 C.0CG0 0 C 6 4

95.300 C. 0 03 334e u. 00 00 083 C. 0 000 0 177

1 0 G . 0 0 0 C. U3Q1067 0 . 30 0G226 0.00000430

135. a 0 c C. 0002915 3 . 00 0 C 555 G .0 G0C G942

lie .3 OC G.0DJ7207 G. 0001239 G .QC03 1881

115. DOG C.0016337 0.0002545 0 .0000 3475

12 0 .DOG 0.0334347 G. 0004868 G. 0 000 5997

125.0 OG 0.0 06760e 0. 00 08749 0.0 000 9759

1 3 C . 0 G C G. 312559 0.0 31 489 0 . C 0 0 1 5C 8 135.300 0. 022167 0 .302414 0. CG0 2228

1 4 G . 0 0 G C. J3739C G .0 03753 0. COO 3164

145. DOG 0. CbQ57«+ 0.005618 3. G03 4339

15l.DOC 3 • 39465 3 0 .0 08135 3 . 0 C 3 5 77

155.3 OC C .14323 0. 01143 0 .GO 0 747

1 6 C .300 0 .21052 3. G 1565 0 .GO C944

165.300 G .30146 0. G2G91 0 .00 1167

17 u . G 0 C G .42162 3. 02736 0 .031415

175.30C u .57722 0. 03511 0 .03 1688

1 8 u . 0 0 0 0.77507 0. 0 4428 0 .03 1984

185. GCC 1. C 226 0 .0550 G. J 3 23 0 1 9 G • j 0 u 1. 3276 3 .0673 0 . 0 0 26 3 195. 30

1.6984 0.0813 C.3 U29 8

2 0 u . 3 0 l 2. 1439 J .0 972 G. 3 0 335

205.303 2. c73

J .1148 0.0 0 37 2 21C .0 0 D 3. 2954 3 .1344 G .(J 0 411

215.300 4.0205 0.1560 C .0 G451

22 3. 3 CC 4. 3585 3.1795 G .3 0492

225. 000 5.8194 0 .2352 C . 3 0 53 3 231 . 3 G C 6.9136 J .2 329 3 . 0 3 57 6

2 35 . JOG 5. 1519 0 .2628 C . 3 0 61

2 4 C . 0 0 0 9.5450 0 .2 948 G .0 0664

245.300 11. 1G4C 0.3292 G.O 071G

25G.30G 12. 8406 3 .3653 G. 3 3757

2 5 5 . 3 0 C 14. 7664 0.4349 G.O 3 606

2 6 0 . 3 0 G 16. 8936 0 . 4465 0 .0 065 8 265.300 19.2357 3 .4907 0 . 0 0 91 3

2 7 C • J u 0 21. 8G56 3 .5378 C . o J 97 2 275. a C C 24. 6190 0 .5880 C . J 1C36

2 8 0 . 3 C 3 2 7. fc914 0.6416 G .3 noe

2 8 5 . 3 C C 31. J 4 1

3 .6990 0.31192

2 9 J . J 0 0 34.0895 0.7610 0.01294

2 9 5 . 3 G D 33.6612 0.8289 0.31429

3 0 u . J 0 0 42.9922 0 .9,153 C . 3 1649

3 J5.0G0 47. 7442 1 .G 029 0 .0 2694

305.330 48. 0770 1.0160 0 . J 0 c 0 -j

JP 11342 A 46
APPENDIX D. (Continued)

Cryoganics Drnaron - NBS Institute for italic Standard* LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-3PACE 13

SUBJECT The Vapor Pressures of Ethane

Table 6. Reduced Vapor Pressure Functions.

NAMi

R. D. Goodwin

DATE July 9. 1973

ETHANE REDUCE? VAPOR PRESSURE FUNCTIONS

T,K X Y (Y-X ) 39.399 0 . 0 vj 0 . G 0 00 G 0. 30 00 C 91.186 0.02 0.G2199 0 .00 199

92.510 0.44 0. 04392 0.00 392

93.373 0.06 G .06578 0.00 57 8 96.277 0 .08 0. 08759 0.00759

96.723 0 .14 3. 1C 93

4

0.00934

98.215 0.12 G. 13102 0.0110 2 99.753 0 .14 0.15264 0.01264

101.339 0.1b 0.17419 0.C1419

10 2.977 0.18 C . 19568 0.31568

10 4.569 C .20 u.2171

0

0.3171C

106.418 G .22 0.23845 0.01345

108.226 0.24 0.25972 0.01972

11C .3 96 0.26 0. 28093 0.02093

112. J 32 0 .28 0. 3G20 5 0 .02 20 5

114.037 0.3 0 0. 32310 0. 0231

G

116.116 0.32 G. 3440 6 0.02406

118.272 0.34 G. 36495 0.02495

12C .509 0.36 0.38574 0.02574

122.332 0.38 0. 40 645 0 .02645

125.247 0 .40 4 .42706 0.02706

127.759 0 .42 0.44758 0.0275 8 13C .373 3 .44 4 • 46 90 o C .02 80 G 133.397 0.46 C. 48832 0 .32332

135.337 0 .43 0.50854 0 .02854

138.301 Q .50 G . 52 856 0.02866

141.997 0.52 0.54866 0.32856

145.234 C . 5 4 0.56855 0. 32 35

5

148.522 0.56 G. 56833 0 .02 83 3

152.172 0.56 G. 60 83 0 0 . G280 0 155.396 0 . 6 u 0.62755 0.G2755

155.307 C .62 G. 6469

8

0.02698

163.919 0.64 C. 66629 0 .02 62 9

168.248 0.66 0,68548 0.3254 8 172.312 0.53 3.70 45 5 0.02455

1 7 7 . 6 3 C 0.70 3.7235 4 0 .32 35 G 182.725 0.72 0. 74233 G.32233

188.121 0 .74 4.76135 0.02105

193.345 0 .76 C . 77965 0 . 0 1 96 5

196.928 0 .7o 0.79815 0.41315

206.405 C .3 J 3.31655 0.41655

213.317 0.82 G. 8343 6 0.01486

2 2 C . 7 3 7 G .84 3.8530 9 0 .31309

228.527 C . 8 6 0.67126 0.01126

237.138 0.39 3.88938 0 . 00 93 8

246.306 G .90 3.90749 0 . J 0 74 9

256.212 u .92 G .92552 0.30562

266.948 0.94 3 .94381 0.00 381

278.523 0.9b C. 96216 0 . 3C 216

291.366 0 .98 G. 98076 3. 3 C 37 8

30 5.33G 1.30 1 . 0 G 0 0 0 0 . 3 0 0 0 C

SP 1134? A 47
APPENDIX D. (Continued)

Cryogmks Drvnton - NSS MiMe for towc Stondords LABORATORY NOTE

PROJECT NO. 275Q364FILE NO. 73-3

PAGE /4-

SUBJECT The Vapor Pressures of Ethane NAMe R. D. Goodwin

DATE July 9, 1973

PROS RAM PSATFIT

ETHANE VAPOR PRESSURES* X = ( 1-TT/ T )/ (1-T T/TC > , LN(PXPTRP) = A 1* X + A2*X2 + A3*X3 + A4*X4 + A 5*X * ( 1-X ) ** E

.

AUTHORS ID = (I)TICKNER* ( 2 ) ROSS IN I * ( 3) CA RR UTH, (4)PAL/P0PE*

( 5 ) L 00 MI S * ( 6 ) PORTER » (7)ZIEGL£R* ( 8 ) 8 ARKE LE W/ TE ST ER

( 9 ) POPE, (10 ) DOUSL IN, PREPRINT (1973 )

,

COMMON TTRP ,TCRT ,PTRP, E,A(9), FZ,F1,F2, DL PDT, D2 LPDT2

C0MM0N/999/NFUN ,Y , F (30)

DIMENSION TEMP(13Q) ,DELT(13G)

D IMENSION 10(999) ,T (999 ) , TX ( 999 ) , P (9 99)

DIMENSION G (30)

1 F ORM A T ( I 5 , 2F10.C)

2 F 0PM A T ( 1 HI 17 X *E THANE VAPOR PRESSURES,

1 18X 6 HTTRP =F7 . 3 , 8 H, TCRT =F8.3//

E = * F5 • 2 //

2 1 8 < 12 M PT RP, MUA TM =F9. 5, 12H, PCRT, ATM =F9 .5// 2 (15X 3F16.

3 FCPMAT

(

iax 2H I D 4X6HT ,XPTL 6X4HT -68 7X5HP,ATM 7X5HCALC0

1 5X5 H DEL T 5X5HP ,PCT)

4 F GRM A T( 1 HI 17X 2HID 4X6 H T , XP TL 6X4HT -68 7X5HP,ATM 7X5HCAL CD

1 5X5 H DEL T 5 X5 HP , PCT

)

5 FCRMAT(15X 15, 2F10.3, 2F12.7, F10.3 , F10.2)

6 F ORMA T ( 1 5X 15, 2F1C .3, 2F12.6, FI C • 3 , F10.2)

7 F OR M A T ( 1 5X 15, 2F10 .3 , 2F12.5, FIG,

3

, F10.2)

8 F ORMA T ( 1 EX 15, 2F10 .3, 2F12.4, F10.3 , F10.2)

9 P ORMA T ( 1 HO 17 X 4HNP =14 , 10H, RMS PCT =F 7. 3)

10 FORMAT(F8#3, F9.t, 63X)

11 F OR.MA T ( 1 HI 16 X *E THANE VAPOR PRESSURES* // 17X3HT,K 6X5HP,ATM

1 6X5HDP/DT 5X^HD2P/DT2 ) 12 F OPM A T ( 1 CX FI j , 3 , 2F11.7, F12.8)

13 FCRMATdlX FIG. 3, 2F11.6* F12.7)

14 FORMATdCX Flu. 3, 2F11.5, F12.6)

19 FORMATdCX FIS. 3, 2F11.4, F12.5)

16 FOPMATdHl 16 X * E TH ANE REDUCED VAPOR PRESSURE FUNCTIONS* //

1 17X 3HT,K 7X1HX 9X1HY 5X5H(Y-X) ) 17 FORMATdCX F 1 0 . 3 , F8.2, 2F10.5)

13 F0RMAT(16X 2HEP b X2HSS)

19 FORMATdCX 2F10.4)

RE AD- IN THE T4 3 - Tb 8 TEMP. CONVERSION TABLE.

20 ? F AO IQ, (( TEMP (J ) ,OELT (J) ) ,J = 1 ,130)

21 TT po =89. 899 5 TCKT=305.33 $ PTRP= 9. 6 3 8E-6 $ E=1 .5 N =0

IF ( I DO ) 23,25

$ T X ( N) = T T

READ (7) ZIEGLER, <ELVIN, MM HG.

22 DC 24 J=l,99 B READ 1, IOD,TT,PP $

23 N = N+l $ IO(N)=IDD $ P(N)=PP/75G

24 T(N) = T 68 (TT, BELT, TEMP)

25 NF1 = N read MIXEC (MPAL, ( 9 ) PO PE , (ldDOUSLlN DATA.

( 4 ) KELVIN, PSIA, ( 9 ) KELV I N , ATMOS , ( 1 0 ) CEN T I G .

, A TM OS

.

26 OC 35 J= 1, 2 G d S READ 1, IDO,TT,FP $ I F ( I DC) 27,36

27 N = N + l 5 1 0 ( N ) = IDD $ IF(ID0-4) 28,30

28 IFQDD-9) 34,32

30 P(N> = PP/14. 69595 $ T ( N) = T 68 ( TT , CELT , T EMP

)

31 T X ( N ) = TT 5 GO TO 35

3? P ( N) = PF f T ( N ) = T 68 (TT, DELT, TEMP)

33 TX(N> - TT S GO TO 35

JP 11942 fl 48
Cryogenics Division - NBS Institute for Bosk Standards LABORATORY NOTE

PROJECT NO. 2751364FILE NO. 73-3

PAGE 15

SUBJECT The Vapor Pressures of Ethane NAME D. Goodv.dn

DATE Tnlv 9. 1973

APPENDIX D. (Continued)

PSATFIT G7/23/7 3

T (N) = TX (N) = TT + 273.15

IF(IOD) 39,41

$ I X ( N ) - 273.15 + TT

34 P ( N) = PP

35 CONTINUE

36 NP = N ? NF = 5

READ (1) DATA, CENTIGRADE, MM HG

.

3d 00 +3 J= 1 , 9 9 S READ 1, IDO,TT,PP $

39 N = N+l $ IO(N) = I DD S P(N) = PP/76Q

43 T ( N) = T66 ( TX <N) , OELT ,TEMP)

41 NP2 = N

READ (2) DATA, CENTIGRADE, MM HG

.

42 DO + 4 J= 1, 9 9 $ RE AO 1, ID0,TT,PP $ IF(IDO) 43,45

43 N - N +1 5 1 0 { N ) = I DD $ P ( N ) = P P/760 $ TXCN) = 273 .15 + TT

44 T ( N) = T68 (TX (N) , CELT, TEMP)

45 N P 3 = N

READ (3) DATA, KELVIN, MM HG.

46 DO -,6 J = 1, 99 t READ 1, IDD,TT,PP $ IF(IDD) 47,49

47 N = N+l $ I D ( N) = I DD $ P(N) = P P/763 $ T X ( N) = TT

48 T ( N) = T68(TT,DELT,TEMP)

49 N P4 = N

READ (5) DATA, KELVIN, ATMOS.

53 DC 52 J= 1 , 9 9 5 READ 1, IOD,TT,PP S

s PP

51 N = N + l $ ID ( N) = I DD % P(N) = PP

52 T(N> = T68( TT,DELT,TEMP)

53 NP5 = N READ (6) DATA, KELVIN, ATMOS.

54 DC 56 J=l,99 t READ 1, IOD,TT,PP

55 N = N+l 5 I D ( N ) = IOD ? P(N) = 56 T(N) = T68(TT,DELT,TEMP)

57 NP6 = N READ (6) DATA, KELVIN, ATMOS,

63 DO 52 J= 1 , 9 9 $ READ 1, IOD,TT,PP

61 N = N+l f ID ( N) =100 S P(N)=PP S 62 T ( N) = T68 ( TT ,DEl_T ,TEMP)

63 N PP = NP7 = N

IF(IDD) 51,53

$ T X ( N) = TT

IF(IDD) 55,57

$ T X ( N ) = TT

$ IF(IDD)

TX (N)=TT

61,63

9.600

EXPLORE VALUES FOP PTPP.

79 E = 1.5 $ PRINT 18 S 80 XK = 1 - TTRP/TC°T

81 DO 32 I P=1 , 26 S PTP = 82 N F UN = NF S DO 85 J = 1,NF $

83 F ( 1 ) = X $ F(2)=X**2 $ F(3)=X**3

Y = L OGF (P ( J) /PT C P)

CALL FIT $ CALL COEFF $ SS

A (K) = F (K)

DO 88 J = 1 , N P S PC = PSA TF (T ( J)

)

CONTINUE S SS=1j3*SQRTF (SS/NP)

SSK = l.CE+010

0 • 3 u 1* IP $ PTRP = PTR*l.QE-6

- ( 1-TTRP/ T ( J) ) /XK

F ( 4 ) =X ** 4 $ F( 5) =X+ (1-X ) **E

84

8 5 86

o7

88

89

90

91

92

9 3 94

95

= n

%

$

« T CK = TCRT $ TTK-TTRP

B DD 8 6 K=l,9

SS = SS + ( P < J) /FC-1 ) **2

IF (SS. LT.SSK ) 89,92

SSK=SS 3 EK=E $ PTK =P TRP

DO 91 K=l,9

G (K) = F ( K

)

PPINT 19, PTR, SS

E = E< l T CRT =TCK t TTRP=TTK $ PTRP = PTK $ DO 94 K = 1 ,9

A ( K) = G(K) 5 PORT = P T FP + EXPF ( A ( 1 ) +A (2 ) + A ( 3) +A (4 )»

PTR = l.CE6*PTRP

IF 11342 k 49
APPENDIX D. (Continued)

CryogwHcs Drmtofi - NCS MIM, ter Beak Stondordi LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3

CnS

SUBJECT The Vapor Pressures of EthaneNAME R. D. Goodwin

DATE July 9, 1973

c PRINT DEVIATIONS, INCLUDING DT = -DP/CCP/DT).

CC

C

C

105 L = 9 5 SS = 0 1G6 PRINT 2, E,TTRP,TCRT»PTR»PCRT, (A(K),K=1,6) J PRINT 3

107 DO 125 J = 1 » NP S L = L*1 $ IF(L-57) 112,106

108 L = u S PRINT 4 112 PC = PS A TF ( T ( J) ) $ DP OT = PC'DLPOT

113 OP = P(J)-PC t DT = -OP/OPOT

114 PCT = 1 3 C’DP/PC B SS = SS * PCT**2

117 IF ( 3 C -0.01) 120,118,118

118 IF(PC-O.l) 121,119,119

119 IF(PC-l.O) 122,123,123

120 PRINT 5, ID(J),TX(J),T( J) , P ( J) , PC , DT , PC T S GOTO 125

121 PRINT 6, ID (J) ,TX ( J) , T( J) ,P( J) , PC ,OT , PCT $ GOTO 125

122 PRINT 7, ID(J),TX (J) ,T( J) ,P< J) ,PC,DT,PCT $ GOTO 125

123 PFINT 3, ID (J) ,TX (J) , T< J) ,P( J) ,PC,DT ,PCT

125 CONTINUE

126 SS = SQRTF ( SS/NP) $ PRINT 9, NP,SS

PRINT OTHER DATA DEVIATIONS.

140 K = NP+1 ? SS = N = 0 $ PRINT 4

141 DC 157 J = K» NPP S IF(J-NPP) 143,142

142 SS = SQRTF ( SS/N) B PRINT 9, N,SS $ GO TO 158

143 N = N+l B PC=PSATF(T< J) ) B DPDT = PC*DLPDT

144 DP = P ( J ) -P C 5 DT = - DP /DPDT

145 PCT = 1CC*DP/PC * SS = SS + PCT**2

146 I F ( 3 C-J • Cl ) 150,147,147

147 IF(PC-O.l) 151,148,148

143 IF(PC-l.O) 152,153,153

150 PRINT 5, ID (J > , TX ( J) , T< J) ,P( J) , PC , OT , PCT $ GO TO 155

151 PRINT 6, ID(J» ,TX(J) ,T( J) ,P(J) ,PC,OT,PCT $ GO TO 155

152 P c I N T 7, ID (J) , TX ( J) , T( J) ,P ( J) , PC ,DT , PCT $ GO TO 155

153 PCINT 3, ID (J) , TX ( J) , T( J) ,P( J) , PC ,OT ,PCT

155 IF(ID(J*l)“IO(J) ) 156,157

156 SS = SQRTF ( SS/N) B PRINT 9, N,SS B SS=N=G B PRINT 4

157 CONTINUE

158 CONTINUE

3 R INTOUT UNIFORM TABLE p Oft PUBLICATION.

230 P p INT 11 B DO 220 J = l,46 B IF(J-l) 202, 201

2L1TT=TT-P B GO TO 235

202 IF(J-46) 204,203

203 TT = TCRT B GO TO 205

204 T T = 8 j 5*J

2 05 PS = PSATF(TT) B DPDT = PS* DL POT B 02 PD T 2 =P S* ( O LPDT ** 2 * 02LPDT2)

2 0 7 IF(°S-0.C1) 210,208,208

2 08 IF (PS -d • 1) 211, 209, 209

2C9 I F ( 3 S -1 . C) 212,215,213

210 P^INT 12 t TT,PS,DPDT,D2PDT2 B GOTO 22 G 211 PRINT 13 TT,PS,0PDT,D2P0T2 S GOTO 22 0 212 PFINT 14 * TT,PS,DPOT,D2PDT2 B GOTO 22 0 213 IF ( J- 46) 215, 214

214 D 2 POT 2 = 0 215 PRINT 1 5 * T T, PS, DPDT, D2PDT2

220 CONTINUE

JP I1J4JI 50
APPENDIX D . (Continued)

Cryogw>icj Drmron - NBS InsMuto for Bosk Standards LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3

Ul 5?^

. SUBJECT The Vapor Pressures of Ethane NAME „R . D. Good)*un

DATi July 9, 1973

PS A TF I T 07/23/73

C PRINT UNIFORM REDUCEO TABLE.

C Y = LN (P/FTRP) /YN, YN = LN ( PORT/ PTR P )

.

C YC = ( A ( 1 ) *X . . . A (5 ) *X*(1-X ) **E)/YN.

253

XN = 1-T TRP/T CRT $ YN = A«l) + A<2> + A(3) + A(4)

251 PRINT 16 S 00 270 J=l,51 t X = Q.L2*(J-1)

252 IF(J-l) 254,253

253 TT = TTRP S GOTO 257

254 IF ( J-51 ) 256,255

255 TT = TORT ? GOTO 257

256 TT = TTRP/ ( 1-X*XN)

257 IF ( J - 51 ) 259, 256

258 Z = 0 S GO TO 260

259 Z = X* ( 1-X

)

260 YC = A ( 5 ) * Z S DO 261 K=l,4

261 YC = YC + A(K»*X»*K

262 YC = YC/YN $ YX = YC - X 270 PRINT 17, TT, X, YC, YX

999 CONTINUE $ STOP t ENO

SINGLE-BANK COMPILATION.

FUNCTION PSATF(T)

C LN(P/PTRP) = A 1* X + A2*X2 A3*X3 + A4*X4 + A5 *X * ( 1 -X ) * * E

.

C ARGUMENT, X = ( 1- TT/T ) / ( 1 -TT/TC )

.

C YIELDS ALSO OLPDT = (DP/OT)/P, AND D2LPT = (D2P/0T2)/P.

COMMON TTRP ,TCRT ,PTRP , E, A ( 9 ) , FZ,F1,F2, DL POT, 02 LP0T2

1 FORMATdHO 9X *PSATF = 0, T EXCEEDS TCRT. * / ) 2 X N = 1 - TT R P/ T CR T $ X= (1-TTRP/T) /XN $ X2=X**2 S X3=X**3 $ X4=X**4

3 OXDT = TTRP/XN/T**2 $ D2XOT2 - -2*DX0T/T

4 0 = 1 -X $ I F « Q) 5,5,7

5 PS AT F = DLPDT = C2LPDT2 = 0 $ PRINT 1 S RETURN SZ=71=Z2=Q % GOTO 9

7 W = Q**£ $ W1 = -E*W/Q $ W2 = <i-E)*Wl/Q

8 Z = X*H S Zi = X*Wi W $ Z 2 = X * K2 2* W1

9 FZ = A ( 1

) *X A(2)*X2 + A(3)*X3 + A(4)*X4 A(5)*Z

10 PSATF = PTRP*cXPF (FZ)

11 FI = A ( 1 ) + 2* A { 2

) * X f 3*A(3)*X2 4*A<4>»X3 + A(5)*Z1

12 OlPOT = FI * OX DT

13 F2 = 2* A (2 ) + 6 * A ( 3

)

# X + 12*A(4)*X2 + A(5)*Z2

15 D2LPDT2 = Fl*O2X0T2 F2*DXDT»*2 S RETURN $ ENO

SP 11342 A 51
APPENDIX D. (Continued)

Cryogenics Divnfon - MBS Inditute for Bone Standards LABORATORY NOTE

PROJECT NO. FILE NO. 73 -3

PAOE \8

SUBJECT The Vapor Pressures of Ethane wms r. I3. Goo'dwin

DATE _ , . ^ . July 9, 1973

FUNCTION T68(X,YMAT,XMAT)

THIS PROGRAM HAS SEEN CHANGED SO THAT THE OSCILLATING NATURE OF

THE MATRIX TO 8E INTERPOLATED EXISTS ONLY AT THE UPPER ENO OF THE

TABLE

THIS ROUTINE WILL TAKE INPUT MATRICES OF UP TO 999 ELEMENTS EACH,

ARRANGEO SO THAT THE X MATRIX(XMAT) IS IN EITHER ASCENDING OR

DESCENDING ORDER, SELECT NMAX OF THESE POINTS, CHOSEN SO THAT

SUCESSIVE X VALUES OSCILATE ABOUT THE VALUE OF THE ARGUMENT X UNLESS THE ENDS OF THE XMATRIX INTERFERE (IN THIS CASE THE

OSCILATORY NATURE IS LOST BUT THE PROGRAM WILL STILL PERFORM AN

INTERPOLATION), INTERPOLATE ON THESE NMAX PAIRS OF DATA PY

AN OSCILATI NG VARIABLE POINT AITKEN INTERPOLATION ALGORITHM

EITHER UNTIL THE PERCENTAGE CHANGE IN THE INTERPOLANT IS LESS

THAN THE ACRCY ARGUMENT ( THE ARGUMENT NESSY INDICATES THE

NUMBER OF THE POINT JUST BEFORE THE LAST ONE CHECKED) OR UNTIL

THE NMAX POINTS ARE ALL USED. IT IS SUGGESTED THAT NMAX

BE LESS THAN 10, AND OF COURSE LESS THAN NELMTS. NELMTS

INDICATES THE NUMBER OF ELEMENTS IN XMAT OR YMAT.

IF NESSY IS ZERO IT INDICATES THAT THE INTERPOLATION REQUIREMENT

HAS NOT BEEN SATISFIED. IF NESSY IS 1 IT MEANS THAT THE VALUE OF

X LIES OUT SIDE THE RANGE OF XMAT.

DIMENSION Y M AT ( 999) , X MAT ( 999) , A ( 21 , 2 0

)

1L0 FORMATC42HINTERPOLATION REQUIREMENT NOT SATISFIED (X= ,E16. 8, 1H)/33H

1 L AST 2 APPROXIMATIONS OF Y A RE ( Y= , E 1 6 . 8 , 1 H, , E 16 . 6 , 1H )

)

2C0 FORMAT ( 55HTHI S REPRESENTS AN EXTRAPOLATION OF THF XMAT MATRIX(X=,

lElo. 3,lH)/3 3HNO CALCULATION HAS BEEN PERFORMED)

3CU FORMAT( 24HNELMTS IS LESS THAN NMAX)

ACC FORMATC 22HNMAX IS LARGER THAN 23)

NELMTS=13G S NMAX=9 I ACRCY=0,01

IF (NMAX -21) 71,71,69

69 WRITE OUTPUT TAPE 6,4)0

To 3 - X $ RfcTURN

71 IF (NMAX-NELMTS) 75,75 ,7 3

73 WRITE OUTPUT TAPE 6,3J&

T 6 3 = X $ RETURN

75 CONTINUE

FIRST TWO SUCCESSIVE VALUES OF THE XMATRIX THAT STRAODLE THE

VALUE X WIL L BE SOUGHT

J J 1 = NEL MTS- 1 DO 2 J I = 1, J J1

D I F 1 = X- XMAT (I ) DIF2=XM A T (

I

1 >- X IF (OIFi ) 16, 15,1 6

15 To 8 = X + Y MA T ( I)

NESSY = NMAX

RETURN

16 IF ( DIF2 ) 18, 17,1 8 17 Tb 8 = X Y M A T ( 1*1)

NESSY = NMAX

KoTURN

18 R A T 1 0 =0 I FI / DIF 2 IF ( RATI 0)20 , 2 C

,

19

19 I MI 0= I GO TO 3 2

2 <3 CONTINU E v n 52
APPENDIX D. (Continued)

SUBJECT

32

98

201

1 C 2

33

34

35

36

3 7

4u

41

2 C 3

l'1

2

356

7

Cryogenics Division - NBS Institute tor Bosic Standards LABORATORY NOTE

The Vapor Pressures of Ethane

PROJECT NO. FILE NO. PAGE

NAME

DATE

73-3 19

R. D. Goodwin _ I

AT THIS POINT ONE COULD PRINT THE FOLLOWING STATEMENT

WRITE OUTPUT TAPE 6 , 2 ) 0 , X N£SSY=1

T68 = X $ RETURN

CONTINUE

NOTE THAT RATIO IS POSITIVE IF THE TWO POINTS STRADDLE X REGARDLESS WHICH IS LARGER

J J J= I MI D JUP = I MI D

JDN = I MI

D

IF( JJJfNMAX-N EL MTS+1) 98,93,102

DO 2 J 1 J = 1 , NM AX

JUJ=IMI0+J-1

A (1 , J)=XMAT (J JJ)

A (2 , J )= YMAT (JJJ)

GO TO 2 J 3 DO *1 J=i,NMAX

JJ=J/2

J0E=J-2*JJ

JOE IS ) IF J IS EVEN AND 1 IF J IS ODD

IF ( J-l) 33,4 3 , 33

IF(J0N-l)34,3o,34

I F ( JUP-NELMTS> 35 ,37 ,35

IF (JOE) 37,36, 37

JUP= JUP+i

JJJ= JUP

GO TO 43

J0N= JDN-1

JJ J= JDN

GO TO 43

A (1, J)=XMAT (JJJ)

A (2 , J )= YMAT (JJJ)

CONTI NJ

E

Thi L

Rdf TM^c/i

NNN=NMA X+l

DO o J= 3 ,NN N

L = J-1

DO 5 K=L ,NM AX

J IS THE COLUMN NUM3ER

K IS THE ROW NUMBER

A(J,K)=(A(J-1,K)-A(J-1,J“2)) MX-A(l,J-2) )/(A(l,K)-A(l,J-2))

+A (J-l , J-2)

IF (<-L) 3,2,3

IF ( A 3 SF ( (A(J,L)-A(J-1,L-1) ) / A ( J , L ) ) - A CRC Y /l C 0 . 0 ) 7 ,7,

3

CONTINUE

CONTINUE

CONTINUE

NESS Y =3

AT THIS POINT ONE COULD PRINT OUT THE FOLLOWING STATEMENT,

WRITE OUTPUT TAPE 6 , 1 J 0 , X , A ( NNN , NMA X )

, A ( NNN - 1 ,N M AX-1

)

T 6 3 = X + A (NNN , NMA X

)

RETURN

NE33Y =J1

Tod = X + A(J,L) S RETURN 2 END

V 1134? A 53
APPENDIX D. (Continued)

Cryogmtcs Drvnion - NBS Institute tor Bosk Standards PROJECT NO. FILE NO. PAGE LABORATORY NOTE 2750364 73-3 20

SUBJECT NAME The Vapor Pressures of Ethane R. D. Goodwin

DATE July 9, 1973

ETHANE VAPOR PRESSURES, E = 1.50

TTRP = 89.899, TCRT = 305.330

PTRP.MUATM = 9.96700, PCRT, ATM = 48.07723 . , J/y/73 10,806922651 8.344715938 - 3.119603823

- 0.642995191 6.059966098 0.000000000

ID T » XPTL T -6 8 P » ATM CALCD DEL T P * PCT

7 90.000 90.010 0 . 00 00103 0 . 0 0 00 103 0.000 - 0.01

7 100.000 100.010 0. 0001096 0. 0001098 - 0.001 0.01

7 110.000 109.998 0. 0007364 0. 0007363 - 0.001 0.02

7 120.000 119.989 0 . 00 34934 0. 0034939 0.001 - 0.01

7 130.000 129.987 0.012728 0 .012732 0.00 3 - 0.04

7 140.000 139.992 0.037792 0 .03780 3 0.003 - 0.03

7 150.000 150.000 0.095474 0 .095476 0.000 - 0.00

7 160. 000 160.010 0.21196 0. 21192 - 0.003 0.02

7 170.000 170.019 0. 42387 0.42 369 - 0.007 0.04

7 180.000 180.027 0. 77824 0.77783 - 0.009 0.05

7 184.520 184.550 1.00000 0.99944 - 0.010 0.06

9 198.181 198.216 1.9737 1.9761 0.027 - 0.12

4 214. 302 214.334 3.9209 3.9159 - 0.032 0.13

4 224.102 224.130 5.6367 5.6402 0.017 - 0.06

4 229.756 229.782 6.8569 6.8598 0.012 - 0.04

4 234. 558 234.581 8.0335 8.0 392 0.022 - 0.07

9 234.692 234.715 8.0741 8.0741 - 0.000 0.00

10 238.150 238.150 9.0097 9.0077 - 0.007 0.02

9 238. 771 238.792 9.1843 9.1905 0.021 - 0.07

4 239. 844 239.864 9.4959 9.5019 0.020 - 0.06

4 240.514 240.534 9.6960 9.7003 0.014 -0 • 04

10 243.150 243.150 10.5063 10 .5045 - 0.006 0.02

4 243. 359 243.377 10.5760 10.5764 0.001 - 0.00

4 246.814 246.830 11.7137 11.7162 0.007 - 0.02

4 247. 816 247.831 12.0502 12.0628 0.036 - 0 . 10

10 248.150 248.150 12.1756 12.1747 - 0.003 0.01

4 249.741 249.755 12.7620 12.7496 - 0.034 0. 10

4 250.146 250.160 12.8985 12.8976 - 0.002 0.01

4 251.587 251.600 13.4425 13.4344 - 0.022 0.06

4 252. 544 252.556 13.8065 13.7997 - 0.018 0.05

10 253 . 150 253.150 14.0310 14.0 30 1 - 0.002 0.01

4 254.290 254.301 14.4898 14.4848 - 0.012 0.03

4 257. 543 257.552 15.8252 15.8266 0.003 - 0.01

10 258 . 150 258.150 16.0835 16.0827 - 0.002 0.00

10 263. 150 263.150 18.3464 18.3452 - 0.003 0.01

4 263.380 263.386 18.4543 18.4573 0 .006 - 0.02

4 267 . 536 267.539 20 .5197 20.5145 - 0.010 0.03

10 268. 150 268.150 20.8318 20.8308 - 0.002 0.00

4 271. 749 271.750 22.7661 22.7662 0.000 - 0. 00

9 272. 949 272.949 23.4515 23.4394 - 0.021 0.05

10 273. 150 273.150 23.5549 23.5536 - 0.002 0.01

4 275.922 275.921 25.1584 25.1702 0.020 - 0.05

4 276. 363 276. 362 25.4558 25.4347 - 0.035 0.08

4 276.385 276.384 25.4491 25.4479 - 0.002 0.00

4 276.514 276.513 25.5472 25.5257 - 0.036 0.08

4 277.813 277.811 26.3185 26.3189 0.001 - 0.00

10 278. 150 278.150 26.5309 26.5290 - 0.003 0. 01

sr HM? < 54
Oyogantci Division - MBS bsMvte for Bose Stamfords LABORATORY NOTE

PROJECT NO. 27'50364

FILE NO. 73-3

PAGE 2/

SUBJECT The Vapor Pressure of Ethane NAME B D n onrlvAn

DATE July 9, 1973

APPENDIX D . (Continued)

10 T.XPTL T -68 P , ATM CA LCD DEL T P , PCT

4 280.041 280.038 27.7039 27.7217 0.028 - 0. 06

4 202.247 282.243 29.1537 29.1647 0.016 - 0.04

10 283 . 150 283.150 29.7763 29.7739 - 0.003 0.01

4 284.635 284.630 30 .7664 30.7893 0.033 - 0.07

9 284.845 284.840 30.9555 30.9353 - 0.029 0.07

4 287. 653 287.648 32.9289 32.9392 0.014 - 0.03

10 288.150 288.150 33.3110 33.3080 - 0.004 0.01

4 288.263 288.257 33.3899 33.3872 - 0 . 00 % 0.01

4 290.040 290.034 34.6873 34.7192 0.042 - 0,09

9 290.214 290.208 34.8748 34.8518 - 0.030 0.07

4 292.236 292.229 36.4440 36.4216 - 0.028 0.06

4 293.098 293.091 37.0816 37.1074 0.032 - 0.07

10 293. 150 293.150 37.1583 37.1547 - 0.005 0.01

9 293. 266 293.259 37.2672 37.2422 - 0.031 0.07

4 296.347 296.339 39.7598 39.7852 0.030 - 0.06

10 298.150 298.150 41.3494 41.3446 - 0.005 0.01

4 299.665 299.657 42.6543 42.6808 0.030 - 0.06

9 299.863 299.855 42.8863 42.8591 - 0.030 0.06

4 300.205 300.196 43.1650 43.1686 0.004 - 0.01

4 301.251 301.242 44.1085 44.1274 0.020 - 0.04

10 302.150 302.150 44.9809 44.9751 - 0.006 0.01

10 303. 150 303. 150 45.9327 45.9268 - 0.006 0.01

4 303.471 303.462 46.2032 46.2273 0.025 - 0.05

4 303.477 303.468 46.2798 46.2331 - 0.048 0.10

9 304.012 304.002 46.7736 46.7533 - 0.021 0.04

4 304.049 304.039 46.7698 46.7896 0.020 - 0.04

10 304. 150 304. 150 46.9040 46.8907 - 0.005 0.01

4 304. 360 304.350 47.0931 47.0953 0.002 - 0.00

4 304.446 304.435 47.2198 47.1802 - 0.040 0.08

4 304.519 304.508 47.2025 47.2525 0.050 - 0.11

4 304. 734 304.723 47.4310 47.4661 0.035 - 0.07

4 304. 796 304.785 47.5185 47.5280 0.009 - 0.02

4 304.924 304.913 47.6846 47.6560 - 0.028 0.06

4 304. 980 304.969 47.7131 47.7122 - 0.001 0.00

4 305.121 305.110 47.8496 47.8541 0.004 - 0.01

10 305.150 305.150 47.8992 47.8945 - 0.005 0.01

4 305. 153 305.142 47.8807 47.8864 0.006 - 0.01

10 305.250 305.250 47.9994 47.9958 - 0.004 0.01

NP = 85 , RMSPCT = 0.050

e = 1.5 7/31/73

» 1134? A 55
APPENDIX D. (Continued)

Cryogenics Division - NSS Institute for Bosk Standards LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-3

FAGE

SUBJECT The Vapor Pressures of Ethane

NAME R

.

D. Goodwin

DATE July 9, 1973

ETHANE VAPOR PRESSURES

T,K P* ATM DP/DT D2P/0T2

89,899 0.0000100 0.0000027 0.00000064

90*000 0.0000102 0.0000027 0.00000066

95*000 0,0000358 0.0000065 0.00000161

100.000 0.0001095 0.0000232 0.00000439

105,000 0.0002985 0.0000567 0.00000960

110.000 0.000736$ 0.0001264 0.0000 1915

115.000 0.0016670 0.0002592 0.00003529

120.000 0.0034991 0.0004948 0.00006077

125.000 0.0068762 0.0008875 0.00009864

130.000 0.012752 0.001507 0. 0001521

135.000 0.022468 0.002439 0. 0002242

140.000 0.037834 0.003785 0. 0003177

145.000 0.061192 0.005656 0. 0004350

150.000 0.095478 0.008177 0.0005776

155.000 0.14426 0.01148 0.000747

160.000 0.21176 0.01569 0.000942

165.000 0.30288 0.02095 0.001165

170.000 0.42317 0,02738 0.001412

175.000 0.57882 0.03511 0.001684

180.000 0.77662 0.04426 0.001979

185.000 1.0239 0.0549 0.00229

190.000 1.3287 0,0672 0.00263

195.000 1.6991 0,0812 0.00298

200.000 2.1440 0.0970 0.00334

205.000 2.6726 0.1147 0.00372

210.000 3.2943 0.1343 0.00411

215.000 4.0188 0.1558 0.00451

220.000 4. 8561 0.1794 0.00492

225.000 5. 8165 0.2051 0.00534

230.000 6.9105 0.2329 0. 00577

235.000 8.1487 0.2628 0.00620

240.000 9. 5420 0.2949 0.00665

245.000 11.1016 0.3293 0.00711

250.000 12. 8390 0.3660 0.00758

255.000 14.7659 0.4052 0.00807

260.000 16.8947 0.4468 0.00858

265.000 19.2381 0.4910 0.00913

270.000 21.8098 0.5381 0.00971

275.000 24.6242 0.5882 0.01034

280.000 27.6972 0.6416 0.01105

285.000 31.0467 0.6989 0.01187

290.000 34.6934 0.7607 0.01288

295.000 38.6630 0.8283 0.01425

300.000 42.9905 0.9046 0.01657

305.000 47. 7433 1.0055 0.03283

305.330 48.0772 1.0228 0.00000

7/31/73, Via Ziegler "Type B " data

if 1134? A 56
APPENDIX D. (Continued)

Cryoganks Division - N8S Institute for Souk Standards LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-3

PAGE 23

suwecT The Vapor Pressures of Ethane name _ ^ „ ,

. R. D. Goodwin

DATE July 9, 1973

ETHANE REDUCED VAPOR PRESSURE FUNCTIONS

T,K X Y CY-X ) 69.899 0.00 0.00000 0.00000

91.186 0.02 0.02190 0.00190

92.510 0.04 0.04376 0.00376

93.873 0.06 0.06558 0.00550

95.277 0.08 0.08734 0.00 734

96.723 0.10 0,10906 0.00906

98.215 0.12 0. 13073 0.01073

99.753 0.14 0.15234 0.01234

101.339 0.16 0.17389 0.01389

102.977 0.18 0.19538 0.01538

10 4.669 0.20 0.21680 0.01680

106.418 0.22 0.23816 0.01816

108.226 0.24 0.25945 0.01945

110.096 0.26 0.28066 0.02066

112.032 0.28 0.30180 0.02180

114.037 0.30 0, 32285 0.02285

116.116 0.32 0. 34382 0,02382

118.272 0.34 0.36471 0.02471

120.509 0.36 0.38551 0.02551

122.832 0.33 0.40621 0.02621

125.247 0.40 0.42682 0.02682

127.759 0.42 0.44733 0.02733

130.373 0.44 0. 46774 0.02774

133.097 0.46 0. 48805 0.02805

135.937 0.48 0.50825 0.02825

L38.901 0.50 0.52835 0.02835

141.997 0.52 0.54833 0.02833

145.234 0.54 0.56820 0.02820

148.622 0.56 0.58796 0.02796

152.172 0.58 0.60760 0.02760

155.896 0.60 0.62713 0.02713

159.807 0.62 0.64654 0.02654

163.919 0.64 0.66583 0.02583

168.248 0.66 0.68501 0.02501

172.812 0.68 0. 70406 0.02406

177.630 0.70 0.72301 0.02301

182.725 0.72 0.74184 0.02184

188.121 0.74 0.76056 0.02056

193.845 0.76 0.77917 0,01917

199.928 0.78 0.79769 0.01769

206.405 0.80 0,81611 0.01611

213.317 0.82 0.83445 0.01445

220.707 0.84 0.85272 0.01272

228.627 0.86 0.87093 0.01093

237.138 0.68 0.88910 0.00910

246.306 0 • 90 0.90726 0.00726

256.212 0.92 0.92544 0.00544

266.948 0.94 0.94369 0.00369

278.623 0,96 0.96208 0,00 208 7/31/73, Via

291.366 0.98 0.98074 0.00074 Ziegler "Type B"

0. 00 00 0

data 305.330 1.00 1.00000

SF 1134? A 57
APPENDIX E.

Oyo9«nic> Division - NBS fratihite for loir Standordi LABORATORY NOTE

HtOJBCT NO. 2750364nu no. 73-4

PAoa

1 SUHJECTEthane Virial Coefficients and Saturated Vapor Densities

NAMB R. D. Goodwin

DATE Aueust 14. 1973

1 . Introduction

The virial equation of state for low densities is needed for thermal computations

to generate P-C-T data, and to obtain saturated vapor densities via the vapor pressure

equation

.

In this report we develop analytical representations for the virial coefficients

of ethane and obtain the corresponding saturated vapor densities.

In the truncated virial equation,

2 3 Z ( T , d ) = P /( R • T • d) = 1 + B(x) • o + C(x).o + D(x)-a , (1)

P is pressure, R the gas constant, T the absolute temperature, d the density, and

a^d/d c is reduced density. The second, third, and fourth coefficients B(x), C(x),

D(x) are dimensionless functions of reduced temperature x =® T/T . We use T

c c s 305.33 K, andV = 1/d = 145.56 cc /mol from Douslin f 2] . In the table s we use

c c symbols B

::

, C' and D'r for the coefficients of (1).

2. The Second Virial Coefficient

Data for B(x) through about I960 are reviewed by Tester [ 16]. Since then we

have data from Gunn [8], Hoover [9], Pope [15], McGlashan [12], and Douslin [2],

Data of Gunn and of Douslin extend from 273 K upwards to 623 K. McGlashan gives

outstanding experimental work on the hydrocarbon series (but not on ethane) down to T/T = 0.5. From his formulations he concludes that the low-temperature data of

c Eucken and Parts [ 4] are wrong. This suspicion also was expressed by Ziegler et

al. [17],

For least squares we have selected for low temperatures only the data from

McGlashan's formula because all other data diverge widely therefrom (Table 2). For

high temperatures we have selected Douslin' s recent data because the experimental

work [ 2J was executed with great care. Table 2 shows that Michels (1D = 3) and Gunn

(1D=8) are in substantial agreement with Douslin. For consistency with Douslin,

we have increased the absolute values of McGlashan's data by one percent, well within

the uncertainty of his V 148 cc/mol.

V I1KM 58
APPENDIX E, (Continued)

Cryogenics Division - NBS InfMwt* for Basic Standards LABORATORY NOTE

MtOJECT HO. 2750364

cite ho. 73-4PAOt ,.2

SUBJECT Ethane Virial Coefficients and Saturated Vapor Densities

NAMe R. D. Goodwin

DATE August 14, 1973

Our formula for B(x), selected from many variations, finally is similar to that

developed for methane [6],

B(x) =!"b + B /x

1/4 + B /x + B /x

Z + B /x

3 Liz 1 • [l-(T /T)

i 4 5Ji_o 1/41

( 2 )

T = 740. 0 K,

o B = 7.99 3156,

B

2 = -10.67 2497,

B

3 = 9. 21 7322,

B = -2.48 1668,

4

B = 0.84 2328.

5

Table 1 gives results for (2) with the data used for least squares: (6) McGlashan;

(10) Douslin. Data not used for l. s . are compared with (2) in Table 2: (1) Eucken;

(2) Lambert; (3) Michels: (4) Hoover; (5) Pope; (8) Gunn.

The Third Virial Coefficient

For C(x) relatively few data are known to us. The data of Michels [13] and

Hoover [9] were generalized in 1967 by Chueh [1], using a formula similar to that developed by Goodwin [5]. In 1971 Pope [15] gave five low-temperature values from 210

to 306 K. For temperatures above 273 K we are fortunate to have the recent, carefullyderived data of Douslin [2].

A comparison of Chueh' s generalized function with Douslin' s data at T/T =2

c shows C =0.20 (Chueh), and C =0.15 (Douslin). Whereas the Chueh formula gives

nearly constant values at high temperatures, the Douslin data are trending asymptotically toward zero.

For least squares we have selected the data of Douslin at high temperature s , and

data generated by Chueh's formula at low temperatures. For consistency we have

diminished these latter values by two percent. (Chueh fails to give his critical densities.

At low temperatures the third virial coefficient is not important in the computation of

sq (1) because the maximum possible density (saturated vapor) is diminishing exponen-

-ry / T

fcially with temperature, e , (see Table 4).

SP 11142 A 59
APPENDIX E. (Continued)

C/yogarncs Divnion - NAS IntMute for Banc Standards LABORATORY NOTE

PROJECT NO. 2750364Pill NO. 73-4

PAOE

3

SUBJECT Ethane Virial Coefficients and Saturated Vapor Densities

NAMI R . D. Goodwin

DAT£ August 14, 1973

Our formula for Cfxl is much simpler than that of Chueh, and is similar to that

developed for methane [6],

C (x

)

O

!~C /x + C „ /x + C /x

51 1-T IT),

o

(3)

T = 217. 80 K,

o C 0. 253 773,

C

2

= 0.865 299 :

C = 0.556 075

,

3 Least squares results are in the upper part of Table 3: (7) Chueh; (10) Douslin.

Other data in the lower part are: (4) Hoover; (5) Pope.

4. The Fourth Virial Coefficient

Recent data of Douslin [2] are plotted in Figure 1. The general behavior expected for D is shown in the book by Mason and Spurling [11]. As present data exist

only at T > T » we use the simple formula, ’ c 100-D ;,: =x • exp^a-b/(x- 1

)~|

, (4)

where x

“ T/T , and a = 4.00, b = 1.84 from Figure 1. c

5. Examination of the Virial Equation

It is valuable to know the relative importance of the terms of eq (1). In Table 4

we compute these for the saturated vapor, using densities from the formula of Plank

and Kambe i tz quoted by Tester [16], We have increased the P.K. den s itie s by 0 . 088%

to agree with the virial equation at 90 K. Pressures are from our vapor pressure

equation [ 7]

.

In the fourth column of Table 4 we give the ratio DI/DN of ideal gas density to

2 the P.K calculated densities. Fifth and sixth columns give B(x).a and C(x).o . If all

data were accurate, we should expect Z(T,d) in the last column to be the same as DI/DN.

The vapor pressures of Ziegler [17] were based on second virial coefficients

of Eucken and Parts [4], the accuracy of which Ziegler questioned. Our selection for

B

:|: also disagrees with Eucken and Parts. We therefore have recomputed our vapor

U 11)4? A 60
APPENDIX E. (Continued)

Cryogenics Division - N8S Institute for Bask Standards LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-4PA@g

4

SUBJECT Ethane Virial Coefficients and Saturated Vapor DensitiesNAM* R . D. Goodwin

DATE August 14, 1973

pressure constants using alternate vapor pressure data of Ziegler, as shown in the

addendum to our Laboratory Note [7], This revised vapor pressure equation is used

in the following to obtain the densities of saturated vapor.

6, Derivation of the Saturated Vapor Densities

For a given temperature we iterate density in the virial equation to obtain a pressure therefrom which is the same as the vapor pressure. Results are in Table 5.

In previous work we have found that this method gives acceptable results at densities

up to about D / 3 , which for ethane occurs near T = 286 K. We see that data from the

c Plank-Kambeitz formula diverge increasingly from our results on approach to T . c The highest temperature at which our results are accurate remains to be seen by comparison with data from other sources. Figure 2 shows ,howeve r , that in the region of

overlap with Douslin's vapor densities [2], our results (the filled circles) appear

reasonable

.

Figure 8 shows the results at lower temperatures. We see that powers of

(1/T) greater U an the first will be needed to describe these data.

7. Discussion of Uncertainties

Experimental uncertainties for virial coefficients vary inversely as the significance of these coefficients in giving departure from ideal gas behavior, see Table 4.

For the second coefficient only, for example,

6B/B 6 Z _ Z

Z

’ Z-l ’

where 6B and 6Z are small variations in B and Z. Assume a tolerable error of 0.0 1 percent in Z. From Table 4 we compute the approximate tolerable uncertainty in B,

neglecting the effect of C(T),

» mm hi
APPENDIX E. (Continued)

SUi

Cryogenics Division - NBS hwtitatle lor Bosk Standards LABORATORY NOTE

PtOJECT NO. 2750364PILE NO. 73-4

PAOf

5

SUBJECTEthant V irial Coefficients and Saturated Vapor Densities

****** R. D. Goodwin

DATE Au£ust 14. 1973

T, K mol/-6 6 B/B, %

100 0.000013 357.0

1 20 0.000349 21.6

1 40 0.00327 3.37

160 0.01626 0.915

1 80 0.05434 0.352

200 0.1401 0. 170

220 0.3035 0.096

240 0. 5864 0.060

2b 0 1.057 0.040

autho r s give estimates of unce;rtainty for experi

however , give these estimates for ethane,

T, K 6B/B, % 6C/C, %

215 1 .

0

10.0

240 0.4 4.0

F 273 0 . 1 1 .

0

and we believe these to be reasonable estimates for very careful work. In Table 2,

however, we see that Hoover's data, ID=4, differ from our selection by up to five percent at low temperatures (215 and 240 K).

Our derived densities depend on the vapor pressure equation. This we estimate

to be uncertain by several percent at the lowest temperatures approaching the triple

point. The virial equation, on the other hand, approaches ideal gas behavior at these

low temperatures. At the higher temperatures above 270 K, we believe the virial coefficients and vapor pressures of Douslin to be accurate as can be derived from the best

of PVT measurements.

62 $1

* 11347 *
APPENDIX E. (Continued)

Cryoganks Drvitron - NBS Institute for Bosk Stamfords LABORATORY NOTE

PtOJECT NO. 2750364Ft IE NO. 73-4

PAOB 6

SUBJECTEthane Virial Coefficients and Saturated Vapor Densities

NAME r. 0. Goodwr in

DATE August 14. 1973

8. Bibliography

[ 1] P, L. Chueh and J. M. Prausnitz, Third virial coefficients of non polar gases

and their mixtures, AlChE Journal 13 (5) 896 (1967).

[2] D. R. Douslin and R. H. Harrison, Pressure-volume-temperature relations

of ethane, (U.S. Bureau of Mines, Bartlesville, Okla. 74003). Manuscript for

J. Cbem. Thermodynamics, July, 1973.

[3] J. H. Dymond and E. B. Smith, The Virial Coefficients of Gases, Oxford

Science Research Papers 2, Clarendon Press, Oxford, England, (1969).

[4] A. Eucken and A. Parts, Z. Phys. Chem. B20, 184 (1933).

[5] R, D. Goodwin, D. E. Diller, H. M. Roder, L. A. Weber, Second and third

virial coefficients for hydrogen, J. Res. NBS 68A (1), 121 (1964).

[6] R. D. Goodwin, Thermophysical Properties of Methane from 90 to 500 K at Pressures to 700 Bar, NBS Tech. Note, manuscript, April, 1973.

[7] The Vapor Pressures of Ethane, Laboratory Note 73-3, July 9, 1973.

[8] R. D. Gunn, M. S. Thesis, University. Calif. (Berkeley), 1958, quoted by

J. A. Huff and T. M. Reed, J. Chem. Eng. Data 8, 306 (1963).

[9] A. E. Hoover, I. Nagata, T. W. Leland, R. Kobayashi, Virial coefficients

of methane, ethane, and their mixtures at low temperatures, J. Chem.

Phys. 48 (6), 2633 (1968).

[10] J. D. Lambert, G. A. H. Roberts, J. S. Rowlinson, V. J. Wilkinson, Proc.

Roy. Soc . (London) A 196, 1 13 (1949).

[11] E. A. Mason and T. H. Spurling, The Virial Equation of State, Pergamon Press,

Oxford (England), 1969.

[12] M. L. McGlashan and D. J. B. Potter, An apparatus for the measurement of

the second virial coefficients of some n-alkanes and of some mixtures of

n-alkanes, Proc. Roy. Soc. (London) A267, 478 (1962).

[13] A. Michels, W. van Straaten and J. Dawson, Physica 2C[, 17 (1954).

[14] Plank and Kambeitz, Z. Ges. Kalte Ind . 1 0

,

209 (1936), quoted by Tester.

[15] G. A. Pope, Calculation of Argon, Methane and Ethane Virial Coefficients, etc.,

Thesis, Rice Univ. , July 1971.

[16] H. E. Tester, ETHANE, in Thermodynamic Functions of Gases, F. Din,

Editor, vol. 3, Butte rworths , London, 1961.

tf 11342 IS ¥3
APPENDIX E. (Continued)

Cryogenics Division - MBS Institute for Bosk Standards LABORATORY NOTE

PROJECT NO. 2750364

PILE NO. 73-4

PAOC7

SUBJECTEthane Virial Coefficients and Saturated Vapor Densities

NAME R. D. Goodwin

DATt August 14, 1973

[]7j Ziegler, Kirk, Mullins, Berquist, Calculation of the vapor pressures, etc.,

VII Ethane, Eng. Expt. Sta. , Georgia Inst. Tech . .Atlanta, Ga. , Dec. 1964.

[ 18) F. Porter, J. Am. Chem. Soc. 4_8, 2055 (1926).

(19) P. Sliwinski, Z. Phys. Chem. 63 263 (1969).

[20] K. R. Hall and P. T. Eubank, Experimental technique for direct measurement

of interaction second virial coefficients, J. Chem. Phys. _59(2), 709 (1973).

[ 21] R. D. Goodwin, Estimation of critical constants T , 0 C from the p(T) and T(p)

relations at coexistence, J. Res. NBS 74A(2), 221 1970).

T able 1 .

Table 2.

T able 3 .

Table 4.

Table 5.

Table Captions

Second virial data of (6) McGlashan, (10) Douslin.

Second virial, (1) Eucken, (2) Lambert, (3) Michels, (4) Hoover,

( 8 ) Gunn.

Third virial, (7) Chueh, (10) Douslin, (4) Hoover, (5) Pope.

Terms of the virial equation for saturated vapor.

Saturated vapor densities derived via V.P. and virial equations.

( 5) Pope

,

» ItMJ I 64
APPENDIX E. (Continued)

Oyog»nici Divnion - MBS Nflvto for Bosk Stondords LABORATORY NOTE

rtOICCT NO. 2750364

me no. 73-4PAW 1

8

1 Ethane Virial Coefficients and Saturated Vapor Densities

NAME D- Good-w.dn

DATE August 14, 1973

Figure 1. Ethane fourth virial coefficients of Douslin [2],

100.

D

1 ' = x ^^.exp[4.0 - 1.84/(x-l)].

I134JI 65
APPENDIX E. (Continued;

Lab. Note 73-4 p. 9

66

Figure

2.

Ethane

saturated

vapor

densities.

Open

circles

from

Douslin

[2];

filled

circles

from

Table

5,

this

report.
APPENDIX E. (Continued)

Figure 3, Ethane saturated vapor densities from Table 5, this report,

67
APPENDIX E. (Continued)

Cryogmics DMwon-NK hwdtaM for Saue Standard* LABORATORY NOTE

Htojecr MO. 2750364nu no. 73-4

PAM

1 1 SUIJfCT Ethane Virial Coefficients and Saturated Vapor Densities

NAM* R. D. Goodwin

DATE August 14, 1973

Table 1. Second virial data of (6) McGlashan, (10) Douslin.

ETHANE SECOND VIRIAL COEFFICIENT

EB = 0.250, TZ = 71*0.0

7. 993156 -10 .672497 9.217322 -2.481668 0. 842328

ID T, K T/TC B* CALC 0 IFF PC NT

6 150. 000 0.4913 -5. 309 -5.310 0.001 0. 01

6 160.000 0.5240 -4.598 -4.597 -0.001 -0.01

6 170.000 0.5566 -4. 031 -4.3 30 -0.001 -0.02

6 180.000 C . 58 95 -3.569 -3.5 69 -0.000 -0.01

6 190.000 0.6223 -3. 188 -3.188 0.000 0.01

6 200.000 0.6550 -2. 868 -2.869 0.001 0. 02

6 210.000 0.6878 -2.597 -2.597 0.001 0.03

6 220.000 0.7205 -2. 353 -2.364 0. 001 0.03

6 230.000 0.7533 -2.161 -2.162 0. 000 0.02

6 240.000 0.7960 -1. 984 -1.984 -0.000 -0.00

6 250.000 0.8188 -1.828 -1.828 -0.001 -0. 04

& 260.000 0.8515 -1.690 -1.688 -0. 002 -0. 09

10 27 3. 150 0.8946 -1. 527 -1.527 0.001 0.06

10 298. 150 0.9765 -1.276 -1.275 -0. 001 -0.08

10 30 3. 150 0.9929 -1.232 -1.232 -0. 001 - 0. 05

10 323. 150 1.0584 -1.077 -1.076 -0. 001 -0.06

10 348.150 1. 1402 -0.914 -0.914 0.001 0.08

10 373. 150 1. 2221 -0.780 -0.781 0. 001 0.10

10 398. 150 1. 30 40 -0.668 -0.670 0. 001 0. 16

10 423. 150 1.3859 -0. 574 -0.575 0.000 0.06

10 448.150 1.4678 -0. 493 -0.493 0.000 0. 10

10 473.150 1.5496 -0. 423 -0.422 •0. 000 -0.08

10 498. 150 1.6315 •0.360 -0.360 -0. 000 -0.01

10 523. 150 1.7134 -0. 306 -0.305 -0. 001 -0.27

10 548.150 1.7953 -0.256 -0.256 -0. 000 -0. 19

10 573. 150 1.8771 -0.212 -0.212 -0.001 — 0.30

10 598.150 1.9590 -0. 172 -0.172 -o. 000 -0.02

10

NP

623. 150 2. 0409

= 23, HEA^PCT = 0.

-0.135

088

-0.135 0. 001 0.53

v ItWI 68
APPENDIX E. (Continued)

Oy°9*nic$ Dwmon - NK 1mMiM it tak Scnckirdt LABORATORY NOTE

MKJJfCT NO. 2750364

nLnSo"

1"

73-4

fAOt 12

Ethane Virial Coefficients and Saturated Vapor Densities

NAME R • D. Good-\vin

DATE August 14 , 1973

Table 2. Second Virial, (l)Eucken, (2) Lambert, (3) Michels, (4) Hoover

(5) Pope, (8) Gunn.

ID T,K me 3 * CALC DIFF PC NT

1 2 0 U • 0 C Ci 0.6550 - 3. 112 -2.869 - 0.243 - 8.48

2 200.000 C .6550 - 3 . 119 - 2.869 - 0. 250 - 8 . 72

5 209.534 0.6863 - 2. 533 -2.609 0.076 2 . 93

1 210.000 0.68 78 - 2.817 -2.597 - 0. 219 - 8.44

2 210.000 0.6378 - 2.817 -2.597 - 0.219 - 8 . 44

4 215.000 0.7042 - 2 . 340 -2.477 0.137 5.52

1 220.000 0.7205 - 2.542 -2.364 - 0 . 178 - 7 . 52

2 220.030 0. 7205 - 2.576 - 2.364 - 0.212 - 8.97

1 230.000 0. 7533 - 2.288 -2.162 - 0 . 126 - 5*84

2 230.000 0.7533 - 2. 343 -2.162 - 0 . 181 - 8 . 38

5 238.759 0.7320 - 1.972 -2.005 0.033 1.63

1 240.000 0.7860 - 2.095 -1.984 - 0.111 - 5 . 61

2 240.000 0.7860 - 2. 116 - 1.984 - 0.132 - 6.65

4 240.000 0.7860 - 1.90 0 -1.984 0 . 085 4.26

1 250.030 0.8188 - 1.924 - 1.828 - 0.096 - 5 . 26

2 250.000 0.8188 - 1. 944 - 1.828 - 0.117 - 6 . 39

5 254.607 0.8345 - 1.733 - 1.759 0.026 1.45

1 250.000 0.8515 - 1.759 -1.688 - 0.070 - 4 . 17

2 250.000 0.8515 - 1.786 -1.688 - 0.098 - 5 . 80

1 270 . JO

j

0.8343 - 1 . 614 -1.564 - 0.051 - 3 . 23

2 270.000 0.8843 - 1. 649 - 1.564 - 0.085 - 5 . 43

3 273.150 0.8946 - 1.521 - 1.527 0.006 0 . 39

4 27 3 . 150 0.8946 - 1. 535 -1.527 - 0. 007 - 0.48

5 273. 150 0.8946 - 1.507 - 1.527 0.020 1 . 33

8 273.200 0.8948 - 1.527 -1.527 0 . 000 0 . 02

1 280.000 0.9170 - 1.470 - 1.452 - 0.018 - 1.25

2 280. 000 0.9170 - 1.511 -1.452 - 0.059 - 4 . 09

2 290.000 0.9498 - 1.408 -1.351 - 0. 058 - 4 . 26

3 298. 138 0.9764 - 1.275 - 1.275 0 . 000 0.03

8 298.200 0.9766 - 1.284 - 1.275 - 0 . 009 - 0.71

2 300.000 u • 93 25 - 1 . 305 -1.259 - 0.046 - 3.68

5 336.052 1 . 03 24 - 1.204 -1.207 0 . 003 0 . 27

3 322.748 1.0570 - 1. 078 - 1.079 0 . 001 0 . 07

8 323.200 1.0585 - 1. 082 - 1.076 - 0.006 - 0. 60

3 347.652 1.1386 - 0.916 - 0.917 0.002 0 . 19

3 372.522 1.2201 - 0.784 -0.784 0.001 0 . 09

8 377.500 1.2367 - 0.752 - 0.760 0.008 1 . 10

3 397.844 1.3030 - 0.671 -0.671 - 0. 001 • 0.08

8 410. 900 1.3458 - 0.616 -0 .619 0 . 004 Q . 61

3 422.700 1.3844 - 0.576 -0.576 - 0.000 - Q . 04

8 444.300 1.4551 - 0.508 -8.505 - 0.003 - 0.69

6 477.600 1.56 42 - 0.423 -0.411 - 0.013 - 3.09

8 510.900 1.6733 - 0. 350 -0.331 - 0. 019 - 5 . 83

» 1TJOI 69
APPENDIX E. (Continued)

Cryogenics Division - NCS Institute for Bosk Stondords LABORATORY NOTE

PROJECT NO. 2750364Fill NO. 73-4

PAM

1 3

SUBJECT Ethane Virial Coefficients and Saturated Vapor Densities

NAME R . D. Goodwin

DATE August 14, 1973

Table 3. Third virial, (7) Chueh, (10) Douslin, (4) Hoover, (5) Pope.

THIRD VIRIAL*

217 •800 0. 253773 0 .865299 C. 556075 0.000000

ID T.K T/TCRT C* CA LCD DIFF

7 210.000 0 ,5878 -0. 251 -0. 247 -0.004

7 220.000 0.7205 0.055 0.055 0.000

7 230. U 0 0 0.7533 0. 249 0.247 0.002

7 240. uQO 0 .7860 0. 367 0.366 0.001

7 230.000 0.8188 0. 436 0.438 -0.002

7 280.000 0.3515 0. 472 0. 477 -0.006

10 273.150 0.3946 0. 489 0. 499 -0.010

10 298. 150 0.9765 0. 500 0 . 489 0.011

10 30 3. 150 0.9929 0. 491 0.483 0.008

10 323.150 1.0584 0. 455 0. 453 0.003

10 343.150 1.1402 0. 409 0. 410 -0.001

10 373. I5u 1.2 221 0. 364 0 . 369 -0.004

10 398. 150 1.3040 0. 328 0 . 332 -0.003

10 423. 150 1.3859 0. 295 0.299 -0.004

10 448. 150 1.4678 0.268 0. 271 -0.003

10 47 3. 150 1.5496 0. 250 0.247 0.002

10 498. 150 1.5315 0. 228 0.227 0.002

1C 523.150 1.7134 0.212 0.209 0.004

10 548. 150 1.7953 0. 195 0 .193 0.002

10 573. 150 1.8771 0. 182 0 • 180 0.002

10 598. 150 1.9590 0.167 0.168 •0.001

10 623. 150 2.3409 0. 154 0.157 -0.003

NP = 22. ME ANDIFF = 0. 004

ID T , < T/TCRT C* CALCD DIFF

5 209.534 0.5863 -2. 770 -0.264 -2.505

4 215. 000 0.7042 -3. 356 -0.079 -3.277

5 238.769 0.7820 0.175 0. 354 -0.180

4 240. 000 0.7860 -0. 121 0. 366 -0.487

5 254.807 0.8345 0. 401 0. 460 -0.059

5 273. 150 0.8946 0. 489 0 . 499 -0.010

4 273. 150 0.8946 0. 501 0. 499 0.002

4 273. 150 0 .8 94 6 0. 537 0. 499 0.038

4 298. 138 0.9764 0. 507 0.489 0.017

5 306.062 1.3024 0. 473 0.479 -0.006

4 322. 748 1.0570 0. 456 0. 453 0.003

4 347. 652 1.1386 0. 405 0.411 -0.006

4 372.522 1.2201 0. 364 0. 370 -0.006

4 397.844 1.3030 0.330 0. 332 -0.002

4 422.700 1.3844 0. 301 0 . 300 0.001

ff 11142 A 70
APPENDIX E. (Continued)

Cryogenics Division - NBS InsMtvte for Bosk Standards LABORATORY NOTE

PROJECT NO. MM HIE NO.

SUBJECT NAME Ethane Virial Coefficients and Saturated Vapor Densities

R. D. Goodwin

DATE August 14, 1973

Table 4. Terms of the virial equation for saturated vapor,

TERMS OF THE VIRIAL EQUATION FOR SATURATED VAPOR

T * K P, ATM MQl/t DI/ON 6* S C*S2 2 CT, 05

90 0. 0000099 0. 0000013 0.999996 -Q.QGG004 -0.000000 0.999996

95 0 • 0000346 0. 0000045 0 .999987 -0 .000011 -0.000 000 0 » 999989

100 0. 0001067 0. 0000130 0.999966 -0.000028 -0.000000 0.999972

105 0.0002916 0. 0000338 0.999920 “0 .000 064 -0.000 000 0.999936

110 0. 0007207 0.0000799 0.999831 -0.QC0133 -0.000 00 0 0.999867

115 0.0016337 J. 00O1732 0.999670 -0.000256 -0.000 00 0 0 .999744

120 0. 0034347 0. 0003490 0.999398 -0.000462 -0.000 000 0.999538

125 0.0067608 0. 0006596 0.998969 -0.000787 -0.000 0Q0 0.999213

130 0 . 0125592 0. Ou 11793 0.998323 -0.001276 -0.000001 0.998723

135 0. 0221670 0. 0020063 0.997397 -0 • 0ui982 -0.000002 0.998016

140 0.0373903 0. 00 32674 0.996119 -0.002961 -0.000 005 0 .997034

145 0 • 0605738 0. 0051196 0.994420 -0 .00427 6 -0.000 009 Q ,995715

150 0 . 0946592 0.0077508 0.992228 -0 .005991 -0.000016 0.993994

L 5 5 0. 1432275 0. 0113809 0 .989479 -0 .008171 -0.000026 0.991803

1 60 0. 2105236 0. 0162608 0 .936113 -0 .010 882 -0.000 042 0.989077

165 0. 30 14633 3. 0226721 0.982082 -0.014185 -0.000063 0.98575?

170 0. 4216243 0. 0309256 0 .97 7343 -0 .018141 -0. 000 090 0 .981769

175 0,5772221 J. 0413607 0 .971866 -0.022806 -0.000124 0 .977070

1 8 C 0. 7750743 J. 0543439 0.965625 -0.028233 -0.000164 0.971603

185 1. 0225573 0. 0702692 0.958606 -0 .034470 -0.000206 0.965324

190 1. 3275553 0. 0695573 0.950796 -0.041563 -0.000248 0.958189

L 9 5 1. 6984137 0. 1126577 0.942186 -0 .049554 -0.00 0 281 0.950164

2 0 0 2.1438785 0. 14Q0503 0 .932771 -0 .058485 -0.0 00 299 0.941217

205 2.6730575 0. 1722494 0.922541 -0.068395 -0.000287 0.931318

210 3.2953721 J. 2098093 0 .911484 -0 .079325 -0.000230 Q. 920445

215 4.0205218 0.2533319 0.899587 -0.091321 -0.000 107 0 .908571

220 4. 85845? 3 0. 3034770 0.886826 -0.104432 0.000108 3.895676

225 5.8193516 0. 3609763 0.873177 -0.118715 0.000 440 0.681732

2 3u 6. 913610 8 0. 4266509 0.858605 -0.134238 0.000 952 Q .866714

235 8. 1518573 0. 5014347 0.843069 -0.151085 0.001 671 0 . 850586

240 9 • 54495 5 1 0. 5864036 0 .826523 -0 .169358 0.002667 0.833309

245 11. 1040386 0.6828144 0 .80 8912 -0 .189185 0.004017 0.814032

250 12.8405603 0. 7921552 0 . 79 0 174 -0 .210 72 5 0.005318 0,795093

255 14. 7663588 0. 9162120 0.770240 -0.234180 0 .008194 0,774014

260 15. 8937542 1. 0571595 0.749033 -0.259804 0.01130

5

0.751500

265 19. 2356771 i. 2176851 0.726466 -0.287925 0.01536 1 0.727436

270 21. 8058475 1. 40 11641 0.702440 -0.318963 0.020 642 0.701679

275 24. 6190249 1. 6119133 0 .676839 -0 .353469 0.027531 3 .674063

280 27. 6913739 1. 8555713 S .649528 -0 .392177 0.036563 0.644386

285 31.0410283 2. 1396981 0.620339 -B. 436086 0.048505 0 .612418

290 34.6890345 2. 4747097 8 .589059 -0 .48660 0 0.0 6449 8 0.577898

295 38.6611522 2. 8756823 0.555393 -Q. 545771 0.086320 0.540549

300 42.9921502 3. 3657409 0.518891 -0.616818 0.116916 0.500098

305 47. 7441963 3. 9859334 0.478608 -0.705645 0.161805 0 .456160

W 1134? A 71
APPENDIX E. (Continued)

Cryogenics Ovnion - MBS Imtitvte for Bosk Stondords

S LABORATORY NOTE

«o*ct NO. 2750364

NU NO. 73-4

PAOC 15

| SUBJECT

" " Ethane Virial Coefficients and Saturated Vapor Densities

MAME R . C). Goodwin

DATE August 14, 1973

Table 5. Saturated vapor densities derived via \7.P. and virial equations

ETHANE SATO. VAPOR DENSITIES VIA V.P. AND VIRIAL EQNS.

ID T,K P. ATM PLANK/KAMB MOL/L PCT

1 69. 699 9.9670-006 1.3511-006 1.3511-006 0.00

1 90.000 1.0238-005 1.3863-006 1 .3863-006 0.00

1 95.000 3.5808-005 4.5936-006 4.5936-006 0.00

1 100.000 1.0952-004 1.3347-005 1.3347-005 0.00

1 105.000 2.9651-004 3.4649-005 3 .4648-005 0.00

1 110.000 7.3654-004 8.1615-005 8.1612-005 0 .00

1 115.000 1,6670-003 1.7671-004 1.7670-004 0.01

1 120.000 3.4991-003 3.5558-004 3.5552-004 0.01

1 125. 000 6.8762-003 6.7110-004 6.7093-004 0.02

1 130.000 1.2752-002 1.1974-003 1.197 0-003 0.04

1 135.000 2.2468-002 2.0336-003 2.032 3-00 3 0.06

1 140.000 3.7834-002 3.3064-003 3.3033-003 0.09

1 145.000 6.1192-002 5.1721-003 5.1653-003 0.13

1 150. 000 9.5478-002 7.8184-003 7.8043-003 0.18

1 155.000 1.4426-001 1.1464-002 1 .1436-002 0.24

1 160.000 2.1176-001 1.6358-002 1.6308-002 0.31

1 165. 000 3.0288-001 2.2781-002 2.2694-002 0.38

1 170.000 4.2317-001 3.1042-002 3.0899-002 0.46

1 175.000 5.7882-001 4.1479-002 4.1252-002 0.55

1 180.000 7.7662-001 5.4457-002 5 .411 1-002 0.64

1 185.000 1.0239+000 7.0369-002 6.9860-002 0.73

1 190.000 1.3287+000 8.9635-002 8.8911-002 0.81

1 195.000 1.6991+000 1.1271-001 1 .1171-001 0.89

1 200.000 2.1440+000 1.4006-001 1.3872-001 0.97

1 205.000 2.6726+000 1.7222-001 1 .704 7- 001 1.03

1 21 0. 0D 0 3.2943+000 2.0973-001 2 .075 0-001 1.08

1 215.003 4.0166+000 2.5321-001 2.5043-001 1.11

1 22 0. 00 0 4.8561+000 3.0 331-001 2 .9993-001 1.13

1 225.000 5.6165+000 3.6077-001 3.5674-001 1.13

1 230.000 6.9105+000 4.2642-001 4.2173-001 1.11

1 235.000 8.1487+000 5.0120-001 4.9585-001 1.08

1 240. 000 9.5420+000 5.8618-001 5.8025-001 1.02

1 245. 000 1.1102+001 6.8262-001 6.7626-001 0.94

1 250. 000 1.2839+001 7.9203-001 7 .8551- 001 0.83

1 255.000 1.4766+001 9.1618-001 9.0997-001 0.68

1 260.000 1.6695+001 1.0572+000 1.0522+000 0.48

1 265.000 1.9238+001 1.2179+000 1.2154+000 0.21

1 270.000 2.1810+001 1.4016+000 1 .4041+ 000 -0.18

1 275.000 2.4624+001 1.6125+000 1 .6245+000 -0.74

1 280. 000 2.7697+001 1.8563+000 1 .886 1+000 -1.58

1 285.000 3.1047+001 2.1404+000 2.2047+000 -2.91

1 290.000 3.4693+001 2.4754+000 2.6108+000 -5.19

* V 111471 72
APPENDIX E . (Continued)

Cryogenics Division - NftS bwtrivte for Boik Standards LABORATORY NOTE

PROJECT NO. 275036^

PIIE NO. 73-4

PAOg

16

NAME Ethane Virial Coefficients and Saturated Vapor Densities

R. D. Goodwin

DATE August 14, 1973

PRO SRAM VIRUS : ““—

ETHANE VIRIAL COEFFICIENTS, X = T/TCRT, Q = X**l/2,

C 3 V - ( B1 32/X**E3 133/X 84/X2 * 05/ X3 ) * ( 1* ( TZ / T ) **1/ 4 ) . C S V = (C1/X**EC *• C2/X3 f C3/X5)* (1-TZ/T) • C ID, (L)EUCKEN, (2 ) - AMBERT » (3)MICHELS, (4)H00VER, (5)POPE,

C ( 6 ) MCGLASHAN, (7)CHUEH, <8)GUNN, (10) OOUSLIN»P RE PRINT*

C V CRT, CC/ MOL , ROSSINI (195 3) /MCGLASH AM= 148 , EU 8ANK/P0PE=146. 2,

C TESTER(1961) =141.7, OOUSLIN (197 3) =1 45 .56.

COMMON/ 1/M, EB,EC»TZB,TZC, BVS,CVS, B(5),C(4)

COMMON/3/ OPSOT

COMMON/999/NP,NF,H(l5) , Y ( 20 0 ) , G ( 2 0 0 , 1 5)

DIMENSION 10(20 0 ) , T ( 2 30 ) , BV ( 20 0 ) , CV ( 2 CO ) , X ( 20 G ) ,XQ(2QQ)

1 F ORMA T ( 15, 2F10.0)

2 F ORM A T ( 1 HI 13X 1HM 5X5HE(BC) 8X2HTZ 8X2HSS)

3 FORMAT(10X 15, 2F10.3, F13.4)

4 F ORMAT ( 1H1 1 7X *E THANE SECOND VIRIAL COEFFICIENT*//

1 18X4HEB = F 6. 3 » EH, TZ =F6.1// 15 X 5F12.6//

2 18X2HID 7 X 3HT » K 5X4HT/TC 7X2HB* 5X4HCALC 5X4HDIFF 5X4HPC NT

)

5 F ORMAT (15X 15, F1L.3, r 9.4, 3F9.3, F9.2)

6 FORMAT(lH117X*THIRD VIRIAL, M =*I2, 6H, EC =F6.3// 16X F10.3,

1 4FL1.6// 18X2HI0 7X3HT , K 4X6HT / T CRT 6X2MC* 5X5HCALCD 6X4HD IFF ) 7 F ORMA T( 15X 15, F1j.3, F1Q.4, 3F10.3)

8 F ORMAT ( 1 8X 4HNP =13, 12H, MEANDIFF = F7.3)

9 F ORMA T ( 1 8X 4HNP =13, 11H, MEANPCT =F6.3)

10 F ORM A T ( 1 HI 15X* TERMS OF THE VIRIAL EQUATION FOR SATURATED VAPOR*//

1 1 7X 3 HT , K 7X5HP,ATM 7X5HMOL/L 5X5HDI/DN

2 7X 3 H B* S 5X4HC*S2 4X6HZ(T,0) ) 11 F ORMAT ( 1 OX F10.G, 2F12.7, 4F10.6)

12 F ORMAT ( 1H1 17X 2MID 7X3HT,K 5X4HT/TC 7X2HB* 5X4HCALC

1 5X4HDIFF 5X4HPCNT)

13 F0RMAT(1H117X2HID 7X3HT,K 4X6HT /T CRT 6X2HC* 5X5HCALCD 6X 4 HD IFF)

15 T TR 3 = 89 • 899 5 TCRT=305. 33 $ DCRT= 1 . 0 / 145. 56

C GENERATE MCGLASH AM DATA FOR BV(T), CC/MOL.

C INCREASE ABS (MCGLASHAM) BY ONE PERCENT (148/145.56 = 1.017).

16 N = 0 $ DO 19 J = 1 , 12 B N = N* 1 $ TT = T ( N) = 140 10 *J

17 X(N)=TT/TCRT B X3 (N) =SQRTF(X (N) ) $ IO (N ) = 6

18 3 V ( M ) = 1. 0 1*GL ABF ( TT ) B Y (N) = 8V(N)*DCRT

19 CONTINUE

C READ DOUSLIN (1973) DATA, CC/MOL.

20 DO 23 J=l, 99 B READ 1, IOD»TT ,BB B IF(IDD) 21,24

21 N = N+l B ID(N) =IOD B T (N) =TT S BV ( N) =BB

22 X ( N) =TT/ TCR T B X 3 (N> =SiRTF(X (N) ) B Y(N)=BB*OCRT

23 CONTINUE

24 NP = N $ NF = 5 B SSK = 1.0E+Q10

C READ SECOND VIRIAL DATA.

25 DO 28 J = 1 , 9 9 B READ 1, IDD,TT ,BB $ IF(IDD) 26,29

26 N = N+l B I D ( N) = I OD B T ( N) =TT B BV(N)=BB

27 X ( N) =TT/ TCRT B X Q ( N) = SQRTF ( X ( N) ) B Y ( N) =3B* DCRT

28 CONTINUE / /

29 NPP = N B M = 0 7/2

6

/23

C EXPLORE VALUES FOR EB AND FOR TZ B.

C MCGLASHAM TZB NEAR 2.7*TCRT = 824 K.

30 EB = 0.25 B TZ = TZB = 740 B PRINT 2

C 31 DO 44 IE*1,3 B EB = 3.25*IE

C 32 DO »4 I T=1 , 17 % TZ = 640 1Q*IT

V 1194? t 73
APPENDIX E . (Continued)

Cryogenics Ownion - NBS bwtihrt. tor Bomc Stondords LABORATORY NOTE

HK5JECT NO. 2750364

FILE NO. 73-4

PAOC 17

; SUBJECT

' Ethane Virtal Coefficients and Saturated Vapor Densities

R. 3. Good-w in

DATI August 14, 1973

33 DO 36 J=1,NP B U=X ( U) $ Q=XQ(J) $ W = 1- ( TZ /T ( J) ) ** 0 . 25

34 G«J,1)=W $ G ( J, 2 ) =W/U**E0 $ G ( J , 3 ) = W / U £ G ( J , 4 ) =W /U**2

35 G ( J, 5 )=H/U**3

36 CONTINUE l CALL EGLNFT £ SS = 0 37 DO 39 J=1,NP £ YC = 3 J DO 38 K=1,N C

38 YC = YC H <K) *G< U,K>

39 SS = SS A8SF(Y( JT/YC-l) $ SS = 100*SS/NP

40 IF (SS.LT.SSK) 41,44

41 S SK= S S S EK-E3 £ TK = T Z S DO 42 K = l,5

42 B(K) = H (K)

44 PRINT 3, M , E8 » T Z * SS $ E 8=EK $ T Z = T ZB=TK $ SS = 0

|i C USE SAVED CONSTANTS FOR DEVIATIONS.

45 PRINT 4, EB, TZ, (B(K),K=1,5)

46 DO 51 J=1,NPP £ U=X(J) £ Q=XQ(J) $ M = 1- ( TZ /T < J) ) ** 0 . 25

47 YC = W* ( B ( 1 ) B(2)/U**EB B(3»/U B(4)/U**2 B(5)/U**3)

48 D I F = Y ( J ) - Y C £ PCT=-1GO*OIF/YC $ S S = S S +A BS F < PCT)

49 PRINT 5, ID (J) , T ( J) ,X ( J ) , Y( J) ,YC, OIF , PCT $ IF(J-NP) 51*50

50 SS = SS/NP £ PRINT 9, NP,SS $ PRINT 12

51 CONTINUE £ N = U C SENERATE THIRD VIRIAL DATA VIA CHUEH(1967), ID = 7.

C DIMINISH CHUEH DATA 8Y 2 PERCENT.

52 DO 55 J= 1, 6 £ N = N + l $ TT = T (N ) = 200 + 10*J

53 X <N> =TT/TCRT £ X Q ( N ) = SORT F i X < N> ) $ ID(N) = 7

54 C V ( N ) = G.98*CHUCF(TT) $ Y ( N) = CV ( N) *DCR 1**2

55 CONTINUE £ K = N + 1 C READ DOUSLIN (1973) DATA, (CC/M0L)**2.

56 DO 58 U = K, 9 9 £ READ 1, 10 ( J) , T( J) , C V( J) $ I F ( ID ( J> > 57,59

57 X (J) =T( J)/TCRT £ X Q ( J ) = SQRTF ( X ( U) ) £ Y ( J) = C V ( J) *DCRT**2

58 CONTINUE

59 NP = U-l £ NF = 3 £ SSK = 1.0E+31G

C READ THIRD VIRIAL DATA. TZC NEAR 220 K.

60 K = NP+1 £ DO 63 U=K, 99

61 RE A3 1, ID ( U) , T ( J ) , C V ( J ) £ IF ( I D ( J ) ) 62,64

62 X(J> = T ( U ) / T C R T £ XD ( J ) =SQRTF< X

(

J

)

) $ Y ( J) =C V ( J) *DCR T* *2

63 CONTINUE

64 NPP = J-l 5 EC = 1.0 $ PRINT 2

C EXPLORE VALUES FOR EC AND FOR TZ.

C 65 00 76 I E = 1 , 4 £ EC = }.5’IE

66 00 7 6 I T = 1 , 11 £ TZ = 217.60 0.05*IT

67 00 59 J=1,NP £ U = X(J) £ W = 1-TZ/TCJ)

68 G (J»1)=W/U**EC £ G(U, 2) =W/U**3 £ G( J, 3 ) =W/U**

5

69 CONTINUE £ CALL EGENFT £ SS = 0 70 DO 72 J= 1, NP £ YC = 3 £ 00 71 K=1,NF

71 YC = YC H(K)*G(U»K) ?/26/V3

72 SS = SS ABSF < Y < J) -YC) £ SS = SS/NP

73 IF (SS.LT.SSK) 7N,76

74 SSK=SS $ TK = T Z £ EK = EC $ MK=M £ DO 75 K*l,4

75 C (K) = H (K)

76 PRINT 3, M » EC » T Z » SS £ M = MK

77 TZC = TZ = TK $ EC s EK $ SS = C C USE SAVED CONSTANTS FOR DEVIATIONS.

79 PRINT 6, M,EC,TZ, (C(K),K=1,4)

80 DO 35 J s 1, NPP £ U = X(J> S W = 1-TZ/TCJ)

81 YC * W* (C(1)/U**EC C(2)/U**3 CC3)/U**5) __ 82 PCT = Y ( J) - YC £ ^

a SS ABSF(PCT)

» 1114? I 74
APPENDIX E. (Continued)

Cryogenics Division - MRS Institute for Bostc StondoHs LABORATORY NOTE

MtOJICT NO. 2750364me no. 73-4BAOE 18

SUBJECT Ethane V irial Coefficients and Saturated Vapor Densities

NAME R. D. Goodwin

August 14, 1973

VIRUS 0 7/26/7 3

83 PRINT 7, ID ( J) , T ( J) ,X ( J) , Y< J) , YC, PCT $ IF(J-NP) 85,84

84 SS = SS/NP 5 PRINT 8, NP,SS $ PRINT 13

85 CONTINUE

j C NOW EXAMINE TERMS OF THE VIRIAL EQUATION AT SATURATION.

: C THE IDEAL GAS DENSITY IS DI = P/(R*T>,

90 PRINT 10 B DO 95 J=l,44 $ TT = 85 5*J

91 PS= 3 SATF (TT ) B ON=DNGSF (TT ) $ Z = ZIPF(TT,DN)

92 01 = PS/TT/0. «923 56156 $ DR = D I/D

N

95 PRINT It, TT,PS»DN» DR, BVS,CVS, Z 99 STOP S ENO

SINGLE-BANK COMPILATION.

FUNCTION CMUCF(T)

C ETHANE THIRD VIRIAL VIA CHUEH FORM ULA ( 1967 > , <CC/M0L)**2.

C CV ( T) /VCRT**2 = F A *F B FC, FA = A/Q + B/X5,

C -B = 1 - EXP (1 - A l

* X2 ) , FC = EXP (- C 0* X - E»X2), X = T/TCRT.

OATA (TCRT=305. 33 ) , < VCR T= 145 . 56 ) , <AL=1.89>

DATA ( A = G • 2 321 , (8 = 0.463 ) , (C=2. 49) , (0 = 2.30 ) , (E=2.7 0)

1 X=T/TCRT $ Q=SQRTF ( SQRTF ( X) ) $ X2=X**2 $ X5=X**5

2 FA = A/Q * 3/ X 5 S FB = 1 - EXPF (1- AL*X2

)

3 FC = EX PF ( - C D*X - E*X2)

4 CHUCF = (FA*FBfFC> *VCRT**2 S RETURN $ END

FUNCTION DNGSF(T)

C

3 L AN</KA MBEI TZ VIA TESTER (P.17D/0IN. VALID 17 0 TO 305 K.

C V = R*T/P - C1/K**A - C2*P**2/X**B , X = T/100,

C V IN CC/GRAM, T IN KELVINS, P IN KG/CM**2,

C l ATI = 1.03323 KS/CM**2, R=2.822, Cl = 69 .0 C 2=2 7. 9, A = 2.4, 8=9.0

DATA (R = 2.822> , ( C 1 = 89. 3 ) , (C2 =27 . 9 ) , ( A =2 .4 ) , (8=9.0 ) , <WM=3 0 .0 7)

1 P = PSATF(T) B P = 1. Q3323*P $ P2 = P**2

2 X = T/100 S XA = X**A B XB = X**B

3 V = R*T/P - Ci'XA - C2*P2/XB

4 DNGSF = 100 0.88/V/WM $ RETURN $ ENO

» 113-4?

«

75
APPENDIX E. (Continued)

CryogwHcs Oviwofi - MBS bMMut. for Bmk Stondordt LABORATORY NOTE

MtOXCT NO. 275036^

me no. 73-4

BAO« 19

Ethane Virial Coefficients and Saturated Vapor Densities

NAMB

J-). Goodwin

DATl August 14, 1973

FUNCTION GLABF(T)

C ETHANE SECOND VIRIAL COEFF. VIA MC GLASHAM FORMULA (1962),

C 1C G. BELIEVES EUCKEN/PARTS ARE WRONG.

0 3 V ( T) / VC R T = 31 - B2/X - B3/X2 - B4/X**4.5, X = T/TCRT.

DATA (TCRT =335.4) * (VC RT =148.0)

DATA (B 1=0.433) , (B2=0.886), (B 3= 0.694) *(04=0.0375)

1 X=T'TCRT S X2=K**2 S XN = X**4.5

2 F = 31 - 3 2 / X - 93/X2 - B4/XN

9 GLA3F = VCRT*F $ RETURN $ ENO

07/26/73

FUNCTION PSATF(T)

LN(P'PTRP) = A*K «• 8*X 2 C*X3 0*X4 E* X* ( 1-X ) *EP

.

COMION/3/ OPSOT

DATA (TTRP =89.899) * (TCRT=305.33), (PT RP=9. 61 6E-6) * (EP = 1.6)

DATA ( A = 8. 454987344 ), (3 = 12.4880 39 775 ) ,(C=-4. 10428 1551)

1 (D=-l. 413860533) * (£= 8. 526522526)

1 F OR1 A T ( 1 H3 9X *PSATF = 0* T EXCEEDS TCRT. * / ) 2 XN=1-TTRP/TCRT $ X= (l-TTRP/TJ/XN $ X2=X**2 $ X3=X**3 $ X4=X**4

3 DXDr = TTRP/XN^T**2 $ Q a 1-X $ IF(Q) 4,5,6

4 PSATF = DPS DT = 3 $ 3 R I NT 1 $ RETURN

5 Z = Z 1 = 0 B GO TO 7

6 W = Q**EP $ HI = -EP*W/Q $ Z = X*H $ Z1 = W + X*W1

7 F = A*X B*X2 «• C*X3 0*X4 + E*Z

8 FI = A 2*B*X f 3*C*X2 4*D*X3 E * Z1

9 PSATF=PTRP*EXPF(F) $ DP SO T=F 1*P SA TF* O XO T S RETURN $ END

07/26/73

FUNCTION ZIPF(T,0)

C Z ( T , 0 ) a 1 BV ( T) *S CV(T)*S**2, S = D/OCRT, X = T/TCRT

•

C 3 V = ( B1 B2/X**EB B3/X B4/X2 B5/X3 ) * ( 1- ( TZ/T) **1/4 )

.

C CV = ( Cl/ X* * EC f C2/X3 C3/X5) * (1-TZ/T)

.

C0M10N/l/i,EB,EC,TZB,TZC, BVS,CVS, B(5),C<4)

DATA (TCRT=305. 33) , ( VCRT = 0 . 1 4556)

1 S = D* VCRT B X= T/ TCRT S Q=SQRTF(X) $ R=X**EC

2 X2=X**2 $ X3=X**3 $ X4=X**4 $ X5=X**5

3 ZB = 1 - (TZB/T) **0.25 S ZC = 1 - TZC/T

4 BV = ZB* (B ( 1) * B ( 2 ) / X* *E B 8(3) /X «• B(4)/X2 B(5)/X3)

5 CV = ZC*(C(1)/R * C ( 2 ) / X 3 C(3)/X5)

6 B VS = B V*S B CVS = CV*S**2

7 ZIP ? = 1 BV S «• CVS $ RETURN $ ENO

tf 1114? I 76
APPENDIX E. (Continued)

Cryoganks DMHon-NK feaMuto ter ink 8*ondord» LABORATORY NOTE

nOJCCT NO. 2750364ms mo. 73-4

fk<m 20

SUBJECTEthane Virial Coefficients and Saturated Vapor Densities

MAMI R . D. Goodwin

DATf August 14, 1973

07/26/73

PROG RAM VAPORDEN

C ETHANE SATVAPORDEN V/ 1 A V.P. AND VIRIAL EQNS.

C ON ISOTHERMS, ITERATE OEN IN VIRIAL EQN. TO MINIMIZE (P-PSAT).

COM M3N/3/ DPSOI

1 FOR.MATUHX ETHANE SATO. VAPOR DENSITIES v/ 1 A V.P. AND VIRIAL EQNS

,

1 *//18X2HID 7 X 3 H T , K 7X5HP,ATM 2 X 1 OHPL ANK/KA MB 7 X5HM0L/L 7 X3HPCT

)

2 FORMA! ( 1 5 X 15, F10.3, 3E12.4, FI 0.2)

3 F0RMAT(I5, F10.3, 2E15.5)

1 9 10= 1 ft T TR 3 = 30.393 ft PRINT 1 20 DO 30 U= 1 » 4 2 4 IF(J-l) 23,22

22 1 - rrRP ft GO TO 24

23 T = HU 4 5 * J 24 D I = DNGSF(T) * P = PSATF(T) ft OEN = FI NOF ( T , P, 01

)

2b PUNCH 3, ID, T , D E N ,

P

27 Dir = DI-DEN I PCT = 100*DIF/DEN

23 PRINT 2, ID, T,P, 01, JEN, PCT

30 CONTINUE ft uTDP ft ENO

SINGwE- 3 A N < COMPILATION.

FU OCT ION F I N Q F ( I , P , 0 I

)

C ON ISOTHERM I, ITERATE OEN TO MINIMIZE (P-PCALC).

COMMON JZOS

data (3K=0. 082056156), <VC2T=0. 14556)

1 FORMAT ( 1H0 9X *FINDF = 0, FAILS TO CONVERGE.* / ) 2 D - JI $ GT = GK* T ft DO 9 J=l,50

3 1 - Z I P r ( T , D ) 4 PC = 0*GT*Z ft DP = P-PC ft AP = ABSF(OP)

4 0 = AP/P-1.0E-6 5 IF ( 0 ) 10,10,5

5 DP DO = 6 T* ( Z 4 D*OZOS* VCRT) ft ADP = ABSFCDPOD)

6 u = AP/ADP/D-i. Cr.-6 ft IF(Q) 10,10,7

7 D = 10 4 OP/DPOD ft IF ( 0 ) 8,8,9

3 D = P/I/GK

3 CONTINUE ft FINDF = 0 ft PRINT 1 ft RETURN

10 FIN JF = U ft RETJRN ft END

» I1MI 77
APPENDIX E . (Continued)

Cryogwncj Drwdon - N>S IndttaN (or Ink Standard, LABORATORY NOTE

MtOJECT NO. 2750364

nu no. 73-4

TAM

21

subject

Ethane V irial Coefficients and Saturated Vapor Densities

**** R. D. Goodwin

DAT* . August 14, 1973

FUNCTION DNGSF(T)

C Pl AiX/KANBEI t z via tested.

DATA (R=2. 822) , (01=39. 0)

,

(C2=27. 9) , (A=2. 4) , (I8=9),(WM=30.07)

1 P = 1.03323*P5ATF(T) $ °2 = P**2

2 X = T/130 f, XA = X**A 5 X3 = X**IB

3 V = R*T/P - C 1 X X A - C2*P2/XB

4 DNGSF = 1000.88/V/WM t RETURN I FND

08/01/73

FUNCTION PSATF(T)

C lN(P/PTRP) = A*X * B*X2 C*X3 0*X4 + E*X* (1-X ) **EP.

C OMMON/ 3/ OPSOT

C CONSTANTS VIA ZIEGLER TYPE B V.P. OATA.

DATA (TTRP=89.899), (TCRT=305.33) » C PTRP=9. 96 7E-6 ) * (EP=1.5)

DATA ( A = 10 • 806922651) ,0=8,344715938) , <C=-3 . 11960 3823)

DATA (D=-0. 642995191) , (6=6.059966098)

1 FORMAT11HO 9X *PSATF = 0, T EXCEEDS TCRT. / ) 4

2 XN=1-TTRP/TCRT S X= ( 1- T TRP/T ) / X N $ X2=X»*2 $ X3=X**3 $ X4=X*»4

3 DXDT = TTRP/XN7T**2 S Q = t-X $ IF(Q) 4,5,6

4 PSATF = DPSDT =0 $ PRINT 1 $ RETURN

5 Z = Z 1 = 0 l GO TO 7 6 W = Q**EP 5 HI = -EP*W/Q $ Z = X*W $ Z1 = W X*W1

7 F = A*X 8*X2 (• C*X3 D*X4 E*Z

8 FI : A 2*8*X 3*C*X2 4*D*X3 E*Z1

9 PSATF=PTRP»EXPF(F) S DPSD T=F 1*P SA TF* DXD T $ RETURN $ END

FU ACTION ZIPF (T , D)

C Z l T , J ) = 1 f 8 V ( X

)

S + CV(X)*S**2#

C b\l = (81 + 32/J 33/ X 34/X2 + 8 5/ X 3

) * ( 1- ( T Z 8/ T

) ** 1 /4 )

.

0 LV = (Gl/X f C 2 X X 3 +• C3/X5) * ( 1-TZC/T) • Condon d z d s data (TCr<T = (0 5. 3 3) , ( V CRT=0 . 1 4556) , (TZ8 = 740. 0 ) ,(TZC=217.8) , 1 (31 = 7.9 93156), ( 92 = -10. 67249 7), (B3 = 9. 217 322 ) , (B 4 = -2 . 4 8 1 66 8 )

,

2 ( 35 = 0 . 3 42 328) ,01=0.2 53 773), ( C 2= 0 . 86 5299 ) , (C3= 0 . 556 0 75 )

1 S=U»VGRT J X=T/TCRT $ Q=X**0.25 S X2=X**2 l X3=X**3 t X5=X*»5

2 ZJ = 1 - (TZ3/T ) *+0. 25 I ZC = 1 - TZC/T

3 b\l = ZBMB1 f 82/0 f 3 3/ X + B4/X2 + B5/X3)

4 ^ = ZCMC1/X 4 02/ X 3 + C3/X5)

o ZIPF = 1 + Q\l* S + CJ + S+* 2 $ DZDS = 9V 2*C\I*S

3 RETURN $ END

» MMil 78 uKom uu.
APPENDIX F.

Cryoyo*ci Dmtton - NBS for laaic Sfcmdords LABORATORY NOTE

MOJECT NO. 2750364

FILE NO. 73-5PAGE

1

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME R . D. Goodwin

DATE Sept. 18, 1973

1 . Introduction.

These densities, and accurate analytical descriptions thereof, are essential

for the computation of thermodynamic functions, in particular to obtain heats of

vaporization via the Clapeyron equation, and to formulate the equation of state which

originates on this locus [4].

We have had difficulties in representing the available ethane data, and therefore have returned to fundamentals. For comparison we shall include oxyge n [18],

fluorine [13], and methane [4]. Previous formulations occur in [4, 7], We start with

the saturated liquid densities because their representation is much simpler than that

of the saturated vapor densities.

2. The Saturated Liquids.

It is well known that these densities are described near the critical point by the

form

p = p + a • (T - T) + b • (T - T)

e (1)

c c c

wherein the first two terms are the rectilinear diameter, and the exponent is near

s =0.35.

Let us constrain (1) at the boundaries by use of the variables,

x ( T ) = ( T - T)/(T - T ), (2) c c t W(p) = (p - p etc )/(p - p ), (3)

where subscripts c and t refer to critical and triple points. Equation (1) now

become s

,

W(p)=a*x + b*x", (4)

and the constraint requires that a + b = 1. If we solve this for the constant b, we may

expect to obtain a function Y(p,x) which is nearly constant over the entire range

0 < x < 1,

Y(p , x) = [W(p) - x]/(x

£

- x). (5)

This sensitive function is useful for examining data.

In past work we found that three arbitrary coefficients are required to describe

saturated liquid densities. We now find the following results via many exploratory

computations. For the smoothed data used here for oxygen and fluorine, the use of

five arbitrary coefficients gives an improvement in the "fit". For the rough experimental data used here for methane and ethane, the use of five arbitrary coefficients

gives virtually no improvement in the "fit" as compared with only three coefficients.

With only three, the first equation used was,

. 79 V 11142 k
APPENDIX F. (Continued)

Cryogenics Drvison - NK IneMute for Basic Stondords LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-5

PAGE 2

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME _ _ , K . D. Goodwin

DATE Sept. 18, 1973

Y(P , x) = + A

^

• x + A^ • x

0-

, (6)

and we found exponent cc = 4/3 for oxygen, fluorine and methane, but a = 8/3 for

ethane. After much exploration we have selected the following representation,

2/3

Y(P , x) = A

i + A

2

• x + A

3

• x (7)

Table 1 gives the fixed-point constants. Table 2A gives the exponent e found

by trial, the least- square s coefficients, the rms of relative density deviations in

percent, and the number of datum pairs, NP.

Tables 3, 4, 5, 6 compare calculated with experimental densities. No

temperature- scale adjustments have been made in present work. Column YX gives

the experimental value of Y(p,x) via (5), whereas column YC gives the value calculated

by the right side of (7). Table 7 compares ethane data not used for least squares.

Tables 8, 9, 10, 11 give saturated liquid densities computed by (7) at uniform

temperatures, and also their slopes and curvatures.

The small deviations for oxygen and fluorine necessarily are systematic because the data were smoothed by the authors. The overall methane deviation is large

because experimental data from various sources are included in the critical region.

The low-tempe rature ethane data of Miller were used to estimate the triplepoint liquid density. Other data are from Canfield et al. , and from Klosek/McKinley

.

The high -tempe rature "data" of Eubank are a correlation of available experimental

data down to the boiling point 184.5 K, (x = 0.561). We estimate uncertainty in our

calculation of these densities to be about 0. 1 percent over the entire range.

Concerning assignment of critical densities, we at first found both P c and

exponent € simultaneously by trial to minimize the overall deviation. The results are rough because these two parameters are mutually compensating for data in the critical

region. Hence we have adjusted P c one step at a time for both saturated liquid and

saturated vapor, examining the values of e found by trial. We select that value of p c which yields reasonable exponents £ for both liquid and vapor. For methane it thus

is necessary to select P c

= 10. 2 mol/T, at the upper limit of uncertainty in the experimental values [4],

3. The Saturated Vapors

Densities of the ethane vapors range thru a factor of about 10^. We have given

reasons for using the logarithm of vapor densities, with arguments in powers of

(1/T), [7]. Define the normalized variables

z(T) h ( T /T-1)/(T /T - 1), c c t (8)

W(p) = In (o /p)/tn(p /P J.

c c t (9)

V 11947 I 80
APPENDIX^^^^Contimj^d^

Cryo9»nia Dwion- Mt6 for Saak Sfondordt LABORATORY NOTE

MOJECT NO. 2750364

FILE NO. 73-5

FAOC 3

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAMf

R. D. Goodwin

DATI Sept. 18, 1973

We write the vapor densities equation for the critical region as follows,

-W(p) = (b-1) . z - b • z

e (10)

wherein the minus sign on the left arises merely from our definition of W(p), Solving

(10) for b yields the dependent variable,

Y(p,z) - [W(0 - z]/(z

£

- z) . (11)

For the present work we have explored all kinds of representations, finally

selecting the expression,

5 Y(p , z) = A

1 + ^

A. • z l/3

. (12)

Table 2B gives results for (12), analagous to table 2A for the liquid. Tables

12, 13, 14, 15 compare calculated with experimental vapor densities. Column YX is

the experimental value of Y(p,z) via (11), whereas YC is calculated by the right side

of (12). Table 16 compares ethane data not used for least squares. Tables 17, 18, 19

20 give uniformly computed densities and derivatives via (12).

Computer programs used in this work are attached as an appendix.

» mu i 81
APPENDIX F. (Continued)

Cryotanks DMaon- NH toltoPt to toe Stamtodi LABORATORY NOTE

PtOJECT NO. 2750364PILE NO. 73-5

PAOC 4

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

HAMC R. D. Goodwin

DAn Sept. 18, 1973

4. Bibliography

[1] C.H. Chui and F. B. Canfield, Trans. Faraday Soc. 67, 2933 (1971).

[2] D. R. Douslin and R. H. Harrison, Pressure-volume-temperature relations

for ethane, (U. S. Bureau of Mine s , Bartlesville, Okla. 74003, Manuscript for

J. Chem. Thermodynamics, 1973).

[3] P. T. Eubank, Thermodynamic properties of ethane: vapor-liquid coexistence,

Advances in Cryogenic Engineering 17, 270 (Plenum Pub. Corp. , New York,

N.Y. 10011, 1971).

[4] R. D. Goodwin, The Thermophysical Properties of Methane from 90 to 500 K

at Pressures to 700 Bar, NBS IR 73-342, October, 1973. Also, NBSIR

73-300, February, 1973.

[5] R. D. Goodwin, The Vapor Pressures of Ethane, Laboratory Note 73-3,

July 9, 1973.

[6] R. D. Goodwin, Ethane Virial Coefficients and Saturated Vapor Densities,

Lab. Note 73-4, Aug. 15, 1973.

[7] R. D. Goodwin, Estimation of critical constants T , p c from the p(T) and T(p)

relations at coexistence, J. Res. NBS 74A ( 2), 221 (1970).

[8] A. Harmens, Orthobaric densities of liquefied light hydrocarbons, Chem.

Engrng. Science 20, 813 (1965); 2]_, 725 (1966).

[9] J. Klosek and C. McKinley, Densities of liquefied natural gas and of low

molecular weight hydrocarbons, paper 22, Session 5, Proc. First Internat.

Conf. on LNG, Chicago, April (1968).

[10] O. Maass and C. H. Wright, J. Am. Chem. Soc. 4_3, 1098 (1921).

[11] Reid C. Miller, Ann. Rpt. to AGA, "Experimental Liquid Mixture Densities

for Testing and Improving Correlations of LNG," Proj. BR-76-1, Univ.

Wyoming, July 1, 1972.

[12] Frank Porter, The vapor pressures and specific volumes of the saturated

vapor of ethane, J. Am. Chem. Soc. 48^, 2055 (1926).

[13] Rolf Prydz and G. C. Straty, The Thermodynamic Properties of Compressed

Gaseous and Liquid Fluorine, NBS Tech. Note 392, October, 1970.

[14] M. J. Shana'a and F. B. Canfield, Trans. Faraday Soc. 64, 2281 (1968).

» 11M1J 82
APPENDIX F . (Continued)

Drvaton NBS IimHuN for Beat Stoidofds LABORATORY NOTE

PBOJECT NO. 2750364FILE NO. 73-5FACE 5

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME R. D. Goodwin

DATE

[15] P. Sliwinski, The Lorenz-Lorenz function of gaseous and liquid ethane, propani

and butane, Zeit. Phys. Chem. NeCie Folge 63, 263 (1969).

[16] H. E. Tester, ETHANE, in Thermodynamic Functions of Gases , vol. 3,

F. Din, Editor (Butte rworths , London, 1961).

[17] J. R. Tomlinson (Gulf Res. and Devel. Co., Pittsburgh, Pa.), Liquid

Densities of Ethane, Propane, and Ethane -Propane Mixtures, Tech. Pub.

TP-1, Nat. Gas Processors Assoc. (808 Home Federal Bldg., Tulsa, Okla.

74103, Feb. 1971).

[18] Lloyd A. Weber, P-V-T, thermodynamic and related properties of oxygen

from the triple point to 300 K at pressures to 33 MN/m^, NBS J. Res. 74A

(1), 93 (1970).

[19] David Zudkevitch (Esso Res . & Engrng. Co., Florham Park, N.J.), The

importance of accuracy in physical and thermodynamic data to chemical

plant design, October, 1972. (Offered for publication in the Proceedings

of the NBS. )

V 1134? A 83
APPENDIX F. (Continued)

Cryo9*nics Drmion- NCS huiJiluU for Ask Stondonfs LABORATORY NOTE

HtOJfCT NO. 2750364

FILE NO. 73-5

PAGE 6

SUWECT The Orthobaric Densities of Ethane, Methane, Oxygen and

HAMt R . D . Goodwin

DATf Sept. 18, 1973

List of Tables

Table 1 . Table 2A.

Table 2B

.

Table 3.

Table 4.

Table 5.

Table 6.

T able 7.

Table 8.

Table 9.

Table 10.

Table 11.

Table 12.

Table 13.

Table 14.

Table 15.

Table 16.

Table 17.

Table 18.

T able 19.

Table 20.

The fixed-point constants.

Constants for vapor equation (12).

Comparison of oxygen liquid densities.

Comparison of fluorine liquid densities.

Comparison of methane liquid densities.

Comparison of ethane liquid densities.

Ethane liquid data not used for least squares.

Calculated oxygen liquid densities.

Calculated fluorine liquid densities.

Calculated methane liquid densities.

Calculated ethane liquid densities.

Comparison of oxygen vapor densities.

Comparison of fluorine vapor densities.

Comparison of methane vapor densities.

Comparison of ethane vapor densities.

Ethane vapor data not used for least squares.

Calculated oxygen vapor densities.

Calculated fluorine vapor densities.

IP I1M7I 84
APPENDIX F (Continued)

LABORATORY NOTE

nojccr no. 2750364

FILE NO. 73-5

FAOC 7

tuuser The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

R. Di.GpQdwm

DATS Sept. 18, 1973

List of Authors for Computer Tables

ID* Author( s) Reference

1 Goodwin (V irial + V . P . ) [6]

6 Porter [12]

9 Tester [16]

10 Douslin [2]

11 Sliwinski [15]

12 Canfield et al. [1. 14]

13 Klosek [9]

14 Miller [11]

15 Eubank [3]

16 Tomlinson [it]

98 Prydz [13]

99 Weber [18]

* For METHANE, see references in [4],

V llttf * 85
APPENDIX F. (Continued)

Cryofmg Dmm-NK InrilMa tar Seat Standard* LABORATORY NOTE

PIOJtCT NO. 2750364

nu no. 73-5

PAOC 8

SUtJKT The Orthobaric Densities of Ethane, Methane, Oxygen andHAm R . D. Goodwin

BAn Sept.* 18, 1973

Table 1 . The fixed -point constants.

Oxygen Fluorine Methane Ethane

T

t- K 54. 3507 53.4811 90.680 89. 899

T

C' K . 154.576 144.310 190. 555 305.330

Pc' mol/t 13.63 15. 15 10. 20 6.87

p f

liquid 40. 830 44. 8623 28. 147 21.680

-4 -4 -2

p

t’ vapor 3.36122- 10 5.670- 10 1.567865- 10 1.35114- 10

Table 2A. Constants for liquid equation (7)

Oxygen Fluorine Methane Ethane

e 0.349 0.354 0.361 0.350

A

1 0.758 8805 0.791 3438 0. 837 0910 0.761 7350

A

2

0. 228 3200 0. 112 9132 0.084 1613 0. 298 6535

A

3 -0. 230 4342 -0. 100 6980 -0.074 7858 -0.327 6239

rms , % 0.014 0.010 0.084 0. 142

NP 50 46 49 29

Table 2B. Constants for vapor equation (12)

Oxygen Fluorine Methane Ethane

e 0.382 0.362 0.382 0.362

A

i 0. 277 3707 0. 257 1572 0.374 1014 0. 192 7743

A

2

-0.338 6621 -0. 227 0644 -0. 261 5731 0.041 5501

A

3 0.769 0708 0.605 3864 0.675 3322 -0 . 789 2263

N -1.576 1185 -1.391 6332 -1.012 2063 0. 357 6675

A

5 0.939 8713 0.792 5719 0.439 8834 0. 124 5438

rms , % 0.052 0. 134 0. 148 0. 104

NP 50 46 96 29

V 1IIUI
, APPENDIX F. (Continued)

NATIONAL 1UREAU OR STANDARDS, CRYOORNIC RNOINORINO LARORATORT LABORATORY NOTE

raOJRCT NO. 2750364

fils no. 73-5

PAG6 9

susjict Qrthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

MA*'- R .D .Goodwin

DATI Saiat. 1ft

Table 3. Comparison of oxygen liquid densities.

TCRT = 154.576, TTRP = 54.3507

CRT = 13.63C, DTRP = 40.630 0 7.5868052-001 2.2632003-001 -2.3043415-001

0 . 0000000*000 0 . 0000000*000 0 . 0000000*000

ID T,K MOL/L CALC PCNT X YX YC YO IF 99 56.000 40.601 40.603 -C.00 0.98354 0.75202 0.75805 -0.00603

99 58.000 40.323 40.326 -0.01 0.96359 0 . 75397 0.75958 -0.00561

99 63.000 40.048 40.049 -0.00 0.94363 0.76038 0.76109 -0.00072

99 62.000 39.777 39.770 0.02 0.92368 0.76779 0.76258 0.00520

99 64.000 39.494 39.491 0.01 0.90372 0.76630 0.76405 0.00225

99 66.000 39.216 39.210 0.01 0.88377 0.76840 0.76550 0.00291

99 68.000 38.926 38.928 -0.00 0.86381 0.76610 0.76692 -0.00081

99 70.000 38.655 38.644 0.03 0.84366 0.77243 0.76831 0.00411

99 72.000 38.358 38.356 -0.00 0.82390 0.76966 0.76969 -0.00002

99 74.000 38.081 38.071 0.03 0.80395 0.77392 0.77103 0.00289

99 76.000 37.779 37.782 -0.01 0.78399 0.77145 0.77235 -0.00090

99 78.000 37.495 37.491 0.01 0 . 76404 0.77482 0. 77364 0.00118

99 60. J03 37.202 37.197 0.01 0 . 7440 8 0.77614 0.77490 0.00124

99 82.000 36.900 36.901 -0.00 0.72413 0.77599 0.77613 -0.00014

99 84.000 36.603 36.602 0.00 0 . 7041 7 0. 77750 0.77733 0.00017

99 66.000 36.298 36.301 -0. Cl 0 .68422 0.77788 0 . 77850 -0.00061

99 68.000 35.997 35.996 0.00 0.66426 0 . 77979 0.77963 0.00016

99 90.000 3 5 . 6o 9 35.688 0.00 0.64431 0.78081 0 . 78073 0.00007

99 92.000 35.373 35.377 -0.01 0.62435 0.78118 0 . 78 180 -0. 00061

99 94.000 35.063 35.062 0.00 0.60440 0.78335 0 . 78262 0.00023

99 96.000 34. 734 34.742 -0.02 0 .58444 0.78261 0. 78381 -0,00120

99 96.000 34.412 34.418 -0.02 0.56449 0 . 78376 0.78475 -0.00099

99 1 0 0 . 0 00 34.083 34.040 -0.02 0 .5445 3 0.78472 0.78565 -0.00093

99 102. J00 33.750 33. 756 -0.02 0.52458 0.78563 0.78651 -0.00088

99 104.000 33.411 33.417 -0.02 0.50462 0.78659 0.78732 -0.00072

99 106.000 33.069 33.072 -0.01 0 .48467 0. 78772 0.78807 -0.00035

99 1 0 8. 0 00 . 32.712 32.720 -0.02 0 . 46471 0.78780 0.78878 -0.00098

99 1 1 0 . 0 00 32.362 32.361 C.OO 0 . 44476 0.78960 0.78943 0.00017

99 112.000 31.990 31.995 -0.02 0.42480 0 .78946 0.79001 -0.00056

99 114.000 3 1 . 6 1 o 31.620 -0. 01 0 . 40485 0.79005 0.79054 -0.00049

99 11b. 000 3 1 .230 31.236 -0.02 0 . 38489 0.79038 0.79100 -0.00062

99 113. J00 30.845 3C .642 0.01 0 . 36494 0.79169 0.79138 0.00031

99 120.000 30.441 30.438 0.01 0 . 34498 0.79208 0. 79169 0.00039

99 122. 000 30.021 30.021 -0.00 0.3250 3 0 . 79190 0.79192 -0.00001

99 124.000 29.595 29.591 0. Cl 0 . 3050 7 0.79239 0.79205 0.00034

99 126. 000 29.146 29.147 -0.00 0.28512 0.79203 0. 79209 -0.00006

99 12 1.000 28.686 26.685 0.00 0.26516 0. 79210 0.79201 0.00008

99 1 10.000 28.209 28.205 0.01 0.24521 0.79216 0.79182 0.00033

99 1 32 . 0 00 27.709 27. 7C4 0.02 C. 22525 0.79192 0. 79150 0.00042

99 1 3 4 . J 00 27.161 27.179 0.01 0.20530 0.79129 0.79103 0.00026

99 136.000 26.631 26.625 0.02 0.18534 0.79103 0.79039 0.00063

99 133.000 26.042 26.037 0 . 02 0 .16539 0.78999 0.78956 0.00043

99 I** 0 . 0 00 25.413 2 5. 4 1C 0.01 0 . 14543 0.L&M3 0. 78851 0.00032

99 142. 000 24, 734 24.733 0.01 0.1254 8 --UT7 8 73 3 0.78719 0.00014

99 144.000 23.992 23.993 -0.00 0 . 105T2 0.78549 0.78555 -0. 00006

99 1 4 6 . 0 uO 23.164 23.170 -0.C2 0 .08557 0.78287 0.78350 -0.00063

99 143.000 22.227 22.230 -0.C1 C . 06561 0.78057 0.78090 -0.00033

99 150.000 21.106 21.108 -0.01 0.04566 0.77724 0.77753 -0.00029

99 152.000 19.646 19. 6h7 -0.00 0.02570 0.77280 0.77264 -0.00004

99 1 5 *, . j 00 1 7.1C6 17.104 0.01 0.00575 0.76528 0.76488 0.00040

NP = 50, RHSPCT = 0.C14

OCILVIK PHKM. INC., IW8IU.TW I*. N. T. 37
APPENDIX F. (Continued)

NATIONAL BUREAU Of STANDARDS, CRYOOENIC ENOINEERINO LABORATORY LABORATORY NOTE

FBOJICT NO. FlU NO. RAM

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAJNI

DATS

Table 4. Comparison of fluorine liquid densities.

E = 0.354

TCRT = 144 . 311 , TTRP = 53.4811

OCRT = 15 . 150 , DTRP = 44.8623

7 . 9134383-001 1 . 1291315-001 - 1 . 0069804-001

0 . 0000000*000 0 . 0000000*000 0 . 0000000*000

10 T,K MOl/L CALC PCNT X YX YC YOIF

98 54.000 44.781 44.781 0.00 0.99429 0.80556 0.80 370 0.00186

98 56.000 44.465 44.464 0.00 0.97227 0.80524 0.80425 0.00099

98 58.000 44.146 44.146 0.00 0.95025 0.80553 0.80479 0.00071

98 60.000 43.825 43.825 0.00 0.92823 0.80574 0.80532 0.00042

98 62.000 43.501 43.501 0.00 0.90621 0.8060 3 0.80583 0.00021

98 64.000 43.174 43.174 - 0.00 0 . 88419 0.80632 0.80633 - 0.00000

98 66.000 42.845 42.845 - 0.00 0 . 8621

7

0.80662 0.80661 - 0.00019

98 68.300 42.512 42.513 - 0.00 0.84015 0.80693 0.80728 - 0.00034

98 70.000 42.176 42.177 - 0.00 0.81813 0.80728 0.80773 - 0.00045

98 72.000 41.836 41.838 - 0.01 0.79611 0.80760 0.80817 - 0.00056

98 74.000 41.493 41.496 - 0.01 0.77409 0.80796 0.80859 - 0.00063

98 76.000 41.146 41.149 - 0.01 0 . 7520 7 0.80831 0.80899 - 0.00068

98 78.000 40.795 40.799 - 0.01 0.73005 0.80368 0.80938 - 0.00069

98 60.000 40 .440 40.444 - 0.01 0.70803 0.80903 0.80974 - 0.00071

98 82.000 40.081 40.085 - 0.01 0.68602 0.80941 0.81009 - 0.00068

98 84.000 39. 717 39.720 - 0.01 0 .66400 0.80977 0.81042 - 0.00065

98 86.000 39.347 39.351 - 0.01 0.64198 0.81011 0.81073 - 0.00061

98 88.000 38.973 38.976 - 0.01 0.61996 0.31347 0.81101 - 0.00054

98 90.000 38.592 38.596 0 o 1 0.59794 0.81080 0.81127 - 0.00047

98 92.000 38 .206 38 . 2 C 9 0 yH 1 CD 0.57592 0.81112 0.81151 - 0.00039

98 94.000 37.613 37.815 - 0.01 0.55390 0.31143 0.81172 - 0.00029

98 96.000 37.413 37.415 - 0.00 0.53188 0.31171 * 0.81191 - 0.00019

98 98.000 37.005 37.006 - 0.00 0.50986 0.81197 0 . 812 C 6 - 0.00009

98 100.000 36.590 36.590 0.00 0.48784 0.31220 0.81219 0.00001

98 1 0 2.

0

00 36.165 36.164 0.00 0.46582 0.31240 0.81229 0.00012

98 104.000 35.731 35.729 0.01 0 .44380 0.81256 0.81235 0.00021

98 1 u 6 .

0

00 35.286 35.283 0.01 0.42178 3.31268 0.81238 0.00030

96 1 0 3.0 00 34.829 34.826 0.01 0 . 39976 0.81274 0.81236 0.00036

98 11 0.000 34.361 34.356 0.01 0 . 37774 0.31276 0.81231 0. 00045

98 112.000 33.878 33.873 0.01 0.35572 0.81272 0.61221 3.00050

98 114.000 33.379 33.374 0.02 0.33370 0.81261 0.81206 0.00055

98 116.000 32.864 32.856 0.02 0.31168 0.81243 0.81186 0.00056

98 118.000 32.330 32. 324 0.02 0.28967 0.81218 0.81161 0.00057

98 120.000 31.774 31.768 0 . C 2 0.26765 0.81183 0.81129 0.00055

98 122.000 31.193 31.188 0.02 0.24563 0.31139 0.81090 0.00049

93 124.000 30.584 30.579 0.02 0.22361 0.81086 0.81342 0.00043

98 126.000 29.942 29.939 0.01 C .20159 0.81020 0.80986 0.00034

98 123.000 2 9 .

2

fc>2 29.260 0.01 0 .17957 0.80942 0.80920 0.00022

98 130.000 28.535 28.534 o.co C .15755 0 .30 850 0.80842 0.00009

98 132.000 27. 750 27.751 - 0.00 0 .13553 0.80742 0.80 749 - 0.00007

98 13 *. 000 26.691 26.894 - 0.01 0.11351 0.30617 0.80638 - 0.00022

98 136.000 25.935 25.939 - 0.01 0.09149 0.30470 0.80506 - 0.00036

98 133.000 24.839 24.843 - C . C 2 0.06947 0.80300 0.80343 - 0.00043

96 140.000 23.521 23.524 - 0.01 0.04745 0.80096 - 0.80137 - 0.00040

98 142.000 21.769 21.770 -o.co 0.02543 0.79843 0.79855 - 0.00012

98 144.000 18.327 18.328 - 0.00 0.00341 0.79340 0.79356 - 0.00016

NP = 46 , RMSPCT = 0.010

OBILVIS WN, INC.. MMMtkYN tT, N. Y. 88
APPENDIX F. (Continued)

NATIONAL BUREAU OP STANDARDS, CAYOORNIC MOMHttNO LABORATORY LABORATORY NOTE

PROJKT NO. 275Q3M

FILS NO. 73^5

RASE

11

subject Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

**** R.D .Goodwin

DATI IS 1Q79

Table 5. Comparison of methane liquid densities.

E 0*361

TCRT =190.555, TTRP = 90.6800

DCRT = 10.200, DTRP = 28.1470

8.370910 3-001 8.4161267-002 -7 .4785753-002

0 . 0000000*000 0 . 0000000*000 0 . 0000000*000

£= 0.361

ID T,K MOL/L CALC PCNT X YX YC YDIP

1 93.512 27.910 27.912 -0.01 0.97164 0.84050 0.84699 -0.00649

1 97.173 27.605 27.605 0. CO 0.93499 0.84830 0.84764 0.00066

1 10 1.434 27.243 27.240 0.01 0.89233 0.85043 0.84836 0.00207

1 105.165 26.916 26.916 0.00 0.85497 0.84900 0.84896 0.00003

1 109.611 26.527 26.521 0.02 0.81045 0.85231 0.84964 0.00267

1 113.772 26.146 26.144 0.01 0.76879 0.85112 0.85023 0.00089

1 117.746 25.782 25.775 0.03 0.72900 0.85327 0.85074 0.00252

1 121.893 25.388 25.380 0.03 0.68748 0.85373 0.85123 0.00249

1 125.825 24.999 24.995 0.02 0.64811 0.85272 0.85165 0.00107

1 129.657 24.611 24.610 0.01 0.60974 0.85236 0.85201 0.00035

10 1 130.000 24.558 24.575 -0.07 0.60631 0.84803 0.85204 -0.00400

1 13 3. 773 24.186 24.182 0 . 01 0.56853 0.85313 0.85233 0.00080

1 133.678 24.176 24.171 0.02 0.56748 0.85338 0.85234 0.00104

102 135.000 24.041 24.052 -0.05 0.55625 0.85002 0.85242 -0.00240

1 1 39. 352 2 3.578 23.579 -0.C0 0.51267 0.85249 0.85266 -0.00017

103 140.000 23.50C 23.507 -0. C3 0.50618 0.85132 0.85269 -0.00137

104 145.000 22.932 22.934 -0.01 0.45612 0.85255 0.85285 -0.00030

1 145.448 2 2 . 8 b 0 22.881 -0.00 0.45163 0.85272 0.85286 -0.00013

105 150.000 22.329 22.328 0.01 0 . 40606 0.85315 0.85287 0.00027

60 1 15 J. J00 22.332 22.328 0.02 C .40606 0.85357 0.85287 0.00070

1 151.553 22.130 22.132 -0.01 0.39051 0.85255 0.85285 -0.00030

106 155. JC0 21.686 21.682 0.02 0.35599 0.85341 0.85274 0.00067

1 15 7.199 21.375 21.363 -0.02 0.33398 0.85201 0.85263 -0.00062

107 lo J. 000 20.991 20.986 0. C2 C. 30593 0.85311 0.85242 0.00069

1 lb 3.659 20.428 2 0.438 -0.05 0.26930 0.85048 0.85205 -0.00157

108 165.000 20.234 20.227 0.03 0.25587 0.85289 0.85188 0.00102

1 169. 326 19.492 19.502 -0.05 0 .21256 0.84962 0.85117 -0.00155

109 170.000 19.387 1

9

. 3 e2 0.03 0.20581 0.85180 0.85104 0.00076

110 1 75.000 18.417 18.414 0.01 0 . 15574 0.85022 0.84981 0.00042

602 175.000 18.42C 16.414 0.03 C . 15574 0.85080 0.84981 0.00100

1 175.053 18.390 18.403 -0.07 0.15521 0 . 84 777 0.84979 -0.00203

111 16 J. 000 17.249 17.250 -0.00 0 .10568 0.84786 0.84800 -0.00014

bO 3 180.000 17.254 17.250 0.02 0.10568 0.84367 0.84800 0.00067

112 16 4. j u

0

16.054 16.061 -0.04 0.C6563 0.84466 0.84588 -0.00121

604 184.000 16.060 16.061 -0.00 0 . 06563 0.84575 0.84568 -0.00013

6 1 65. J 30 15.710 15.688 0.14 0.05532 0.84922 0.84517 0.00405

113 186.000 15.286 15.299 -0.08 0.04561 0.34203 0.84442 -0.00240

b 1 6 6 . 0 30 15.3C2 15.286 0.11 0 .0453 0 0.84765 0.84440 0.00325

6 1 8 7 . 0 31 14.836 14.826 0.07 0 .03528 0 • d 45 72 0.84351 0.00221

5 187. *89 14.582 14.589 -0.05 0.03070 0.84158 0.84305 -0.00147

114 186.000 14.284 14.298 -0.10 0.02558 0.33922 0.84248 -0.00327

6 18 6.0 31 14.285 14.279 0.04 0.02527 0.84388 0.84245 0.00143

6 189.032 13.578 13.578 0.00 0.01525 0.84114 0.84113 0.00002

5 1 89. 331 13.3Gu 13.315 -0.11 0.01226 0.83640 0.84065 -0.00425

5 189. 7C7 12.879 12.920 -0.31 0 .00849 0.82667 0.83996 -0.01329

6 190.032 12.474 12.477 -0.02 0 .00524 0.83812 0.83924 -0.00111

5 190.066 12.367 12.418 -0.17 0.00488 0.83082 0.83915 -0.00833

7 190.070 12.440 12.415 0.20 0.00466 0.84908 0.83914 0.00994

7 190.170 12.270 12.235 0.28 0.00385 9.85369 0.63887 0.01462

NP - 49, RMSPCT = 0.084
APPENDIX F. (Continued)

NATIONAL BUREAU Of STANDARDS, CRYOGENIC ENGINEERING LABORATORY PROJECT NO. FILE NO. PAOE

- LABORATORY NOTE 2750364 73-5 12

oubject Orthobaric Densities of Ethane, Methane, Oxygen and NAM£ R.D, Goodwin

Fluorine DATE _SeDt . 18. 1973

T able 6 9 Comparison of ethane liquid densities .

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oaiLVIE PNBS0. INC.. BROOKLYN 17. N. Y. STOCK NO. 4BO 90
APPENDIX F. (Continued)

NATIONAL BUREAU Of STANDARDS, CRYOGENIC ENOINORINO LABORATORY LABORATORY NOTE

PROJECT NO. 27*50364

PI LB NO. 73.5

PAQf

13

subject Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

HAM£ R . D . Goodwin

DATE Sent. IB. Km

Table 7. Ethane liquid data not used for least squares,,

u. © •H © ® 4 Ps in Ps CM © PO O' 9 9 y-8 y>8 CM CM 4 po « CM CM s4 © N- © © ps © <5*4 © CM 4

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osilvik rime*, me.. Brooklyn it. n. . STOCK NO. 4*0 91
APPENDIX F. (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-5

PAGE 14

subject Orthobaric Densities of Ethane , Methane, Oxygen and

Fluorine

name r .D. Goodwin

DATE Sent. 18. 1973

Table 8. Calculated oxygen liquid densities

T,K R, MOL/L

54.351 40.830

56.300 40.603

58.000 40.326

60.000 40.049

62.000 39.770

64.000 39.491

66.000 39.210

68.000 38.928

70.000 38.644

72. 000 38.358

74.000 38.071

76.000 37.782

78.000 37.491

80.000 37.197

82.000 36.901

84.000 36.602

86.000 36.301

83.000 35.996

90.000 35.688

92.000 35.377

94.000 35.062

96.000 34.742

98.000 34.418

1 0 0.0 00 34.090

102.000 33.756

104.000 33.417

106.000 33.072

108.000 32.720

110.000 32.361

112.000 31.995

114.000 31.620

116.000 31.236

118.000 30.842

120.000 30.438

122 .000 30.021

124.000 29.591

126. 000 29.147

128.000 28.685

130.000 28.205

132.000 27.704

134.000 27.179

136.000 26.625

133.000 26.037

1 4 0 . 0 Q 0 25.410

142.000 24.733

144.000 23.993

146.000 23.170

143.000 22.230

150.000 21.108

152.000 19.647

154.000 17.104

154.576 13.63C

DR/OT D2R/DT2

-0.1377 -0.00019

-0.1380 -0.00021

-0 .1385 -0.00023

-0 .1390 -0.00026

-0.1395 -0.00029

-0.1401 -0.00032

-C .1408 -0.00035

-0 .1415 -0.00038

-0.1423 -0.00041

-0.1432 -0.00045

-0 .1441 -0.00049

-0.1451 -0.00053

-0 .1462 -0.00057

-0 .1474 -0.00061

-G .1487 -0.G0066

-0 . 1500 -0.00071

-0.1515 -0.00077

-0 .1531 -0.00083

-0.1548 -0.00089

-0 .1567 -0.00096

-0.1586 -0.00103

-0 .1608 -0.00111

-0.1631 -0.00119

-0 .1655 -0.00129

-0 .1682 -0.00139

-0 . 1711 -0.00150

-0 .1742 -0.00162

-C .1776 -0.00176

-0.1813 -0.00191

-0 .1852 -0.00207

-C .1896 -0.00226

-C .1943 -0.00248

-0.1995 -0.00272

-0 .2052 -0.00300

-0.2115 -0.00332

-0.2185 -0.00369

-0.2263 -0.00413

-0.2351 -0 .00466

-0 .2450 -0 .00530

-0.2564 -0.00608

-0.2695 -0.00707

-0.2848 -0.00833

-0 . 30 31 -0.01000

-0 .3253 -0.01229

-0 . 3529 -0.01555

-0 .3886 -0.02051

-C .4370 -0.02869

-0 .5079 -0.04396

-0.6253 -0.07893

-0 .8749 -0.2C084

-2.1732 -2.34479

0 .0000 0.00000

OaiLVIK PRKS®. INC.. BROOKLYN 17. N. Y. •TOCK NO. 480 92
APPENDIX F . (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. ?7RmA4

FILE NO. 73-5PACE 15

subject Or thobaric Densities of Ethane, Methane, Oxygen and

Fluorine

name q .Goodwin

°ATE Sent. 18. 1973

Table 9. Calculated fluorine liquid densities.

T,< R, MOL/L DR/DT D2R/DT2

53.481 44.862 -0.1573 -0.00054

54.000 44.781 -0.1576 -0.00055

56.000 44.464 -C .1587 -0.0005b

58.000 44.146 -C .1599 -0.00061

60.000 43.825 -0.1612 -0.00065

62.000 43.501 -0.1625 -0.00068

64.000 43.174 -0 .1639 -0.00072

66.000 42.845 -C .1654 -0.00076

68.000 42.513 -0.1670 -0.00081

70.000 42.177 -0 .1686 -0.00085

72.000 41.838 -0.1704 -0.00090

74.000 41.496 -0.1722 -0.00095

76.000 41.149 -0.1742 -0.00101

78.000 40.799 -0 .1763 -0.00107

80.000 40.444 -0 .1785 - C • 0 0 11

4

82.000 40.085 -C . 18 C

8

-0.00121

84.000 39.720 -0.1833 -0.00129

86.000 39.351 -0 .1860 -0.00137

88.000 38.976 -0 .1888 -0.00146

90.000 38.596 -0 .1918 -0.00156

92.000 38.209 -0.1951 -0.00167

94. 000 37.815 -0 .1985 -0.00179

96.000 37.415 -0 .2022 -0.00192

98.000 37.006 -0 .2062 -0.00207

10 0.0 00 36.590 -C . 2105 -0.00223

102.000 36.164 -0 .2151 -0.00242

104.000 35.729 -0 .2202 -0.00262

10 6. JQQ 35.283 -0 .2257 -0.00286

108.000 34.826 -0 . 2316 -0.00313

110.000 34.356 -0 .2382 -0.00344

112. 000 33.873 -0.2454 -0.00380

114.000 3 3 . 3 74 -C .2534 -0.00422

116.000 32.858 -0.2624 -0.00472

118.000 32.324 -0.2724 -0.00533

120.000 31.768 -C .28 38 -0.00606

1 2 2 . J 0 0 31.188 -0 .2967 -0.00696

124.000 30.579 -0 . 3118 -0.00811

126.000 2 9 . 9 3 9 -0 .3294 -0.00959

128.000 29.26G -0.3505 -0.01156

1 3 J . J 0 0 28.534 -0 .3762 -0.01428

132.000 27. 751 -0.4084 -0.01821

134.000 26.894 - 0 .4504 -0. 02426

13o. 000 25.939 -0.5081 -C .0 3440

138.000 24.843 -0.5939 -0.05377

140.000 23.524 -0.7400 -0.09999

142.000 21.770 -1.0696 -0 .2770 4

144.000 18.328 -3.6894 -7.49794

144. 310 15.150 0 . 0 0 0 0 0.00000

OGILVIE PRESS. INC., BROOKLYN 17. N. Y. STOCK NO. 480
APPENDIX F. (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-5PAGE 16

subject Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

name r ,D .Goodwin

DATE Sept. 18, 1973

Table 10. Calculated methane liquid densities

T,K

90.680

92.000

94.000

96.000

98. 000

1 0 0 . 0 00

102.000

104.000

106.000

108.000

11 J . 000

112.000

114.000

116.000

118.000

12 0.300

122.000

124.000

126.000

128.000

1 3 0 . 000

132.000

1 34. 300

136.000

138.000

140.000

142. 0 00

144. 000

146. 000

148.000

15 0. J00

152. 000

154.000

156. 000

153.000

160.000

162.000

164.000

166.000

163.000

170.000

172. 000

174.000

176.000

178. 000

180.000

182

.0

00

184. jCQ

186.000

188.000

190.000

190.555

OGILVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. 430

R, MOL/L DR/DT D2R/DT2

28.147 -C .0825 -0.00031

28.038 -0.0829 -0.00032

27.871 -0 .0836 -0.00033

27.704 -0 .0842 -0.00035

27.534 -0.0849 -0.00036

27.364 -0 .0857 -0.00038

27.192 -0 .0865 -0.00040

27.018 -0.0873 -0.00041

26.843 -0.0881 -0.00043

26.665 -0 .0890 -0.00045

26.486 -C .0899 -0.00048

26.306 -0 .0909 -0.00050

26.123 -0.0919 -0.00052

25.938 -0 .0930 -0.00055

25.751 -0 .0941 -0.00058

25.561 -0.0953 -0.00061

25.369 -0.0966 -0.00064

25.175 -0.0979 -0.00068

24.978 -C .0993 -0.00072

24.778 -C .1008 -0.00076

24.575 -0.1023 -0.00080

24.368 -0.1040 -0.00085

24.158 -0.1057 -0.00090

23.945 -0 .1076 -0.00096

23.728 -0.1096 -0.00103

23.5G7 -0.1117 -0.00110

23.281 -C .1140 -0 .00117

23.051 -0 .1164 -0.00126

22.815 -0.1190 -0.00136

22.574 -0.1219 -0.00147

22.328 -0 .1249 -0.00159

22.0 75 -u .1282 -0.0G173

21.815 -0.1318 -0.00188

21.547 -0 .1358 -0.00207

21.271 -0 . 1401 -0.00228

2G.986 -0 .1449 -0.0C253

20.691 -0.1503 -0.00282

20 .385 -C .1562 -0.00318

20.066 -C .1630 -0.00361

19.732 -0 .1707 -0.00414

19.382 -0.1797 -0.00481

19.012 -0 .1901 -C . 0 0568

18.620 -0.2026 -0.00683

18.200 -0 .2177 -0.00841

1 7.747 -0.2367 -0 .0 1068

17.25G -0.2612 -0.01415

16.696 -0 .2947 -0.01988

16.061 -0 .3440 -0.03064

15.299 -0 .4261 -0.05538

14.298 -0 .6021 -0.14217

12.527 -1.5385 -1 .72796

1 0.2C 0 0 . 0 0 00 0.00000

94
APPENDIX F. (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-5

PAGE 17

SUBJECT The Orthobaric Densities of Ethane . Methane, Oxygen and

Fluorine

NAME , R.D .Goodwin

DATE Sept . 18 . 1973

Table 11. Calculated ethane liquid densities.

ETHANE SATURATED LIQUID DENSITIES

T,K R, MOL/L DR/DT D2R/DT2

83.899 21.680 -0.0360 0.00000

90.000 21.676 -0.0360 0.00000

95.000 21.496 -0 .0360 -0 .ocooo

1 0 0 .000 21.316 -0 .0360 -0.00001

105.000 21.136 -C .0361 -0.00001

110.000 20.955 -0 .0362 -0.00002

115.000 20.774 -0.0363 -0 .0000 2 120.000 20.593 -C .0364 -0.00003

125.000 20.411 -0.0365 -0.00003

130.000 20.220 -0.0367 -0.00004

135.000 20.044 -0 .0369 -0.00004

143.000 19.859 -0 .0371 -0.00005

145.000 19.673 -0 .0374 -0.00006

150.000 19.485 -0 .0377 -0.00006

155.000 19.296 -0.0380 -0.00007

1 6 0 . J 0 0 19.105 -0 .0384 -0.00000

lb5.000 18.912 -0 .0388 -0.00009

170.000 18.717 -0 .0392 -0.00010

175.000 18.520 -0 .0398 -0 . 0 0 01 1 180.000 lb. 320 -0 .0403 -0.00012

185.000 18.116 -0.0410 -0.00013

190.000 17.910 -0.0417 -0.00015

195.000 17.700 -0 .0424 -0.00016

200.000 17.405 -0.0433 -0.00018

205.000 17.266 -0.0443 -0.00020

210.000 17.042 -0.0453 -0.00022

215.000 16.813 -0 .0465 -0.00025

22 5.000 16.577 -C .0478 - 0 .00028

225.000 16.335 -0.0493 -0.00031

233.000 16.085 -0 .0509 -0.00035

235. 000 15.826 -0 .0527 -C.0C039

240.000 15.557 -0.0540 -0.00045

245.000 15.277 -0.0572 -0.00051

250.000 14.984 -0 .06GG -0.00059

255.300 14.676 -0 .0632 -0 .00069

260.300 14.351 -0 . C 6 69 -0.00082

265.000 14.005 -0.0715 -0.00099

270.000 13.635 -0 .077C - 0 . QC123

275.000 13.233 -0 .0839 -C.0C156

280.300 12.792 -0.0929 -0.00208

285.000 12.299 -0 . 1053 -0.00295

290.000 11.729 -0.1238 -C .00463

295.000 11.040 -C .1554 -0.00871

3 Q 0 . 3 0 0 10.112 -u .2206 -0.02539

305.000 8.048 -1.2696 -2.44167

30 5 . 330 6.870 0.0000 0. OCOOO

OGILVIE PRESS. INC.. BROOKLYN T5 17. N. Y. STOCK NO. 490
APPENDIX F . (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-5

PAGE 18

subject TRe Qrthobaric Densities of Ethane, Methane, Oxygen and NAME R D .Goodwin

Fluorine °ATE Sept . 18, 1973

Table 12. Comparison of oxygen vapor densities.

6. = 0.3e2

T CRT = 154.57b, TTRP = 54. 3507

DCRT . = 13.631, DTRP = 3.36122-004

2.7737066-001 -3.3666205-001 7.6907075-001 -1 . 5761185*000

9.3987130-001 0.0000000+000 0.0000000+000 0.0000000+000

ID T,K MOl/L CAL CD PCNT Z YX YC YDIF

99 56.000 5.3300-004 5.3288-004 0.02 0.95458 0.07082 0.07159 -O.OOC77

99 58.000 8.9930-004 8.9941-004 -0.01 0.90296 0.07289 0.07270 0 . 00019

99 60.003 1.4640-003 1.4644-003 -0.03 0 .85479 0.07505 0.07474 0.00031

99 62.000 2.3057-003 2.3068-003 -0.05 0.80972 0.07792 0.07752 0 . 0 0 C 4 3 99 64.000 3.5233-003 3.5251-003 -0.05 0 . 76747 0. 08123 0.08089 0.00034

99 66.000 5.2367-003 5. 2388-003 -0.04 0.72778 0.08497 0.08473 0.00024

99 68.000 7.5880-003 7. 5899-003 -0.02 0 . 69042 0 .08906 0.08893 0.00013

99 70.000 1. 0742-002 1. 0742-0 32 -0.00 0.65520 0.09343 0.09341 0.00001

69 72.000 1 . 4885-002 1.4883-002 0.01 0.62194 0.09804 0.09811 -0.00006

99 74.000 2. 0227-002 2. 0220-002 0.04 0.59048 0.10281 0.10 296 -0.00015

99 76.000 2.6996-002 2.6983-002 0.05 0.56067 0.10773 0.10 792 -0.00019

99 78.000 3 . 5441-002 3.5421-002 0.06 0.53239 0.11275 0.11296 -0.0002 1 99 80.000 4.5831-002 4.5602-002 0.06 0 .50552 0.11781 0.11804 -0.00023

99 82. 000 5.8449-002 5.8412-002 0.06 0.47996 0.12292 0.12314 -0.00022

99 84.000 7.3595-002 7.3552-002 0.06 0.45562 0.12804 0.12823 -0.00019

99 8 6 . J 0 0 9.1589-002 9. 1542-002 0.05 0.43242 0.13313 0.13330 -0.00017

99 88.000 1 . 1276-001 1.1271-001 0.04 0.41026 0.13821 0.13833 -0.00012

99 93.000 1. 3745-001 1. 3741-001 0.0 3 0 .38910 0.14323 0.14331 -0.00C03

99 92.000 1 .6603-001 1. 660 1-C01 0.0 1 0.36885 0.14820 0.14824 -0 .00 00 4 99 94.000 1 . 968 7-00 1 1. 9887-C01 -0.00 0. 34946 0.15311 0 .15 310 0.00000

99 96.000 2. 3637-001 2.3641-001 -0.01 0. 33088 0.15794 0.15790 0.00004

99 98. 000 2. 7894-001 2.7902-001 -3.0 3 0.31306 0.16270 0 .16262 0.00009

99 10 3.0 00 3.2702-001 3.2716-001 -0.04 0.29596 0.16738 0.16726 0 .00 01

2

99 102.000 3. 8108-001 3.6127-001 -0.05 0 .27952 0.17196 0.17182 0 . 0001 + 99 104.000 4.4162-001 4.4186-001 -0.05 0.26372 .0.17645 0.17630 0.00015

99 106.000 5.0914-001 5.0943-001 -0.06 0 .24851 3 .18086 0.18070 0 .00 01 6 99 1 u 8 . 0 00 5.8421-001 5.8455-001 -0.06 0.23387 0.18518 0.185C2 0.00016

99 11 3.000 6. 6747-001 6. b783- 0 0

1

-0.05 0 . 21975 0.18940 0.18925 0.00015

99 1 12. JOU 7. 5953-001 7.5992-0 01 -0.05 0 .20615 0.19355 0.19341 0.00014

99 1 1 4 . J 0 0 8.6121-001 8.6155-001 -0.0 4 0.19302 0.19759 0.19748 0.00011

99 116.000 9. 7325-001 9. 7353-031 -0.03 0.18034 0.20156 0.20148 3.000G3

99 118.000 1. 0965+000 1.0967+000 -0.02 0 . 16809 0.20545 0.20540 0.00005

99 120.000 1.2321+000 1. 2322+ 000 -0.00 0 .15625 0.20926 0.20925 0.00000

99 1 2 2 . 0 0 0 1.3812+000 1.3810+000 0.01 0 .14480 0.21299 0 .21 303 - 0 . C 0 0 0 4 99 124. 000 1 . 5450+000 1.5445+030 3.0 3 0.13372 0.21666 0 .21674 -0.00009

99 126.000 1 . 7250 +00 0 1. 7243+0U0 0.04 0.12299 0.22027 0.22039 -0.00012

99 128.000 1.9230+000 1.9220+0^0 3.05 0.11259 0.22383 0.22398 -0.00015

99 13 .000 2.1411+000 2.1399+030 0.06 C. 10252 0.22735 0.22751 -0.00017

99 1 32.000 2. 3819+000 2. 3e05+000 0.06 0. C9275 0.23083 0.23100 -0.00017

99 1 8 *4 • 0 0 0 2.6483+000 2. 64 70+000 0.05 0.08327 0.23429 0 . 23444 -0.00016

99 1 3 o . 0 0 0 2. 9444+000 2. 9433+000 0.04 0. 07407 0.23773 0.23786 -J.OOC12

99 1 3 8 . 0 0 0 3.2750+000 3 . 27 4 5 + C 30 0.01 0.06514 0. 24119 0 .24124 -0.00005

99 14 3.000 3.6468+000 3.6474+000 -0.02 0.05646 0 . 24466 0.24462 0.00006

9 6 1 2 . 0 0 0 4. 0692+000 4. 0712+000 -0.05 0. 04803 0.24819 0.24801 0.00013

99 1 4 4 . J 0 J 4.5552+000 4.5592+000 -0.09 0.03983 0.25176 0.25143 0.00033

99 1 4 6 . 0 0 0 5 . 1261+000 5.1316+000 -0.11 0.03185 0.25536 0.25493 0 .0 0 04 3 99 1 h 8 . 0 0 0 5.6177+00C 5.6225+CjC -0.C8 0.02410 0.25892 J .25 857 0.00035

99 1 5 0 . 0 0 0 6 . 7 U56 + 000 6.6967+000 0.13 0.01654 0.26182 0.26247 -0.00065

99 152.000 7 . 9239+000 7.9138+000 0.13 0.00919 0.26616 0.26692 -0.00076

99 1 5 * . J 00 1.C225+001 1.0230+001 -0.05 0. CQ203 0.27367 0.27313 0.00054

NP = 50, RHSPCT = 0.052

OOILVIK PMtaa. INC.. BROOKLYN 17. N. . STOCK NO. «RO 96
APPENDIX F. (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-5

PAGE 19

subject ,pke Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME R .D .Goodwin

DATE Sent. 18. 1973

Table 13. Comparison of fluorine vapor densities.

E = 0.362

TCRT = 144 . 310 , TTRP = 53.4611

OCRT = 15 . 150 , DTRP = 5 . 67000-004

2 . 5715721-001 - 2 . 270 6443-001 6 . 0538644-001 - 1 . 3916332*000

7 . 9257188-001 0 . 0000000*000 0 . 0000000*000 0 . 0000000*000

ID T,K MOL/L CflLCD PCNT z YX YC YDIF

98 54.000 6 . 6000-004 6 . 6001-004 - 0.00 0.98473 0.03779 0.03766 0.00010

98 56.000 1 . 1500-003 1 . 1518-003 - 0.16 0.92853 0.04645 0.04297 0.00348

98 58.000 1 . 9300-003 1 . 9272-003 0.14 0.87621 0.04693 0.04877 - 0.00184

98 60.000 3 . 1100-003 3 . 1038-003 0.20 0.82738 0.05309 0.05493 - 0.00184

98 62.000 4 . 8400-003 4 . 8291-003 0.23 0.78169 0.05968 0.06135 -0 .00167

98 64.000 7 . 2900-003 7 . 2821-003 0.11 0.73887 0.06725 0 .06792 - 0.00067

98 66.000 1 . 0660-002 1 . 0675-002 0.05 0.69063 0.07434 0.07459 - 0.00026

98 68.000 1 . 5250-002 1 . 5253-002 - 0.02 0.66077 0.08139 0.08130 0.00009

98 70.000 2 . 1280-002 2 . 1293-002 - 0.06 0.62507 0.08827 0.08799 0.00028

98 72.000 2 . 9(37 0-002 2 . 9105-002 - 0.12 0.59135 0.09515 0.09464 0.00051

98 74.000 3 . 8970-002 3 . 9029-002 - 0.15 0 .55945 0.10181 0.10121 0.00063

98 76.000 5 . 1350-002 5 . 1434-002 - 0.16 0 .52923 0.10829 0.10769 0.00063

98 76.000 6 . 6600-002 6 . 6713-002 - 0.17 0 .50057 0.11466 0.11406 0.00060

98 80.000 8 . 5150-002 8 . 5291-002 - 0.17 0.47333 0.12086 0.12030 0.00056

98 82.000 1 . 0745-001 1 . 0761-001 - 0.15 0.44742 0.12691 0.12641 0.00053

98 64.000 1 . 3397-001 1 . 3416-001 - 0.14 0.42275 0.13281 0.13238 0.00044

98 86.000 1 . 6523-001 1 . 6541-001 - 0.11 0.39923 0.13854 0.13820 0.00034

98 88.000 2 . 0174-001 2 . 0191-001 - 0.08 0. 37677 0.14413 0.14388 0.00025

98 90.000 2 . 4407-001 2 . 4420-001 - 0.05 0.35532 0 .14956 0.14940 0.00015

98 92.000 2 . 9280-001 2 . 9286-001 - 0.02 0.33479 0.15484 0.15478 0.00006

98 94.000 3 . 4857-001 3 . 4852-001 0.01 0.31514 0.15997 0.16001 -0.00004

98 96.000 4 . 1203-001 4 . 1184-001 0.05 . 0.29631 0.16496 0.16509 - 0.00013

98 98.000 4 . 8389-001 4 . 8352-001 0.08 0 .27824 0.16981 0.17003 - 0.00021

98 10 J . 000 5 . 6491-001 5 . 6432-001 0.10 C . 26090

' 3.17453 0.17482 - 0 .00029

98 102. 0 00 6 . 5591-001 6 . 5507-001 0.13 0 . 24424 0.17912 0 .17947 - 0.00035

98 10 9.000 7 . 5778-001 7 . 5667 - 001 0.15 0.22822 0.18356 0.18398 - 0.00040

96 106.000 8 . 7151-001 8 . 70 1

2

-

C

0 1 0.16 0.21281 0.18792 0.18836 - 3.00044

98 1 U 8.000 9 . 9617-001 9 . 6651-001 0.17 0.19796 0.19215 0.19261 - 0.00046

98 110.000 1 . 1390*000 1 . 1371*000 0.17 0.18366 0.19627 0.19673 - 0.00046

98 1 1 2 . 000 1 .

2

^ 53*000 1 . 2932*000 0.16 0 .16986 0.20028 0.20072 - 0.00044

98 114.000 1 . 4687*000 1 . 4666*000 0.15 0.15655 0.20419 0.20460 - 0.00041

96 116 . 0 CJ 1 . 6610*000 1 . 6590*000 0.12 0. 14370 0.20801 3.20836 - 0.00035

98 118.000 1 . 8743*000 1 . 6725*000 0.09 0.13129 0.21174 0.21200 - 0.00027

98 1 2 0.

0

00 2 . 1111*000 2 . 1099*000 0.06 0.11928 0.21538 0.21554 - 0.00016

98 122.000 2 . 3744*000 2 . 3741*000 0.01 0.10768 0.21894 0.21898 - 0.00004

98 124.000 2 . 6680*000 2 . 6690*000 - 0.04 0.09644 0.22243 0.22232 0.00011

96 1 2 o . 0 0 0 2 . 9965*000 2 . 9992+000 - 0.09 0. 08556 0.22584 0.22556 0.00027

98 126. 000 3 . 3661*000 3 . 3709+000 - 0.14 0.07503 0.22917 0.22873 0.00045

98 130.000 3 . 7 o 48*000 3 . 7921*000 - 0.19 0.06481 0. 23243 0.23181 0.00062

98 1 3 2 .

0

0 0 4 . 2641*000 4 . 2735 +OuO - 0.23 0.05491 0.23560 0.23484 0.00076

98 1 34 .

0

00 4 . 8207*000 4 . 8319*000 - 0.23 0.04530 0.23862 0.23782 0.00031

98 1 3 b . 0 0 0 5 . 4816*000 5 . 4905*000 - 0.16 0.03598 0.24138 0.24077 3.00061

98 138.000 6 . 2910*000 6 . 2909*000 o.co 0 . C 2692 0.24374 0.24375 - 0.00003

98 140.000 7 . 322 6 * 00 C 7 . 3133*000 0.13 0.01813 0.24625 0.24683 - 0.00058

98 142.000 8 . 7654*000 6 . 7644*000 0.24 0.00958 0.24889 0.25 0 23 - 0.00133

96 144. 000 1 . 1668*001 1 . 1893*001 - 0.04 0.00127 0.25552 0.25509 3.00044

NP = 4 b , RMSPCT = 0.134

OttlLVII PRKSt. INC.. BROOKLYN 17. N. T. STOCK NO. 97
APPENDIX F. (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

PROJECT NO.

NAME

FILE NO. 73-5

PAGE ML

R . D . Goodwin

DAT! Sent. 18. 1973

Table 14„ Comparison of methane vapor densitie:

TCRT s 190.555s TTRP OORT s i 0 o 20 0 « DTRP

3 . 7410143-001

4 « 3988336=001

• 2 e 61 5 730 9-0 01

0 . 0000000 * 00(2

E = 0 o 382

90.6800

1 . 56787=002

6 . 7533217=001

o . oooooaa+ooo

1 . 0122063*000

0 . 0000000*000

10 T,K MOL/L CALCO PCNT 2 YX YC YDXF

2 92.000 1 . 8280=002 1 . 8280-002 0.00 0.97263 0=21853 0 .21874 - 0.00021

2 94.000 2 . 2860-002 2 . 2858-002 0.01 0.93261 0.22329 0.22354 - 0.00025

2 96.000 2 . 8290-002 2 . 8294=002 - 0.01 0.89427 0=22864 0 .22828 0.00036

2 93.060 3 . 4690=002 3 . 4691=002 = 0.00 0.85749 0.23301 0.23295 0.00006

2 100.000 4 . 2160=002 4 . 2159=002 0.00 0.82218 0.23752 0.23755 - 0.00003

2 102.

3

00 5 . 0810-002 5 . C 813-002 - 0.01 0.78826 0.24213 0.24207 0 .0000 7 2 104.000 6 . 0770-002 6 . 0772=002 - 0.00 0.75 564 0. 2465 3 0.24650 0.00003

2 106.000 7 . 2160=002 7 . 2161 = C 02 - 0.00 0.72425 0.25086 0=25084 0.00002

2 106.060 8 . 5110=002 8 . 5110=002 - 0.00 0.69402 0.25510 0 .25510 0.00003

2 110.000 9 . 9750-002 9 . 9753-002 - 0.00 0.66490 0.25928 0.25926 0.00002

2 112.000 1 . 1623-001 1 . 1623-001 0.00 0.63681 0.26332 0.26333 - 0.00000

2 114.000 1 o 3468-001 1 -. 34 6 8 - 0 0

1

- 0.00 0.60971 0 .26732 0.26730 0.00002

2 116.000 1 . 5527-001 1 . 5527-001 3.00 0 .58354 0.27117 0.27119 - 0.00002

2 118. 000 1 . 7814-001 1 . 7813=001 0.00 0.55826 0 .27495 0.27498 - 0.0000 2 2 120.000 2 . 0346-001 2 . 0345-001 0.01 0.53383 0.27864 0.27668 - 0.00004

2 122.000 2 . 3139=001 2 . 3138-001 0.00 0.51019 0.28226 0.28228 = 0.00003

2 124. 000 2 . 6212-001 2 . 6211-001 0.00 0.48732 0.28577 0.28500 - 0.00003

2 126.000 2 . 9583-001 2 . 9582-001 C . Q 0 0 . 46517 0.28921 0.28923 - 0.00002

2 128.000 3 . 3272-001 3 . 3271-001 0.00 0. 44372 0.29255 0.29257 - 0.00002

2 130.000 3 . 7299-00

1

3 . 7299-001 0.00 0 . 42292 0.29582 0.29583 - 0 .0000 1 2 132.000 4 . 1686-001 4 . 1687-001 - 0.00 0.40276 0.29902 0.29900 0.00002

2 134.000 4 . 6457-001 4 . 6461-001 - 0.01 0. 38320 0. 30213 0.30209 0.00004

2 136.000 5 . 1638-001 5 . 1644-001 - 0.0 1 0 . 36421 0.30515 0.30510 0.00006

2 136.000 5 . 7255-001 5 . 7264=001 - 3.02 0 . 34577 0 . 30811 0.30003 0=00003

2 140 .000 6 . 3337-001 6 . 3351=001 - 0.02 0 .32786 0.31099 0.31088 0 = 00011

2 142.000 6 . 9916-001 5 . 9937-001 - 0.03 0. 31046 0.31380 0.31366 0=00014

2 144.000 7 . 7028-001 7 . 7055=001 - 0.04 0.29353 0 . 31654 0.31637 0=00016

2 146.000 8 . 4711-001 8 . 4745-001 - 0.04 0 .27703 3. 31920 0.31901 0.00019

• 2 143 . Q 0 9 . 3007-001 9 . 3049-001 - 0.05 0.26106 0.32179 0.32158 0=00021

2 15 0. 000 1 . 0196*000 1 . 0201*000 - 0.05 0.24548 0.32431 0 .32409 0=00022

2 152.000 1 . 1164*000 1 . 1169*000 - 0.05 0.23030 0.32675 0.32653 0.00022

2 154.000 1 . 2209*000 1 . 2214*000 - 0.05 0.21552 0.32912 0.32891 0.00021

2 156.000 1 . 3333*000 1 . 3343*000 -0 o 0 4 0.20111 0.33140 0.33123 0.00017

2 158.000 1 . 4560*000 1 . 4563*000 - 0.02 0.18707 0. 3336 1 0.33350 0.00011

2 160.000 1 . 5884*000 1 . 5884*000 - 0.00 0.17339 0.33571 0.33571 0.00003

2 162.000 1 . 7322*000 1 . 7316*000 0.03 0. 16004 0=33772 0.33788 - 0.00016

2 164.000 1 . 8886*000 1 . 8670*000 0.06 0.14701 0.33981 0 o 34 0 0 0 - 0.00039

2 166.000 2 . 0593*000 2 . 0561*000 0.16 0.13430 0 . 34135 0.34208 - 0.00073

2 163.000 2 . 2465*000 2 . 2408 * 000 0.26 0.12190 0.34291 0=34412 - 0.00121

1616 169.067 2 . 3438*000 2 . 3463*000 0.11 0.11540 3.34469 0,34520 - 0.00051

1614 169.270 2 . 3687*000 2 . 3670*000 0.0 7 0.11417 0.34506 0.34540 - 0.00035

912 169.417 2 . 3858*000 2 . 3821*000 0.16 0.11328 0 . 34480 0.34555 - 0.00075

1612 169.468 2 . 3801*000 2 . 3873*000 0.03 0.11297 0. 34545 0=34560 - 0=00015

910 169.601 2 . 4 C 54*000 2 . 4011*000 0.18 C . 11217 0. 34488 0.34573 -0 .00085

308 169.794 2 . 4236*000 2 . 4213*000 0.10 0.11101 0. 34547 0.34593 - 0.00046

1716 173.088 2 . 7972*000 2 . 7964*000 0.03 0.09162 0.34905 0.34920 - 0.00015

1714 173.290 2 . 6203*000 2 . 8215*000 - 0.04 0=09046 0.34961 0=34940 3=00021

oaiLVIC PMIt. INC., 1MMLTN 17. N. . 9TM* N*. tn 98
APPENDIX F. (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-5

PAGE 21

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME _ . R . D . Goodwin

DATE Sent. 18, 1973

Table 14 (Continued) . Methane vapor densities.

ID T,K MOL/L CftLCD PCNT z YX YC YOIF

1712 173.469 2.8457+000 2.8465+000 -0.03 0.08931 0.34973 0.34959 0.00014

1012 173.473 2.8480+000 2.8445+000 0.12 0.08940 0.34896 0.34958 -0.00062

1010 1 73.675 2 . 8700+000 2.8701+000 -0.00 0.08824 0.34980 0.34978 0.00002

1006 173.857 2.8935+000 2.8934+000 0.00 0.08720 0.34995 0.34996 -0.00001

161b 1 7 7. 094 3.3501+000 3.3513+000 -0.03 0.06901 0. 35333 0.35315 0.00013

1814 1 77.292 3.3601+000 3.3822+000 -0.06 0.06792 0. 35369 0.35335 0.00034

1114 177.328 3.3863+000 3.3879+000 -0.05 0.06772 0. 35364 0 .35339 0.00025

1612 1 77.485 3.4108+000 3.4128+000 -0.06 0.06686 0. 35386 0 .35354 0.00031

1112 177.509 3.4209+000 3.4166+000 0.12 0.06673 0.35290 0 .35357 -0.00067

1110 177.700 3. 4602+000 3. 44 73+ 0 C C 0.37 0.06568 0.35175 0.35376 -0.00200

1916 181.105 4. 0663+000 4.0686+000 -0.06 0.04738 0.35755 0.35722 0.00033

1914 181.304 4. 1077 + 00 0 4. 1101+000 -0.06 0. 04633 0. 35778 0.35743 0.00034

1213 181.389 4 . 1269+000 4. 1281+000 -0.03 0 .04588 0.35769 0 .35 752 0 .0001 7 1912 181.506 4.1496+000 4.1530+000 -0.08 0.04527 0.35813 0 .35765 0 .00048

1211 181.589 4.1656+000 4. 1708+000 -0.12 0.04483 0 . 35848 0.35774 0.00074

1209 181.763 4.2042+000 4.2097+000 -0.13 0. 04389 0.35870 0 .35793 0.00078

1516 183.117 4 . 5212+000 4. 5240+000 -0.06 0.03688 0.35978 0 .35940 0 .00 0 3 9 1514 18 3. 322 4.5704+000 4. 5754+ 0CC -0.11 0. 03582 0 . 36032 0.35963 0.00069

1512 IS 3.514 4.6189+000 4.6246+000 -0.12 0 . 03484 0. 36063 0 .35985 0.00078

1316 164.125 4 . 7622+ J00 4. 7880+000 . -0.12 ' 0.03171 0.36134 0.36055 0.00079

2108 164.087 4. 7625+000 4. 7775+000 0.10 0. 03190 0 . 35982 0.36051 -0.00068

210 7 164.285 4. 8263 + 00C 4. 8327+000 -0.13 0.03089 0.36161 0.36074 0 .00 087

1314 184. 370 4. 8462+000 4. 8567+000 -0.22 0.03046 0.36228 0 .36 0 84 0.00144

2 1 0 b 184.471 4.8797+000 4.6857+000 -0.12 0.02994 0. 36177 0 . 360 96 0.00081

1312 184.510 4. 367b+00U 4.8969+000 -0.19 0.02975 0. 36228 0.36101 0.00127

6 185.030 5. j38G+00u 5. C524+O0C -0.28 O'. 02711 0.36359 0.36164 0.00195

6 1 8o. 030 5.3640+000 5. 3838+000 0.00 0. 02208 0. 36290 0.36292 -0.00002

22 0 6 166.103 6. 4077+000 5.4098+000 -0.04 0.02172 0.36331 0.36302 0.00029

141b 130.129 5. 4096+000 5.4192+0C0 -0.18 0.02159 0 . 3b43 6 0.36305 0.00131

1414 18-.. 319 5. 4795+00

J

5.4691+000 -C.17 0.02064 0.36461 0.36331 0.00130

22 0 7 18o.304 5 . 4627+000 5.4835+000 -0.01 0. C2072 0.36339 0.36329 0.00010

22 0 b 136.501 5. 5571+000 5.5581+000 -0.02 0. 0 1974 0. 36369 0.36356 0.00013

1412 130.518 5.5591+000 5.5646+0CC -0.10 0 . C 1965 C. 36434 0 . 36359 0.00075

6 1 6 7.0 51 5. 7360 +00C 5 . 7 7 2 3 0 0 u 0.2 4 0.01711 0. 36244 0.36433 -0.00189

b 1 8 3 . 0 31 6. 2750+ 000 6.2474+0OG 0.44 0. 01219 0. 3620

1

0.36592 -0.00392

2306 138.140 6. 2930+000 6. 3064+000 -0.21 0.C1165 0 . 3680 4 0.36612 0.00193

2 10 7 183.343 6.4067+000 6. 4218+000 -0.24 0. r 1066 0 . 36868 0.36648 0.00219

230b 168.545 6.5278+000 6.5441+0U0 -0.25 0.0 0 968 0.36926 0 . 36686 0.00239

6 1 6 9 . 0 32 6. 916O+OU0 6.6777+000 0.59 0. C0732 0. 36167 0.36787 -0.00620

5 16). 765 7.561C+000 7.5576+0C0 -0.09 0.00378 0.37093 0.36975 0 .00117

6 190. J32 7.9oU0+30Q 7.9153+000 0.56 0.00250 0 . 3618b 0.37065 -0 .C0879

c, 130.046 7.9-5 50+^00 7.9371+000 -0.0 3 0 . C 0 243 0.37113 0.37070 0.00043

7 190.070 8. OOOC + OOG 7.9756+000 0.31 0.00232 0 . 36588 0.37079 -0.00491

7 1 9 J . 1 7 J 6.170C+000 8. 1508+000 0.24 0.00184 0 . 36709 0 .37120 -0 .0041 2

7 190.270 8.360C+OOL 8.3595+000 0.0 1 0.00136 0 . 37154 0.37166 -0.00013

5 1)0.279 S . 390 0 0 C 0 8.3805+000 0.14 0.00132 0.36899 0.37171 -0.00272

7 1 9 0 . 570 8. b 200+000 8.6242+ 000 -0.05 0.00088 0. 37333 0.37221 0.00112

7 1 9 0.4 70 9. ouUC+OjC 9 . C 1 16+CuC -0.13 0 . C a 041 0.37689 3.37291 0.00397

r, 13'. 500 9.1610+006 9.ie67+0C0 -C.26 C . C 0 026 0.36333 0.37319 0.01014

NP - 96, RHL^CT = 0.146

OQILVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. 480 yy
APPENDIX F . (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-5

PAGE 22

subject 'ppg Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

name p . p) ^ Goodwin

DATE Sent. 18 1973

pm

03

ro

• O

II

Table 15. Compari son of ethane vapor densities.

Ll_ on ro 4 4 CD 4 T m 03 o- J- 03 in -»-4 CM rw CD N. in K- ro co ro r- U3 IH 4 of j- ^4 H ro ro CM vH o CD H CM CM CM CM =?4 4 t4 CM r4 CD N. o ro O' in o 4- D o o O CD O o O o S' CD CD O o CD o o O CD O CD O CD o o CD o o •S' o

>- CD o Q •S' a o o o CD O CD o o CD CD o O CD o CD O O o o O G O o o

o G O o CD CD o o O CD O CD o CD O o CD CP CD O o CD a o o CD O o o

CD

1 CD CD a O• 0

1 0

1 o

• 0

1 O1 CD CD CD O CD o CD a O

1 CD

• o• CD

1 o

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1 CD CT> O 01 01

C-3 K- ro CM N- tH CO O' ro 03 cp in <x> N- H ro 03 *4 •X) in *4 ^4 B0 CM 4 O' to 4- in GO

>- in os VO CO 4 CM CD C\J 03 ro 4 CO 03 CP 03 OO CO M3 03 O' <=0 ro 03 iO •n >*4 N. N. 00 CO CO in CT P- CO oo CM i£> CP rl ro J- in in CD in CO p- M3 in ro N. o •*4 CVJ CM CM 4 CM o CD CM ro in 03 P- O' CD CM ro 4 4 j- in iO N- GO BO O' O' O' O' O' o o o o a CD CD o CD o CD O •H 4 W <5-4 *4 4 *4 4 4 4 4 *4 ^4 ^4 -*H 4

CD

1 CD1 CD

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X in CP ro 4 GO in ro 4 CM ro O r^ CO N- CO CO CO *4 in TO in in i£> 4 N. BO ro

>- CD 4 4 CM cr N. O' 4 ro in CD CP 4 <JD CD O' K. 4 p- 03 ro <o in ro 4- v£> •n ro

ro ao CM in O' 03 CM N. CM 03 O' CM ro in in O) o in GO p- 03 in CM r- o CM CM CM CM

N- m 4 CM a O CM TO in 03 CP CD 4 CM ro J- 4 Jf in 03 OO B0 O' O' O' O' O'

rH CD CD CD CD CD CD CD CD CD CT o o CD *4 4 *4 •*4 4 4 t4 4 4 t4 t4 4 t4 4 ^4 ^4

CD CD

CD CD CD CD CD CD CT CD CD CD CD CD o CD O CD CD CD CD O CD O a CD O O CD CD O O CD

i 4- i » i i • CD CD

in O

N- CD M *4 4 *4 03 *4 CD ro 4 C

P

os CD ro in N- O' 03 03 4 O' o> O' 4- in CP o r\j in 4

03 G j- <© O 4 ao •JO 4 CD 4 in ro N» 4 CO \D in ro CD oo H 03 P0 G ro cj iD CM 4

03- CD X) vO rl j- oj ro rj cr> 00 CD ro CP CP 4 03 ro 00 CM 03 03 O' 0J r- CD 4- ro o CD

N* CD (T in 4 n O' ro N- ro CP in 4 OO 03 ro *4 o O' 03 03 J- ro ^4 4 CD CD CD CD O

in CD CP <x> N- 03 in J- j- ro ro CM CM OJ 4 H 4 *4 t4 CD CD CD o G a O G o o G O

ro O o o o CD o CD o o o o CD o CD CD O CD CD CD O O O O o a O O CD O O

cD CP G 1— O r^ G -t in ro cO in CD ro 4 O' ro 4 4 t4 CP 10 03 G n- nj in CM r- CO CO 4 ro UJ G 0J o z O G 4 o o *4 4 t4 G UJ O *4 4 *4 4 CD CD G p4 a o ro o a *4 CD CD o

G ID o o

i CM CD a G CD CD G CD O O CD CD CD G CD a CD O CD O G O CD a o CD G CD O CD CD a

CO O 4- CM CD 1 i t i i • t i i • i i i UJ O' 4 CP CD

1—

1

O' t4 00 CD

y— a0 in • • H4 • ro 0- CD o n in in 4 ro ro ro CvJ CM 0J CM 4 *4 ^4 ^4 4 t4 4 t4 CD a G O CD CD a a CD CD

(/I O' • 1 o a o a G CD a CD CD CD "D LJ CD CD CD O CD a CD CD CD o CD G CD O o CD CD CD z CO 4 —J o o CD G CD G CD o CD O G O CD O G CD a CD G o CD v-D O O O o o CD O

UJ rvj G < i « i i i i » 1 i i i i i t i i t • i 4- 4- 4- 4- 4- 4- 4- 4 4 4

Q II II o O o ro 03 03 ro CD B0 4 CP 4 4 in p- lO CD cO in CP N- CP O' 03 4 CD ro O' N- 4 4

o O n in CP i0 •D O' 4 TO O' 4 ao ro ro <D ao CP ro 4 in 03 0J t4 4 CM ao CM CO CD

Ct a CL 1 4- GO ro <£> in CP CP CP CM ao t-D CP CO o CM o vU in (M in ro 03 1^ a CD 4 ro *4 4 4

O O' ac •£> CD ro ro *4 in ^4 CM N- cO G 4 GO ro CD o 0J CO r^. 03 C0 t4 in Cl ao in ro 03 CD CP *4 • a 1- 1

CO O LD d 1— o a O *4 *4 ao ro ro N. t4 ro ln CO 4 0J ro 4 in iO ao ^4 *4 0J 0J ro 4 4 in in 03

CD CD

in ct o f-D G in G

UJ ro N. »4 a -j 03 in in 4 ro ro ro CM (M CM (\J 4 4 4 4 *4 4 4 *4 O O CT CT O CD CT CD CT CT

¥— ro GO • • CD CD CD a G G o G CD CT O CD O CD O CD CD CD O CT o CT G o CD CT CT O CD C_3 d • • 4 o _i CD CD CD CD a G o G CD CD CT CT CT CT CT CT CD CD CT CT o CT G o CD CT O CT CD a

QC in 03 o i « i i i i 1 i i i i | i i i i i i i 4- + 4- 4- + + 4- 4» + 10

r> CD r <0 0J tM G rp ro JO CP t4 'H PM O 0J PM in 03 4 CT CT o CD G CT G O CT O CD X

w- TO *4 4 0) 4 'H in r^ m 4 G CP 4 4 P* in O' s. 00 0J in 4 ro fs. N. CT PM N- 4 in ro o CL

cl a CD r P3 03 in CP CD o ro GO 4 O' CO 0- CP 4 o 03 in ro in ro 03 <X3 CD CD CT ro ^4 in

in II II o CD ro ro 4 in 4 ro a0 03 O 4 B0 ro o CP CVJ CO N» CO 03 4 in CT ao in ro 03 CT O' 4

UJ kl 0J 03 4 4 rO ro *4 ro N. *4 ro in ao 4 PM 0J 4 in 03 r^ CO 4 ^4 PM 0J ro 4 4 in in 03 0J z nc CL ro

<r o O 4 ro II X 1— Q N- 4

1— rc in a O CD CD CD CD G CT G CT CT CT CT CT o CD CD CT CD O O CT CD CT CT CT CT CT CD CL UJ CM 4 •L CD o CD CD CD G O CT O CD a CD o CD CT CT CT CD in in in tn in in in in in in in z

0J CD G CD n fD CT CD CT CD CD CD CD CT CT CT CT CT CT 4 4 "«4 4 4 4 *4 4 4 •4 OJ 4 4 CD CD CD o CT CD r D CT CT CD CD CT CT CD CD CT in CD ro ro ro m ro a0 PM ro 4 in in

<T> O 4 oo ro 4 in 03 O O' O 4 PM ro 4 4 in in 03 N. ao O' CP CT G CT CT CD

•*4 -4 4 4 4 4 4 4 t4 *4 PsJ PM PM PM PM PM PM PM CM PM OJ PM PM ro ro ro ro ro

Q r4 4 H 4 H 4 4 *4 4 4 *4 4 4 4 *4 t4 *4 *4 o o CT CD CT CT o CD CD CT o

1-4 4 t4 4 ^4 4 4 t4 *4 4 *4

OGILVIE PRESS. INC., BROOKLYN 17, N. Y. STOCK NO. 490 100
APPENDIX F. (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-5PAGE 23

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

NAME „ ^ R.D . Goodwin

F luorine DATE IS 1 Q7T

Table 16. Ethane vapor data not used for least squares.

u. vi> rvj CVJ <30 ro CO CV in vD O' X rr> LT» CT x 3 f\J x in in eo 3 X <50 in CD CM ao

fr—4 cd CD 9-4 CVJ X X 00 CD CD ro CM ao PO 3 ee o <r> ® o O' O' O' 4 ao 3 3 3 O' TO CM in 9-4 fO o o CD CD CD CO o H j- CM CM CD CD CD CD 9-4 o CD 9"4 SD O 9-4 CD o o o o o H 9-4 CM 3 O

V CD a CD CD CD o O CD CD CD O o O O o a o o CD O o O O o o o o o CD O CD CD O o o CD CD o O CD CD CD CD o CD CD CD CD CD o o cd o o CD © o o o o CD O O CD CD

CD CD CD CD CD CD CD CD O O CD o CD O o CD CD CD CD CD CD CD CD CD CD cd CD CD CD CD CD O

i i i i i i i i i i • i i 1 1 • i i • o CD j- O' in CM 9-4 TO X in CM CD CO ® in 3 3 CM X in 3 ro CM P- in X ro X CD j- 3 P- in

>- 3 o in CD 3 N. O’ o ro XI 3 a ro in O' C3 O' p- m N. X 3 in X X X Lf\ IV. 3 9-4 3 N. O in O' 3 ® CM X •=H CM 9-4 CD 3 O' 3 to TO ® CM X 9-4 in o' in O' ro X N* O' o 9-4 CM CM CM

in in m x P. N- OO CM ro ro eo 3 3 in IT' X X P- P. r^ p» eo ® to X O' O' X X X 9-4 9-4 9“4 9-4 9H 9-4 9-4 9-4 o 9-4 9-4 9=4 9-4 4 9-4 9-4 9—4 9-4 9-4 9-4 ^4 9~4 9-4 9-4 9-4 9-4 9-4 9-4 9-4 9-4 9—4 9-4

CD O CD CD CD O O CD O CD CD CD CD CD CD CD CD CD CD O CD O CD CD CD CD CD CD O rD CD O

X X CM X N- X ro 3 9-4 X ro 3 CD ro IO p. CO ao 9-4 CM 9-4 X X ® CM X CM CM ao X at X ro

>- 3 o 3 N. to p- o a CM CM 9-4 X p- X X to 9-4 9-4 X X X X -t o *r4 CD X o X X X 9-4 CD X X ro P» 9-4 X p- o X X ro eo TO p. CM K CM X O X 9-4 X O 3 X ® CD CM CM 3 X ro X X in X X p. r^ p- 9-4 CM ro ro 3 3 X X X X N. p. ao P- ® co ® ® X X X X X a

9-4 9-4 4 9-4 9-4 9-4 9-4 9-4 CD 9-4 9-4 9-4 9-4 9-4 9—4 9-4 9-4 9—4 9-4 9-4 9-4 9-4 4 9—4 9-4 9-4 9-4 9-4 4 9-4 9—4 9-4 CM

CD O CD CD CD O CD CD CD CD O CD O CD CD CD CD CD CD O CD CD O CD CD O CD CD CD CD CD rrj a

PJ X IT. 9*4 O CM in p. X X X 9-4 X CM X ro 9-4 ro X 9-4 CM 9-4 CM X ro CM ® GO X CM ro X

ro X X O r^ CD CM X ® X X o CM CD X ® CM X CD p- X ® CM X O ro X X X CM

CM CM ro 3 X N> X CM ro X in X X X X X X X X X nj -r (M ro O X CM 9-4 CD CD ® X X 3 ro CM CM K. 3 CM 9-4 CD X <o N- X X ro ro CM ro (M 9-4 9-4 9-4 CD o a O a O

o a O O CD o o CD CM 9-4 9-4 9-4 9-4 o o O CD CD o CD o CD o CD CD CD CD a CD o CD CD o

o o CD a CD o o CD o o O o a o o CD CD CD CD O CD CD CD O CD CD CD CD O o CD CD CD

ro 9-4 X P0 ro 9-4 ro at CM 9-4 K- ® ro CM 4 p» X X X CD X 9-4 X ef CM ro X ro CD GO z o CD O 9-4 CM 3- p- J- 9-4 ro X j- 9-4 CM j- X j- ro ro ro p» o ro 9-4 9*4 9-4 CM CM CM ro X NCL CD

l CD CD CD CD CD CD 9-4 9-4 9-4 CD CD O CD CD CD a CD CD o o

1 o

• CD C)I a

1 CD

1 CD

8 CD

8 CD

J o

• CD1 CD

1 CD1

9-4 CJ a a CD CD a CD CM 9-4 9-4 9—4 9-4 9-4 9-4 CD CD CD O O CD CD o <o GO CD CD CO CO CD CO CD CD o 'ID CD CD CD CD CD CD CD CD O O CD O CD CD CO o CD CD CD CD CD o CD O CD CD CD o CD o O O

a CD o O o CD o O O CD o CD CD CD CD CD CD CD CD CD CD CD o CD CD o Q Q CD O CD CO CD < i 4* 4- <» •f 4- 4- 4- i t 1 • i i i 4- 4- 4 4- 4- •+• 4- 4* 4 V 4- 4- 4- 4- 4 4 4* o X 9-4 ro r^ J- X X ro N- CM ro CM X 3 X 3 9-4 CM N» X X ® X rO X X X N* X) X 3

PJ MJ -3 CM o ® ® ro 3- 9-4 CM X 3 X X X CM ro ro ro CO X ro X CO 3 X X tn ® 3 CM CD X 9—4 CD CM P- ® r- 9-4 CM o 9-4 9-4 X X 9-4 X X ro CD X CM X CM X o 3 O 9-4 ro X 9-4

9-4 D CM df X GO 9-4 X ® p~ X X -J in X CD 94 ro X GO GO J* a 3 ® 9-4 X X ro X CD ro X

X 9-4 9-4 9-4 9-4 9-4 CM CM X ro 3 in X p. CO 9-4 9-4 9-4 9-4 9-4 CM CM CM CM CM ro ro ro •J* 3 X X X

X 9-4 O CD O O CD O o CM H 9-4 9-4 9-4 94 9-4 CD CD CD a a CD O a CD CD CD a o o CD CD CO o

N. CO O a CD O r D CD o o CO O O CD O CD CD CD CD o o CD o CD CD O CD o o o ro a CD CD X CD o o o a CD CD CD CD ' ) CD O O CD CD CD CD CD CD CD CD o CD rC) o CD o o CD CD CD CD CD o i 4- 4- + 4- 4- 4- 4- i 1 i i i i i 4 4- 4- + 4- 4- + 4* 4* 4- 4- 4> 4- 4- 4- 4- 4- 4- s: CM 3 9-4 X 9-4 N. CD X ro N- CD N. x> X 9-4 9-4 ro ao CM X X CO X ro CM cO ro ro ro X ro X CM X 3 3 X 3 CD o X ro ® 9-4 3 9=4 ^4 rs* CD o X 9-4 ® X 9-4 3 o O 3 X CD N- X

X X 9-4 CD CM ® CD 9-4 X r^ ro 3 CM ro CM X in 3 9-4 ® 9-4 X 9-4 X CD 3 X CD (M CM X

CD CD CM 3 X ® CM X ® p- X X 3 X X CD 94 ro X GO CD 3 CD 3 CO 9—4 in X CM CD ro ®

X 9-4 9-4 9-4 9*4 9-4 CM CM X ro 3 X X N. GO 9-4 9-4 9-4 9-4 9-4 (M CM CM CM CM ro ro ro 3 3 X X X

y CD CD CD O O CD O CD Q> N- ro 9-4 ® m CM X X CM CD ao X 3 a CD CD O CD CD CD CD CD o O

•t O CD o a C3 O o CD GO O o CM ro X 3 a ® ro X ro rw X o X ® X X X in in in

4— O C7D CD CD CD CD CD CD X CM X X r\j X o ® nj N» O X in CM CM —4 9-4 X 9—4 X 9-4 9—4 X 9-4

CD in CD X 'D in O 3 X cr ao ro GO ro ao ro ao ro ao ro GO *o GD ro m CO rD CM ro 3 3 X

in X X K. r^ GO cO X ® CM ro ro 3 3 in X D X N. ® GO o aO X X O’' CO ID o D D O

CM CM CM CM CM CM CM CM 9-4 CM CM (M CM CM CM CM CM CM CM (M CM CM CM CM CM CM CM ro ro ro ro ro ro

a 9-4 9—4 9-4 9-4 9-4 9-4 9=4 9-4 X X X X X X X X X X X X X X 9-4 9-4 9-4 9=4 9-4 9-4 9f=4 9—4 9^ 9-4 9-4

OGILVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. 480 101
APPENDIX F. (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-5PAGE 24

The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

name p Goodwin

DATE Spot. 18 1 973

Table 17. Calculated oxygen vapor densitie s

.

T, K R, MOL/L DR/DT D2R/DT2

54.351 3.3612-004 9.6727-005 2.4354-005

56.000 5.3288-004 1.4452-004 3.4007-005

53.000 8.9941-004 2.2709-004 4.9253-005

6 J. 000 1.4644-003 3.4449-004 6.8929-005

62.000 2.3068-003 5.0609-004 9.3527-005

64.000 3.5251-003 7.2213-004 1.2342-004

66.000 5.2388-003 1. 0035-003 1. $884-004

63.000 7.5899-003 1.3613-003 1.9990-004

7 0 . 0 0 0 1 . 0742-002 1.8068-003 2.4655-004

72.000 1 . 4883-002 2.3511-003 2.9868-004

74.000 2.0220-002 3.0050-003 3.5605-004

76.000 2.6983-002 3. 7786-003 4.1840-004

73.000 3.5421-002 4.6817-003 4.8543-004

30.000 4.5802-00

2

5. 7233-003 5 • 5684-0 0 4 32.000 5.8412-002 6.9118-003 6.3239-CC4

84.000 7. 3552-002 8.2554-003 7.1185-004

86.000 9.1542-002 9.7617-003 7.9510-004

88.000 1. 1271-001 1.1438-002 8.8208-004

90.000 1.3741-001 1.3293-002 9.7286-0C4

92.000 1.6601-001 1. 5332-002 1.0676-003

94.000 1 . 9887-00 1 1.7566-002 1.1666-003

96.000 2. 3641-001 2. GO 02- 0 02 1.2703-003

93.000 2. 7902-00

1

2.2651-0G2 1.3793-C03

100.000 3.2716-001 2. 5523-002 1.4944-003

102.000 3.8127-001 2. 6633-002 1.6164-003

104.000 4.4186-001 3.1994-002 1.7466-003

106.000 5. C943-001 3.5626-002 1.8865-003

1 0 3

.

0 0 0 5.8455-001 3.9548-002 2.0377-003

110.000 6.6783-001 4. 3785-002 2.2023-003

112.000 7.5992-001 4.8368-002 2.3830-003

114.000 8.6155-001 5.3330-002 2.5829-003

116. 000 9. 7353-001 5. 8715-002 2.8059-003

113.000 1.0967+000 6.4572-002 3.0569-003

12 J. 000 1 . 2322+000 7 . Q9b5- 0 02 3.3422-CG3

122. 000 1.3810+000 7. 7969-002 3.6695-003

124.000 1 . 5445+000 8.5678-002 4.0493-003

12o. 000 1. 7243+000 9.4210-002 4.4951-003

128.000 1.9220+000 1. 0371- 0 01 5.0254-CC3

13. .000 2. 1399+000 1.1438-001 5. 6657-C 0 3 132.000 2.3605+000 1. 2647-001 6.4520-003

134.000 2.6470+000 1.4032-001 7.4368-003

1 3 6 • J 3 Q 2.9433+000 1. 5641-001 8.6997-C03

1 3 5 . 0 00 3.2745+000 1.7539-CGi 1.0366-002

140.000 3 . 64 7 4 + 000 1.9828-001 1.2644-002

142.000 4. 3712+000 2.2661-001 1.5903-002

1 44. J 00 4.5592+000 2.6300-001 2.0854-002

1 4 b . 0 0 0 5. 1316+GOO 3.1214-001 2.9031-002

143.000 5.8225+000 3. 8373-001 4.4334-C 02

15 0. 000 6.6967+300 5.G204-C 01 7.9575-002

152. OUO 7 .9138+300 7. 542G-001 2.0346-001

154.000 1. 023C+001 2. 0622+000 2.4109+000

154.576 1 . 3bJG+001 0. 0000 + 000 0 . 00 0 0 + 0 0 0

OG1LVIE PRESS, INC., BROOKLYN 17. N. Y. STOCK NO. 490 102
APPENDIX F. (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY PROJECT NO. FILE NO. PAGE LABORATORY NOTE 7750364 73-5 75

subject Tkg Orthobaric Densities of Ethane, Methane, Oxygen and

NAME R.D Goodwin

Fluorine DATE ...13. 19,71

Table 18. Calculated fluorine vapor densities.

T,K R» MOL/L DR/DT D2R/DT2

53.481 5.6700-004 1.6771-004 4.2852-005

54.000 6.6001-004 1.9119-004 4.7718-005

56.000 1.1518-003 3.0817-004 7.0323-005

58.000 1. 9272-003 4.7699-004 9.9683-005

60.000 3.1038-003 7.1188-004 1.3650-004

62.000 4. 8291-003 1. 0283-003 1.8127-004

64.000 7.2821-003 1.4424-003 2.3426-004

66.000 1 . 0675-002 1.9709-003 2.9554-004

68.000 1.5253-002 2.6301-003 3.6499-004

70.000 2. 1293-002 3.4361-003 4. 4236-004

72.000 2.9105-002 4.4046-003 5 .2731-004

74.000 3.9029-002 5.5501-003 6.1945-004

7o. 000 5.1434-002 6.6869-003 7. 1844-0 04

78.000 6.6713-002 8.4282-003 8.2395-004

80.000 8.5291-002 1.0187-002 9. 3580-004

82.000 1.0761-001 1.2176-002 1.0539-003

64.000 1.3416-001 1. 4407-002 1.1783-003

3 6. J 0 0 1 . 6541-001 1.6893-002 . 1.3094-003

68.000 2.0191-001 1.9649-002 1.4475-003

90.000 2.4420-001 2.2689-002 1.5935-003

92.000 2.9286-001 2. 6029-002 1.7482-003

94.000 3.4852-001 2.9688-002 1.9129-003

96.000 4.1184-001 3.3688-002 2.0693-003

99.000 4. 8352-001 3. 8054-002 2.2793-003

1 0 0 . 0 00 5.6432-001 4.2816-002 2.4854-003

102.000 6.55G7-001 4.8009-002 2.7105-003

104.000 7. 5667-001 5.3674-002 2.9585-C03

106.000 8 . 7012-001 5.9861-002 3.2339-003

108.000 9.9651-001 6.6631-002 3.5426-003

il 3. J00 1. 1371+000 7. 4058-G02 3.8918-003

112.000 1.2932+00

0

3.2232-032 4.2910-003

114.000 1.4666+000 9.1264-002 4.7523-003

116.000 1.6590+000 1.0129-001 5.2919-003

113. UG0 1.8725+000 1.1250-031 5.9315-003

120.000 2. 1099 + 000 1.2511-001 6.7C13-003

122. 000 2 . 3741+000 1.3942-001 7.6437-003

124.000 2.6690+000 1. 5584-001 8.8210-003

1 2 6 • 0 0 0 2 . 9992+000 1.7492-001 1.0328-002

126.000 3.37C9+0C0 1.9746-GC1 1. 2313-0 02

130.000 3 . 7921+000 2.2465-001 1.5026-002

132.000 4.2739+000 2.5834-001 1.8913-002

134.000 4. 8319+000 3.0165-001 2.4841-002

136.000 5 . 49C5+000 3.6028-001 3.4720-CC2

139.000 6.2909+000 4.4628-001 5.3532-002

140.000 7.3133+000 5.9079-001 9.6476-002

1 <+ 2 . J 0 0 8.7644+000 9.1469-001 2.72 51-001

144. 000 1.1893+001 3. 5620+00

0

7.7289+000

144. 310 1 . 5150+001 0.0000+000 0.0000+000

OG1LVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. 450 103
APPENDIX F. (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. 2750364FILE NO. -73-5

PAGE 26

SUBJECT The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME R . D . Goodwin

DATE ciopf 18 1Q78

Table 19. Calculated methane vapor densitie s

.

T,K Rf MOL/L DR/DT D2R/DT2

90.680 1.5679-002 1.8523-003 1.7385-004

92.000 1.8280-002 2.0919-003 1.8937-004

94.000 2.2858-002 2.4952-003 2.1409-004

96.000 2.8294-002 2.9492-003 2.4020-004

98.000 3.4691-002 3.4569-003 2.6763-004

100.000 4.2159-002 4.0206-003 2.9634-004

102. 00C 5.0813-002 4.6430-003 3.2628-004

104.000 6. 0772-002 5. 3265-003 3.5744-004

106.000 7.2161-002 6.0736-003 3.8980-004

106.000 8.5110-002 6.8866-003 4.2339-004

11 0.000 9.9753-002 7. 7680-003 4.5823-004

112.000 1.1623-001 B. 7204-003 4.9439-004

114.003 1.3468-001 9. 7465-003 5.3195-004

116.000 1.5527-001 1.0849-002 5.7100-004

113.000 1.7813-001 1.2032-002 6.1170-004

120.000 2.0345-001 1.3297-002 6. 54 20-004

122.300 2.3138-001 1.4650-002 6.9870-004

124.000 2 . 6211-001 1.6093-002 7.4545-004

126.000 2.9582-001 1.7633-002 7.9471-004

128.000 3.3271-001 1. 9274-002 8.4681-004

130.300 3.7299-001 2. 1023-002 9.C214-0C4

132.000 4. 1687-001 2.2885-002 9.6113-004

134.000 4.6461-001 2.4870-002 1.0243-003

136.000 5.1644-001 2.6986-002 1.0922-003

138.000 5.7264-001 2.9242-CG2 1. 1657-00 3 14 0. 000 6.3351-001 3.1652-002 1.2454-003

142.000 6.9937-001 3.4229-002 1.3325-003

144.000 7. 7055-001 3.6988-002 1.4280-003

146.000 8.4745-001 3.9948-C02 1.5335-C03

148.000 9.3049-001 4. 3130-002 1.6506-003

150.000 1.0201+000 4.6559-002 1.7815-003

152.000 1 .1169+000 5. 0267-002 1.9288-003

154.000 1 . 2214+000 5.4288-002 2.0957-003

156. 300 1. 3343+000 5. 8665-002 2.2865-003

156.000 1.4563+000 6. 3453-002 2.5065-003

160.000 1 . 5884+000 6.8715-002 2.7627-003

162. J00 1 . 7316+000 7.4534-002 3.0643-003

164.000 1 .8870+000 8.1011-002 3.4240-003

166.000 2.0561+000 8.8280-002 3 . 85 92-0 G 3 168.000 2.2408+000 9.6514-002 4.3945-003

170.000 2. 4430+000 1. 0595-0C1 5.0661-003

172.000 2.6656+000 1.1691-001 5.9289-003

174.000 2.9119+000 1.2985-001 7.0695-003

176.000 3.1867+000 1.4546-001 8.6322-003

178.000 3.4963+000 1.6482-0C1 1.0873-002

180.000 3.6497+000 1.8973-001 1.4288-002

182.000 4.2610+000 2.2344-001 1.9949-002

164.000 4.7537+000 2. 7274-001 3.0592-002

186.000 5. 3730+000 3.5464-001 5.5251-002

168.000 6.2307+000 5. 3071-001 1.4281-001

190 . 000 7 . 8668+000 1.4868+000 1.7833+000

190.555 1. 020C+001 G . 000 0 + 000 0.0000+000

OQILVIE PRESS. INC., BROOKLYN 17. N. Y. STOCK NO. 4SO 104
APPENDIX F. (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-5PAGE 27

subject Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

name p Goodwin

DATE SeDt. 18. 1 073

Table 20. Calculated ethane vapor densities.

ETHANE SATURATED VAPOR DENSITIES

T,K R, MOL/L DR/DT D2R/DT2

89.699 1. 3511-006 3.4416-007 7.9422-006

90.000 1 .3863-006 3.5229-007 8.1081-008

95.000 4.5944-006 1. G378-0C6 2.1037-C07

i o o . o o o 1.3356-005 2.6924-006 4.8256-0 0 7 105.000 3.4683-005 6.2648-006 9.9665-007

110.000 8.1696-005 1.3276-005 1.8818-006

115. J00 1. 7684-304 2. 5955-005 3.2903-006

120.000 3.5568-004 4.7323-005 5.3851-006

125.000 6.7091-004 8. 1216-005 8.3256-006

1 3 . 0 0 0 1 .1963-003 1. 3223-004 1.2254-005

135.000 2. C304-003 2.0559-004 1.7283-005

1 4 0.0 00 3.2990-003 3.0703-004 2.3493-005

145.000 5. 1575-003 4.4257-004 3.0926-005

150.000 7. 7918-003 6.1835-004 3.9592-005

155.000 1. 1418-002 8. 405 1-004 4.9474-005

160.000 1.6284-002 1.1151-003 6.0539-005

165.000 2.2666-002 1.4478-003 7.2744-005

i 7 0 . 0 0 0 3.0869-002 1.8443-003 8. 60 50-005

175. OGu 4. 1225-002 2. 3101-C03 1.0C43-CC4

1 8 0. 0 00 5.4094-002 2.8504-003 1.1588-004

135.000 6. 9862-002 3.4707-003 1. 3243-004

19 J .000 8.8944-002 4.1767-003 1.5C14-C04

195. 000 1 . 1178-00 1 4.9742-003 1.6912-004

2 u 0.000 1 . 3885-001 5.8703-003 1 . 8956-004

205.000 1. 7066-301 6. 8727-003 2.1170-004

210.000 2. 0777-301 7.9907-003 2.3587-C04

215. 0C0 2. 5u78-JQi 9. 2355-Cu3 2.6252-004

22 0. 0 00 3. 0036-001 1. 0621-0G2 2.9224-004

225.000 3.5725-001 1.2164-002 3.2581-004

230.000 4. 223 C -3 01 1.3887-002 3.6425-004

235.000 4.9647-001 1. 5817-002 4.0894-C04

240.000 5. 8386-001 1.7990-002 4.6176-004

245.000 6. 7685-001 2.0453-002 5.2532-004

250 . 000 7.6599-001 2.3267-002 6.0 3 30 -0 0 4 255.000 9. Iu25-J0l 2 . 6519-C 02 7.0116-004

260.000 1.0521+000 3.0325-002 8.2712-C04

265.000 1.2147+000 3.4858-002 9.9430-004

270.000 1 « 4G23 + 30G 4. 1373-CC2 1.2246-003

275.000 1 . 6207+000 4. 7273-002 1.5572-003

280.000 1.6784+000 5. 6239-002 2.0691-003

285.000 2. 1686+300 6.8532-002 2.9298-003

290.000 2. 5736+000 8. 68 20-002 4.58 76-CG3

295.000 3 . C777 + 30 0 1.1613-001 8.6241-003

3 0 U . 0 00 3.8180+000 1.9083-001 2.5135-002

305.300 5.6689+000 1. 2377+000 2.4827+GCC

305.330 6. 870G+000 0. 0000+000 0 . 0000+000

OGILVIE PRESS. !MC.. BROOKLYN 17. N. Y. STOCK NO. 4SO 105
APPENDIX F . (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. 2750364FILE NO. 73-5

PAGE 28

subject Orthobaric Densities of Ethane, Methane. Oxygen and

NAME R.D . Goodwin

Fluorine DATE Sent. 18. 1973

10/10/73

PROGRAM LICKFIT

C REPRESENT ETHANE SATURATED LIQUID DENSITIES.

C DEFINE X = ( TC-T ) /TC-TT) , Q = X»*l/3, XE = X**E, AND -

C DEFINE YY = < 0 - DC ) / ( D T-0 C ) , WHEN THE EQN. IS -

C (YY-X)/ (XE-X) = A1 A2*Q2 + A3*Q3 . . . C DCRT = 6.86, 6.87 POSSIBLY VIA MY VAPORDEN EQN.

C DTRP = 21.68 ESTIM. VIA REIO C. MILLER.

C ID, (9) TESTER, (lO)DOUSLIN, ( 1 1 ) SLIWINSKI , (12) CANFIELD ET AL.,

C 10, (13) KLOSEK, ( 14) MI LLER, (15) EUBANK ,

( 16) TOMLI NSON

COMMON E,AZ, TTRP,TCRT , DTRP, DCRT, DRDT, D2RDT2 , A(6)

C0MM0N/999/NP,NF ,H(15 ),Y(200),G(200,15)

DIMENSION I D C 9 9 ) ,T (99) ,0EN(99) , U ( 99 ) , W ( 99 ) , XQ ( 99

)

1 F ORM AT (15, 2F10.0)

2 FORMAT (1H1 13X 1HE 8X2HAZ 6X4HDCRT 8X2HSS)

3 F ORMAT ( 5X 4F10.3)

4 FORMAT (1H1 1ZX ETHANE SATURATED LIQUID DENSITIES, E =* F6.3//

1 20 X 6HTCRT -F8.3, 8H , TTRP =F8.4//

2 20 X 6HDCRT =F6.3, 8H, DTRP =F8.4// 2(13X 3E15.7/) /

3 8X2HID 7 X 3 H T , K 5X5HM0L/L 6X4HCALC 4X4HPCNT

4 1 4 X 1 H X 8 X 2HY X 8X2HYC 6X4HYDIF ) 5 F OR TAT ( 5X 15, 3F10.3, F8.2, F15.5, 3F10.5)

6 F ORMAT ( 1H1 16X ETHANE SATURATED LIQUID DENSITIES* //

1 17X 3 H T , K 3X7HR,MOL/L 5X5HDR/0T 3X 7HD2R/DT 2 ) 7 FORMAT ( 1 0 X 2F1C.3, FIG. 4, F10.5)

9 F ORMAT ( 1 8X 4HNP =13, 10H, RMSPCT =F7.3/)

C

C DO ALL FOUR, OXYGEN, FLUORINE, MFTHANE, AND ETHANE.

1C DO T9 I G= 1 , 4 $ GOTO (11,13, 15,17) , IG

C CONSTANTS FOR OXYGEN.

11 TTRP=54.3507 t TCRT=154.576 S TZ=52 « DT=2 I NZ=52

12 D TRP = 4 0.63 $ OCR T = 13 . 63 S DZ=13.58 t EZ = 0.340 $ GOTO 19

C CONSTANTS FOR FLUORINE

.

13 T T R 3 = 5 3.481 1 J TCRT = 144.31 S TZ = 50 $ DT=2 t NZ = 48

14 D T RP = 44 .862 3 { DCRT = 15.15 $ DZ = 15.10 J EZ = 0.342 S GOTO 19

C CONSTANTS FOR METHANF.

15 TTRP=90.680 * TCRT=19C.555 * TZ=88 i OT=2 ? NZ=52

16 DTRP =2 3.147 S DCRT=10.20 S DZ=10.05 t EZ=0.350 S GOTO 19

C CONSTANTS FOR ETHANE.

17 TTRP =89. 899 S TCRT=305.33 S TZ=8C t DT=5 t NZ=46

lb D TRP = 2 1.68 $ OCR T= 6.87 $ DZ= 6.82 S EZ = 0.349

19 XN = TCRT-TTKP t YN = DTRP- OCR T C RtAU NP DATA FOR LEAST SQUARES.

C READ L. A. WEBER S OXYGEN VOLUMES, CC/MOL.

20 OO 27 J = 1 , 9 9 t READ 1, I D ( J ) , T ( J ) , DEN ( J ) t IF(IO(J>> 21,28

21 XF(ID(J>— 15) 23,22

22 CONTINUE

23 I F ( I 0 ( J

) -99) 25,24

24 DEN(J) = 10Gv'/DEN(J)

25 U(J> = X = ( TCRT-T ( J) ) /XN $ Q = CU3ERTF ( X ) I DO 26 K=2,6

26 G ( J,K) = Q* * K $ G (J ,1) = 1 27 W(J) = (DEN (J) -DCRT) /YN

28 NPP = NP = J-l i NF = 3 $ E = 0.36

C EXPLORE E, AZ, AND DCRT.

29 AZ = NF % SSK = 1.CE+01C

30 DO *9 I E= 1 , 21 i E = EZ 0.001*IE

OGILVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. 480 106
APPENDIX F. (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-5

PAGE 29

SUBJECT . _ , w , „ , The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME _ R .D .Goodwin

DATE Sent. 18. 1973

LICKFIT 1C/10/73

C SET UP THE LEAST SQUARES ARRAYS.

36 00 40 J = 1 , N P $ X = U(J) $ XQ ( J ) = XE = X**E

37 Y < J ) = (W ( J

) -X) / (XE-X

)

40 CONTINUE $ CALL EGENFT J SS=0 $ DO 43 J=1,NP $ YC = 0 l 00 41 K=1,NF

41 YC - YC 4 H(K)*G(J,K) $ X = U(J) $ XE = XQ(J)

42 UC = DCRT 4 (X 4 (XE-X)*YC)*YN

43 SS = SS 4 ( DEN ( J ) /DC - 1

) * *2 $ SS = IOC *SQRTF (SS/NP)

44 IF (SS.LT.SSK) 45,46

45 S 3K = SS i EK = E i AZK = AZ S DK = DCRT

46 DO h 7 K = 1 ,

6

47 A (K) = H (K)

46 CONTINUE

49 CONTINUE

50 E=E< % AZ = A ZK i OCRT= DK J YN = DTRP - OCRT

C USE SAVED CONSTANTS FOR DEVIATIONS.

60 PRINT 4, E, TCRT , TTRP, DCRT, DTRP, <A(K> ,K=1,6> $ SS = 0 61 00 7 U J=1,NPP J X = U(J) t XE = X**E t XEX = XE-X

62 YC = 0 $ 00 63 K=1,NF

63 YC = YC 4 A ( K

) *G (J,K)

64 YS = X 4 XEX*YC l DC = DCRT 4 YN*YS

65 YX = (W ( J

) -X) /XEX $ YD = YX-YC

66 PCT = ICO* (OEN ( J) /OC-1) J SS = SS 4 PCT**2

67 PRINT 5, ID (J) , T ( J) ,DEN< J) , DC, PCT, X,YX,YC,YD

68 IF(J-NP) 70, b9

69 SC = S QR T F (SS/NP) J PRINT 9, NP, SS

70 CONTINUE

C PRINT UNIFORM TABLE FOR PUBLICATION.

71 PRINT 6 * DO 8J J=1,NZ $ IF(J-l) 73,72

72 TT = TTRP $ GO TO 76

73 IF(J-NZ) 75,74

74 TT = TCRT f GO TO 76

75 TT = TZ 4 Q T* J 76 R = DENLIQF (TT)

60 PRINT 7, TT , R , D R D T ,D2RDT2

99 CONTINUE

C 00 OTHER ETHANE DATA WITH EXISTING COEFFICIENTS.

100 PRINT 4, E, TCRT, TTRP, DCRT, DTRP, CA(K) ,K = 1, 6) J SS = 0 101 00 110 J = 1 , 99 $ READ 1, I DD , TT , DN $ IF(IDD) 1 3 2,99 3 102 X= (TCRT-TT) /XN $ Q = CUBERTF ( X) * XE=X**E J XEX = XF-X

103 YC = A ( 1) S DO 104 K=2 ,NF

104 YC = YC 4 A ( K ) * Q

* * K

1 J 5 DC = DCRT 4 YN* ( X4XE X*YC) J P CT = 1 0

C ( DN / DC - 1

)

106 YY - (DN-DCRT) /YN S YX = (YY-X)ZXEX $ YD = YX-YC

110 PRINT 5, I DO , T T , DN , DC, PCT, X,YX,YC,YD

999 STOP I END

OOILVIE PRESS. INC., BROOKLYN 17. N. Y. STOCK NO. 480 107
APPENDIX F. (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTEPROJECT NO. 2750364FILE NO. 73-5

PAGE 30

suBJtd Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME K .D .Goodwin

DATE Sent. 18. 1973

10 / 10/73

PROGRAM VAPORFIT

C REPRESENT ETHANE SATURATED VAPOR DENSITIES.

C THIS FORM IS CONSTRAINED AT THE TRIPLE POINT, ANO

C DEFINE X ( T ) AS FOR THE VAPOR PRESSURE EQUATION -

C Z = ( 1- X ) = (TC/T-1) / ( TC/TT-1) , ZE = Z’*E, Q = Z”l/3, AND -

C DEFINE YY = L N ( DC/D) /L N ( DC/ D T) , AND THE DEPENDENT VARIABLE - C Y (Z,YY) = (YY-Z) / (ZE-Z) , WHEN THE L.S. EQN. IS -

C Y ( Z » Y Y ) = A1 + A 2 ’Q2 + A3*Q3 + A4’Q4 + . . . C ID., (1) VIRIAL/V.P. , ( 6 ) PORTER , (lO)OOUSLIN, (11 ) SL IWINSKI

.

COMMON E , A L , TTRP, TCRT , DTRP , DCRT , DRDT,D2RDT2, A ( 9

)

C0MM0N/999/NP,NF , H ( 1 5 ) ,Y(23C),G(2C0,15>

DIMENSION ID(99) *T (99) ,DEN(99) , U(99),W<99), ZQ(99)

1 FORMAT ( 15 , F10.C, E15.5)

2 FORMAT ( 1 HI 10X 1 HE 8X2HAL 6X4HDCRT 8X2HSS)

3 FORMAT ( 1C X 4F10.3)

4 F ORMAT { 1 HI 17X * E T H A N E SATURATED VAPOR DENSITIES, E =* F6.3//

1 2 0 X 6HTCRT =F8.3, 8H , TTRP =F8.4/

2 2 u X 6HDCRT =F8.3, 6H, DTRP =E12.5// 2(13X 4E15.7/) /

2 3 X 2 HI D 7X 3HT , K 8X5HMOL/L 8X5HCALCD 4X4HPCNT

3 12X 1HZ 8X2HYX 3X2HYC 6X4HY0IF ) 5 FORMAT ( 5X 15, F1U.3, 2E13.4, Fd.2, F13.5, 3F10.5)

6 F ORMAT (15, 2F1C.0)

7 FORMAT (1H1 1 6X ’ETHANE SATURATED VAPOR DENSITIES’ //

1 1 7 X 3 H T , K 6X7HR,M0L/L 8X5HDR/DT 6X7HD2R/DT 2 ) 8 F ORMAT ( 1 G X F10.3, 3E13.4)

9 FORMAT (18X 4HNP =13, 10H, RMSPCT =F7.3/)

61 FORMAT (1H1 7X2HIO 7X3HT,K 8X5HMOL/L 8X5HCALCD 4X4HPCNT

1 1 2 X 1HZ 8X2HYX 8X2HYC 6X4HYDIF ) CC DO ALL FOUR, OXYGEN, FLUORINE, METHANE, ETHANE.

10 DO 31 I G = 1 , 4 $ GOTO (11,13,15,17) ,IG

C CONSTANTS FOR OXYGEN.

11 T TRP=54. 35C 7 $ TCRT=154.576 t TZ=52 $ CT=2 S NZ=52

12 DTRP=3. 36122E-4 « OCRT=13.63 ? DZ=13.58 * EZ=0.360 * GOTO 19

C CONSTANTS FOR FLUORINE.

13 TfRP=53.4811 £ TCRT=144.31 £ TZ=50 £ DT=2 £ NZ=48

14 DTRP=5.670E-4 I DCRT=15.15 « DZ=15.1G * EZ=0.340 t GOTO 19

c Constants for methane.

15 T T RP = 9 J . 6 8 0 $ TCRT = 190.555 £ TZ = 88 S DT=2 £ NZ = 52

16 DTRP=0. 01567865 l OCRT=1C.20 J DZ=1C.05 J EZ=0.360 ? GOTO 19

C CONSTANTS FOR ETHANE.

C OMIT 24, AND FIX DTkF.

17 T T RP = 8 9. 899 % TCRT = 30 5.3 3 S TZ = 8C l 0T=5 t NZ = 46

16 OTRP= 1.35114E-6 $ DCRT=6.P7 S DZ=6.84 S EZ=0.34J

19 ZN = TCRT/TTkP-1 £ YN = L OG F ( DCRT / 0 TRP

)

C READ OUR I D ( 1 ) DATA MIXED WITH DOUSLIN.

C INCREASE OUR DEN BY 0.15 PCT TO AGREE WITH COUSLIN.

20 DO 27 J = 1 , 2 0 0 £ IF(IG-4) 22,21

21 READ 1, ID ( J) , T ( J) ,DEN (J) $ I F < I D ( J ) ) 23,28

22 READ 6, I D ( J ) , T ( J ) , DE N ( J ) $ I F < I D ( J ) ) 25,28

23 IFlIO(J)-l) 25,24

24 CONTINUE

25 U(J> = Z = (TCRT/T ( J) -1) /ZN T Q = CUQERTF ( Z) f DO 26 K =2,7

26 G ( J , K) = Q”K $ G (J,l) = 1 27 W(J) = LOGF (DCRT/DEN ( J) ) /YN

OOILVIE PRESS. INC., BROOKLYN 17. N. Y. STOCK NO. 490 108
APPENDIX F. (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. FILE NO. 73_5

PAGE

T. 1 subject The Orthobaric Densities of Ethane, Methane, Oxygen and

Fluorine

NAME R .D .Goodwin

DATE Sept 18 1Q77

VA PORFIT 10/10/73

26 NP = J-l 2 AL = NF = 5 $ E = 0.360

C EXPLORE OCR T , AND EXPONENT E.

33 SSK = 1.GE+01C

34 DO 48 I E= 1 , 2 1 2 E = EZ + 0.002*IE

C SET UP THE ARRAYS FOR LEAST SQUARES.

36 DO 39 J=1,NP $ Z = U(J) $ ZQ(J) = ZE = Z**E

37 Y ( U ) = (W(J)-Z)/ (ZE-Z)

39 CONTINUE 2 CALL EGENFT $ SS = 0 C NOW GET THE RMS DEVIATION.

40 DO 44 J=1»NP 2 YC = 0 $ DO 41 K=1,NF

41 YC = YC + H < K > * G (U » K

)

42 Z = U<J) S YS = Z + (ZQ(J)-Z)*YC

43 DC = OCRT*EXPF ( - YN* Y S

)

44 SS = SS + ( DC/ DEN ( J ) - 1

) **2 2 SS = 100 *SQRTF (SS/NP)

45 IF (SS.LT.SSK) 46,46

46 S SK = SS 2 EK = E 2 ALK-AL 2 DK = DCRT 2 DO 47 K = l,9

47 A (K) = H ( K

)

46 CONTINUE

49 E = E< 2 AL= ALK 2 DCRT = DK 2 YN = LOGF (DK/DTRP)

C USE SAVED CONSTANTS FOR DEVIATIONS.

50 PRINT 4, E, TCRT , TTRF , DCRT,DTRP, ( A ( K ) ,K=1,8) 2 SS = 0 51 DO 59 U=1,NP 2 Z = U(J) 2 ZE = Z**F 2 ZEZ = ZE - Z 52 YC = 0 2 DO 53 K=1,NF

53 YC = YC A (K) *G (U,K)

54 YS = Z + ZEZ*YC 2 DC = CCRT * EX PF ( - YN* Y S

)

55 YX = (W(J)-Z)/ZEZ 2 YD = YX - YC

56 PCT = 100* (DEN (J)/DC-1) 2 SS = SS + PCT **2

57 IF (IG.EQ.3. AND.J.EQ.46) 58,59

58 PRINT 61

59 PRINT 5, ID ( J) ,T (J) ,DEN( J) , DC, PCT, Z,YX,YC,YO

60 SS = SQRTF ( SS/ NP ) 2 PRINT 9, NP, SS

C PRINT UNIFORM TABLE FOR PUBLICATION.

71 PRINT 7 2 DO 60 J=1,NZ 2 IF(J-l) 73,72

72 TT = TTRP 2 GO TO 76

73 IF(J-NZ) 75,74

74 TT = TCRT 2 GO TO 76

75 TT = TZ * D T*U

76 R = DENGASF (TT)

80 PRINT 9, T T , R, DRDT , D2RDT2

81 CONTINUE 2 PRINT 61

C DO OTHER ETHANE DATA WITH EXISTING COEFFICIENTS.

82 DO 88 J = 1 , 9 9 2 READ 6, I DO, T T , DN 2 IF(IDO) 83,99

83 Z = (TCRT/TT-1) /ZN 2 ZE = Z**E 2 ZEZ = ZE - Z 84 Q = CU3ERTF (Z) 2 YC = A(l) 2 DO 85 K=2,NF

a 5 YC = YC + A ( K

) *Q**K

86 YY = LOGF (OCRT/DN) /YN 2 YX = (YY-Z)/ZEZ 2 YD = YX-YC

87 DC = DCRT*EXPF(-YN*(Z 4-ZEZ*YC) ) 2 PCT = 1C0MON/DC-1)

86 PRINT 5, I D D , T T , DN , DC, PCT, Z,YX,YC,YD

99 STOP 2 ENO

CGILVIE PRESS. INC.. BROOKLYN 17. N. Y. STOCK NO. 450 109
APPENDIX F. (Continued)

NATIONAL BUREAU OF STANDARDS, CRYOGENIC ENGINEERING LABORATORY LABORATORY NOTE

PROJECT NO. 2750364

FILE NO. 73-5

PAGE

- \

*>

bUBJECT i . f , .

1 he Ortnonaric Den ~ 1 ti- *s of Kthane, Methane, Oxygen and

*\1 no One

NAME _ _ _ R . O . Goodwin

DATE Sent. 18.

10/ 10/ 73

FUNCTION DENLIC)F(T)

C ETHANE SATURATED LIQUID DENSITIES, MOL/L.

C y = A1 + A2*Q2 + A3* C 3 + . . . , YN = DTRP-DCRT,

C C-N - DCRT Y N * ( X + ( X E - X

) * Y ) . CUM 'ION E,AZ,TTRP,TCRT ,DTRP,DCRT, DRDT ,D2RDT2 , A ( 6 )

1 FORMAT (1H0 9X * DENL IGF = 0, T EXCEEDS T CRT . * / ) 2 IF(TCRT-T) 3,4,5

3 PRINT 1 t STOP

4 DENlIQF = DCRT $ DRDT = D2RD T2= G S RETURN

5 XN=TCRT-TTRP i YN=DTRF-OCRT S X = ( TCR T- T ) / X N ? DXCT=-1/XN

6 X E = X

* * E S XE1 = E * X E / X $ X E 2 = <E-1)*XE1/X

7 n = CU 3E R T F ( X ) i W1 = W/3/X $ W2 = -2*Wl/3/X

tt Q = XE-X $ Qi = XE1 - 1 $ Q2 = XE2

S N F = A Z f Y = A ( 1 ) f Y1 = Y2 = 0 f D0 11K = 2,NF

1C Y = Y + A ( K ) * W

* * K J Y 1 = Y 1 + K* A ( K

) *

W * * ( K- 1

)

11 Y2 = Y2 K* (K-l ) *A ( K

) *W** ( K-2

)

12 Y 2 = Y1*W2 + Y2*W1**2 S Y1 = Y1*W1

13 OENLIQF = DCRT ( X Q* Y

) * YN

14 OROT = (1 f Q* Y 1 + Q 1 * Y ) * Y N* D X 0 T 15 D2R0T2 = ( Q * Y 2 - 2*C1*Y1 Q2 * Y ) * YN * OXO T* * 2 $ EET'JRN t END

1 0 / 1 J / 7 3

FUNCTION DENGASF(T)

C ETHANE SATURATED i/APGR DENSITIES, MOL/L.

C Y = A1 * A 2 * G2 * A 3 * C 3 . . , NF = AL, YN = L N ( D CR T / 0 T RP ) , C U = Z + (ZE-Z)*Y, DEN = DCRT*EXP(-YN*U)

.

C NOTE THAT Z - C ONLY AT T = TCFT, WHICH IS EXCLUDED.

COMMON t , A L , TTRP,TCRT, DT RP , OCR T , DRDT , D 2 R 0 T 2 , A(9)

1 c OR MAT (1HC hX *DENGASF = 0, T EXCEEDS TCRT. * / )

2 IF(TCRT-T) 3,4,5

3 PRINT 1 $ STOP

4 D E No AS F = DCRT S L^OT = D2RDT2 = C ? RETURN

5 ZN = TCRT/TTRP-1 $ Y N = L OOF ( DC R T/ D TR P ) t Z= < TCR T / T - 1 > / ZN

f n Z DT = -TCRT/ZN/T**2 % D2ZD T 2 = -2*DZDT/T

7

7 r = Z* * E % Z E 1 = E

* ZE/Z S ZE2 = (E- 1 ) * Z E 1 / Z

t X = ZE-Z % XI = ZF 1 - 1 9 X 2 = ZE2

5 1 = CU3ERTF (Z) l Cl = G/3/Z i Q2 = - 2*01 /3/Z

1C NF = AL t Y - A ( 1

)

-< K* II Y 2 = u * DO 13 K=2,NF

1

1

T - Y +• A ( < ) *Q**<

L 2 Y 1 = Y 1 * <*m<K)*Q**(K -1

)

13 i l = Y 2 + K*(K-1)*A(K) Q** (K- 2 ) 14 Y 2 = Y

1 *G2 Y 2 * Ql * * 2 S Y

1

= Y 1 * Q 1

1

c, U = Z y X * Y i UA = 1 + X * Y 1 y x 1 Y t U 1 = U A * D Z D T lb J 2 = UA*D2ZDT2 (X*Y2 r\) X H* * Y 1 + X 2 * Y ) *DZDT**2

1 7 k 2 r E X P F ( - Y N * U ) t CENGASF = F = DCRT*XP * YU = -YN*Ui

IE DOT = Y U * F l D2RDT2 = ( YU* YU- YN* U2 ) * F l RETURN $ Fn

1 G I LV I E PRECIS, INC , BROOKLYN 17. N Y. STOCK NO. 450 110
1

APPENDIX G.

Cryogenics Division — NBS Institute for Basic Standards LABORATORY NOTE

COST CENTER 2750364

FILE NO 73-6

PAGE

SUBJECT Liquid-Vapor Saturation (Orthobaric) Temperatures of

Ethane and Meth£ne_

name

£). Goodwin

DATE Nov. 28, 1973

1. Introduction . The present, new investigation has been necessary to accommodate the

extreme range of ethane saturated vapor densities (a factor of 10

7

). Our previous

work on ethane appears in Lab. Notes 73-2,3,4,5.

Analytical description of the two-phase, liquid-vapor equilibrium (temperature-density relationship) is needed for our new equation of state which originates on this locus (NBS IR 73-342). In particular, the forms used below give the important

property that all derivatives are zero at the critical point.

In the following we split the range, using different functions according

P ^ P c . In each case the dependent variable is

Y(T) = (Tc /T-1)/(TC /Tt -1) (1)

The symbols used here appear in a LIST.

2. The Saturated Vapor Temperatures . The analytical formulation is

Y(T) = U (t

)

. [1 + Ao • In (a /ct

6 ) + W(a )] where

U(a) ~ exp[a . (ug - u)],

and n

W('-r) -

l

At • (q

1 - cp5 ).

i = 1

1/3 1 / 3 The notation is q

o'

, q^ 0g , and Ug 1 / 1 crg - l j .

This equation is constrained at the vapor triple point.

Fixed-point constants are given by table 1, and coefficients by table 2. The comparisons of results for ethane and for methane are in tables 3,5. Deviations

necessarily are systematic because the "data" are smoothed analytically (Lab. Note

73-5). We believe all deviations to be well within the real accuracy of the data.

3. The Saturated Liquid Temperatures.

The analytical formulation is

f.n(Y) = 8 •

( ut - u) + W(o ) (3)

where n

W(cr) o

; Bt

• (x1 - x|). (3 -a)

iYl

( 2 )

( 2-a)

( 2-b)

SP 11342 A 111 U S. Government Printing Office. 1973- a 780-339
APPENDIX G. (Continued)

Cryogenics Division-NBS Institute for Basic Standards LABORATORY NOTE

COST CENTER 2750364

FILE NO 73-6

PAGE 2

SUBJECT Liquid-Vapor Saturation (Orthobaric) Temperatures of

Ethane and Methane

namEr.d. Goodwin

DATE Nov. 28, 1973

The notation is xt = | (J t - 1 1 , = 1 /xt .

This equation is constrained at the liquid triple point.

The comparisons of results for ethane and for methane are in tables 4,6,

Computer programs are attached.

LIST OF SYMBOLS

d,

d c ,

d* ,

dt .

q>

D,

CT,

,

T,

Tc , Tt ,

x,

density, mol/t, DEN

critical-point density, DCRT

vapor triple-point density, DGAT

liquid triple-point density, DTRP

1/3

qg =_ _ 1/3

s d/dt , density reduced at liquid triple point

d / cl, , density reduced at the critical point

d ? /d c , reduced triple-point vapor density

dt /dc , reduced triple-point liquid density

Ta (p), the saturation temperature

critical-point temperature, TCRT

triple-point temperature, TTRP

1 /x, ug = 1 /xg , Ut = i /xt

| a - 1 1 , Xg s | ag - 1 1 , xt s | at - 1

1

Table 1. The fixed-point constants

Ethane Methane

Tt , K 89.899 90.680

T c , K 305.330 190.555

d c , mol/T 6.87 10. 20

d t , liquid 21.68 28. 147

d ? , vapor 1.35114. 10" 6

1. 567 865. nr 2

SP 11342 A 112U S. Government Printing Office 1973- # 730-339
APPENDIX G. (Continued)

Cryogenics Division — MBS Institute for Basic Standards LABORATORY NOTE

COST CENTER 2750364

FILE NO 73-6PAGE 3

SUBJECT Liquid-Vapor Saturation (Orthobaric) Temperatures of

Ethane and Methane

name R.p). Goodwin

DATE Nov. 28, 1973

Table 2. Coefficients for the equations

Ethane Methane

V apor a 3/2 1/2

At -0.0610 6983 -0. 1596 5159

At -0.5510 7806 -0.6669 5380

As 1.8906 0757 1.0242 2995

A? -4.8476 0684 -0.5885 7993

A* 8. 5887 8625 0. 2042 8358

As -8.3103 1296 - Ag 3.3001 3887 - rms, % d 0.111 0.043

T 0.009 0.004

Liquid 6 1/3 1/3

Bi 9. 1071 7170 8. 5837 7917

b2 -7.9603 9387 -7.0525 4699

b3 4. 8472 6284 4. 1610 2443

b4 -1.5919 0104 -1.3691 9291

b5 0.2253 7899 0. 2067 1342

rms, % d 0.004 0.006

T 0.016 0.006

SP 11342 A 113 •ir U S Government Printing Office. 1973- tbo-339
APPENDIX G. (Continued)

Liquid- Vapor Saturation (Orthobaric) Temperatures of

Ethane and Methane

COST CENTER 2750364

FILE NO 73-6

PAGE 4

SUbJ- Table 3. Ethane Saturated Vapor Temperatures

NAME R.D. Goodwin

DATE Nov. 28 1973

NF = 7, AL = 1.500, PE = 0.000, DGAT = 1.35114-006

TTRP = 89.899, TCRT = 305.330, DTRP = 21. 680, DCRT = 6.870

-0 . C6106983 -0. 55107806 1.89060757 4.84760684

8 . 58878625 -8. 31X31 296 3.3 0813887 0.03000000

o • UOOOQOOO C. 0LC 0 0 000 0.00000000 0.00000000

MOL/L CALC PCNT T,K CALC PCNT DTS/DD

V

1.35 114-006 1. 35114-006 0.00 89.899 89. 899 0.00 2-915+006

1 .38631-006 1. 38619-006 -0.01 90 .0 00 90.000 0.00 2.848+0G6

4.59443-006 4.58134-006 -0.28 95.000 95. 013 0.01 9.651+005

1 • 33561 — Q05 1. 33129-005 -0.32 100.000 100. 016 0.02 3.714+005

3 .46326—005 3.46067-005 -0 .22 105.000 105. Q12 0.01 1.594+005

8 . 16960-005 3. 16454-005 -0.06 110.000 110. 004 0.00 7.518+004

1.76344-004 1.76987-004 0 .08 115.000 Ilk. 995 -o.o a

_

3.346+004

3 .55631-004 3.56292-004 0 .17 120 .0 00 119.907 -0.01 2.111+004

6.7 0 90 3-Q 04 6.72259-004 0.20 125.000 124. 983 -0.01 1.231+004

1 . 19634-JG3 1. 19845-003 0.18 130.000 129. 984 -0.01 7.567+003

2. 03041-0 G

3

2. 03275-003 Q .12 135.000 134. 969 -0.01 4.970+003

3.29903-003 3.30029-003 0.04 140.000 139. 996 -0.00 3.262+003

5 . 15754-o03 5.15568-033 -0.04 145. 000 145. Q 04 0.00 2.263+003

7 .79177-003 7. 73449-003 -0 .09 150.000 150. 012 0.01 1.619+003

1 . 14133-002 1. 1404 0-002 -0.13 155.000 155.017 0.01 1.191+003

1.62542-002 1. 62620-002 -0.13 160.000 160.019 0.01 8.969+002

2 .26660-002 2.2640 2-002 -0 .11 165.000 165. 018 0.01 6.903+002

3.08636-002 3. 08446-00

2

-0.08 170.000 170. 013 0.01 5.415+002

4. 12247-03

2

4. 12114-002 -0,03 175. 0QQ 175.006 0.00 4.322+002

5.4C 1 39-002 5.41016-002 0 .01 180.000 179. 997 -0.00 3.502+002

6 . 98623-002 6. 990C 3-002 0 .05 185 .0 00 184. 989 -0.01 2.877+002

3.89439-002 8. 90172-002 0.08 190.000 189. 982 -0.01 2. 392+002

1. 117 32— C o

1

1. 11888-G01 0.10 195.000 194. 979 -0.01 2 .009 + 00 2 1.38350-001 1 . 33978-001 0 .09 200.000 199. 978 -0.01 1.704+002

1.7(1662-001 1 . 73 78 7-0 01 0.07 205.000 204.982 -0.01 1.457+002

2. j777Q-G01 2 . 0786 2-0 01 0 .04 210.000 209. 988 -0.01 1.253+002

2 .50780-001 2. 5080 3-001 0 .01 215.000 214. 997 -0.00 1.085+002

3.00 559-00 1 3 . 0 328 0 -0 01 -0.03 220.000 220. 007 0.00 9.434+001

3 . 5 7 7 5 3 - 0 0

1

3.57050-031 -0 . 06 225.0011 . 225.017 0.01 9.234+001

4.22301-001 4. 21977-001 -0 .08 230.000 230. 023 0.01 7 .2G8 + 001

4. 96469-001 4.96061-001 -0.08 235.000 235. 026 0.01 6.322+001

5 .80*77-001 5 . 30460-001 -0.07 240 . 000 240.023 C . 01 5.553+001

6.76*52-001 6. 76541-001 -0.05 245.000 245.015 0.01 4.879+001

7.85990-001 7. 85922-001 -0 .01 250.000 250.003 0.00 4.286+001

9.10251-001 9. 13553-001 0.03 255.000 254. 989 -0.00 3.760+001

1.J5210+030 1. 0528 3 +0 00 0 . 07 260.000 259. 976 -0.01 3.291+001

1 .21471+000 1. 21579+000 0 .09 265.000 264. 969 -0.01 2.367+001

1 . 4 C 2 3 1 + 0 0 0 1 . 40343+000 0 .08 270.000 269.972 -0.01 2.482+001 A 1.62073+00

0

1.62131+000 0 .04 275.000 274. 988 -0.00 2.124+0C1 i'

1 . 37345+003 1.37773+000 -0.04 280.000 280. 013 0.00 1 .788 + 00 1 2.16363+uGG 2 . 1861 8 + 0 00 -0.11 285.000 285. 035 0.01 1.463+001

2.57 357 + uOO 2 .57381+000 -0.11 290.000 290.032 0.01 1.146+001

3.07773+309 3 . 0301 1+0CQ 0.00 295 .0.00 294. 980 .... -0.01 8.351+00C

3.31 3 0 3 + 00 0 3. 82166+OOG 0 . 10 300.000 299. 980 -0.01 5.426+0CC

= 0.009

1 14

P 44, DNRMSPCT 0.111, TSRMEPCT
APPENDIX G. (Continued) 1

Cryogenics Division — N B S Institute for Basic Standards LABORATORY NOTE

COST CENTER 2750364

FILE NO 73-6

PAGE 5

subject Liquid-Vapor Saturation (Orthobaric) Temperatures of

Ethane and Methane

NAME R.D. Goodwin

° ATE Nov. 28. 1973

Table 4. Ethane Saturated Liquid Temperatures

NF = 5 , AL = 0.000 , BE = 0 . 333 , DGAT = 1.35114 - 006

TTRP = 89 . 899 , TCRT = 305 . 330 , OTRP = 21 . 660 , OCRT = 6.970

9. 10717170 - 7 . 96039387 4.84726284 1 .59190104

0 . 22537699 0 . 00000000 0.00000000 0 .00000000

0 . 00000000 0 . ooocoooo 0.00000000 0 .00000000

MOL/L CALC PCNT T,K CALC PCNT DTS/OO

2. 1680 0 + 001 2 . 16800+001 0.00 39.899 89.899 0.00 - 2 . 753+001

2 . 16764+001 2 . 16763+001 - 0.00 90.000 89.999 - 0.00 - 2 . 753+001

2 . 14963+001 2 . 14951 + 001

' -0 .01 95.000 94.967 - 0.04 - 2 . 764+001

2 . 13162+001 2 . 13145 + 001 - 0.01 100.000 99.952 - C .05 - 2 . 771+001

2 . 11359+001 2 . 11341 + 001 - 0.01 105.000 104.951 - 0.05 - 2 . 773+001

2 . 09553+001 2 . 09538+001 -0 .01 110.000 109.958 - 0.04 - 2 . 771+001

2 . 07743+001 2 . 07732 + 00 1 - 0.01 115.000 114.969 - 0.03 - 2 . 766+00

2 . 05928 + 001 2 . 05921 + 00 1 - 0.00 120.000 119.983 - 0.01 - 2 . 758+00

2 . 041 06 + 0 01 2 . 041 05 + 001 - 0.00 125.000 124.997 - 0.00 - 2 . 746+001

2 . 02276+001 2 . 02280 + 00 1 0.00 130.000 130.010 0.01 - 2 . 733+001

2 . 00438+001 2 .00445 + 0 0 1 0.00 135.000 135.020 0.0 1 - 2 . 717+001

1 . 9 Q 588+001 1 .98598 + 00 1 0.01 140.000 140. 027 0.02 - 2 . 698+001

1 . 96727+001 1 . 96739 + 0 C 1 0 .01 145.000 145.0 31 0.02 - 2 . 673+001

1 . 94852+001 1 . 94964+001 0.01 150.000 150.032 0.02 - 2 . 655+00

1 . 92961+001 1 . 92972+001 0.01 155.000 155.031 0.02 - 2 . 631+001

1 . 91052+001 1 . 91062+001 0 .01 160.000 160.027 0.02 - 2 . 604+001

1 . e 9123 + 0 0 1 1 . 89132 + 00 1 0.00 165.000 165.021 0.01 - 2 . 575+001

1 . 87173+001 1 . 37178+00

0 .00 170.000 170.014 0.01 - 2 . 544+001

1 . 85190+001 1 . 85201+001 0.00 175.000 175.006 0.00 - 2 . 511+001

1 . 83196+001 1 . 83195+001 - 0.00 160.000 179.999 - 0.00 - 2 . 476+001

1 . 61164+001 1 . 811 60 + 00 1 - 0.00 185.000 184.992 - 0.00 - 2 . 438+00

1 . 79098+001 1 . 79092+001 - 0.00 190.000 109.986 - 0.01 - 2 . 397+001

1 . 76996+001 1 . 76987 + 0 0 1 - 0.00 195.000 194.981 - 0.01 - 2 . 354+001

1 . 74652 + 0 01 1 . 74843+001 - 0.01 200.000 199.978 - 0.01 - 2 . 308+001

1 . 72664 + 0 01 1 . 72653+001 -0 . 01 205.000 204.977 - 0.01 - 2 . 260+001

1 . 70425+001 1 . 70415+001 -0 .01 210.000 209.973 - 0.01 - 2 . 203+001

1 . 68130+001 1 . 60121+001 -0 .01 215.000 214.981 - 0.01 - 2 . 153+001

1 . 65774+001 1 . 65767+001 - 0.00 220.000 219.985 - 0.01 - 2 . 094+00

1 . 63348+001 1 . 63344 + 0 0 1 - 0.00 225.000 224.990 - 0.00 - 2 . 033+001

1 . 60845+001 1 . 60043+001 - 0.00 230.000 229.996 - 0.00 - 1 . 967+001

1 . 58255 + 001 1 . 58256+001 0 .00 235.000 235.002 0.00 - 1 . 898+00

1 . 55567+001 1 . 55571+001 0.00 240 .00 0 240.007 0.00 - 1 . 825+00

1 . 52767+001 1 . 52773+001 0.00 245.000 245.011 0.00 - 1 . 749+001

1 . 49638+001 1 . 49846+001 0 .01 250.000 250.013 0.01 - 1 . 668+001

1 . 46761+001 1 . 46770+001 0.01 255.000 255.014 0.01 - 1 . 582+001

1 . 43511+001 1 . 43518+001 0 .01 260.000 260.012 0.0 0 - 1. 49 3 + 00 1

1 . 40054+001 1 . 40059+001 0.00 265.000 265.0 0 3 0.0 0 - 1 . 399+001

1 . 36340+001 1 . 36350+001 0.00 270 .0 0 0 27 0 . 0 0 2 0.0 0 - 1 . 298+00

1 . 32333+001 1 . 32331 + 0 0 1 -0 .00 275 . 00 0 274.997 - 0.00 - 1 . 191+001

1 .27923 + 001 1 . 27917+001 - 0.00 280.000 279.994 - 0.00 - 1 . 076+001

1 . 22965+001 1 . 22978+001 - 0.01 285.000 204.993 - 0.00 - 9.500 +00 0 1 . 17293+001 1 . 17290+001 - 0.00 290.000 289.997 - 0.00 - 8. 090 + 00 0

1 . 10398+001 1 . 10403+001 0.00 295.000 295.003 0.00 - 6 . 441+000

1 . 01117+001 1 . 01117+001 0.00 300.000 300.000 - 0.00 - 4.358 + 00 0

NP 44, DNRMSPCT 0.004, TSRMSPCT 0.016 115
APPENDIX G. (Continued)

Liquid-Vapor Saturation (Orthobaric) Temperatures of

Ethane and Methane

Table 5. Methane Saturated Vapor Temperatures

NP = 5, AL = 0.500 , 35 = 0. 0 00 , DGAT = 1. 56787 -002

TTOp - 90.680, TC P T = 190.555, DTRP = 28. 147, DCRT =10. 200

-0 . 15965159 -0. 66695380 1.02422995 0 .53857993

0 . 20428358 0. o o ooooon 0.00000000 0.00000999

0 . 00000000 0. 00000000 0.00000000 0.00000000

MOL/L CALC PCNT T , K CALC PONT DTS/OD

t .5678 6-00? 1 .56786-002 0.00 90.680 90.630 0.00 5 . 39 1 +-99-2

1 . 6?79 1-002 1 .8 2830-00 2 0.02 92.000 91.998 -0.00 4. 775+002

2.? 6 579-00? 2.28663-002 0.0 4 94,000 93 .996 -9.0 0 4* 0 05 +90 2

2. 8?943-00? 2 . 6 3066-002 0.0 4 96.000 95 .996 -0.0 0 3. 390+002

3.46926-002 3.47064-002 0.04 98.000 97.996 -0.00 2^8934-002

4.2162 5-002 4.21756-002 0.03 100.000 99.9 97 -0.0 0 2.488+002

5.06166-00? 5.0 8288-00? 0.02 102.000 101.998 — 0 »0 9 A. 1544-002

5.07803-00? 6,0785 r -002 0.01 104.000 103.999 -0.00 1.878+002

7 .*1719-902 7 .21702-00? -0. 00 106.000 106. 0 90 0.09 1.6474-90 2 3.51224-00? 8.51123-002 -0. 01 103.000 108.091 0.00 1. 453+002

9. 9 765 6-00 2 9.97466-002 -0. 0? 110.000 110*092 0.00 1. 289+092

1 . 1624 1-00 1 1 .16213-001 -0. 0? 112.000 112.093 0.0 0 1.147+002

1 . 3469 2-001 1 .34655-001 -0.03 114. 000 114.094 0.00 1. 026+902

1 . 5526 9-00 1 1.55226-001 -0. 03 116.000 115.094 0.0 0 9. 221+001

1 . 761? 8-no

1

1.7 308 f1 -OOl -0.0 3 113.000 113 .094 0.0 0 8.314+091

2.0 343 1 -00 1 2.03383-001 -0. 02 120.000 120.014 0.00 7. 522+001

2.7134^-001 2.31304-001 -0.02 122.000 122.013 0.00 6.827+091

2 . 6205 8-001 2.62022-001 -0. 0 1 124.000 124.092 0.0 0 6.215+001

2 . 9574 4—001 2.9572 c -001 -0. 0 1 126.000 125.091 0.00 5.672+991

3 . 1261 6-0 0 1 3.3261 1-001 -0.00 128.0 00 128.010 0.0 0 5.189+001

3. 72670-001 3.72889-001 0. 01 130.000 129.999 -0.00 4. 757+991

4 . 1673 7-0 0 1 4.16790-001 0. 01 132.000 131.998 -0 .0 0 4. 370+001

4.641+44-001 4,64520-001 0.02 134.000 133.997 -0 .00 4. 0 2 1 + 901

5.16255-001 5. lo3 62-001 0.0? 136.000 135.996 -0.0 0 3. 706+001

5.7?44 l-0 n l 5.72576-001 0. 02 133.000 177.995 -a .o o 3.420+001

6. 3729 7-001 6.33462-001 0.03 140. 000 139.9 95 -0.00 3. 159+001

5 . 99144-ng 1 6.9 9 331-001 0.03 142.000 141 .995 -0.00 2.921+001

7.70734-001 7.70534-001 0.0 3 144.000 143.995 -0.00 2. 704+001

3 .4725 1 -00 1 0.4745 1-001 0.0? 1 4 6. 000 145.995 -0.0 0 2.503+001

9 . 70 32 0- 00 1 9.30504-001 0. 0? 148.000 147 .9 96 -0.00 2. 319+001

1 . 0?00 1+000 1.02016+000' 0.01 150.000 149.997 -0.00 2. 146+001

1 . 1 1 68 5 +0 o n 1.11694+000 0.0 1 152.000 151 .9 98 -0.0 0 1.989+001

1.?? 147+000 1.22144+000 0,00 154.000 1 54 . 0 1

0

-0.00 1. 842+901

1.33441+000 1. 33437+000 -0.0 1 156.000 156.011 0.0 0 1. 705+001

1 .+5656 + 00 0 1.45636+000 -0. 01 158.000 158.013 0.0 0 1. 576+001

1. . 5*87 '’+000 1.58943+000 -0.0? 160.000 150.015 0.0 0 1. 455+001

1 .7 3 20+ + 0 00 1.73156+000 -0.0 3 162.000 162.017 0.00 1.341+001

1 . 6 3 75 ° + 0 0 0 1 »o 3697 + 000 -0. 03 164.000 164.0 9 8 0.0 0 1.234+001

2.05665+000 2.0561 0+000 -0,04 166.000 166.099 0.01 1. 132+001

?.?4l5 p +90n 2.24077+000 -0. 04 168.000 168.098 0.0 1 1. 036+001

2.44331+000 2.44300+000 -0.03 170.000 170.098 0.00 9. 433 + 000

2 ,6663 1+000 2.66564+000 -0.03 172,000 172.096 0.00 8 . 548+000

?. 9 124 P +000 2.91214+000 -0. 0 1 174.000 174.013 0.00 7.696+000

3. 13601 + 0 no 3.13711+000 0.0 1 176.000 1 7 5 . 9 99 -0.0 0 6.871 + 00 0 3. -*•9531 + 0 00 3.49685+000 0.0 3 178.000 177.994 -0.00 6. 066+000

3.343? 7 + 0 0 n 3.95039+000 0.0 6 180.000 179.939 -0.0 1 5. 275+00 0 4 .25606+000 4.26143+Q00 0.08 132.000 1 31.935 -0 .0 1 4.486+000

4.74367+300 4.75265+000 0.08 184.000 133.935 -0.0 1 3. 690+000

5 . 3 65 ? 6 + 0 0 0 5,36670+000 0.0 3 186.000 135.9 96 -0.0 0 2. 858+090

6.2^000+000 6.20577+000 -0.23 183.000 138.028 0.01 1.935+000

p -in

,

n iPMs°rT (1.0 43 , TS’MSPCT 0.00 4 H6
M

(\l

CMM

CVJ

(VI

PU

<\l

CVJ

fvl

C\J

CM

CM

CM

CM

<\J

CM

(\J

(\J

CM

CM

CM

(VI

CM

CM

CM

CM

(\f

APPENDIX G. (Continued) File 73.6

Liquid-Vapor Saturation (Orthobaric) Temperatures of

Ethane and Methane

Table 6. Methane'Saturated Liquid Temperatures

NF = 5, AL = 0.000 , BE = 0 .333, DGAT = 1.56787- 002

T7RP = 90.680, TCRT = 190.555 , DTRP = 28 .147, OCRT = 10. 200

8.53377917 -7. 05254699 4.16102443 -1 .36919291

0.20671342 0. 00000000 0.00000000 0 .00000000

1 MOL/L CALC PCNT T , K cal: PCNT DTS/DD

2.81470+001 2.81470+001 0.00 90.680 90.630 0.0 0 - 1.208+001

2.80376+001 2.60375+001 - 0 . 00 92.000 91.996 -0 .0 0 - 1.203+001

2.7871 4+001 2.76706+001 - 0 . 00 94.000 93.9 n - 0.0 1 - 1. 194+001

2.77036+001 2.77026+001 - 0 . 00 96.000 95,936 - 0.0 1 - 1.186+001

2.75344+001 2.75332+001 - 0 . 00 95.000 97.936 - 0.01 - 1.176+001

2. 7363 e + 001 2.73625+001 - 0 . 00 100.000 99.935 - 0.01 - 1. 167+001

2.71916+001 2.71904+001 - 0 . 00 102.000 101.936 - 0 .01 - 1. 157+001

2.70179+001 2.70167+001 - 0 . 00 104.000 103.937 - 0.01 - 1.147+001

2.68425+001 2.63415+001 - 0 . 00 106.000 105.938 - 0.0 1 - 1. 136+001

2.66654+001 2.6o645+001 - 0.00 108.000 107.990 - 0.0 1 - 1. 125+001

2 . 64 8 6 5 + 001 2.64657+001 - 0 . 00 110.000 109.992 - 0.0 1 - 1. 113+001

2 . 6305 6 + 001 2.63051+001 -0. 00 112.000 111.994 -0 .0 1 - 1 . 101+001

2.61226+001 2.61224+001 -0. 00 114.000 113.996 -0.00 - 1.089+001

2.59379+001 2.59377+001 -0.00 116.000 115.998 -0.00 - 1 . 076+001

2.57507+001 2.57507+001 0.00 113.000 113.000 0.0 0 - 1. 063+001

2.55612+001 2.55615+001 0.00 120.000 120.002 0.0 0 - 1 . 050+001

2.53693+001 2.53697+001 0,00 122.000 122.004 0.00 - 1. 036+001

2.51749+001 2.5175^+001 0.00 124.000 124.006 0.00 - 1 . 022+001

2.41777+001 2.49784+001 0. 00 126.000 126.007 0.0 1 - 1 . 008+001

2 . 47776 + 00 1 2 .47784+001 0.00 128.000 128.005 0.0 1 - 9.928+000

2 .45745+001 2.^5754+001 0.00 130.000 130.009 0.0 1 - 9. 775+000

2.43632+001 2.43692+001 0.00 1 32. 0 00 132.009 0.0 1 - 9.616+000

2.41535+001 2.41595+001 0. 00 134.000 134.009 0.0 1 - 9.457+000

2.39452+001 2.39462+001 0 . 00 136.000 1 36 . 0 0 9 0.0 1 - 9.292+000

2.37230+001 2.37290+001 0. 00 138.000 138.009 0,0 1 - 9. 122+000

2.35067+001 2.35076+001 0. 00 140.000 140.008 0.01 - 8.948+000

2.3281 0+001 2.32816+001 0. 00 142.000 142.007 0.0 1 - 8.768+000

2.30506+001 2.30513+001 0. 00 144.000 144.006 0.0 0 - 8.584+000

2.26152+001 2.28156+001 0. 00 146.000 146.005 0.0 0 - 8.395+000

2 .25744+001 2.2574^+001 0.00 148.000 148.003 0.0 0 - 8 . 200+000

2.2327 6 + 00 1 2.23278+001 0.00 150.000 150.002 0.0 0 - 7.999+000

2.20746+001 2.20745+001 -0.00 152.000 152.000 -0.00 - 7. 793+000

2.18146+001 2.16143+001 -0.00 154. 000 153.933 “0.0 0 - 7. 579+000

2. 1547 1+001 2.15466+001 -0.00 156.000 155.9 35 -0.00 - 7. 359+000

2.1271 3+001 2.12705+001 -0.00 153.000 157.995 -0.0 0 - 7.132+000

2 . 0 986 3 + 00 1 2.09853+001 -0. 00 160.000 159.9 93 -0.0 0 - 6 . 896+000

2.06912+001 2.06901+001 - 0.01 162.000 161.932 -0.00 - 6.652+000

2.03349+001 2.03835+001 -0.01 164.000 163.9 91 - 0.01 - 6. 399+000

2.00656+001 2.00643+001 - 0.01 166.000 165.9 91 -0 .0 1 - 6.135+000

1 . 9732 2 + 0 0 1 1.97307+001 -0.0 1 168.000 167.932 -0.00 - 5. 859+000

1 . 9332 0 + 0 0 1 1.93607+001 - 0.01 170.000 169.933 “0.0 0 - 5.570+000

1.90125+001 1.90114+001 -0. 01 172.000 171.9 34 -0.0 0 - 5. 265+000

1.86201+001 1.86195+001 -0. 00 174.000 173.997 -0.0 0 - 4. 943 + 00 0

1 .3200 4 + 0 0 1 1.82004+001 0.00 176,000 176.000 “0.0 0 - 4. 60 0+000

1 . 7745 7 + 001 1.77475+001 0.00 176.000 173.003 0.0 0 “ 4.232+000

1 .72^9 9 + 00 1 1.72516+001 0 . 0 1 180 . 0 0 0 130.0 35 0,00 - 3. 833+000

1 .6695 8 + 00 1 1 .669o3+001 0.01 182,000 1 32.0 0 8 0.0 0 - 3. 394+000

1.60606+001 1.60632+001 0.02 184.000 1 84.0 0 8 0.0 0 - 2.903+000

1 .52986+001 1.52997+001 0.01 186.000 136.033 0.0 0 - 2.338+000

1.42978+001 1.42937+001 -0.0 3 183.000 187. y 33 -0.0 0 - 1.65 2 + 000

1.25270+001 1.25276+001 0 . 00 190.000 190.000 0.0 0 - 6. 700-001

=51, DNRMSPFT = G.OOo, T SR M S PC T = 0.006 117
APPENDIX G. (Continued)

Cryogenics Division — N B S Institute tor Basic Standards LABORATORY NOTE

COST CENTER 2750364

FILE NO 73-6PAGE 8

subject Liquid-Vapor Saturation (Orthobaric) Temperatures NAME „ _ R D Goodwin

of Ethane and Methane DATE TV T Nov. 28, 1973

11/28/73

Appendix I. The Computer Programs

PROGRAM TSATFIT

C DESCRIBE ETHANE SATN. TEMPS., TSAT(QEN).

C DEFINE R=D/DTRP, S=D/DCRT, S T = D TRP/DCR T , AND -

C YYJTSAT) = ITCRT/T-1J/ ITCPT/ITRP-l) , AND. -

C

COMMON NG,AL*££,TTRP.,I£RJ,_ OGAT , DTRP , QCRT-* DTSQR, A(15J,B(15)

C0MM0N/999/NP,NF ,H(15),Y(200),G<200,15)

DIMENSION T (99) * DEN ( 991 *Y Y ( 99) _»E115J

DIMENSION UL (99)

_2 FORMAT ( 1H1 3.0X * ETHANE. SATURATION TEMPERATURES* //

1

16X4HNF =13, 6H , AL =F7.3, 6H , BE =F7.3, 8H, OGAT =E13.5//

1 16X 6HTTRP =F7 • 3 , 8H , TCRT =F 8 . 3 , 8H, DTRP =F7.3,

2 8 H » DCRT =F6. 3/ / 3(12X 4F16.8/ ) /

315 X5HMOL/L 11X4HCALC 5 X4HPCNT 8X3HT,K 6X4HCALC 5X4HPCNT6X6HDTS/DD)

3 FORMAT (1H1 14X 5HMOL/L 11X4HCALC 5X4HPC NT

3 8X3HT,K 6X4HCALG 5X4HPCNT 6XEHDTS/DD ) 4 FORMAT ( 5X 2E15.5, F9.2, F11.3, F10.3, F9.2, E12.3)

5 FURMAT E13X 2HNF 13X2HAL 13X2HBE 8X2HSSI

6 FORMAT (10 X 15, 2E15.5, F10.3)

9 FORMAT (1HC 6X 4HNP =13, 12H , DNRMSPCT =F6.3, 12H , TSRMSPCT =F6.3)

11 TTRP=89.899 $ TCRT=3D5.33 $ YN = TCRT/TTRP-1

1.2 DTRP = 21.68 S D CRT = 6 67 $ DGAT=1. 351 14 E-6

13 ST = DGAT /DCRT $ VT=1/(1-ST) S QT = CUBE RTF ( S T)

C

C SATO. VAPOR TEMPS. CONSTRAINED AT T.P. BY SUBTRACTION -

C EQUATION, YY = U < S) * ( 1 +W ( S ) ) , U = E XP ( A L* ( VT- V ) )

,

C V = 1/ABS(S-1), Q = S** (1/3) , AND -

C W = A1*LN(S/ST) * A2MQ.-QT) + A3MQ2-QJ2) + . . . C GENERATE THE SATO. VAPOR CAT A

.

25 DO 29 J=1 ,44 $ IF(J-l) 27,26

26 T ( J) = TTPP $ GO TO 28

27 T ( J ) = 80 + 5* J

2« DEN (J) = DENGASF ( T ( J)

)

29 YYIJ) = ( TCRT/T { J) -1) / YN $ NP = 44

C PRINT FOR NF, GET AL BY TRIAL.

30 AL = 1.50

31 DO 69 NF=4,10 $ NG = NF $ SSK = 1.0E+100

32 DO 40 J=1,NP t S=DEN ( J) /DCRT $ Q = CU BE RT F ( S) J V=l/(1-S)

33 U = EXPF ( AL* (VT- V) ) $ C-(J,1) = U*LOGF(S/ST)

...35, DO 36 K=2,NF $ N = K-i„ . 36 G ( J , K ) = U*(Q**N - QT * *N

)

40 Y ( J) = YY ( J) - U 49 CALL EGENFT $ DO 50 K=1,NF

5C A ( K) = H(K) $ SD = SS = 0 51 OO 52 J= 1 , NP S TC = TS A T F ( DE N ( J )

)

52 SS = SS + (TC/T(.J)-1) **2 . $ SS = 100*SQRTF (SS/NP)

53 IF (SS.LT.SSK) 54,56

54 SS K = SS $ NGK = NG $ A L K = A L $ BEK = BE S DO 55 K=1,NF

55 F ( K) = AIK)

56 CONTINUE

57 CONTINUE S NG=- NG K $ AL = ALK $ BE = BEK $ DO 58 K=1,NF

58 A ( K ) = F ( K) $ SS = SD = 0

SP 11342 A 118

U S Government Printing Office 1973- H 790-339
APPENDIX G. (Continued)

Cryogenics Omiion-NBS Institute tor Bone Stindords LABORATORY NOTECOST CENTER 2750364

FILE NO 73-6PAGE 9

SUBJECT Liquid-Vapor Saturation (Orthobaric) Temperatures of

Ethane and Methane

name

j-j Goodwin

DATE Nov. 28, 1973

Appendix I. (continued)

C PRINT CONSTANTS AND DEVIATIONS.

60 PRINT 2, NG» AL + BEtDGAT , TTRP,TCRT ,DTRP^DCRT j_ (A_( K) , K=1 , 12)

61 DO 67 J= 1 * NP $ 0=0 E N ( J ) $ X=T(J) $ DC=FIND S AT F ( 0 , X

)

TSATFIT 11/28/73

62

DPCT = 100MOC/D-1) $ SD = SD + DPCT*0PCT

64 T.C = TSATF(D) $ DTSDD = D TSDR/DTRP

65 TPCT = 1 0 0 * { TC/X- 1) $ SS = SS + TPCT*TPCT

67 PRINT 4 4 0 ,QC,OPCT . X. TC.JPCT* DTSQO

68 SD=SQRTF (SD/NP) $ SS=S0RTF < SS/NP) $ PRINT 9, NP, SD, SS

69 CONTINUE $ AL = 0

C

C SATD. LIQUID TEMPS. CONSTFAI NED AT THE T.P. 3Y SUBTRACTION, - C EQN . , LN(YY) = W(S), WHFRE X = ABS(S-1), XT=ABS { ST-1) , AND -

C W(S) = BE* LL/XT-l/X) + B1MX-XT) + 82MX2-XT2) + . . . C GENERATE LIQUID DATA.

70 DO 74 J=1 , 44 $ IF(J-l) 72,71

71 T « J ) = TTRP $ GO TO 73

72 TtJ) = 30 + 5*

73 DEN ( J) = DENLIQF ( T ( J) ) 74 YYU) = LOGF { (TCRT/T ( J) -1) / YN)

75 NP = 44 $ NG = NF = 5 $ XT = DTRP/DCRT - 1 C SET UP FIXED LEAST SQUARES FUNCTIONS,.

30 DO 35 J= 1 , NP S S = DEN ( J ) /DCRT $ X = ABSF(S-l)

31 UL ( J ) = 1/XT - 1/X $ DO 82 K=1,NF $ N = K

32 G ( J , K ) = X**N - XT**N

35 CONTINUE _

C FIND NF, BE BY TRIAL.

90 BE = 1. 0/3.0 S DO 91 J = 1,NP

91 Y ( J ) = YYU) - BE*UL(J) $ CALL EGENFT $ DO 92 K= i , NF

92 9 ( K) = H ( K ) S SD = SS = 0 C PRINT LIQUID DEVIATIONS.

1QJL PRINT 2, NG, AL, BE, DGAT, TTRP, TCRT,DTRP, DCRT, (B ( K) , K=1 , 12

)

101 DO 105 J = 1 , N P $ D = DEN<J) $ X = T(J) $ DC = F I ND S AT F ( 1 , X

)

102 DPCT = 10 0*1 DC/D - 1) $ SO = SD + DPCT**2

103 TC = TSATF(D) $ DTSDD = DTSDR/DTRP

104 TPCT = 100* (TC/X-1) $ SS = SS + TPCT**2

105 PRINT 4, D, DC, DPCT, X,TC,TPCT, DTSDD

106 3U = SORT F (SO/NP ) S SS = SGRTF<SS/NP)

107 PRINT 9, NP, SO,SS

11C CONTINUE

S9 C STOP $ END

SP 11342 A 119

fr US Government Printing Office. 1973- # 790-339
APPENDIX G. (Continued)

Cryogenics Division — NBS Institute for Basic Standards LABORATORY NOTE

COST CENTER 2750364

FILE NO 73-6

PAGE 10

SUBJECT Liquid-Vapor Saturation (Orthobaric) Temperatures

of Ethane and Methane

name R.D. Goodwin

° ATE Nov. 28, 1973

Appendix I. (continued) 11/28/73

FUNCTION TSATF1DEN)

CQ-MWON NG ,AL *BE,-J TRP ,-ICRT , OGA T *-DTRP ,-DCRT , DTSDR * A(15),B(15J

1 R= DEN/OTRP $ S=DEN/DCRT ! QS = S-l $ OSOR=DTRP/D CRT S IF(QS) 2,30

2 X„J5._ABS£ I QS3 S- XI = OS£R*QS/X $ YN = TCRT/TTRP - 1

3 V = 1/X $ Vi = -DSOR/QS/X $ IF(QS) 4,30,15

C SAT D • VAPOR TEMPS. CON-STRAINED AT T.P. BY SUBTRACTION -

C EQUATION, YY = U t S) * < i+W <S ) ) , U = EXP ( A L* < VT- V )>

,

C = l/ABSCS-i), a = S** (1/3) , AND_=—

C W = Al*LN(S/ST) + A2*<Q-QT) + A3MQ2-QT2) . . . -k_-ST ^DGAT /HCRX S.JI L=1/X1-ST) QI-.CUBERI.EAS T)

5 U = EXPF(AL*(VT-V)) $ U1 = -AL*V1*U

- 6 Q—= CU-BERTF (ST S Q1 = -£*OS0R23VS7 W = 1 + A t 1

)

*L0GF (S/ST) $ W1 = A<i)*DSDR/S

B M ID JC~2 , NG $ N = X-l - _

9 W = W + A{K)*(Q**N - QT**N)

IQ HI = W1 + N* A ( K) * Qi * Q** Xfclr.l 1 12 F = U*W $ Fi = U*W1 L'l * W $ 0=1 + YN*F

14 TSATF = TCRT/Q $ DTSDR = - YN*F 1*TSATF/Q $ RETURN

C SATO. LIQUID TEMPS. CONSTRAINED AT THE T.P. BY SUBTRACTION, -

C EQN . , LNIYY) = W ( WHERE X=ABS(S-1), XT = ABS ( ST- 1) , AND -

C W(S) = BE* (1/XT-l/X) + B1MX-XT) + B2*(X2-XT2) + . . . .15 XT = OSDR-1 S H- = BE* (l/XT.-VJ $ -BE*V1

17 DO 19 K= 1 , NG $ N = K 18 W = W + B X K ) * ( X* *tX - XT **N

)

19 W 1 = W 1 + B(K)*N*X1*X**(N-1)

20 F = EXPFIW). ,„i FI = W1*F $ Q =_ 1 + YN* F 22 TSATF = TCRT/Q $ OTSDR = - YN *F 1* TS A TF /Q S RETURN

3 C TSATF = TCRT- S DTSOR.= 0 _J .RETURN .. $ END

FUNCTION DENGASF { T)

C ETHANE SATURATED VAPOR DENSITIES, MOL/L.

C Y = A1 + A2*Q 2 A 3* Q3 + . . , NF = AL, YN = LN (OCRT/OTRP) , C U = Z + (ZE-Z) *Y* QEN = DCRT*£ XP l- YN*U)

.

DIMENSION A ( 5

)

DATA (TTRP=89.899) ,(TCRT=305.33J, (E=fl.362)

DATA ( DCRT = 6.87) , (OTRP = 1 . 3 5 1 14 E- 6 ) 3 AT A { A = 0.19277431, 0.041550G9, -fl. 78922629,

1

0.35766750, 0.12454376)

1 FORMAT (1H0 9X *OENGASF = 0, T EXCEEOS TCRT. * / ) 2 IF (TCRT-T) 3,4,5

3 PRINT 1 $ STOP

4 DENGASF = OCRT $ DRDT = D2RDT2 =0 $ RETURN

5 ZN=TCRT/TTRP-1 $ YN= L OC-F { OCR T / D TRP) $ Z= ( TCRT/T-1) /ZN

6 D ZD T = -T CRT /ZN/ T /T $ ZE = Z**E $ Z El = E*ZE/Z

a. X = ZE-Z $ XI = ZE1-1 $ Q = CUBERTF ( Z

)

$ Q1 = G/3/Z

10

11

Y = A ( 1 ) $ Y 1 = 0 $

Y = Y + AIK) *Q**K

ro 13 <=2,5

12 Y 1 = Y 1 + K* A ( K) * Q** ( K- 1

)

13 CONTINUE £ Y1 =-Yi*Ql

15 U = Z + X * Y $ UA = 1 + X Y1 + XI *Y $ U1 = UA *DZDT

16 XP = E XPF ( - Y N*U) .$ DENGASF = F._= DCRT*XP

17 DRDT = -YN*U1*F $ PFTURN $ END

SP 11342 A 120

U S. Government Fainting Office; 1973- # 790-339
APPENDIX G. (Continued)

Cryogenics Division — NBS Institute for Basic Standards COST CENTER FILE NO PAGE LABORATORY NOTE 2750364 73-6 1 1 subject Ljquicl_ "Vapor Saturation (Orthobaric) Temperatures NAME R. D. Goodwin

of Ethane and Methane DflTE Nov. 28, 1 973

Appendix I. (continued) 11/23/73

12

3

4

5

6

7

8o 11

11

12

13

14

15

16

17

18

2 C 21

22

23

FUNCTION F I NOS AT F (M,T)

THIS FINDSATF AOJUSTED FOR ETHANE,

ITERATE DEN TO MINIMIZE (T-TS) VIA TSATF(DEN).

1 = 0 FOR VAPOR, M = 1 FOR LIQUID.

COMMON NG,AL,BE, TTRP»TCR7 , OGAT , DTRP, DCRT , DTSDR , A(15),B<15)

DATA (DGT = i. QE-6) , (QLT=23. Q)

FAILS TO CONVERGE.

T EXCEEDS T CRT • * / ) FORMAT (1H0 9X *F I NOSATF = 0, / ) FORMAT (1H0 9X *F INDSATF - 0,

IF { T-T CRT ) 4,22,23

IF(M.EQ.O) 5,6

= DENGASF ( T ) $ GO TO 7

D = DENLIQF ( T)

DO 20 J= 1 , 5 0 $ D T =T-TS ATF ( 0 ) $ I F ( ABSF ( OT /T ) - 1 . 0 E -6 ) 21,21,8

DT D-D = DTSDR/DTRP $ IF (DT OD. EQ. 0 . 0) 22,9

DD = OT/DTDO $ IF ( A BSF (CD /D) - 1 • 0E-6 ) 21,21,10

D = D + DL S IF (M.EQ.0) 11,15

IF ID, GT . DGT ) 13,12

O = DGT $ GO TO 20

IF ( 0 , LT. DCRT) 20,14

D = DCRT - 0.02 I GO TC 20

IF (D.GT.OLT) 16,17

D = DL T $ GO VO 20

IF (O.GT.OCRT) 2C , 18

O = DCRT + 0.02

CONTINUE $ FINDSATF

FINDSATF =0 $

FINDSATF = DCRT

FINDSATF = 0 $ PRINT 2 $ RETURN $ END

= t $ PRINT 1 $ RETURN

RETURt

$ RETURN

PRINT 2 $

11/28/73

FUNCTION DENLIQF (T)

ETHANE SATURATED LIQUID DENSITIES, MOL/L.

Y = Al + A 2* Q 2 f A3*Q3 + . . . , YN = QTRP-OCRT,

DEN = DCRT . YN*(X + (XE-X)*YL*. . DATA (TCRT=3G5.33),(TTPP=89.899), (DCRT=6 . 87),(DTRP=21.68),<E=0.35»

DATA (A=Q. 76173503) , (B = 0. 29365351) , ( C =- 0 . 3276 23 94

)

1 FORMAT (1HC 9X DENLIQF = 0, T EXCEEDS TCRT. * / ) IF { T CRT -T ) 3,4,5

PRINT 1 $ STOP

DENLIQF=DCRI $ DRDT = D2FD T 2 = 0 . $ RETURN

XN = TCRT-TTRP $ YN=DTRP-DCPT $ X = ( T CRT -T ) / XN $ DXDT=-1/XN

XE = X**E $

Q = XE-X $

WW = W*W $

1C Y 1 = 2*B*W + 11 Y 1 = Y 1 * W

13 DENLIQF = DCRT + 14 DRDT - (1 + Q*Y1

XE 1 = E*XE/X

Q 1 = XF1-1

Y = A + B*WL + 3*C* WW

$ H = CUBERTF(X)

C*X

W1 = W/3/X

(X + Q*Y)*YN

* Q1*Y) *YN*DXDT RETURN END

SP 11342 A 121 U S Government Printing Office. 1973- # 7&0-339
APPENDIX G. (Continued)

Cryogenics Division — NBS Institute for Basic Standards LABORATORY NOTE

COST CENTER 2750364

FILE NO 73-6

PAGE 12

subject Liquid- Vapor Saturation (Orthobaric) Temperatures name r . d t Goodwin

of Ethane and Methane 0ATE Nov. 28, 1973

Appendix I. (continued) 11/28/73

1

2

3

4

5

6

8

10

11

12

13

15

16

17

FUNCTION DENGASF(T)

METHANE SAT*. VAPOR DEN, MOL/L, VIA VAPORFIT,

Y = Ai A 2 * Q2 A3*Q3 . . , NF = AL, YN

U = Z_ + <ZE-Z)*Y, J3EN = DCRT*EXP (-YN*U) • DIMENSION A (5

)

D ATA (TTRP = 9Q.,68) , (TCRT= 190. 555) , <E = 0 . 3 88)

OAT A (DCRT=10.2) , (DTRP=0 . 01567365

)

3 AT A ( A = 0,3925579, -0.4976888, 1.3200516,

1 -1.6817790, 0.6848609)

FORMATUHO 9X DENGASF = 0, T EXCEEOS TCRT , * / ) I F ( TCRT-T ) 3,4,5

PRINT 1 $ STOP

DENGASF - DCRT % DROT = 02RDT2 = 0 ZN=TQRT/TTRP-1 l YN=LOGF(DCRT/DTRP)

DZOT = -TCRT/ ZN/T/T $ ZE = Z**E $ X = ZE-Z $ J(1 = ZE1-1 $ Q = CU8ERTF ( Z

)

Y = A (1 ) $ Y 1 = 0 $ DO 13 < = 2,5

Y = Y A(K)*Q**K

Y 1 = Y1 + K*A <K) *Q**(K-l

)

CONTINUE $ Y1 = Y1*Q1

U = Z X *Y $ UA = 1 * X*Y 1 f X 1*Y $ U1

XP = EXPF(-YN*U) $ DENGASF J= F = DCRT*XP

DPDT = -YN*U1*F $ RETURN $ END

11/19/73*1

= LN( OCRT/DTRP)

% RETURN

S Z= (TCRT/T-1) /ZN

ZE1 = E*ZE/Z

$ Q1 = Q/3/Z

= UA* DZ DT

LAB • NOTE 73-5.

= DTRP-OCRT,

12

3

4

56

8

9

10

11

13

14

FUNCTION OENLIQF(T)

METHANE SATD. LIQUID DEN, MOL/L,-VIA

Y = Al + A2*Q2 A3*Q3 * . . . , YN

DEN = DC P.T Y N* ( X + (XE-X)*Y).

DATA ( T TRP= 90 .68) , ( T CRT = 1 90 . 55 5 ) , (E= 0.361)

DATA (DCRT=10.2) , ( DT RP=2 8 .147

)

DATA ( A =0.8 37 0910 3) , (B=0. 08416127) , (C=-0. 07478575)

FORMAT ( IHO 9X *DENLIQF = 0, T EXCEEDS TCRT. * / ) I F { TCRT-T) 3,4,5

PRINT 1 $

DENLIQF=DCRT

X N=TCRT-TTRP

XE = X* *E $

Q = XE-X $ W H = W* H S Y 1 = 2* 9* W +

Y 1 = Y1*W1

DENLIQF = DCRT

DPDT = (1 + Q*Y

1

STOP

$ DRDT = D2 ROT2 = 0 t RETURN

$ YN=DTR p - DCRT $ X= ( TCRT-T ) /XN $

XE1 = E*X E / X t W = CUBERTF ( X

)

Q1 = XE1-1

Y = A + 8* W W C*X

3*C* WW _

DXDT = -l/XN

$ rfl = W/3/X

(X + Q* Y

)

Y N

+ Q1*Y> *YN*DX DT RETURN $ END

SP 11342 A 122 U S Government Printing Office 1973- # 780-3 3 9

USCOMM ERL
oo

OOOOOOOOOO

06/05/74

APPENDIX H„

Computer Programs for Equation of State

PROGRAM ETHANE

GOODWIN EQUATION OF STATE APPLIED TO ETHANE.

EQN. (Y-YSAT) = F(R,T), WHERE Y = (Z-1)*X/R, AND -

F (R,T) = 9* XBF E*XEF, NOTE ONLY TWO TERMS.

XBF = SQRT CT/TC) *LN (T/TS)

XEF = PSI-PSISAT, PSI - (1-W*LN d+l/W)) /X, W = EP*(T/TH-i).

9 = 81 + 82*R B3*R2/(1+BE*R2) , BE = 1, APPROX.,

E = (S-l) * (S-ER) * (El + E2*R), ER - 1.9, NF = 5.

NOTE, PRESSURE IN BARS, 1.01325 BAR/ATM.

LET GAS CONSTANT GK = 0.0831434*DTRP, PN = R*GK*T.

AUTHOR 10. VIRIAH2), PAL(4), REAMER (8) , MICHELS<9), DOUSLIN(IO).

COMMON B1,B2,B3,B4, ER, E1,E2,E3

COMMON/l/AL ,BE,EP, GK, DCRT , TCRT , PCRT , DTRP, TTRP , PTRP

COMMON/2/NP ,NF,IO<999) ,T (999) , P (999) ,OEN (999)

COMMON/ 3/0 POT ,D2POT2,DPSDT,OPMCT,DPDO,DPCR,DTSOR,DTHOR

COMMON/4/ XB1 ,XB2 , XC1,XC2, XE1,XE2, OXBOR,DXCDR , DXEDR

COMMON/6/ TSAT, THETA, PSAT

COMMON/7/ XB,XC,XO,XE

COMMON/ 8/IP ,NPP, PI ,P2,P3,P4,P5, I DP (99) , TPS (99) ,PPS(99)

COMMON/ 9/ IS , NPS »EG ,EL,ALS,BES,AL1,AL2,AL3,CG(5) , AY (8) , AW (5)

COMMON/ 10 / IDS (99) , TSS(99), DNS(99)

COMMON/11/ MP4, NP5

COMMON/999/ NFUN,Y,F(30>

DIMENSION G ( 30 ) , DND (30) ,TD (16) , PPO(30,16)

1 FORMAT (15, 3F10.0)

2 FORMAT ( 15 , F10.3, E15.5)

3 FORMAT ( 1H0 9X *EQN. OF STATE, OTRP =*F7.3, 8H, DCRT =F7.3,

1 8H , TCRT =F8. 3//1 0X4HAL =F5.2, 6H, BE =F5.2, 6H, EP =F5.2//

2 10X 4HNP =14, 10H, PAVPCT =F6.3)

6 FORMA T ( 1H1 16X *THE ISOCHORE AT* F6.2, * MOL/L* //

1 17X 3HT , K 5X5HP,B AR 5X5HDP/DD 5X5H0P/DT 4X7HD2P/0T2)

7 FORMATdOX F10.1, 2F10.3, F10.4, F11.5)

8 FORMAT ( 1H1 14X *THE ISOTHERM AT* F7.2, * OEG. K* //

1 10X 5HM0L/L 5X5 HP, BAR 5X5H0P/CD 5X5HDP/0T 5X 7HD2P/DT 2 ) 9 FORMA T ( 5X F10.2, 2F10.3, F10.4, F12.6)

11 FORMAT ( 1H1 7X *EQU ATION OF STATE VS. PVT DATA* //

1 8X 2 HI D 7X 3HT , K 5X5HMCL/L 5X5HCALCD 4X5H0,PCT

2 6X5HP, BAR 5X5HCAL CD 4X5HP,PCT)

12 F ORMA T ( 5X 15, F10.3, 2F10.4, F9.2, F11.3, F10.3, F9.2)

13 FORMA T ( 1H0 8X 4HNP =14, 12H, DNRMSPCT =F6.3, 12H, PMEANPC T =F6.3)

14 FORMAT ( 8F1 0 . 0)

15 FORMAT ( 16X 8F8.0)

16 FORMATdOX 7F10.0)

22 TTRP= 89. 899 $ 0TRP = 21.68 $ 0 = 1.01325 f PTRP=Q*9 . 967E-6

23 TCRT = 305.37 $ DCRT = 6.74

24 WM=30 .07 $ QP=Q/14. 69595 J GKK=0 .0831434 f GK = DTRP*GKK

25 AL=2 • 0 J BE=1. 0 $ EP=0.5 i ER=1.9

READ MIXED VAPOR PRESSURE DATA, ALL IN T-68, BAR.

26 DO 27 J=1 , 99 S READ 2, I OP ( J ) , T PS ( J) , PPS ( J) f IF(IOP(J) ) 27,28

27 CONTINUE

C READ TSAT (DEN) DATA (ORTHOBARIC DENSITIES).

28 NPP = J-l 5 DO 29 J=l,28

29 READ 2, I DS ( J) , TSS ( J ) , DNS ( J ) $ DO 31 J = 29,99

30 REAO 1, IDD,TSS(J) ,DNS(J) S IF(IDD) 31,32

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ETHANE

APPENDIX H. (Continued)

06 / 85 / 71*

31 XDS«J) - IOD

32 NPS = J — 1

GENERATE VIRIAL PVT DATA BELOW 1 MOL/L.

34 NP1 =38 2 DN = 0,4 2 OO 37 J=i,NPl f N = J

35 TT = 220 «• 10*N 2 ID(N> = 2 $ T (N) = TT 2 DEN (N) = ON

37 P (N) = ON*GKK*TT*ZIPF(TT,DN)

READ DOUSLIN ETHANE PVT DATA.

39 N=N«-1 2 DEN (N) =0.7 0 2 T(N)=248.15 S P(N ) =Q* 11 . 6 0 87 S ID(N) = 10

SET UP HIS DENSITIES, AND READ HIS TEMPERATURES.

40 ONO(l) = 0.75 $ OO 41 1=2,30

41 OND(I) = 0.5*1 2 REAO 14, (TO ( J ) , J=i, 16)

READ PRESSURES (ATM) ALONG ISOCHORES (MANY BLANKS).

42 00 43 1=1,30 S READ 15, ( PPO ( I , J) , J=1 , 16)

CONVERT TO ONE PVT POINT PER INDEX, N.

43 CONTINUE 2 OO 46 1=1,30 $ OO 46 J=l,16 $ IF(PPOfI,J)) 44,46

44 N = N41 2 ID (N) =10 2 T (N) = 273.15 TD(J)

45 0ENCN) = ONO(I) S P(N) = Q*PPD(I,J)

46 CONTINUE 2 DO 48 J=i,5 2 READ 1, IDD,ON,TT,PP

47 N=N*1 2 ID ( N) = IOO S OEN (N) =ON I T (N) =TT $ P(N> = Q*PP

READ MICHELS, DEG. C, AMAGAT DEN, AMAGAT (PM).

48 CONTINUE 2 NP2 = N * READ 16, (TO ( J) ,J=1 ,7) S DO 49 1*1,17

49 READ 14, ONO(I), (PPD (I, J) , J=i ,7)

50 00 53 1=1,17 S DC 53 J=i,7 2 IF(PPD(I,J)) 51,53

51 N = N*1 $ ID (N) = 9 J T (N) = 273.15 TO(J)

52 DEN (N ) = 0. 045064*DND(I) J P(N) = Q*DN0(I)*PPD (I , J)

53 CONTINUE 2 NP3 = N

READ 8 PAL/POPE ISOCHORES NO. 17 THRU 24, GRAM/CCf PSIA.

THESE DATA AOJUSTED BY RICE UNIV., APRIL, 1974.

57 CO 62 1=1,12 2 DO 61 J=l,99

58 READ 14, DN,TT,PP 2 IF (DN) 59,62

59 N = N*1 2 ID ( N) = 1200 100*1 J

60 T (N) = TT 2 P (N) = QP*PP S OEN(N) = 1000*DN/HM

61 CONTINUE

C READ REAMER ET AL UP TO NP5.

62 CONTINUE 2 NP4 = N I CALL REAOIT

C USE ONLY OATA THRU PAL/POPE FOR LEAST SQUARES.

63 NP = NP4 2 NF = 5 2 SSK = 1.0E+100 2 IP = IS = 1 C

C EXPLORE NONLINEAR PARAMETERS DTRP , DCRT ,TCRT,AL,BE,EP.

64 CALL PSATFIT $ PCRT = PSATF(TCRT)

65 CALL OSATFIT 2 CALL TSATFIT

C 66 CO 74 MA=i , 3 2 AL = 0.5MMA+2)

C 67 00 74 ME=1 , 3 f EP = 1.0/(6-ME)

66 CALL SETUP 2 SS = 0 2 DO 69 J=1,NP

69 SS = SS ABSF ( 1-PVTE (T(J) , DEN ( J) )/P(J) ) 2 SS = 100*SS/NP

70 IE ( SS -SSK ) 7 1,74,74

71 SSK=S S 2 DC R=DCRT 2 TCR=TCRT 2 AL K= AL 2 BEK=BE 2 EPK=EP

72 CO 73 K=1 , NF

73 G (K) = F (K)

74 PRINT 3, DTRP, DCRT, TCRT, AL ,BE»EF , NP,SS

76 DCRT = OCR 2 TCRT =TCR 2 AL =AL K 2 BE=BEK 2 EP=EPK

77 81=G ( 1) 2 82=G (2) 2 B3=G(3)

7e E 1=G ( 4) 2 E2=G (5)

80 CALL PEEK 2 CALL ISOTHERM

124
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ETHANE

APPENDIX H. (Continued)

06/05/74

GET DEVIATIONS FOR INDIVIDUAL AUTHORS.

83 DO 100 IG=1,5 I G0T0<84, 85,86,87,88) ,IC84 M=1 S N=NP1 $ GO TO 90

85 M=N*1 * N = NP2 S GO TO 90

86 M = NM $ N=NP3 $ GO TO 90

87 R=N*- 1 t N = NP4 $ GO TO 90

88 R=N + 1 $ N=NP5 $ GO TO 90

90 PRINT 11 t SO = SS = K = L = 0 91 DO 98 J=M , N $ K=K+1 I L = L*1 S IF(L-53) 93,92

92 L = 0 * PRINT 11

93 FC = PVTF (T (J) , DEN (J) ) $ DC = FINOENF (T(J),F(J),CEN(J) ) 94 PPCT=10Q* <1-PC/P(J) ) S SS-SS+AESF (PPCT) $ IF(DC) 95,96

95 DPCT = 100* (l-DC/DEN (J) ) $ GC TO 97

96 DPCT - 0.0

97 SO = SO « DPCT**2

96 PRINT 12, ID(J),T(J), DEN ( J) , DC , DPCT , P(J),PC,PPCT

99 SS = SS/K J SD = SQRTF (SD/K) f PRINT 13, K, SD,SS

100 CONTINUE

PRINTOUT ISOCHORES.

130 DO 160 1 = 1,22 S I F ( I -7 ) 132,131

131 DN = OCRT $ GO TC 133

132 DN = I 133 FRINT 6, DN

138 IF ( ON-OTRP ) 140,141,141

140 TS = TSATF(DN) $ GO TO 142

141 TS = TTRP* (ON/DTRP) **4

142 IF(I-ll) 143,143,144

143 IT = 8 $ GO TO 150

144 IF (1—15) 145,145,146

145 IT = 4 % GO TO 150

146 IF (I - 19) 147,148,1 48

147 IT = 2 $ GO TO 150

148 IT = 1 150 00 159 J= 90, 600, IT $ TT = J $ IF(TT-TS) 159,159,151

151 FP = PVTF ( T T ,ON) J PX = DPDRF ( T T , DN)

153 IFCPP-700.0) 155,155,160

155 PRINT 7, T T , PP , DPDD , OPDT , 02PDT2

159 CONTINUE

160 CONTINUE

C PRINTOUT ISOTHERHS (NEED FINDSATF).

200 DC 230 1=1,99

201 READ 1, IDD,TT,DS ? IF(IDD) 210,999

210 PRINT 8, TT

211 OH = OTRP* (TT/TTRP) **0.25 S IF(TT-TCRT) 212,212,213

21? DG = FINDSATF(TT,0) J 01 = F I NCSA T F ( T T , 1

)

213 DO 220 N= 1 , 5 0 0 $ DN = N*DS I IF ( TT- T CRT ) 214,215,215

214 IF(ON.GT.DG.AND.DN.LT.DL) 220,215

215 IF (ON.GT.OH) 230,216

216 FP = CPORF ( TT, DN ) I IF(PP-750.0) 217,217,230

217 PX = PV TF ( T T , DN

)

219 FRINT 9, ON,PP, DPDD, 0PDT,D2PDT2

220 CONTINUE

230 CONTINUE

999 CONTINUE S STOP J END

125
APPENDIX H. (Continued)

06/15/74

SUBROUTINE READIT

C REAO ETHANE PVT DATA OF REAMER ET AL. T,F, PSIA, Z(P,R,T).

C IND. ENG. CHEM. 36, 956-958, (OCT. ,1944).

C0MM0N/2/NP , NF ,IO(9S9),T (999), F (999) ,DEN (999)

COMMON/ll/ NP4 , NP5

DIMENSION TA(7) ,PSI (22) ,Z(22,7)

DATA (GKK = 0.0831 43 4) , ( 0= 1. 0 1325 ) , (PA=14 . 69595

)

1 FORMAT ( 24X 7F8.0)

2 FORMA T ( 15, F11.0, 8X 7F8.0)

3 FORMAT ( 15 , F11.0, F16.0)

C REAO THE SUPPLEMENTARY PVT DATA. ONE POINT PER CARD.

9

CO 15 1=1,99 $ REAP 3, I00,PF,ZA $ IF(IDO) 10*16

10 N = NP4 I 11 ID(N) = IOO t P ( N ) = Q*PP/PA J IF( I - 13) 12,12,13

12 TF = 100 $ GO TO 14

13 TF = 160

14 T (N ) = 273.15 (TF-32)/1.8

15 DEN(N) = P(N)/ZA/GKK/T (N)

16 CONTINUE

C NCW REAO 22 ISOBARS OF THE SQUARE TABLE 1.

20 EFAD 1, (TA (J) , J=1 ,7) $ DC 21 1=1,22

21 READ 2, IOO, PSI (I ) , (Z ( I , J ) , J = 1 , 7) C NCW CONVERT TO ONE FCINT PER INCEX, N.

25 DO 29 1=1,22 $ DC 29 J=l,7

26 N = N+l S ID (N) = 8 $ P(N) = Q*PSI(I)/PA

27 T (N) = 273.15 (T A ( J ) -3 2 ) / 1 .

8

28 DEN(N) = P (N)/Z (I, J)/T (N) /GKK

29 CONTINUE J NP5 = N 30 RETURN I ENO

SINGLE-BANK COMPILATION.

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APPENDIX H. (Continued)

06/05/7**

SUBROUTINE OSATFIT

FIND COEFFS. FOR DENGASF(T), DENLICF(T), ETHANE.

FUNCTIONS VIA GOODWIN LAB. NOTE 73-5.

DATA ARRANGED IN OROFR OF INCREASING DENSITIES.

COMMON/l/AL ,BE,EP, GK, DC RT , TCP T , F CRT , D TFP , TT RF , F T R

C0MM0N/9/IS,NPS,EG,EL, ALS,BES, AL1 ,AL2,AL3,CG(5) ,AV(8),AW(5)

COMMON/iO/ IDS(99), TSS(99>, DNS(99)

COMMON/ 999/ NFUN,Y,F(30)

DIMENSION G ( 9)

OATA (DGAT = 1.35114E-6)

1 FORMA T(1H19X*SATURATED VAPOR DENSITIES, E = *F6 . 3 // 1 0 X 6HT TRP =F7.3,

1 8H , TCRT =F8. 3 , 8H, OCRT =F6.3, 8H, DGAT =E12.5// 7X 5F13.6//

2 13X2HI0 7 X 3HT , K 8X5HM0L/L 8X5HC A LCD 4X4HPCNT ) 2 F CRM A T ( 1 0 X 15, F10.3, 2E13.4, F8.2)

3 FORMAT (1H19X*SATD. LIQUID DENSITIES, E = * F6.3// 1IX6HTTFF =F7.3,

1 8H , TCRT = F 8 • 3 , 8H, DCRT =F6.3, 8H, DT R F =F7.3// 9X 3F15.9//

2 13X2 HID 7 X 3HT , K 5X5HMCL/L 5X5HCALC0 5X5HPRCNT)

4 FORMA T ( 10X 15, 3F10.3, F10.2)

5 FORMAT(1HO 15X 4HNP =13, 10H, RMSFCT =F6.3>

FCR THE SATURATED VAPOR, DEFINE -

Z = (TC/T-1) /(TC/TT-1) , Q = Z**l/3, ZF = Z**E,

YY = LN(DC/D) /LN (DC/DT) , ANO THE DEPENDENT VAFIAELE - Y ( Z, Y Y ) = (YY-Z) /(ZE-Z) , WHEN THE L.S. ECN. IS - Y(Z,YY) = Al A2*Q2 A3*Q3 A4*C4 A5*Q5.

6 ZN=TCRT/TTRP-1 S Y N=LOGF ( OCR T / D GA T ) 5 SSK=1.0E+100

EXPLORE VALUES FOR EXPONENT EG.

7 CO 18 1=1,11 S EG = 0.33 + 0.01*1

8 NFUN =5 $ DO 12 J = l,99 $ I F ( CNS ( J ) - OOP T) 9,13,13

9 Z = ( TCRT/TSSC J)-l ) /ZN S Q = CUBERTE ( Z

)

10

YY = LOGF (OCRT/DNS (J) )/YN $ F(l) =1 $ OO 1 1 K=2,5

11 F (K) = Q**K t Y = (YY-Z) / (Z** EG-Z)

12 CALL FIT

13 NP = J-l $ CALL CCEFF J SS = 0 S DC 14 K = 1 ,5

14 CG ( K

)

= F ( K ) l DO 15 J = 1 , NP i DC - DENGASF ( T SS ( J)

)

15 SS - SS ( OC/ DNS ( J

) -1 ) * * 2 t IF (SS .LT .SSK) 16, 18

16 SSK = SS t E GK = EG * DO 17 K=l, 5 17 G (K) = F ( K ) 16 CONTINUE $ EG = EGK J 00 19 K = l, 5 19 CG(K) = G ( K ) $ IF(IS) 20,26

20 PPINT 1, EG, TTRP, TCRT , DCRT, DGAT, (G(K),K=1,5)

21 SS = 0 t OO 24 J = 1 , N P $ DC = DENGAS F ( TSS ( J )

22 FCT = 100* (DNS(J)/DC-1) J SS = SS PCT**2

24 FRINT 2, IDS(J), T S S ( J ) , DNS ( J ) , CC,PCT

25 SS = SQRTF ( SS/NP) $ FRINT 5, NP, SS

FCR THE SATURATED LICUID, DEFINE - X = (TC-T) / (TC-TT), Q = X**l/3, XE = X**E,

YY = ( O-DC) / (DT-OC) , WHEN THE L.S. EQN . IS - (YY-K) /(XE-X) = A1 + A 2*Q2 A3*Q3.

26 M = NP 1 % SSK = 1.0E+100

27 XN = TCRT-TTRP $ YN = DTRP-DCRT

C EXPLORE VALUES FOR EXPONENT EL.

26 CO 37 1=1,14 * EL = 0.25 * 0.01*1 J NFUN = 3 29 00 32 J = M , NPS $ X = (TCR T-TSS ( J ) ) / XN

30 C = CUBERTF(X) 5 YY = ( DN S ( J

) -C CRT ) / Y

31 F ( 1 ) = 1 S F ( 2 ) =Q * Q $ F ( 3 ) = X $ Y = ( YY- X ) / ( X* F L - X )

127
DSATFIT

APPENDIX H. (Continued)

06/85/74

32 CALL FIT $ CALL CCEFF $ AL1=F(1) * AL2=F(2) f AL3=F(3)

33 SS = 0 $ DO 34 J=M,NPS $ DC = DENLIQF (TSS ( J)

)

34 SS = SS (DC/DNS(J)-1)**2 * IF (SS .LT. SSK) 35,37

35 SSK = SS J ELK - EL $ DO 36 K=l, 3

36 G (K) = F ( K

)

37 CONTINUE $ EL = ELK $ AL1=G(1) S AL2=G(2) $ AL3=G<3)

36 IF(IS) 40,99

40 PRINT 3, EL, TTRP, TCRT , OCRT , OTRP , <G(K),K=1,3>

41 SS = N = 0

42 00 44 J=M , NPS l N = N+l S DC = DENL I QF ( TSS < J > 43 PCT = 100* (DNS (J)/OC-l) t SS = SS PCT**2

44 PRINT 4, IDS (J) ,TSS (J) ,DNS ( J) , OC,PCT

45 SS = SQRTF ( SS/N) $ PRINT 5, N, SS

99 RETURN J END

SINGLE-RANK COMPILATION.

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APPENDIX H. (Continued) 06/85/71*

SUBROUTINE TSATFIT

FIT TSAT DATA VIA FUNCTIONS OF TSA TFI T (METHANE ) , 4/19/74 AT 09.00.

NCTE, ALS = BES = 0.5, E - 1/4, VAPOR NF=6, LIQUID NF = 3.

NOTE DIFFERENT FUNCTIONS AS OEN L . T. OR G.T. DCPT.

DEFINE YY(TS) = ( TC R T /T -1 ) / ( TCR T /T TRP-1 ) FOR EACH FUNCTION.

DATA ARRANGED IN ORDER OF INCREASING DENSITIES.

COMMON/l/AL,BE,EP, GK, DCRT , TCRT , PCRT , D T RP , TT RF , P T R

COMMON/3/ OP OT,D2PDT 2, DPS DT,DPM0T, OPOD , O PDR , D TSDR , 0 THOR

COMMON/ 9/1 S,NPS, EG , EL, ALS, BES, AL1 , AL 2 , AL 3 , C G ( 5 ) , AV (8) *AW (5)

COMMON/10/ IOS( 99) , TSSI99), DNS 1 99

)

COMMON/999/ NFUN,Y,F(30)

OATA (DGAT = 1.35114E-6)

1 FORMAT ( 1H1 3 OX ’ETHANE SATURATION TEMPERATURES’ //

1 16X 4HAL =F 6.3, 6H, BE =F6.3, 8H, DGAT =E12.5//

2 16X 6HTTRP =F7.3, 6H, TCRT =F8.3, 8H, DTRP =F7.3,

3 8H , DCRT =F6. 3 // 2(13X 4F15.9/) ) 2 FORMATdHO 12X 2HI O 10X5HMOL/L 1 1 X4HCAL C 5X4HPCNT

1 8X3HT,K 6X4HCALC 5X4HPCNT 6X6HDTS/0D ) 3 F ORMA T ( 10 X 15, 2E15.5, F9.2, Fll.3, ri0.3, F9.2, E12.3)

4 FORMATdHO 12X 4HNP =13, 12H, DNFMSPCT =F6.3, 12H, TSRMSPCT =F6.3)

FOR SAT. VAPOR DEFINE, X=ABS(S-1), XT= ABS ( ST- 1 ) , WHEN EQN. IS - IN(YY) - AL’ (1/XT-l/X) = Al’LOG (LN ( 1 + E/S ) /LN ( 1 «-E / ST ) ) W«S),

W ( S > = A2MQ-QT) A3*(02-QT2) + A4’(S-ST) A5*(S2-ST2) . . . WHERE, Q = S” 1/3, AND OT = ST”l/3.

5 ALS = BES =0.5 S E = 0.25 S YN = T CRT/TTRP - 1 6 ST = DG AT /DCRT I XT= 1-ST $ EK=LOGF ( 1 + E/ST)

7 GT = CUBERTF (ST ) % NFUN = NF = 8

9

OO 16 J = 1 , NPS $ IF (DNS (J) -OCRT) 10,17,17

10 S = DNS ( J ) / DCRT $ X = 1-S * 0 = CUBERTF (S

)

11 F ( 1 ) = LOGF (LOGFC1 +E/S) /EK)

12 F ( 2 ) = Q-QT $ F ( 3 ) = Q’O - OT’CT

13 DO 14 K=4 , NF $ N = K-3

14 F(K) = S”N - ST” N 15 Y = LOGF( (TCRT/TSS C J) -1) /YN) - AL S’ (1/ X

T - 1/ X)

16 CALL FIT

17 NF = J-l $ CALL CCEFF * DO 18 K=1,NF

18 A V ( K ) = F ( K ) $ IF (IS) 20,28

20 PRINT 1, ALS, BES, DGAT, TTRP,TCRT , DTRP, DCRT, {F ( K ) , K = 1 , N f

21 PRINT 2 J SD = SS = N = 0 22 CO 26 J = 1 , N P $ T = TSS(J) $ C = DNS(J)

23 CC = FINDSATF (T, 0) * DPC T= 1 0 0 ’ ( 1 - DC /O ) $ S0=SD+DPCT”2

24 TC = TSATF(O) $ DTSCD = DTSDR/DTRP

25 TPCT = 10 0’ (1-TC/T ) J SS = SS TPCT”2

26 PRINT 3, IDS ( J ) , 0,CC,CPCT, T,TC,TPCT, OTSDD

27 SD = SORT F ( S O/N P ) f SS = SQRTF(SS/NP) $ PRINT 4, NP, C C,SS

FOP SATO. LIQ. USE, X=ABS(S-1), XT=ABS(ST-1) IN THE EON. - LN(YY) = BE’ C 1/XT-l/X) Bl’(S-ST) + 92’(S2-ST?) + . . . 28 NFUN = NF = 5 $ M=1 f ST= OTRP/DCRT « XT = ST-1

29 00 35 J= 1 , N PS * IF (DNS (J) -DCRT) 30,30 , 31

30 M = M *• 1 % GO TC 35

31 S = D NS ( J ) / OCR T $ X = S-l % DC 32 K = 1,NF

32 F(K) = S”K - ST” K

33 YY = (TCRT/TSS (J)-l) /YN % Y = LOGF(YY) - BES’ (1/ X T- 1 /X )

34 CALL FIT

35 CONTINUE $ CALL COEFF $ OO 36 K=1,NF

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TSATFIT

APPENDIX H. (Continued)

06/85/74

36 AW < K) = F(K) $ IF(IS) 40,99

40 PRINT 1, ALS ,8ES,0GAT , TTRP , TCRT , 0TRP,0CRT, (F ( K) , K= 1 , NF

)

41 PRINT 2 $ SD = SS = N = 0 42 DO 46 J=M , N PS * N = N+l « D = ONS(J) $ T = TSS(J)

43 CC=FINOSATF <T, 1) $ DPCT= 1 0 0 * < 1 -DC /O) J SD=S0+0FCT**2

44 TC = TSATF(D) $ DTSDD = DTSOR/DTRP

45 TPCT = 10 0 * ( 1— TC/T ) $ SS = SS TPCT**2

46 PRINT 3, IDS(J), D,DC,DPCT, T,TC,TPCT, DTSDD

47 SD = SQRTF ( SD/N ) I SS = SQRTF(SS/N) t PRINT 4, N, SO, SS

99 RETURN S END

06/05/74

SUBROUTINE PSATFIT

FIT GOODWIN EQN . TO VAPOR PRESSURE DATA, ALL ON T-68, BAR.

LMP/PT) = P1*X + P 2* X 2 P3*X3 P4* X4 P 5*X* < 1 -X ) * * 1 . 5

.

COMMON/l/AL,BE,EP,GK» DCRT , TCRT , PCRT , D TRP , TTRP , P TRP

COMMON/8/IP,NPP,Pl ,P2,F3,F4,P5, I0P(99) , TPS ( 9 9 ) , FPS ( 9 9

)

C0MM0N/999/NFUN,Y, F (30)

1 FORMAT ( 1H1 14X *VAFOR PRESSURES, TTRP =*F7.3, 8H, TCRT = F 8 . 3

)

2 FORMA T ( 1H0 12X 5F13.8)

3 FORMAT ( 1H0 17X 2HI D 7X3HT,K 10X5HP,BAR 10X5HCALCD 6X4HPCNT ) 4 FORMAT (15X 15, F10.3, 2E15.5, F10.3)

5 FORMAT ( 1H0 16X 4HNP =14, 10H, RMSPCT =F6.3)

6 NFUN =5 « XK = 1 - TTRP/TCRT J DO 10 J=1,NPP

7 X = ( 1-TTRP/TPS ( J) )/XK $ QC = X* (1 -X) SQRTF (1 -X)

8 F ( 1 ) = X t F(2) = X*X $ F ( 3) =X*X*X J F < 4 > =F ( 2) * F ( 2 ) ? F(5)=QC

9 Y = LOGFtPPS (J) /PTRP)

10 CALL FIT $ CALL COEFF

11 P 1=F ( 1) S P2=F (2) $ P 3=F ( 3 ) I F4 = F<4> f F5 = F(5) * IF(IF) 12,20

12 SS = L = 0 $ PRINT 1, TTRP, TCRT

13 PRINT 2, PI ,P2,P3, P4,P5 S FRINT 3

14 DO 18 J = 1 , NPP $ P = PPS(J) ! PC = PSATF (TPS ( J)

)

15 L = L 1 J PCT=10 0* (P/PC-1) I SS=SS+PCT**2 $ IF(L-45) 18,17

17 L = 0 l PRINT 1, TTRP, TCRT I PRINT 3

18 FRINT 4, IOP(J) ,TPS ( J) , P,PC,PCT

19 SS = SQRTF ( SS/NPP) I PRINT 5, NPP, SS

20 RETURN $ END

130
APPENDIX H. (Continued)

06/85/74

SUBROUTINE PEEK

C EXAMINE BEHAVIOR OF THE COEFFICIENTS.

COMMON B1,B2,B3,B4, ER * E1,E2,E3

COMMON/l/AL , BE, EP,GK, DC RT , TCRT , F CRT , DTRP, TTRP , FTRF

COMMON/6/ TSAT, THETA, PSAT

4 FORMA T ( 1H1 14X ’EQUATION OF STATE, COEFFICIENTS* //

1 15X 6H0TRP =F8 • 4, 8H, TTRP =F 8 . 3 , 8H, PTRP =F13.9/

2 15X 6H0CRT =F8.4, 6H, TCRT =F8.3, 8H, PCRT =F13.9//

3 15 X 4HAL =F5. 2 , 6H, BE =F5.2, 6H, EP =F5.2//

5

12X 3F15.9/ 12X 2F15.9/ ) 5 FORMAT ( 15X 5HM0L/L 6X4HTSAT 5X5HTHETA 6 X4HPSAT

1 9X1HB 9X1HC ) 6 FORMAT (10X F10.1, 5F10.3)

70 FRINT 4, DTRP, TTRP, FTRP, DCR T , T CR T , PCRT , AL ,BE , EP ,

1

B1,B2,83, E1,E2

71 PRINT 5 $ DO 77 J=l,46 $ ON = 0.5*J $ S = ON/DCRT

72 R=DN/ DTRP % R2=R**2 J R3=R**3

73 5 = 31 t B2*R «• 83*R2/(1+BE*R2)

74 E = (S-l)* (S-ER)*(E1 E2*R)

76 TS=TSAT=TSATF(ON> S TH=THETAF (DN) $ PS=PSATF(TS)

77 PRINT 6, DN, TS,TH,PS, B, E 99 RETURN % END

06/05/74

SUBROUTINE ISOTHERM

C PRINTOUT THE CRITICAL ISOTHERM.

COMMON/l/AL , BE, EP, GK, CCRT , TCPT , FCRT , D TRP, TTRP , FTRF

C0MM0N/3/DPDT ,D2PDT2,DPSDT , DPMCT ,DPDC,DPCR, OTSCP , 0 THOR

C0MM0N/4/XBl,XB2, XC1,XC2, XE1,XE2, DXB 0 R , D XC OR , C X E CR

1 FORMAT ( 1H1 14X *THE CRITICAL ISOTHERM* //

1 10X 4HTC =F8.3, 6H, OC =F7.3, 6H , PC =F8.4//

2 11X 4HD/DC 9X4HP/PC 8X5HDP/DD 4X6H0TS/0R 4X6HDTH/DR

3 4X6HDPS/DR 4X6HDX B/DP 4X6HDXC/DF ) 2 FORMA T (5X F10.2, 2F13.9, 5F10.5)

5 FRINT 1, TCRT, DCRT , FCRT $ CO 8 J=l,51

6 OR : 0.74 < 0.01*J $ DN = OCPT’DR

7 FR = OPORF ( TCRT , ON ) /PCRT $ DPSOR = OPSDT’DTSOR

8 PRINT 2, DR , PR , DPD D , D TS DR , DTH DR , DPS DR , CXBDR ,DXEDR

9 RETURN t END

131
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APPENDIX H. (Continued)

06/85/74

SUBROUTINE SETUP

C SET UP THE ARRAYS FOR LEAST SQUARES.

COMMON B1,B2,B3,B4, ER, E1,E2,E3

COMMON/l/AL ,BE,EP, GK, DCRT , TOR T , PCRT , DTRP, TTRF, PTSP

COMMON/ 2/NP,NF, 10 (999) ,T(999) , P (999) , DEN (999)

COMMON/6/ TSAT, THETA, PSAT

COMMON/999/ NFUN,Y,F(30)

1 NFUN = NF $ DO 10 J=1,NP

2 TT = T ( J) J X = TT/TCRT $ 0 = DEN(J) f S = D/OCRT

3 R = D/OTRP S R2 = R*R $ R3 = R*R2 $ RG = R*GK

4 TS=TSAT=TSATF(D) I THETA=THETAF (D) « PS = PSATF(TS) t XS=TS/TCRT

5 XB = XBF (TT , D) $ XE = ( S- 1

) * ( S- ER) *XEF (TT , D

)

6 F (1 ) =XB * F(2)=XB*R $ F ( 3) =XB*R2/ (1+BE* R2)

7 F (4 ) = XE $ F ( 5) = XE* R

9

Y = (P( J)/RG/TT-1) *X/R - ( PS/RG / T S-l ) *X S /R

10 CALL FIT $ CALL COEFF J CALL STAT

11 8i = F ( 1 ) S B2=F(2) $ B 3=F ( 3

)

12 Ei=F(4) * E2=F (5)

30 RFTURN $ END

06/05/74

FUNCTION THETAF (OEN)

THFTA = TS AT *EXP (U ( S ) )

.

LET Q = (S-l) /(ST-1) , WHERE ST = DTRP/D CRT , THEN - IF S < 1, U = AL*Q**3, IF S > 1, U = -AL*Q**3,

YIELOS ALSO THE FIRST DERIVATIVE RSP, TO RHO r OEN/DTRP.

COMMON/1/ AL , BE, EP, GK, DC RT , TCRT , PCRT , D TRP, TTRP , PTRP

COMMON/3/DPOT,D2PDT2,OPSDT , OPMC T , DPO C , D P CR , DTSCR,OTHOR

COMMON/6/ TSAT, THETA, PSAT

1 S = DEN/DCRT t D SDR = DTRP/DCRT S C = DSOF-1

20= (S-l)/C $ Q2 = Q*Q $ U = AL*Q*Q2

3 U1 = 3*AL*Q2*DSDR/C * IF(Q) 5,9,4

4 U = -U $ U1 = -U

1

5 XP = EXPF(U) J THETAF = TSAT*XP

6 CTHDR = ( TS A T* U1 OTSOR)*XP f RFTURN

9 THETAF = TCRT f OTHDR =0 $ RETURN f END

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APPENDIX H. (Continued)

06 / 05/74

FUNCTION PVTF(T,DEN)

C YIFLDS P,8AR, ALSO DP/DT, D2P/DT2.

COMMON 81, 82, 83, B4 , ER, E1,E2,E3

COMMON/l/AL ,BE,EP, GK, OCRT , TCRT , PCRT , D TRP, TTRP , PTRP

COMMON/3/DPDT,D2PDT2, DPSOT, DPMCT, CPOO,DPCR, DTSDR,0TH0R

C0MM0N/4/X81,XB2, XC1,XC2, XE1,XE2, OXBOR , DXCDP , CXEDR

C0MM0N/6/ TSAT, THETA, PSAT

1 Q = DEN * S = Q/DCRT £ R = Q/DTRP

2 R2 = R*R $ R3 - R*R2 $ RG = R *GK

3 TS=TSAT=TSATF(Q) I THETA =THETAF ( C ) * PS=FSATF(TS)

4 XB = XBF (T , Q ) $ XE = XEF (T , Q

)

5 e = B1 + B2*R + B3*R2/(1+BE*R2)

6 E - (S-l) * (S-ER) *( El + E2*R>

9 F = B*X8 + E*XE $ FI = B*XB1 + E*XE1 $ F2 = E*XB2 + F*XF2

11 YS = <PS/RG/TS-1)*TS/TCRT/R

15 FVTF = (T R* (F+YS)*TCRT)*RG £ DPOT = (1+R*F1)*RG

17 C2P0T2 = R* RG*F 2/T CRT $ RETURN £ END

06/05/74

FUNCTION OPDRF CT ,DEN)

DPORF = P,BAR. OP/DR IS IN COMMON • GK = 0* 08 31434*DTRP.

EQNSTATE IS Y = YS AT + F (R , T ) , WHERE Y = (Z-1)*X/R, AND -

F (R , T ) = B*XB + C*XC + 0*XD + E«XE, YIELDS DFR I V . - DP/DR = 2*P/R - GK*T + R2*GK*TCRT* (F 1 + YS1).

COMMON B1,B2,B3,B4, ER, E1,E2,E3

COMMON/l/AL, BE, EP,GK, DC RT , TCR T , P CRT , D TRP , TTRP , PTRP

COMMON/3/DPDT, D2PD T 2 , DPS DT , OPMD T , DPD D, D P CR , DTSDR , D THOR

C0MM0N/4/XB1 ,XB2, XC1,XC2, XE1,XE2, DXB O R , D XC DR , D X E DR

COMMON/6/ TSAT, THETA, PSAT

COMMON/7/ XE,XC,XD,XE

1 X=T/TCRT S Q=DEN £ S=Q/DCRT f CS D F=DTRP / DCR

2 R-Q/DTRP £ R2=R*R $ R3=R*P2 £ RG - R* GK

3 TS=TSAT = TSATF (O) £ THETA =THETAF (C ) $ PS = PSATF(TS) £ XS = TS/TCRT

4 XB = XBF (T , G ) $ XE = X EF ( T , G

)

5 BS = 1 + BE *R2 £ BS1 = 2*BE*R 66=91+ B2*R + B3*P2/BS

7 ED = B2 + B 3* ( 2*R/ 8S - R2* BS1/BS/BS)

6 SX = (S-l)MS-ER) £ E = El + E2*R

9 ED = SX *E2 + (2*S - 1 - ER)*OSOR*E £ E = SX*E

12 F = B * X B E*XE £ YS = < P S/R G / T S- 1 ) * X S /R

13 FI = 8*0XB0R + BO*XB + E*OXECR + EQ*XE

16 YS1 = (TS - R* D TSO R + DPSDT*DTSDR /GK - 2*PS/RG) /TCRT

17 C = <F+YS)*R/X £ DP DR = (1 + 2*Q + <R2*Fi + YS1)/X)*GK*T

16 CPORF = ( 1 +Q ) *RG*T £ DPOD = CPCR/DTRP £ RETURN £ ENC

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APPENDIX H. (Continued)

06/05/74

FUNCTION XBF(T,0)

C XEF = SORT <T/TC)*LN (T/TS) = Q<T)*Z(R,T),

C Z(R,T> = LN(U), U(R,T) = T/TS(R).

COMMON/l/AL,BE,EP,GK, DCRT , TCRT , PCRT , 0 TRP , TTRP , PTRF

COMMON/3/DPOT,D2PDT2,OPSOT,OPMCT,CPOO,DPCR, OTSCR ,OTHDR

C0MM0N/4/XBi,XB2, XCi,XC2, XE1, XE2, DXBDR ,DXCOR , DXEOR

COMMON/6/ TSAT, THETA, PSAT

1 TC = TCRT t TS = TSAT $ X = T/TC

2 U = T/TS S U1X = TC/TS J U1R = -U*DTSDR/TS

3 Z = LOGF(U) $ Z1R=U1R/U $ Z1X=U1X/U $ Z2X=-Z1X*Z1X

4 C = SQRTF(X) $ Qi = 0.5/Q $ 02 = -Q1/2/X

5 X8F = Q*Z $ OXBDR = Q*Z1R $ XB1 = Q*Z1X Cl*Z

6 XB2 = Q*Z2X 2*Q1 *Z1X + Q2*Z I RETURN t END

06/05/74

FUNCTION XEF (T , D)

XEF = PSI-PSISAT, PSI = <l-W*l_N (1+1/W) ) /X, W = EPMT/TH-i).

XEF = F(R,T)/X - FS (R ) / XS

F (R , T ) = 1-W*P<R,T> , P (R , T ) = LN(U), U = i+l/W(P,T),

FS (R) = 1-WS*PS(R), PS (R) = LN(V>, \l ~ 1 + 1/HS(R).

COMMON/l/AL ,BE,EP, GK, DCRT , TCRT , PCRT , D TRP, TTRP , PTRP

C0MM0N/3/DPDT,D2PDT2, DPSDT, DPMOT, DPDD, DP CR , DTSDR , D THOR

C0MM0N/4/XBl,XB2, XC1,XC2, XE1,XE2, DXB D R , OXC DR , DX EDR

COMMON/6/ TSAT, THETA, PSAT

1 E=EP t TC = T CRT $ T F=THET A $ TS = TS AT J W = E*(T/TH-i) $ IF(W) 30,30,2

2 WW = W*H J MIX = E*TC/TH t W 1 R = -E * T*D THDR/ TH / TH

3 U=l*l/W I U1R=-W1R/WH $ U1X=-W1X/WW $ U2X = -2»U1X*N1X/W

4 F=LOGF(U) t P1R = U1 R/U * P1X=U1X/U $ P 2 X = U2X/L - PIX*P1X

5 F = 1 - W*P $ FIR = -W*P1R - W 1 R*

P

6 FIX = -W*P1X - W1X*P t F 2 X = -H*P2X - 2*W1X*P1X

7 WS = E* (TS/TH— 1) $ IF(WS) 8,8,9

6 FS = 1 * FS1 =0 $ GO TO 12

9

WS1 = E* ( DTSDR - TS*DTHDR/TH)/TH J U = 1M/WS

10 PS = LOGF(U) I PSI = -WSl/U/fcS/WS

11 FS - 1-WS*PS $ FS1 = -WS*PS1 - WS1*PS

12 X=T/TC t X2=X*X % XS=TS/TC I XS1=CTS0R/TC

13 XFF = F/X - FS/XS I XE1 = F1X/X - F/X2

14 XE2 = F2X/X - 2*F 1X/X2 2*F/X/X2

15 CXEDR = F1R/X - FS1/XS FS*XS1/XS/XS $ RETURN

30 XEF - XE1 = XE2 = OXEDR =0 f RETURN $ END

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APPENDIX H. (Continued)

06/95/74

FUNCTION DENGASF (T

)

ETHANE SATD . VAPOR DENSITIES, MCL/L, VIA LAB. NOTE 73-4, 73-5 . Y = Ai A2*Q2 A3 *0 3 . . , NF = AL , YN - L N < DC RT / DT R F ) , U = 2 (ZE-Z) *Y , DEN = DCRT* E XP (-Y N*U ) . COMMON/l/AL,BE,EP,GK, DCRT , TCRT , FCRT , D T RP , TTRF , F T R

C0MM0N/9/IS,NPS,EG ,EL, ALS,BES,AL1 ,AL2,AL3,CG(5),AV(8),AW(5)

DATA (OGAT = 1.35114E-6)

1 FORMAT ( 1H0 9X *DENGASF = 0, T EXCEEDS TCRT. * / ) 2 IF (TCRT-T) 3,4,5

3 PRINT 1 * STOP

4 CENG A SF = DCRT $ RETURN

5 YN = LOGF (DCRT/DGA T) f Z = ( TCP T/T -1 )/( TCRT /T T RP - 1

)

6 C = CUBERTF(Z) $ Y = CG(1> $ DO 7 K=2,5

7 Y = Y CG(K)*Q**K J U = Z (Z**EG-Z)*Y

8 CENG A SF = OCRT*EXPF ( - YN* U) $ RETURN * END

06/05/74

FUNCTION DENLIQF (T

)

ETHANE SATD. LIQUID DENSITIES, MOL/L, VIA LAB. NOTE 73-5.

Y = Al A2*Q2 + A3*G3 + . . . , YN = DTRP-DCRT,

DEN = DCRT YN*(X + (XE-X)*Y).

COMMON/l/AL ,BE,EP,GK, CC RT , TCR T , F CRT , D TRP , TT RF , F T R

C0MM0N/9/IS ,NPS,EG ,EL ,ALS,BES,AL1 ,AL2,AL3,CG(5),AV(8),AW(5>

1 FORMAT ( 1H 0 9X *DENLIQF = 0, T EXCEEDS TCRT. * / ) 2 IE (TCRT-T) 3,4,5

3 PRINT 1 t STOP

4 OENLIQF = OCRT S RETURN

5 X = ( TCRT-T) / (TCRT-TTRP) S W = X**EL - X 6 0 = C U8 ER TE ( X ) $ Y = A L 1 «- AL2*C*Q AL3*X

7 CENLIQE = DCRT ( D TR P -D CR T

) * ( X W*Y) J RETURN % END

06/05/74

FUNCTION PMELTF(T)

C ETHANE MELT P TO 42 ATM., CL US I US / WE I GAN D , 1940 . C SIMON EON., P = PT RF + A*(X**2 -1), X = T/TTRF.

C0MM0N/3/DPDT,D2PDT2, DPSDT, OPMD T , DPD D, D P CR , DTSCR,OTHDR

CATA (TTRP = 8 9. 8 99) , ( PTRP =9 . 96 7E -6 ) ,(A= 2840.0) ,(Q = 1.013 25 ) 1 X = T/T TRP « PMELTF = QMPTRF + A*(X*X-1))

2 CPMOT = 0*A*2*X/TTRP $ RETURN S END

* SINGLE-BANK COMPILATION.

ROGRAM LENGTH 00063

135
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APPENDIX H. (Continued)

0

6/ 1) 5/ 74

FUNCTION PSATF(T)

C ETHANE V.P., BAR , VIA LAB. NOTE 73-3.

COMMON/l/AL,BE,EP,GK, OCRT , TCRT , PCRT , DTRP, TTRP , PTRP

COMMON/3/DPDT,D2PDT2,DPSOT,DPMCT,DPDO,DPDR, DTSDR ,QTH0R

COMMON/ 8 /I P*NPP,P1*P2»P3,P4,P5» IDP(99) ,TPS(99) ,PPS(99)

1 FORMAT ( 1H0 9X *PSATF = 0, T EXCEEDS TCRT. * / ) 2 XN = 1-TTRP/TCRT $ OXDT = TTRP/XN/T/T

3 X=(i-TTRP/T)/XN $ X2=X*X $ X3=X*X2 S X4=X2*X2

4 V = 1-X I IF (V ) 5,6,7

5 PSATF = OPSOT =0 $ PRINT 1 $ RETURN

6 Z = Z 1 = 0 t GO TO 9

7 C = SQRTF(V) $ W = V*Q $ W1 = -3*Q/2

8 Z = X*W * Z1 = W X*W1

9 F = P1*X P2*X2 P3*X3 P4*X4 P5*Z

10 FI = PI * 2*P2*X 3*P3*X2 4*P4*X3 P5*Z1

11 PSATF = PTRP*EXPF ( F ) f DPSDT = FI* DXO T *PS ATF $ RETURN « ENC

06/85/74

FUNCTION TSATF (DEN

)

C THIS NEW TSATF VIA TSATFIT, 4/19/74 AT 09.00.

COMMON/1/AL,0E,EP,GK, DCRT , TCRT , PCRT , D TRP, TTRP , P TRP

C0MM0N/3/0P0T,D2P0T2, OPSOT, OPMOT, DPDD, DP DR, DTSDR, 0 THOR

C0MM0N/9/IS,NPS,EG,EL,ALS,BES,ALl ,AL?,AL3,CG(5) , AV (8) , AH (5)

DATA (NFG= 8 ) , (NFL=5

)

DATA (E = 0.25) , (DGAT = 1.35114E-6)

SATD* VAPOR TEMPS. CONSTRAINED AT T.P. BY SUBTRACTION - DEFINE X = ABS(S-l), XT = ABS(ST-l), WHEN THE FQN • IS - LN(YY) = AL* ( 1/XT-l/X) A 1* LOG ( LN ( 1 * E/S ) /L N ( 1 +E / ST ) ) W(S>,

W(S) = A 2* ( Q— QT ) A3* ( Q2-QT 2) A4*(S-ST) «• A5*(S2-ST2) . . . WHERE, Q = S**l/3, AND OT = ST**l/3.

1 S = OEN/OCRT $ D SDR = DTRP/DCRT t QS = S-l $ IF(QS) 2,30

2 X = ABSF(QS) $ XI = OSDR*QS/X S YN = TCRT/TTPP - 1 3 V=l/X $ Vl=— OSDR/X /CS $ ST=OGAT/CCRT $ IF(QS) 4,30,15

4 XT = 1-ST t V T = l/ XT I U=ALS*(VT^V) $ U1=-ALS*V1 f EK=LOGF(l* E/ST)

5 P = 1 « E/S $ PI = -E*DSDR/S/S $ PG = LCGF(P)/EK

6 G = LOGF(PG) t Gi = Pl/P/PG/EK

7 0 = C U8ERTF ( S) $ QT = CUBERTF (ST) S 01 = 0*DS09/3/S

8 W = U A V ( 1

) *G AV (2 )* (Q-QT) AV ( 3) * ( G*C-Q T* Q T

)

9 HI = Ui A V (1 ) *G1 + A V ( 2

) * Q 1 + AV(3)*2*0*Q1

10 CO 11 K = 4 , NFG f N = K- 3 $ W = W + A V (K) * ( S**N-ST**N) ft 11 HI = HI N*OSDR*A V (K) *S** (N-l) t GO TO 18

SATO. LIQUID TEMPS. CONSTRAINED AT THE T.P. 8Y SUBTRACTION, - EQN. , LN(YY) = H (S ) , WHERE X = ABS(S-1), XT= ABS (ST-1 ) , AND - W (S) = BE* (1/XT - 1/X) El* (S-ST) <• B2*(S2-ST2) . . . 15 ST = DSDR S XT = ST-1 $ W = eES*(l/XT-V) $ Wi = -BES*V1

16 CO 17 K=1

,

NFL $ W = W AW(K)*(S**K - ST**K)

17 Wl = Wl AW (K)*K*OSOR*S** (K-l

)

18 F = EXPF(H) $ FI = Wl* F $ Q = 1 Y N*F

19 TSATF = TCRT/Q $ OTSDR = -YN*Fi*TSATF/Q * RETURN

30 TSATF = TCRT $ DTSDR =0 t RETURN S END

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APPENDIX H. (Continued)

06 / 0/ 7*4

FUNCTION FINDENF(T,P,DI)

ON ISOTHERM T, ITERATE DEN TO MINIMIZE (P-PCALC).

NEWTON-RAPHS0N ITERATION. INITIAL OEN = 01.

NOTE STATEMENTS 14,15 FOR ETHANE

COMMON/l/AL » BE,EP, GK, OCRT , TCRT , PORT , D TRP , TTRP , P TRP

COMMQN/3/OPDT,D2PDT2, DPSDT, OPMD T , DPDD, D P OR , DTSDR » 0 THOR

1 FORMATdHO 9X *FINDENF = 0, FAILS TO CONVERGE. * t ) 2 FORMATdHO 9X FINDENF = DCRT, DP/DR ZERO OR N EG • * / ) 3 FORMATdHO 9X *F IN DENF = 0, 01 INSIDE DOME.* / ) 4 D=DI $ Dr1=OTRP* < T/ TTPP ) * 0 . 25 % DX=DM+1 $ IF(T-TCRT) 5,7,8

5 DG=DENG ASF ( T ) % OL =DENLI OF ( T) % P S=PSATF(T)

6 IF CO. GT.OG.AND.O.LT .DL) 32,8

7 OG=OL =OCRT $ PS=PCRT $ IF (0 . EQ. DCRT ) 33,8

8 DO 30 J=l,50 * DP = P - DPDRF ( T ,D

)

9 IF(ABSF(OP/P)-1.0E-6) 31,31,10

10 IF ( DP DO ) 33,33,11

11 CD = DP/DPDD $ IF (ABSF (DD/D) -1. OE-6) 31,31,12

12 0 = 0 + DO $ IFtO.GT. 0.001) 14,13

13 0 = 0.001 S GO TO 30

14 IF(O.GT.OX) 15,16

15 0 = DM $ GO TO 30

16 IFCT-TCRT) 17,22,30

17 IF(P.LT.PS) 18,20

18 IF(D.GT.OG) 19,30

19 C = OG J GO TO 30

20 IF(O.LT.DL) 21,30

21 C = DL % GO TO 30

22 IF(P.LT.PCRT) 23,25

23 IFCO.LT.DCRT) 30,24

24 C = DCRT - 0.02 $ GO TO 30

25 IFtO.GT. DCRT) 30,26

26 0 = DCRT 0.02

30 CONTINUE $ FI NOE NF = 0 $ PRINT 1 $ RETURN

31 FINDENF = D $ RETURN

32 FINOENF = 0 $ PRINT 3 $ RETURN

33 FINDENF = DCRT % PRINT 2 * RETURN t END

SINGLE-BANK COMPILATION.

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APPENDIX H. (Continued)

06/85/74

FUNCTION FINDSATF ( T , M)

ITERATE OEN TO MINIMIZE (T-TS) VIA TSATF ( DEN)

.

THIS FINOSATF ADJUSTED FOR ETHANE,

M = 0 FOR VAPOR, M = 1 FOR LIQUID,

COMMON/ 1/AL , BE, EP, GK , DCRT , TCR T , FCRT , D TRP , TTRP , PTRP

COMMON/ 3/OPOT, 02PDT2, DPS DT , DPMCT , DPDD, DP CR,DTSOR,D THOR

DATA (DGT=5.0E-7>, <DLT=23.0>

1 FORMATdHO 9X *FINOSATF = 0, FAILS TO CONVERGE.* / ) 2 FORMATdHO 9X *FIN DSA TF = 0, T EXCEEDS TCRT.* / ) 3 IF ( T- TCRT ) 4,22,23

4 IF(M.EQ.O) 5,6

5 D = OENGASFCT) S GO TO 7 60= DENLIQF (T)

7 00 20 J = l, 50 t DT=T-TSATF ( D) $ IF ( A BSF ( D T/T ) - 1 . 0 E-6 ) 21,21,8

8 OTDD = DTSOR/OTRP $ IF ( DTDO. EQ . 0. 0 ) 22,9

9 DO = DT /OTDD $ I F ( A BSF ( DO /0 ) - 1 . 0E-6) 21,21,10

10 D = 0 t DO $ IF(M.EQ.O) 11,15

11 IF(O.GT.OGT) 13,12

12 0 = OGT t GO TO 20

13 IF(O.LT.OCRT) 20,14

14 0 = DCRT - 0.02 $ GO TO 20

15 IF(D.GT.DLT) 16,17

16 D = DLT $ GO TO 20

17 IF CD.GT .DCRT) 20,18

18 0 = DCRT «• 0.02

20 CONTINUE $ FINDSATF = 0 $ PRINT 1 $ RETURN

21 FINOSATF = D S RETURN

22 FINDSATF = OCRT $ RETURN

23 FINDSATF = 0 t PRINT 2 $ RETURN * END

06/05/74

C

FUNCTION Z I PF ( T , D)

ETHANE VIRIAL EON. VIA LAB. NOTE 73-4.

DIMENSION B (5) , C( 3)

CAT A (TCRT = 3 05. 33) , ( VCRT = 0 . 1 45 5 6 ) ,(TB=7 40.0),(TC = 217.8)

CATA ( B = 7.993156, -10.672497, 9.217322, -2.481668, 0.842328)

DATA ( C = 0.253773, 0.865299, 0.556075)

S = 0 *VCRT

X2 = ZB = BV = CV = ZIPF

t X = T/T CRT

X*X $ X 3 = X* X 2 2

1 - ( T B/T ) **0 .25 2 ZBM8<1) + 8<2)/C

ZC*(C(1)/X + C ( 2 ) /X 3 = 1 B V*S CV*S*S

* 0 = X* *0 • 2 5 X5 = X 2* X 3

ZC = 1 - TC/T

B (3) /X B (4) /X2 B ( 5 ) / X 3

)

+ C ( 3 > / X5 ) f RETURN t END

138
APPENDIX H. (Continued)

05/09/74

SUBROUTINE FITTER

COMMON/999/ NCOF,V,G(30)

OIMENSION A(30,31) ,B<30,31)

COMMON /77 7/ A,SY,SYY,RES

TYPE DOUBLE SY , SYY ,RES , A,

DATA <NTR=-1), <NDIM=30)

EQUIVALENCE (A,B)

37 FORMAT (*i T HE COEFFICIENTS AND THEIR ESTIMATED ERRORS ARE 0 */ /)

38 FORMAT <*0 * /*0*/*OE STIMATE D RESIDUAL SUM OF SQUARES =*E17.9/

1 * ESTIMATED REGRESSION SUM OF SQUARES =*E17.9/

2 * ESTIMATED TOTAL SUM OF SQUARES =*E17.9/

3* VARIANCE OF FIT =*E17.9/* DETERMINANT OF THE MATRIX =*E17.9/

4* CORRELATION COEFFICIENT =*E17.9/* NUMBER OF POINTS = *I5)

45 FORMAT (*1 THE ARRAYS IN THE FITTING PROGRAM ARE TOO SMALL TO HOLD T 1HE NUMBER OF CONSTRAINTS AND FUNCTIONS ASKED FOR IN THE CALLING PR

20 GRAM*

)

371 FORMAT (E19.10,* +0R-*E9.2>

C ENTER HERE TO FIT THE DATA

ENTRY FIT

IF(NTR) 1,3,3

1 NP = 0 NF=NCOF

IF ( NF • GT. N DIM) GO TO 44

NCO N= 0 S Y= 0 • SYY =3.

NY=NF+1

DO 2 1=1, NY

DO 2 J = 1 , N

2 A (J ,1) =0.

IF(NTR.EQ.O) GO TO 11

N TR = 0 3 SY=Y+SY

SYY =SY Y +Y * Y DO 4 J= 1 , NF

A ( J , NY ) =A ( J , NY ) +Y* G (J)

00 4 1=1, NF

4 A (I , J) =A ( I , J) *G (I) *G ( J ) N P= NP+ 1 RETURN

C ENTER HERE TO CONSTRAIN THE EQUATION

ENTRY CONS TR

IF(NTR) 10,11,11

10 N TR = Q

GO TO 1 11 N = N Y—l

IF( (NY *NC0N*2) .GT.NDIM) GO TO 44

00 12 1=1,

A (I ,NY + 1) =A (I, NY)

A (NDIM-NCON,!) =G(I

)

A(NY,I)=G(I)

12 A (I , NY ) =G ( I

)

NCON=NCON+l

DO 13 I =NF , N

A (NY,I + 1) = 0.0

139
o

O

«->

APPENDIX H. (Continued)

FITTER

13 A ( I +1 , NY) = 0 • 0 NY=NY+1

A (NY-1 , NY) =

Y

RETURN

C ENTER HERE TO INVERT MATRIX ANG GET COEFFICIENTS

ENTRY COEFF

N =N Y-l

00 20 1=1, NF

20 G(I)=A(I,NY)

DO 22 1=2,

N

DO 21 J=I , N

Y

21 A (1-1, J)=A (1-1, J)/A(I-1,I-1)

DO 22 J=I ,

N

DO 22 K=I , NY

22 A (J,K) =A( J,K)-A (J, 1-1) *A(I-i,K>

A (N ,NY ) =A (N,NY) / A ( N , N

)

DO 24 1=2,

N

1 =N -I

2

DO 24 J=L , N

24 A (L -1 , NY) = A (L-l , NY > - A ( L-l , J ) *A ( J , NY > RES=SYY

DO 25 1=1, NF

RES=RES-A(I,NY)*G(I)

25 G (I ) =A (I, NY)

DF=NP-NF+NCON

Y=NCON

N TR = -1

RETURN

C ENTER HERE FOR STATISTICS OF COEFFICIENTS

ENTRY STAT

DO 27 1=1 , NCON

DO 27 J=1 , NF

2

7 RES=RES-A (NDIM-I+i , J

) * A ( J , NY ) * A (NF + I ,NY

)

TOT=SYY-SY*SY/NP

REG=TOT-RES

S Y Y =RE S/DF

ST=l*96+2»72/DF+8. 04/DF**3

D ET = 1

•

DO 30 1=1, NF

0ET=DET*B (1,1)

30 A (I ,1) =1. 0/A (I , I)

DO 32 1=2, NF

DO 32 J=2 ,

I

S Y= 0 • 00 31 K=J ,

I

31 SY=SY-A(I,K-1) *A(K-1,J-1)

32 A (I ,J-1)=SY*A(I ,1)

PRINT 37

DO 36 1=1, NF

L =NF-I

DO 33 J = 1 , L

K = NFJ

DO 33 H =1 ,

J

N=NF-M

1

33 A (K,I) =A(K,I)-A (K, N) # A (N» I

)

05/09/74

140
APPENDIX H. (Continued)

FITTER 05/09/74

DO 34 J~2 t I 34 A < J-l, I) = A <I,J-1)*SYY

DO 35 J=1,I

35 A (I ,J)=A(I,J)*SYY

88= 8 ( 1 , 1 ) C 88 IS THE VARIANCE OF THE COEFFICIENTS

IF< 8B.LT. 0 .0)BB=-8B

FF=ST*SGRT (BB)

B3B=B(I,NY)

36 PRINT 371, BBS, FF

IF(SYY.LT. 0.0) SYY =-SY Y CORR=REG/TOT

PRINT 38, RES, REG, TOT, SYY, DET,CORR,NP

Y = SQRT (RES/OF)

RETURN

44 PRINT 45

STOP

END

SINGL E-9ANK COMPILATION.

141
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APPENDIX I. Computer Programs for Thermofunctions 06/06/74

PROGRAM ETHERM02

C START ETHANE PROVISIONAL THERMOFUNCTIONS, 14 FEB., 1974.

COMMON B1,B2,B3, ER, E1,E2

COMMON/l/AL,BE,EP,GK, OCRT , TCR T , PORT , D TRP , TTRP , PTRP

C0MM0N/3/DPDT,D2PDT2,CPSDT ,DPMCT ,DPDO,DTSDR,OTHDR

COMMON/4/ XB1,XB2, XE1.XE2, OXeDR,OXEDR

COMMON/6/ TSAT, THETA, PSAT

COMMON/7/ T B , PB , H B , SB

COMMON/8/ P , T, DEN, E,H,S, CV,CP,CSAT, W,WK

CCMMON/9/ El (60), SI (60), CVI (60)

COMMON/ 10/ 0F(34),EF (34) ,SF (34) , C VF (34)

COMMON/99/ TI,EZZ, EZ,SZ,CVZ, HZ,CPZ

DIMENSION PP (99

)

3 FORMATdHl 11X *LOOF CLOSURE CHECK FOR SATURATED LIQUID,* /

1 12 X ^ENTHALPY, H, VIA FURTADO CP(T). HC VIA CLAPEYRON EQN • * //

2 12X 3HT,K 9X1HH 8X2HHC 7X3HFCT 9X1HS 8X2HSC 7X3HPCT » 4 F ORM A T ( 5X 3F10.0, 4F10.2)

5 FORMAT(IX)

1C FORMATdHl 9X * ETH ANE FUNCTIONS AT TB ON THE CP ISCEAR AT PE.*//

1 10X 5HT9 =F8.3, 6H

,

PB = F 8 . 3 , 6 H,

2 10X 5HEZ =F 1 0 • 2

,

6 H

,

E =F10.2//

3 10X 5HHZ =F10.2, 6 H

,

H =F10.2//

u 10X 5HSZ = FI 0 . 4, EH, S =F10 .4//

5 10X 5HCVZ =F 1 0 . 3

,

6 H

,

C V = F 1 0 • 3/ /

6 10X 5HCPZ =F1 0 . 3

,

EH, CP =F10. 3//

7 10X 21HFURT ADOS VALUE t CP =F 1 0 • 3)

15 FORMA TC3F10.0)

16 FORMA T(//////// 1H1 18X ETHANE ISOBAR AT P =*F6.1, 4H EAR//

1 19 X 1HT 6X3HDEN 6X3HV0L 5X5HDP/DT 5X5HDP/PO 8X1HE 8X1HH 8X1HS

2 6X2HCV 6X2HCP 5X1HW /

3 1 5 X 5HDEG K 4X5HMCL/L 4X5HL/MCL 5X5HBAR/K 1X9HB AR-L/MOL 4X5HJ/M0L

4 ^X5H J/MOL 2X7HJ/MCL/K 1X7HJ/MCL/K 1X7H J/MCL/K 1X5HM/SEC ) 17 FORMAT ( 10X F10.3, F5.3, F9.5, F10.4, F10.3, 2 F9 . 1 , F 9 . 3 , 2F 8 . 2 ,F 6. 0

)

18 FCRMATdOX F10.3, F9.5, F9.3, F10.6, F10.3, 2F9 . 1 , F9 . 3 , 2F8 . 2 ,F6. 0 ) CONSTANTS OF EQNSTATE, 6/5/74 AT 8.21.

NOTE, EZZ FROM TESTER.

30 WM = 30.07 I WK = 100000/WM $ Q = 1.01325 $ GKK = 0.0831434

31 TTRP = 89.899 * DTRP = 21.68 ? PTRP = 0*9.6676-6

32 TORT - 305.37 I DCRT = 6.74 t PORT = PSATF(TCRT)

33 GK - DTRP*GKK $ EZZ = 4.1868*4827.2

34 AL =2 $ BE = 1 $ EP = 0.5 $ ER = 1.90

35 ei = 1.348167996 $ B2 = 1.569704511 * B3 = 5.560186452

36 El = -1.042842462 $ F2 = 0.224978299

C INTEGRATE ON ISOTHERM TB UP TO POINT (TB , FB) , THFN -

C GET FURTADO, S CP(T) FOR COMPARISON, AND PRINT ALL VALUES.

40 TP = T = 340 $ PB = P = 137.895

41 CALL SAVIDEAL $ CALL HOMO THRM ? TI = T * CALL IDEAL

4? HB = H $ SB = S $ CPX = CPXF(T)

43 PRINT 10, T , P , D EN , EZ,E, HZ,H, SZ,S, CVZ,CV, CFZ,CF, CPX

44 CALL MEMORY

C

C NCW COMPARE SATLIQ FUNCTIONS VIA FURTADO WITH CLAPEYRON.

50 PRINT 3 S DO 60 J=l,43 S T = 85 + 5*J

51 P = PS - PSATF(T) ? CALL SATC-STRM ? CG = DEN

142
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APPENDIX I. (Continued)

ETHERM02 06/06/74

52 DL = FINOSA TE ( T , 1) $ Q = 100*T*DPSDT* ( 1/DL-1/DC-)

53 HC = H + Q « SC = S + Q/T

55 CALL SATLQTRM $ HF = 100MHC/H-1) $ SR = 100*(SC/S-1)

60 PRINT 4, T, H,HC,HR, S,SC,SR

98 CALL JTLOCUS * CALL TA6LIQ

COMPUTE THERMOFUNCT ICNS ON ISOBARS.

EACH ISOBAR STARTS ON THE MELTING LINE.

ISOBARS AT P UNDER PORT TRAVERSE THE OOME.

LET THE FIRST ISOBAR BE AT P = 0.1 BAR.

ENTER COMPRESSED LIQUID V/ 1 A FUPTACC CP(T) ON 1 37.695 BARISC0AR.

10C NI = 68 $ PP ( 1 ) = 0.1 % READ 15, ( P P ( I ) , I = 2 , N I

)

102 DO 30 0 1 = 1, NI * P = PP < I > % PFINT 16, P 103 CALL MELTHERM * V = 1/DEN

104 PRINT 17, T , DEN , V, DPDT , DPDD, E,H,S, CV,CP,W

105 IT = T/10 $ IF(P.LT.PCRT) 110,199

C

C

C

C

r

C

CASES FOR P LESS THAN PCRT.

110 TS = FINDTSF (P) $ TX = TS + 10 $ K = L = 111 DO 150 J= 1 ,99 ? T = JT = 10*(IT*J)

112 IF(T.LT.TS) 113,115

113 call LIQTHERM % V = 1/DEN

114 PRINT 17, T , DEN , V, DPDT, DPDD, E,H,S, CV,CP,W

115 IF(T.LT.TX) 118,130

CASE FOR THE SATURATED LIQUID AND VAPOR.

116 T = TS I CALL SATLCTPM J V = 1/DEN

119 PRINT 17, T , OEN , V, DPDT , DPDD, E,H,S, CV,CP,W

120 CALL SATGSTRM * V = 1/DEN

121 IF(P.LT.20. 0) 122, 123

122 PRINT 18, T , D E N , V , DPDT, DPDD, E,H,S, CV,CP,W

123 FPINT 17, T , DEN , V, CPCT,CFDC, E,P,S, CV,CP,W

124 T = JT

CASES FOP THE HOMOGENEOUS DOMAIN.

130 IF (JT-5Q9) 135,135,131

131 K = K + 1 * T = JT = JT + 10*K

132 IF (JT-600) 135,135 , 300

135 CALL HOMOTHRM f V = 1/DEN

13C IF(P.LT.20. 0) 137,138

137 PFINT 18, T , DEN , V, DPDT, DPDD, E,H,S, CV,CP,W

13fc PRINT 17, T,DEN,V, DPDT, DPDD, F,H,S, CV,CP,W

1 5 C CONTINUE

0

f

f

?

CASES FOR P GREATER THAN FCRT.

199 K = L = 3 200 DO 25 0 J = 1 , 9 9 J T = JT = 10MIT+J)

201 IF (T.LT.TB) 202,21 0 202 IF ( T . GT .TCRT ) 203,205

203 PX = PVTF (T ,QCRT,0 ) J IF(P.GT.FX) 205,220

CASE FOR THE COMPRESSED LIQUID.

205 CALL LIQTHERM $ V = 1/DEN

206 PRINT 17, T , OEN , V, DPDT, DPDD, E,H,S, CV,CP,W ? CASES FOR THE HOMOGENEOUS DOMAIN.

210 IF(JT-500) 220,220,211

211 K = K+t ? T = JT = JT + 1 0 * K

GC TC 1 5 C

PRINT 5

GC TO 1?4

GC TC 150

GC TO 2 5 C

143
APPENDIX I. (Continued)

ETHERM02

212 IF (JT-600) 220,220,300

220 CALL HOMOTHRM $ V = 1/DEN

221 PRINT 17, T , DEN , V, DPDT , DPDD, E,H,S, CV,CP,W

250 CONTINUE

300 CONTINUE

999 STOP % END

SUBROUTINE SAVIDEAL

C MEMORIZE IDEAL GAS FUNCTIONS EVERY 10 K THRU 600 K.

C NCTE USE BY HOMOTHRM ONLY.

COMMON/9/ El (60) ,SI (60) ,CVI (60)

COMMON/99/ TI , EZZ , EZ,SZ,CVZ, HZ,CPZ

1 DC 9 J = 9 , 6 0 * TI = 10* J J CALL IDEAL

2 E I ( J ) = EZ $ SI < J ) = SZ $ C VI (J) = CVZ

9 CONTINUE J RETURN J END

SUBROUTINE MEMORY

C MEMORIZE CPSUMIT RESULTS EVERY 1C K FROM 90 TO 340

C NOTE USE BY L IQTHERM ONLY.

COMMON/3/P, T ,DEN, E,H,S, CV,CP,CSAT, W,WK

COMMON/ 10/ DF(34),EF (34) ,SF(34),CVF(34)

1 00 9 J= 9, 33 J T = 10*J $ CALL CPSUMIT

2 C F ( J ) = DEN * EF ( J) = E J SF ( J) = S $ CVF ( J)

9 CONTINUE * RETURN S END

06/06/74

06/06/74

06/06/74

K.

= CV

144
APPENDIX I. (Continued)

06/06/74

SUBROUTINE JTLOCUS

C DERIVE THE J-T INVERSION CURVE. USE ROUTINE DEL TAP ( T ,01) . DIMENSION TT (99) ,PP (99) , ON (99)

DATA (QCRT=6.76)

,

( TCP T = 3 0 5 . 4 3

)

1 FORMAT ( 1H1 16X *THE JCULE-THCMSON INVERSION LOCUS FOR ETHANE*//

1 17X3HT,K 5 X5HP * BA R 5X5HM0L/L 7X3HT,K 5X5HP,BAR 5X5HM0L/L)

2 FORMAT ( 10X F10.0, F10.1, F10.2, F1C.C, F1C.1, F10.2)

6 TA = 240 « NP = 72

7 PRINT 1 I DO 25 1=1, NP S DX = 1.6

8 T = TA + 5*1 $ X - T/TCRT

o Cl = OCRT* (2.40 - 0. un OD * X + 0. 2 4 / X ) 10 IF(T-TCRT) 11,12,12

11 CL = DENLIQF(T) $ IF (DI -DL) 25,12,12

12 SS = DELT AF ( T, 01 ) ? DO 20 I T = 1 , 15

14 0 =D I - DX ? SL = OELTAF(T *D) $ D = DI DX t SP=DEL T AF ( T 15 IF(SS-SL) 18,16,16

16 IF(SP-SL) 19,17,17

17 SS = SL S DI= D

- DX $ GC TC 20

18 IF(SS-SP) 20,20,19

19 SS = SP $ DI = D

+ DX

20 OX = DX/2

23 T T ( I ) = T J D N ( I ) = DI $ PP(I) = PVTF(T,OI,0)

25 CONTINUE $ N = NP/2 $ DO 2 9 J =1 ,

29 PRINT 2, TT ( J) ,PP( J) * D N ( J ) , TT (J+N) ,PP (J + N) , CN (J + N)

30 RETURN $ END

06 /06/74

FUNCTION DEL TAF (T, D)

C GET (T*OR/OT - D*DP / DD ) FOR THE J-T INVERSION CURVE.

C0MM0N/3/DPDT, D2PD T2,DPSDT ,DPMCT ,DPDD,DTSDF,DTHDF

DATA (DCRT = 6.76) ,

( TCPT = 305. 43)

1 IF(T-TCRT) 2,4,4

2 DL = DENLIQF(T) $ IF(O-DL) 3,3,4

QFLTAF = 1 . 0E+10 0 I RETURN

P = PVTF (T, D , 1

)

DELTAF = ABSF ( T*DPOT - D*OPDO

)

RETURN

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APPENDIX I. (Continued)

06/86/74

SUBROUTINE TABLIQ

C TABULATE THE ETHANE SATURATED LIQUID FUNCTIONS.

COMMON/l/AL,BE,EP,GK, DCRT , TCRT , FCRT , D TRP , TTRP , PT RP

COMMON/3/DPDT,D2PDT2,DPSDT,DPMOT, DPDD, D TSDR ,D THDR

COMMON/3/ P,T,DEN, E,H,S, CV,CP,CSAT, W , WK

DIMENSION TSA<46), PSA(46>

4 FORMA T ( 1H1 13X ’PROPERTIES OF SATURATED LIQUID ETHANE* //

1 14X1HT 10X1HP 5X3HDEN 4X5HV,LIQ 6X5HV,GAS 5X6HDFS/DT 3X6HDCL/DT

2 6X5H0P/0T 6X5H0P/0D 2X5HQ,VAP 2X5HQ,XPT /

3 10X5HOEG K 8X3HBAR 3X5HMOL/L 4X5HL/M0L 6X5HL/M0L 6X5H3AR/K

4 2X7HM0L/L/K 6X5HBAR/K 2 X9H B A R-L / MOL 2X5 H J/ MOL 2X5HJ/M0L ) 5 FORMAT(5XF10.3, Ell. 3, F8.3, F9.5, 2E11.3, F9.4, 2E11.3, 2F7.0)

11 FORMAT ( 1H1 13X ’PROPERTIES OF SATURATED LIQUID ETHANE* //

1 14X1HT 1 1 X 1 HP 9X1 HE 9X1 HH 9X1HS

2 6X2HCV 6X2HCS 6X2HCP 6X1HW 2X6HCS,XPT /

3 10X5HOEG K 9X3HBAR 5X5HJ/MOL 5X5HJ/MOL 3X7HJ/M0L/K

4 1X7H J/MOL/K 1X7HJ/M0L/K 1X7HJ/MCL/K 2X5 HM/SEC 1X7HJ/M0L/K ) 12 FORMA T ( 5X F10.3, E12.3, 2F10.1, F10.3, 3F8.2, F7.0, F8.2)

C FOR PAGE ONE OF TABLIQ.

140 PRINT 4 J NP = 46

141 DO 151 J-1,NP t IF(J.EQ.l) 142,143

142 r = TTRP $ GO TO 147

143 IF(J.EQ.NP) 144,146

144 T = TCRT J OG = DL = DCRT $ CDLDT = 0 145 VG = VL = 1/OG J GO TO 149

146 T = 80 + 5 * J

147 OL = FINOSA TF ( T , 1) $ DDL DT = DT RP/DTSDR

146 DG = FINOSATF (T ,0) J VG = 1/DG $ \ll = 1/OL

149 TSA(J) = T t PSA(J) = PS = PSATF(T)

150 QC = 100*T* DPSDT* ( VG-VL) $ PX = PVTF(T,DL,1) S QX = CVAFXF(T)

151 PRINT 5, T,PS,OL, VL,VG, DPSDT, DDLDT, DPDT, OPDD , QC,OX

FOR PAGE TWO OF TABLIQ.

NOW INTEGRATE ALONG FB, THEN ON ISOTHERM T DOWN TO THE SATLIQ.

USE SUBROUTINE SATLQTRM FOR THIS OPERATION.

1 6 C PRINT 11 % OO 165 J = 1,NP

161 T = TSA (J ) J P = PSA ( J)

162 CALL SATLQTRM J CSX = CSATXF(T)

165 PRINT 12, T,P, E,H,S, C\/,CSAT,CP, W, CSX

999 RFTURN $ END

SINGLE-BANK COMPILATION.

146
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APPENDIX I. (Continued)

06/06/74

FUNCTION PVTF(T,D,M>

P V TF = P,3AR. M= 0 YIELDS DP/ 0 T , C 2 F /DT2 . M = 1 YIELDS ALSC DF/DC.

NOTE GK = 0. 0831434*DTPP, AND R = DEN/DTRP*

P = PS (R) + R*GK*(T-TS) + R2 *GK* TC * ( B*XB + E*XE>.

COMMON B1,B2,83, ER, E1,E2

COMMON/l/AL, BE,EP,GK, DCRT , TCRT , FCRT , D TRP , TTRF , P TRP

C0MM0N/3/0PDT,02PDT2,DPSDT, DPMCT,DPOC,DTSDR, OTHDR

COMMON/4/ XB1,XB2, XE1*XE2, OXBDP,DXEDR

COMMON/6/ TSAT, THETA, PSAT

1 S = 0 /DCRT f DSD R = DTRP/OCRT J R = D/D TRP

2 R2=R*R * R3=R*R2 S R4=R2*R2 I RG = R*GK

3 TC = TCRT $ TS = TSAT = TSATF(D) J THETA = THETAF(C)

4 PS = PSATF(TS) S XB = XBF(T,C) * XE = XEF(T,D)

5 BN = 1 + 3E* R2 $ B = B1*R2 + B2*P3 + B3*R4/8N

6 EM = E1*R2 E2*R3 * S X = (S-1)*(S-ER) $ E = SX*EM

7 F = 8*XB + E*XE J Fi = B*XP1 + E*XE1 S F2 = P*XB2 E*XE2

g PVTF = PS + (T-TS) *RG + GK*TC*F

9 DPDT = RG + GK*F1 f D2PDT2 = GK*F2/TC t IF(M.EQ.l) 10,20

10 3D = 2* 91 * R 3* B2 *F 2 + (2-BE*R2/PN) *2*B3*R3/PN

11 ED = SX*(2*E1*R + 3* E 2* R 2 ) + (2*S-1-ER) *EM*OSDR

12 FI = B*DXBDR + BD* X B + E*OXECR + ED* X E 13 DPDR = OPSD T*DTSDR + GK* ( T - TS-R* 0 TSD R) + GK*TC*F1

14 OPDO = OPDR/DTRP

20 RFTURN $ END

06/06/74

FUNCTION THETAF (DEN)

THETA = TS A T *EXP (U( S ) ) . LET Q = (3-1 ) / (ST-1 ) , WHERE ST = DTRP/D CRT , THEN - IF S < 1, U = AL *Q* * 3 , IF S > 1, U = -AL*Q**3,

YIELDS ALSO THE FIRST DERIVATIVE RSP. TO RHO = DEN/DTRP.

COMMON/l/AL , BE, EP, GK, DCRT , TCRT , F CRT , D T RP , TT RP , F T R

COMMON/3/DPDT ,D2POT2,DPSDT ,OPMCT,OPOC,OTSDP,OTHDF

COMMON/6/ TSAT, THETA, PSAT

1 S = DEN/OCRT * D SDR = DTRP/DCRT $ C = DSDR-1

2 Q = (S-l)/C S Q2 = O *Q S U = AL*Q*02

3 U1 - 3*AL*Q2*DSDR/C f IF(O) 5,9,4

4 U = -U $ U 1 = -U1

5 XP - EXPF(U) J THETAF = TSAT*XP

6 OTHDR = ( T S AT* U 1 + CTSDR)*XP S RFTURN

9 THETAF = TCRT $ OTHDR =0 $ RETURN J END

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APPENDIX I. (Continued)

06/86/74

FUNCTION XBF(T,D)

XBF = SORT (T/TC) *LN (T/TS) = Q(T)«Z<R,T>,

Z(P,T) = LN(U>, U(R,T) = T/TS (R )

•

COMMON/i/AL,BE,EP,GK, OCRT , TCRT , PCRT , 0 TRP , TTRP , PTRP

C0MM0N/3/DPDT,D2PDT2, DPSDT, DPMOT , DPDO, D TSDR ,DTHOP

COMMON/4/ XB1,XB2, XE1,XE2, OXBDR , DXEDF

COMMON/6/ TSAT, THETA, PSAT

TS = TSAT $ X = T/TC

U1X = TC/TS $ U1R = —U*D TSOR/TS

2 Z1R=U1R/U 2 Z1X=U1X/U 2 Z2X=-Z1X*Z1X

$ Q1 = 0.5/Q 2 G2 = -Q1/2/X

OXBDR = C*Z1R $ XB1 = Q * Z1X *• Q1*Z

• 2*Q1*Z1X + Q2*Z $ RETURN 2 END

1 TC = TCRT I

2 U = T/TS $

3 z = LOGF (U)

4 Q = SQRTF (X

)

5 XBF = Q*Z 2

6 XB2 = Q*Z2X

06/06/74

FUNCTION XEF (T, D)

XEF = PSI-PSISAT, PSI = (1-W*LN (1+1/W) ) /X, W = EPMT/TH-l).

XEF = F (R, T) /X - FS (R) /XS

F(R,T> = 1-W*P(R,T), P (R , T ) = LN(U), U = i+l/W(R,T),

F S ( R) = 1-WS*PS(R>, PS ( R ) = L N < V/ ) , \J - l + i/WS(R).

COMMON/l/AL ,BE,EP,GK, OCRT , TCRT , PCRT , 0 T RP , TT RP , PT R

F

COMMON/ 3/ D POT, D2PD T2 , DPSOT , DPMCT,DPDD,DTSOR,DTHDP

COMMON/4/ XB1,XB2, XE1,XE2, OXBDR, DXEOR

COMMON/ 6/ TSAT, THETA, PSAT

1 E = EP 2 TC = T CRT $ TH = THET A $ TS = TS AT 2 W = EMT/TH-1> 2 IF(W) 30,30,2

2 W W = W*W 2 H 1 X = E*TC/TH 2 W1P = -E # T*DTHDP/ TH/TH

3 U=l+1/W 2 U1R=-W1R/WW 2 U1X=-W1X/WW 2 U2X = -2*U1X*H1X/H

4 P=LOGF ( U) S P1R = U1 R/U $ P1X=U1X/U 2 P 2 X = U2X/U - P1X*F1X

5 F = 1 - H*P * FIR = -W * P 1 R - W1P*P

6 F IX = - W* P 1 X - W IX # F 2 F 2 X = -R*P2X - 2*W1X*F1X

7 WS = E* ( T S/ T H— 1 ) 2 IF(WS) 8,8,9

8 FS = 1 2 FS1 =0 2 GO TO 12

9 WS1 = EMDTSOR - T S *D T HDR/ T H ) / T H $ U = 1+1/WS

10 PS - LOGF(U) $ PSI = -WS1/U/WS/WS

11 FS = 1-WS*PS 2 FS1 = -WS*PS1 - WS1*PS

12 X = T / T C 2 X 2 = X* X S XS=TS/TC $ XSl = DTSOR/TC

13 XEF - F/X - FS/XS 2 XEl = F1X/X - F/X2

14 XE2 = F2X/X - 2*F1X/X2 + 2*F/X/X2

16 OXEDR = F1R/X - FS1/XS + FS*XS1/XS/XS 2 RETURN

3 C XFF = XEl = XE2 = DXEDP = 0 2 RETURN 2 ENO

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APPENDIX I. (Continued)

06/06/7*4

FUNCTION DENGASF (T

)

C Y = A 1 + A2*Q2 A3*C3 + . . , NF = AL , YN = L N ( DCRT /D T RF) , C U = Z (7E-Z)*Y, DFN = DCRT*EXP (-YN*U ) . DIMENSION A (5)

DATA (TTRP=89.899) , ( DTRP = 1 . 35 1 1 4

E -6

)

DATA (TCRT=305.37) , (DCRT =6. 74) , ( E = 0 . 39)

OATACA = 0.21587515, - 0 . 0 8 5 2 2 3*4 2 , - 0 .61 5 23457 ,

1

0.25452490, 0.15177230)

1 FORMAT (1H0 9X *DENGASF = 0, T EXCEEDS TCRT. * / ) 2 IF(TCRT-T) 3,4,5

3 PRINT 1 $ STOP

4 DENGASF = DCRT $ RETURN

5 ZN=TCRT/TTRP-1 $ Y N = LO GF ( OCR T / C TRP ) $ Z= ( TCP T / T - 1 ) / Z

6 Q = CUBERTF ( Z) S X = Z**E -2 3 Y = A(l) 3 DO 8 K=2,5

8 Y = Y + A(K)*Q**K $ U = Z + X*Y

9 DENGASF = DCRT* EXP F ( - Y N* U ) 3 RETURN 3 FNO

06/06/74

FUNCTION DENLIQF (T

)

ETHANE SATO. LIQUID DENSITIES, NOL/L, VIA LAB. NOTE 73-5.

Y = A 1 + A2*Q2 A3*C3 . . . , YN - DTFP-DCRT,

DEN = OCRT + YN*(X + <XE-X)*Y).

DATA (TTRP = 89.899) , (DTRP = 21.66)

DATA (TCRT = 3 05. 37) ,(DCRT = 6.74) , (F = 0.33)

DATA ( A = 0 . 72 190943 8), ( 6=0.2965778 99 ),(C = -0. 30 0365476)

1 FORMAT (1H0 9X *DEN LIQF = 0, T EXCEEDS TCRT. / ) 2 IF(TCRT-T) 3,4,5

3 PRINT 1 3 STOP

4 OENLIQF - DCRT S RETURN

5 XN = TCRT-TTRP 3 YN = OTRP-DCRT 3 X = (TCRT-D/XN

6 W = CUBERTF ( X ) 3 G = X**E - X 3 Y = A + C*X

6 CENLIQF = DCRT + (X + C*Y)*YN 3 RETURN 3 END

06/06/74

FUNCTION PMELTF(T)

C ETHANE MELT P TO 42 ATM., C L US I U S / WE I GA N D , 1940 . C SIMON EQN . , P = PTRF + A*(X**2 -1), X = T/TTRF.

C0MM0N/3/DPDT, C2PDT2,DPSDT , DPMCT,CPDD,DTSDF,OTHDP

OATA ( T T RP= 8 9 . 6 99) , ( PT PP = 9 . 96 7

E -6 ) ,

( A=2 8 4 0 . 0 ) ,( Q = 1 . 0 1 3 25 ) 1 X = T /T TRP S PMELTF = GMPTPF + AMX*X-1>)

? CFMDT = 0*A*2*X/TTRF 3 RETURN 3 END

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APPENDIX I. (Continued) 06/06/714

C

C

FUNCTION PSATF(T)

C ETHANE V.P., BAR, VIA LAB. NOTE 73-3.

COMMON/3/DPDT,D2PDT2,DPSDT,DPMOT,OPOO,DTSDR,DTHDR

DATA (TTRP = 89.899) , ( TCPT = 3 0 5 . 3 7 ) , <PTRP= 9 .967E-6)

DATA <P1= 10. 795491 66 ), <P 2=8. 35899 001) , <P3=-3. 11498770 >

,

1 (P4 = -0. 64969799) , (F5 = 6. 07349549)

1 FORMATdHQ 9X *PSATF = 0, T EXCEEDS TCPT. * / ) 2 XN = 1-TTRP/TCRT $ DXDT = TTRP/XN/T/T

3 X=(1-TTRP/T)/XN S X2=X 4 X f X3=X 4 X2 S X4=X2 4 X2

47= 1-X $ IF (V ) 5,6,7

5 PSATF = DPSDT =0 $ PRINT 1 S RETURN

6 Z = Z 1 = 0 $ GO TO 9

7 Q = SQRTF(V) % W = V

4 Q $ HI = -3 4 Q/2

8 Z = X 4 W S Z1 = W + X 4 W1

9 F = P1 4 X 4 P2 4 X2 4 P3 4 X3 + P4 4 X4 + P54 Z 10 FI = PI 4- 2 4 P2 4 X 4 3

4 P34 X2 + 4

4 P4 4 X3 + P5 4 Z1

11 FSATF = 1.01325 4 PTRF 4 EXPF(F)

12 DPSDT = F

1

4 OXDT 4 PS AT F T RETURN * END

06/06/74

FUNCTION TSATF(DEN)

C THIS NEW TSATF VIA TSATFIT, 4/19/74 AT 09.00.

COMMON/3/ OP DT, 02PD T2 , DPS OT , DPM C T , DPD 0, 0 T S DR , 0 THO

P

DIMENSION A V ( 8 ) , AW(5)

DATA (ALS=0.5),(BES=0.5),(E=0.25),(DTRP=21.68),(DGAT=1.35114E-6)

DATA (TTRP = 89. 899) , ( TORT = 3 0 5 . 37 ) , (DCRT=6.74)

D AT A ( AV = 0.868105174, 0 .015169784, -0.7 296 0432 2, 1.0096514932,

1

-8.734027096, 21.107128228, -31.449940867, 17.863703965)

OATACAW = 23.724518399, -14.886051613, 5.431774425,

1 -1.071505659, 0.091351825)

SATO. VAPOR TEMPS. CONSTRAINED AT T.P.

DEFINE X = ABS(S-l), XT = ABS(ST-l), WHEN THF FQN . IS - IN(YY) = AL 4 ( 1/XT-i/X) + Al 4 LOG (LN (H-E/S) /LN (1 + E/ST) ) W(S),

W(S) = A2MQ-QT) + A3 4 (Q2-QT2) + A4MS-ST) 4 A5 4 (S2-ST2) + . . . 1 S = DEN/DCRT $ D SDR = DTRP/DCRT S OS = S-l ? IF(QS) 2,30

2 X = ABSF(QS) $ XI = DSDR 4 QS/X $ YN = TCRT/TTRP - 1

3 V = l/X t Vl = -OSOR/X/CS S ST = DG AT/C CRT $ IF(QS) 4,30,15

4 XT = 1 - ST t V T = l/ XT $ U=ALS 4 (VT-V) $ U1=-ALS 4 V1 J EK=LOGF(l+ E/ST)

5 P = 1 + E/S $ PI = -E 4 DSDP/S/S $ PG = LOGF(P)/EK

6 G = LOGF(PG) J G1 = Pl/P/PG/EK

7 Q = CU9ERTF (S) $ CT = CUBERTF (ST) $ Q1 = Q

4 DSOR/3/S

e W = U 4 AV(1)*G 4 AV ( 2

)

4 (O-CT) 4 AV ( 3) * (

C

4 C-QT 4 QT)

9 W 1 = U1 4 AV(1)*G1 4 A V ( 2

) * 0 1 4 AV(3) 4 24 G 4 Q1

10 DO 11 <=4,8 $ N = K-3 $ W = W 4 AV(K) 4 (S 44 N-ST 44 N)

11 W 1 = W1 4 N

4 DSDR 4 AV (K) 4 S 44 (N-l) t GO TO 18

SATD. LIQUIO TEMPS. CONSTRAINED AT THE T.F.

ECN., LN(YY) = W(S), WHERE X = APS(S-1), X T= APS (S T- 1 ) , ANO - W(S) = BE 4 ( 1 / XT - 1/X) 4 B1 4 ( S-S T ) 4 B2 4 (S2-ST2) 4 . . . 15 ST = DSDR I XT = ST-1 T W = BESM1/XT-V) f W1 = -BES 4 V1

16 CO 17 K = 1 , 5 $ W = W 4 AW ( K) 4 (S 44 K - ST 44 K)

17 W1 = W1 4 A W ( K ) 4 K

4 DSDR 4 S 44 (K-l)

18 F = EXPF(W) $ FI = W l 4 F I C = 1 4 Y N

4 F

19 TSATF = TCRT/Q $ DT SDR = -YN 4 F1 4 TSATF/G $ RETURN

30 TSATF = TORT $ DTSDP =0 « RETURN S END

150
APPENDIX I. (Continued)

06/06/7A

FUNCTION FINOTMF (P

)

C GIVEN MELTING PRESSURE P, ITERATE T TO MINIMIZE (P-FC).

COMMON/ 3/DPDT, 02PDT2, DPSOT , OPM C T , DP D 0 , D T S DR , DTHO

1 FORMAT ( 1H0 9X FINOTMF = 0, FAILS TO CONVERGE) / ) 2 T = 100 $ DO 6 J = 1 » 5 0 f DP = P-PMELTF(T) J A DP = AESF(DP)

3 I F t ADP/P-1. OE-6) 7,7,4

4 IF( ADP/DPMDT/T-1.0E-6) 7,7,5

5 T = T DP/DPMDT

6 CONTINUE $ FINOTMF =0 $ PRINT 1 $ RETURN

7 FINOTMF = T $ RETURN $ END

06/86/74

FUNCTION FINDTSF(P)

C GIVEN VAPOR PRESSURE P, ITERATE T TO MINIMIZE (P-PC).

COMMON/l/AL , BE , EP, GK , DC RT , TOR T , F CRT , D T RP , TT RP , F TR

COMMON/ 3/ DPDT, D2POT2, DPSDT , OPMOT ,DPDO,DTSDP,DTHDR

1 FORMA T ( 1H0 9X FINDTSF = 0, FAILS TO CONVFRGE. / ) 2 FORMAT ( 1H0 9X FINDTSF =0, P EXCEEDS PCRT. / ) 3 IF (P-PCRT ) 4,11,12

4 T = 2 00 $ DO 9 J = 1 , 5 0 $ DP = P - PSATF(T) $ AOP = AeSF (DP)

5 IF(ADP/p-1. 0E-6) 10,10,6

6 IF ( ADP/OPSDT/T-l.O E-6) 10,10,7

T = T + OP/DPSDT S IF(T-TCPT) 9,9,

T = TCRT

CONTINUE $ FINDTSF = 0 $ PRINT 1 RETURN

FINDTSF = T $ RETUPN

FINDTSF = TCRT * RETURN

FINDTSF = 0 $ PRINT 2 $ RETURN $ ENO

151
APPENDIX I. (Continued)

06/06/74

FUNCTION F INDENF (T , P)

C ON ISOTHERM T, FIND DEN, MOL/L, TO MINIMIZE (P-PC) VIA EQNSTATE.

COMMON/l/AL,BE,EP,GK, DC RT , TCRT , F CRT , D TRP, TTRF , FTRP

COMMON/3 /DPDT,D2PDT2,DPSDT,0PM0T,DPD0,DT SDR, D THOR

DATA (DM=23. 0) ,

( DG AT = 1 . 3 51 14E- 6

)

41 FORMA T ( 1H0 9X FINOENF = 0, FAILS TO CONVERGE. * / ) 42 FORMAT ( 1H0 9X ’FINDENF = DCRT, DP/DR ZERO OR NEG. * / ) 43 FORMAT ( 1H0 9X ’FINOENF = 0, DOUBL E- VALUED AT P = PSAT. * / ) 1 IF(T-TCRT) 2,5,8

2 DG=FINDSATF (T,0) $ DL=FI NDSATF < T , 1) $ PS=PSATF(T>* IF(P-FS) 3,32,4 30= DG/ 2 $ GO TO 11 40= (DL+DM)/2 $ GO TO 11

5 DG=DL=DCRT $ PS=PCRT $ IF(F-FS) 6,33,7 60= DCRT/2 * GO TO 11

7 0 = 2 ’DCRT $ GO TO 11

6 IF(T.LT. 400.0) 9,10

9

PC = PVTF ( T , OCRT , 0 ) $ IF(P-PC) 6,33,7

10 0 = OCRT

11 DO 30 J = 1 , 5 0 I DP=P-PVTF (T ,D,1) S IF ( ABSF ( DP/F) - 1 . OE-6) 31,31,12

12 IF(OPDD) 34,34,13

13 OD = DP/OPDD $ IF (ABSF (DO/D) -1. OE-6) 31,31,14

14 C = 0 + DO $ IF (D.GT.OGAT) 16,15

15 0 = OGAT $ GO TO 30

16 IF(D.GT.OM) 17,18

17 0 = D TRP S GO TO 30

16 IF ( T-TCRT ) 19,24,30

19 IF(P.LT.PS) 20,22

20 IF(D.GT.DG) 21,30

21 0 = D G $ GO TO 30

22 IF(D.LT.DL) 23,30

23 D = OL * GO TO 30

24 IF (P.LT.PCRT) 25,27

25 IF (D.LT .OCRT) 30,26

26 0 = OCRT - 0.02 $ GO TO 30

27 IF(D.GT.DCRT) 30 ,20

28 0 = OCRT 0.02

30 CONTINUE $ F INDENF = 0 $ PRINT 41 t RETURN

31 FINDENF = D $ RETURN

32 FINDENF = 0 t PRINT 43 $ RETURN

33 FINDENF = DCRT $ RETURN

34 FINDENF = DCRT $ PRINT 42 $ RETURN l END

SINGLE-BANK COMPILATION.

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APPENDIX I. (Continued)

06 / 06/74

*v>

FUNCTION FINDSATFt T,M)

C ITERATE OEN TO MINIMIZE (T-TS) VIA TSATF(OEN).

C M = 0 FOR VAPOR, M = 1 FOR IIQIIC.

COMMON/i/AL ,BE,EP,GK, DCRT , TCP T , P CRT , 0 TRP , TTRP , PTPP

C0MM0N/3/DPDT,02PDT2,DPS0T, DPMDT, DPDD, DTSDR , DTHDR

DATA (DM = 23.0» ,

< DG A T = 1 . 3 5 1 1 4E- 6 ) 1 FORMA T ( 1H0 9X FINDSATF = 0, FAILS TO CONVERGE.* / > 2 FORMAT ( 1HG 9X *FIN OS A TF = 0, T EXCEEDS TCPT.* / ) 3 IF(T-TCRT) 4,22,23

4 IF(M.EQ.O) 5,6

5 0 = DENGASF (T) S GO TO 7

60= DENLIQF (T)

7 CO 20 J = 1 , 5 0 $ D T =T-TS ATF (D ) S IF(ABSF (DT/T) -1.0E-6) 21,21,8

8 OTDD = DTSDR/OTRP $ IF ( D T DO . EQ . 0 . 0 ) 22,9

9 DD = OT/DTDD $ I F < ABSF ( DD/O > - 1 . OE-6) 21,21,10

10 0 = D + DO $ IF(M.EQ.O) 11,15

11 IF(D. GT.DGAT) 13,12

12 0 = DGAT $ GO TO 20

13 IF ( 0. LT. DCRT) 20,14

14 0 = DCRT - 0.02 $ GO TO 20

15 IF(D.GT.DM) 16,17

16 0 = DM I GO TO 20

17 IF (D.GT .DCRT) 20,18

18 0 = DCRT «- 0.02

20 CONTINUE S FINDSATF =0 $ PRINT 1 $ RETURN

21 FINDSATF =0 J FETURN

22 FINDSATF = OCRT $ RETURN

23 FINDSATF = 0 J PRINT 2 $ RETURN * END

06/06/74

SUBROUTINE IDEAL

ETHANE IDEAL GAS (1 ATM) TH ERMO F UN CT I ONS (CHAO, 1973).

EQN., Y = ( EZ-EZZ) /FT = 3 + F(X), X = T/100, 0 = X**l/3,

F ( X ) = A 1* Q4 + A2*Q5 + A3*Q6 + . . . + AN*Q**(N+3).

(HZ-HZZ)/RT = 1 + Y, CVN = CVZ/R = 0(EZ/R)/DT, CPZ/F = 1 + CVZ/F,

SZ/P = AZ + INTEGRAL (CVZ/R/X + 1/X)*DX.

CCMM0N/99/TI , EZZ, EZ,SZ,CVZ, HZ,CPZ

DIMENSION A (9)

OATA (R = 8. 3143) ,<AZ=21. 705718)

0

A T A ( A = 65.498641, -362.0 1 15914, 853. 3408616, - 1 123.601622 ,

1

°06. 2184427, -459.2302545, 143.0300226, -25.07495605,1.897540044)

1 X = TI/100 S 0 = CUPERTF (X) $ DQDX = Q/3/X * F = FI = S = C 2 DO 4 J=i,9 $ K = J + 3 $ L = J + 6

3 Y = A ( J

) * 0

* * K $ F = F + Y $ F1 = F1+ K*Y/C

4 S = S f L * Y/K $ S = AZ + S + 4*L0GE(X) 5Y=3fF I CV = Y + X*E1*CQCX

C CONVERT TO DIMENSIONED RESULTS, JOULES, MCLES, KELVINS.

6

E 7 = R* T I * Y I HZ = R*TIMi + Y) f CPZ = R*(1+CV)

9 SZ = R*S $ CVZ = P*C V ? RETURN * ENC

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APPENDIX I . (Continued)

06/06/74

SUBROUTINE HOMOTHRM

GIVEN P,T, GET DEN AND FUNCTIONS FCR HOMOGENEOUS DOMAIN.

USE MEMORIZED IOEAL GAS FUNCTIONS EVERY 10 K.

COMMON/l/AL , BE,EP, GK, DCRT , TCR T , PCRT , D T RP , TTRP , FTRP

CCMM0N/3/DP0T,02PDT2,DPSDT , DPMD T , OPDO, D TSDR , D THOR

C0MM0N/8/ P,T,DEN, E,H,S, CV,CP,CSAT, W , WK

COMMON/9/ El (60) ,SI (60) ,CVI (60)

COMMON/ 39/ TI ,EZZ, EZ,SZ,CVZ,HZ,CFZ

DATA (DA=0. 0) , (Q=l. 01325) , ( G= 0 . 0 8 31 4 34)

1 K = T/10 t EZ = EI(K) J SZ = SI ( K) J CV7 = CVI(K)

2 OEN = OB = FINOENF (T , P) $ N = 5*(l+OB)

3 E = EZZ + EZ ESUMF(N,T,DA,DB) $ H = E + 100*P/DB

4 S = SZ + SSUMF(1,N,T,DA, OB) - 100*G*LOGF (G*T*DB/G)

5 X = 1 0. 0* A 8SF (T /TCRT-1) J IF(X.LT.3.0) 6,7

6 N = N + DB*DB*EXPF (-X)

7 CV = CVZ «- CSUMF(N,T ,DA, DP) $ PX = PVTF(T,DB,1)

6 CP = CV f 1 00*T/DPDD* (DPDT/DB ) **2

9 W = SQRTF ( WK*CP*DPOD/CV) J RETURN $ END

06/06/74

SUBROUTINE LIQTHERM

FOP DEN ABOVE DCRT, AND T UNDER TP = 340 K.

GIVEN P , T , GET DEN ETC. FIRST USE CPSUMIT TO GET FUNCTIONS

AT POINT (T , P B , 0 B ) , THEN INTEGRATE ALONG ISOTHERM T.

USE MEMORIZED FUNCTIONS FROM CPSUMIT CN ISOBAR PB(FURTADO).

COMMON/3/OPOT,D2PDT2,DPSDT,DPMOT, OPDO, D TSDR ,D THD R COMMON/8/ P , T , DEN, E,H,S, CV,CF,CSAT, W,KK

COMMON/ 10/ DF(34),EF (34) ,SF(34),CVF(34)

1 K = T/10 $ D8 = DF ( K) f DEN = DN = FINOENF (T ,P)

2 E = EF ( <) $ S = S F ( K ) $ CV = CVF(K)

C INTEGRATE ALONG ISOTHERM T FROM DE TO DN

.

3 CX = ABSF ( DN-D3 ) J N = 5M1+CX)

4 E = E f ESUMF (N,T, OP, DN) t H = E 100*P/DN

5 S = S + SSUMF ( 0 ,N, T ,DB,DN) * N = N DX*DX

6 CV = CV f CSUMF (N, T ,DP,DN) t PX = PVTF(T,DN,1)

7 CP = CV * 100*T/OPDD* (OPDT/DN ) **2

9 W = SQRTF ( WK*CP*DPDO/CV) t RETURN S END

154
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vn

.tAPPENDIX I. (Continued) 06/06/74

SUBROUTINE SATGSTRM

C GIVEN P,T AT SATURATION, GET OEN ETC. - COMMON/l/AL , BE, EP,GK, DC RT , TC R T , F CRT , D TRP , TTRF , FTRP

COMMON/ 3/ DP DT, D2P0 T2, DFSDT , DPMD T , DPDD, D T SDR , D THD

COMMON/8/ P,T,DEN, E,H,S, CV,CF,CSAT, W,V<K

COMMON/99/ TI,EZZ, EZ,SZ,CVZ, HZ,CPZ

CAT A (A = 0 . 0 ) , <Q = 1. 0132 5) , ( G = 0 . 0 8 31434)

1 TI - T S CALL IDEAL

2 DEN = OG = FINOSATF (T , 0) $ N = 5M1+ DG)

3 E = EZZ f EZ + ESU MF ( N , T , A , DG ) S H = E + 100*P/DG

4 S = SZ + SSUMF( 1,N ,T,A,OG) - 100*G*LOGF (G*T*OG/Q)

5 IF(T.EQ.TCRT) 6,7 6CF=CV=W=Q S RETURN

7 N = N + DG * DG SCV = CVZ + C S UN F ( N ,T , A , DG

)

8 PX = PVTF ( T , DG , 1) ? CP = CV + 1 00 * T/ D P CD* (DPD T / 0G ) * * 2 9 W = SQRTF(WK*CP*DPDO/CV) $ RETURN S ENC

06/06/74

SUBROUTINE SATLQTRM

C GIVEN P,T AT SATURATION, GET DEN ETC. - C AT TEMP. T, GET FUNCTIONS AT P = FP VIA CFSUMIT,

C THEN INTEGRATE ON ISOTHERM T FROM CB OOWN TO DL OF THE SATLIC.

COMMON/l/AL, BE, EP,GK, PC RT , TC R T , F CRT , D T RP , TT RF , F T R

COMM ON/ 3/ DP DT, 02PDT2, DFSCT ,DPMCT,DPDD,DTSDP,DTHDP

COMMON/8/ P , T , DEN, F,H,S, CV,CP,CSAT, W , WK

1 CALL CP SUM I T S D8 = DEN S CEN = DL = F I ND S A T F ( T , 1

)

2 DX = ARSF(DB-OL) S N = 5M1 + CX)

3 S = S + SSUMF(0,N,T ,Oe,OL) S E = E + ESUMF ( N , T , OB , CL

)

H = E + 100*P/DL S IF(T. EQ.TCRT) 5,6

CSAT = CV = CP = W = 0 S FETl’RN

N = N + D X* DX S CV = CV + CSL M F (N , T , D 8 , DL

)

PX = PVTF(T , CL , 1 ) f CDLDT = C TF F/DTSOR

8 CSAT = CV-1 00*T*OPDT*DDLDT/DL/CL S CP = C V 10 0* T / O P CD * ( D P C T / DL ) * * 2

9 W = SQRTF ( WK*CP # DPDP/CV) S RETURN f END

06/06/74

SUBROUTINE MELTHERM

C GIVEN P, GET T , DEN, ETC. FOR FREEZING LIQUID.

COMMON/3/DPDT,02PDT2,DPSDT,DPMCT,CPDD,DTSDR,DTHDP

COMMON/8/ P , T , DEN, E,H,S, CV,CF,CSAT, W , WK

1 T = FINOTMF(F) S CALL CPSUMIT $ DB = DEN

2 DEN = DM = FIN DENE (T , F

)

C NON INTEGRATE ON ISOTHERM T FROM DB TO DM

3 N = 5 + 5* A8SF COM- DE ) S E = E + ES UMF ( N , T

,

O,

M

)

4 H = E + 100*P/CM S S = S + SSUME(0,N,T,DB,DM)

5 CV = CV + CSUMF (N, T , D E , DM ) S PX = PVTF(T,DM,1)

6 CP = CV + 1 00*T/DPDD* (DPDT/CM) **2

9 W = SQRTF (WK*CP*DPOP/CV) * RETURN S END

155
o

oo

APPENDIX I. (Continued)

36/06/74

SUBROUTINE CPSUMIT

USE FURTAOO CP(T) ALONG ISOBAR FB = 137.895 BAR.

START AT TB = 340 K WITH VALUES HB , SB, THEN - INTEGRATE DOWN TO ANY T, YIELDS DEN, E, H, S, CP, C V, AT (T,FE).

C0MM0N/3/DPDT,D2PDT2, DPSDT , DPMO T , DP DO, 0 T SDR , D TH D

R

COMMON/7/ TB ,PB , H B , SB

COMMON/8/ P , T , DEN, E,H,S, CV,CF,CSAT, W , WK

DATA (TX = 250.0)

1 H = H B t S = SB ? IF(T.LT.TX) 6,2

2 TP = T-T3 I N = 2 +A BSF ( TR ) $ DT = TR/N

3 CO 5 J=i,N J TJ = TB + (J-3.5)*DT I CP = CFXF(TJ)

4 H = H + CP* OT $ S = S + C P* D T /T J

5 CONTINUE « GO TO 15

6 TP= TX-TB J N = 2 + ABSF ( TR ) $ OT = TP/N

7 00 9 J=1,N I TJ = TB + (J-0.5)*DT S CP = CPXF(TJ)

8 H = H + CP*DT $ S = S + CP* DT/T J 9 CONTINUE

10 TP = T-TX $ N = 2+ABSF (TR) /2 J DT = TR/N

11 DC 13 J=1,N $ TJ = TX + ( J- 0 • 5

) *DT S CP = CPXF(TJ)

12 H = H + CP* DT * S = S + CP*DT/TJ

13 CONTINUF

15 DEN = FINDENF (T ,PB) $ CP = CPXF(T)

16 E = H - 100*PB/DEN J PX = P VTF ( T, DEN , 1

)

20 CV = CP - 1 00*T/DPOD* (DPDT/OEN) **2 S RETURN $ END

156
<D

Ui

oj

r\)

.X)

vn

c*j

no

APPENDIX I. (Continued)

06/06/74

FUNCTION CSUMF<N,T ,CA ,08)

C OELTA C V = -T*INTEGPAL ( ( 0 2P/ DT 2 ) / C** 2

> * D D . COMM ON/3/ DP DT,02PDT 2 , DPSDT , DPMCT,OPDD,OTSOP,DTHDF

DX = (03-DA ) /N S CSUHF =0 t DO 5 J=1,N

DN = DA (J-0.5)*DX $ P = PVTF(T,DN,0)

CSUHF = CSUMF - D2PDT2*0X/ DN/DN

CSUHF = 100*T*CSUMF $ RETURN $ END

06/06/74

FUNCTION ESUMF (N,T ,DA, DB)

GET DELTA E OVER DENSITY RANGE FRCH DA TO DP.

DELTA E - INTEGRAL (P-T* (DP/DT) ) * DX/ DN* * 2.

C0MM0N/3/DPDT,D2PD T2, DPSDT, DPMO T , DPD D, D T SDR , OTHDR

CX = (D3-DA ) /N $ ESUMF = 0.0

DO 5 J=1,U % ON = DA + <J-0.5)*DX t P = PVTF(T,DN,0>

ESUMF = ESUMF (P - T* DPD T

) * DX/ 0 N/ ON

ESUMF = 10 0 *ESUMF $ RETURN J END

06/06/74

FUNCTION SSUMF (L,N , T , DA, DP

)

C DENSITY- DEPENDENT CHANGE OF S FROM DA TO CB.

C DELTA S = INTEGRAL (GK-(DP/DT)/DN)*DX/DN.

CCMMON/3/OPDT , D2PDT2, DPSDT , DPMDT ,OPDO,OTSDR,DTHDF

DATA (GC = 0.0831434)

1 SSUMF = 0 ? DX = ( DB-D A ) / N J IF(L.EQ.O) 4,2

2 00 3 J=1,N * DN = DA + (J-0.S)*DX t F = PVTF(T,DN,0)

3 SSUMF = SSUMF + (GC-DPCT/DN)*DX/DN $ GC TO 9

4 DO 5 J= 1 , N * DN = DA + (J-0.5)*OX * F = PVTF(T,DN,0>

5 SSUMF = SSUMF - DP QT* OX/ ON/ DN

9 SSUMF = 1 0 0 * SS UMF $ RETURN ? END

157
!i APPENDIX I. (Continued)

06/86/74

FUNCTION CPXF(T)

C ETHANE CP, J/MOL/K, OF ANDRE FURTADO AT P = 137,895 BAR.

C DEFINE X = (T-TTRP) /(TMAX-TTRP), WHEN THE EQN. IS - C LN(CM-CP) = Al A2*X2/(1-X) + A3*X2 A4*X3 + A5*X4.

C NOTE THIS FORMULA VALID ONLY UP TO 345 K.

C NOTE FACTOR 1.874 FOR ETHANE VS. METHANE CONVERSION.

DIMENSION A (5)

DATA (TTRP=89.899) , (TM=354. 0) , <CM=62.60

)

DAT A ( A = 3.2632884, -0.1544225, -0.1414889, -0.5064375, 0.2769915)

1 X = (T-TTRP ) / (TM-TTRP) S X2 = X*X

2 Y = A (1 ) A (2) *X2/ ( 1-X) + A(3)*X2 + A(4)*X*X2 A(5)*X2*X2

3 CPXF = 1.87 4335* (CM - EXPF(Y)) $ RETURN S ENO

10/15/74

FUNCTION CSATXF(T)

C F

Q

RM U L A T

I

QN-QF ETHANE DA T A O F AUTHORS

C WIEBE/HUBBARD/BREVOORT, AND WITT/KEMP, J/MOL/K.

C VIA PROGRAM CSAT-2, 3/27/74.

C FOR 59 POINTS, THE RMS IS 0.50 PCT.

C CS = A t X = T/TCRT

C REVISED FOR TCRT = 305.37, 10/7/74.

DATA (E = 0 .5) , ( TC=3Q 5. 37 ) DATA ( A=67 .3153) , (B =-16. 5 87 6) , (C =16. 3526)

1 X = T/TC $ U = 1-X $ IF ( U ) 2,2,3

2 CSATXF =0 $ RETURN

3 CSATXF = A + B*X *_CfX/U*»_E t- ..... RETURN $ END

10/15/74

FUNCTION QVAPXFCT)

C VIA PROGRAN SWAB-2+ USING OATA OF^

C DOUSLIN, RIEDEL, FURTADO. FOR 49 POINTS, RMS = 0.56 PCT.

£ DE FINE X = (TC-T)

/

( TC-TT) , U = X»»l/3, WHFN EQN. IS -

C QV = A1*U A2*U2 . . . A6*U6.

C REVISED FOR TGRT = J3G5-.37,- 10/7/74.

DIMENSION A ( 6

)

DATA- lTX=aR.A9Rl , (

T

C = 3Q5. 37 I DATA (A = 12.102730, 11.165588, 16.539265,

1 -71^8 54 6 95 . 82 ^166239, -3? . fil (151 1.1 1 U = CUBERTF ( (TC-T)/ (TC-TT)) $ Q = 0 $ DO 2 K=l,6

2 Q = Q ACK)*U**K S QVARXF = 1G0G*CI $ RETURN S__END

158
CD

CD

UD

So

COUD-3-CVJ •— CDCOCOCj-CNI CD !

«—•

.—I —I 1—

L/LOUJ 'AilSNBd

159

Figure

1.

The

locus

of

recent

P-p-T

data.
Figure 2. Generalized locus of isochore inflection points.

Figure 3. Generalized behavior of the critical isotherm.

160
DENSITY

TEMPERATURE

Figure 4. Gene ralized behavior of the locus 0(p).

161
$(p,

T)—

$

(p,

T)

Figure 5. Generalized behavior of the function $(p,T).

Figure 6. Generalized behavior of the function Y(p, T).

162
+ .5

0

~T~ 1

1

1

0 ©OOOOo

o _ o

~ ^ O

o o

o o

o ©

Q.

~’ 5 - o O —

o o

o o

-1.0 — o © —

o 0

o o

-1.5

1 1 1 ^ 1 1

0 12 3 P/Pc *

Figure 7. Behavior of coefficients B(p), C(/o) for methane.

163
P/Pz~~

Figure 8. Presumed behavior of C(p) for hydrogen.

164
TEMPERATURE

Generalized density-temperature phase diagram.

1 6 5

Figure 9.
o

o

ro

• o

• o

-• o

o«

p

o

o

o

o

o

o •

o

o

o

o

<_>

TOu

cr

I +JCLX

cr

M

SCJ

TOO

O

CM

I LOUi/r ‘ 33N3U3J3K3

o

o

co

I

Figure 10. Comparisons for saturated liquid ethane. Q is heat of vaporization,

and H is enthalpy. Calculated values are via the Clapeyron equation. See

section 4.3 of the text.

166

o

LDCM

+ o

o

CM

O

ID

OO

TEMPERATURE
2400

o

o

CO

o

CO

CM

o

CMCM

t

o

CO

o

o

o

s/uj a n n o s jo a 3 3 d

Figure 11. Speeds of sound for saturated liquid ethane

167

TEMPERATURE
Table 1. Experimental and calculated vapor pressures

ID: (4) Pal; (7) Ziegler; (9) Popej^lO) Douslin

VAPOR PRESSURES, TTRP - 89.899, TCRT = 305.370

10.79549166 8.35899001 -3.11490770 -0.64969799 6.07349549

ID T,K P , BAR CALCD PGNT

7 90.010 1.03991-005 1.04012-005 -0.120

7 100.010 1.11231-004 1.11214-004 0.015

7 109.998 7.46205-004 7.460 84-004 0.016

7 119.989 3.53971-003 3.54004-003 -0.009

7 129.987 1.28963-002 1.29009-002 -0.835

7 139.992 3.82929-002 3.83041-002 -0.029

7 150.000 9.67387-0U2 9.67415-002 -0.803

7 160.010 2.14770-001 2.14725-001 0.821

7 170.019 4.29490-0D1 4.29303-001 0.044

7 180.027 7.88547-001 7.88122-001 0.054

7 184.550 1.01 325 + 00 0 1.01269+000 0.055

9 198.216 1 .99985 + 0 00 2.00235+000 -0.125

4 214.334 3.97283+000 3.96786+000 0.125

4 224.130 5. 71141+000 5.71485+000 -0.860

4 229.782 6.94778+000 6.95075+000 -0.043

4 234.581 8.13995+000 8.14562+000 -0.870

9 234.715 8.18108+000 8.18100+000 0.801

10 238.150 9.12908+000 9.12702+000 0.823

9 238.792 9.30599+000 9.31232+000 -0.068

4 239.864 9.62177+000 9.62783+000 -0.863

4 240.534 9. 82448+000 9.82894+000 -0.845

10 243.150 1.06455+001 1.06436+001 0.818

4 243.377 1.07162+001 1.07165+001 -0.803

4 246.830 1.18689+001 1.18715+001 -0.022

4 247.831 1.22099+001 1.22225+001 -0.103

10 248.150 1.23369+001 1.23360+001 0.007

4 249.755 1.29310+001 1.29184+001 0.097

4 250.160 1.30694+001 1.30685+001 0.007

4 251.600 1.36207+001 1.36124+001 0.861

4 252.556 1.39895+001 1.39824+001 0.851

1 0 253.150 1.42169+001 1.42160+001 0.007

4 254.301 1.46818+001 1.46766+001 0.036

4 257.552 1.60349+001 1.60 361+001 -0.007

10 258.150 1.62966+001 1.62958+001 0.005

10 263.150 1. 85895+001 1 .85882+001 0.007

4 263.386 1. 86989+ 0U1 1.87019+001 -0.816

4 267.539 2.07916+001 2.07864+001 0.825

1 0 268.150 2.11078+001 2.11067+001 0.805

4 271.750 2.30678+001 2.30680+001 -0.001

9 272.949 2.37622+001 2.37499+001 0.852

10 273.150 2.38670+001 2.38656+001 0.006

4 275.921 2.54917+001 2.55038+001 -0.047

4 276.362 2.57931+001 2. 57719+001 0.082

4 276.384 2.57863+001 2.57854+001 0.804

168
Table 1 ID

4

4

10

4

4

10

4

9

4

10

4

4

9

4

4

10

9

4

10

4

9

4

4

1 0

1 04

4

9

4

1 04

4

4

4

4

4

4

4

4

10

10

. Experimental and calculated vapor pressures, (continued).

T »

276.513

277.811

278.150

280.038

282.243

283.150

284.630

284.840

287.648

288.150

288.257

290.034

290.208

292.229

293.091

293.150

293.259

296.339

298.150

299.657

299.855

300.196

301.242

302.150

303.150

303.462

303.468

304.002

304.039

304.150

304.350

304.435

304.506

304.723

304.785

304.913

304.969

305.110

305.142

305.150

305.250

P,8AR

2.58857+001

2.66672+001

2.68824+001

2. 80710 + QtJl

2.95400+001

3. 01708 + QU1

3.11740+001

3.13657+001

3.33652+001

3.37524+001

3.38323+001

3.51469+001

3.53369+001

3.69269+001

3.75729+001

3. 76506+001

3.77610+001

4.02866+001

4.1897 3 + O’0

4.32194+001

4.34545+001

4.37369+001

4.46929+001

4.55769+001

4.65413+001

4.68154+0D1

4.68930+001

4.73934+001

4.73895+001

4.75255+001

4.77171+001

4.78455+001

4.78280+001

4.80594+001

4.81482+001

4.83164+001

4.83453+001

4.84837+001

4.85152+091

4.05339+001

4.86354+001

CALCD PCNT

2. 58642+001 0.883

2.66676+001 -0.002

2.68805+001 0.807

2.80 889+001 “0.064

2.95509+001 -0.837

3.01685+OQi 0.008

3.11970+001 *0.074

3.13450+001 0.866

3.33761+001 -0.033

3.37495+001 0.009

3.38295+001 0.008

3.51795+001 -0.893

3.53139+001 0.865

3.69041+001 0.962

3.75992+001 -0.070

3.76472+001 0.8 09

3.77359+001 0.067

4.03123+001 -0.S64

4.18927+001 0.811

4.32470+001 -0.064

4.34277+001 0.0 62

4.37404+001 -0.808

4.47120+001 -0.043

4.55712+001 0.013

4.65354+001 0.013

4.68403+001 -0.053

4.68462+001 0.100

4.73730+001 0.043

4.74097+001 -0.043

4.75201+001 0.011

4.77197+001 -0. 105

4.78048+001 0.985

4.78781+001 -0.105

4.80947+001 -0.873

4.81574+001 -0.019

4.82871+001 0.061

4.83440+001 0.003

4.84878+001 -0.008

4.85205+001 -0. Oil

4.85287+001 0.011

4.86313+001 0.808

NP = 85, RMSPCT = 0.050

169
Table 3. Experimental and calculated saturated liquid densities

ID: (5) via isochores of Pal; (10) Douslin; (12) Chui;

(13) Klosek; (14) Miller; (16) Tomlinson

SATO. LIQUID DENSITIES » E = 0.330

TTRP = 89.899, TCRT = 305.370, DCRT = 6.740, DTRP = 21.688

0.721909438 0.296577899 -0.300365476

ID T,K MOL/L CALCC PRC NT

10 304.150 8.737 8.740 -0.03

10 303.150 9.201 9.200 0.01

10 302.150 9. 544 9.544 0.00

10 298.150 10.499 10.487 0.12

10 293.150 11. 297 11.292 0.05

10 283.150 12.458 12.454 0.04

10 273.150 13. 342 13.344 -0.02

10 263.150 14. 089 14.091 -0.02

5 255.963 14. 554 14.570 -0.11

10 253.150 14.753 14.747 0.04

5 247.962 15. 050 15.060 -0.07

5 240.700 15. 455 15.475 -0.13

5 229.917 16. 037 16.048 -0.07

5 222.618 16. 423 16.413 0.06

5 214.942 16.754 16.781 -0.16

5 207.941 17. 125 17.103 0.13

5 197.888 17.529 17.548 -0.11

5 188.451 17. 941 17.950 -0.05

5 176.512 18. 446 18.440 0.03

5 167.366 18. 823 18.805 0.10

12 161.360 19. 027 19.040 -0.06

5 156.875 19.226 19.213 0.07

13 133.150 20. 126 20.107 0.10

13 127.594 20. 323 20.312 0.05

13 122.039 20. 521 20.516 0.02

13 116.483 20. 717 20.719 -0.01

12 115.770 20. 747 20.745 0.01

14 115.050 20. 771 20.771 0.00

13 110.928 20.915 20.921 -0.03

14 1 08.110 21. 025 21.023 0.01

12 108.150 21. 027 21.022 0.02

14 100.020 21. 313 21.315 -0.01

14 91.010 21. 639 21.640 -0.00

NP = 33, RMSPCT = 0.068

170
Table 4. Vapor densities via vapor-pressure and virial equations

ETHANE SAID. VAPOR DENSITIES VIA V.P. AND VIRIAL EQNS *

ID T,K P, ATM PLANK/ KAH0 MOL/L PC T

1 69. 699 9.9670-006 1.3511-006 1.3511-006 0 .00

i 90.000 1.0233-005 1.3863-006 1 .3863-006 0.00

1 95.000 3.5303-005 4.5936-006 4.5936-006 0.00

1 100.000 1.0952-004 1.3347-005 1.3347-005 0.00

1 105.000 2.9851-004 3.4649-005 3 .4648-005 0.00

1 110.000 7 .3654-004 8.1615-005 8.1612-005 0.00

1 115.000 1.6670-003 1.7671-004 1.7670-004 0.01

1 120.000 3.4991-003 3.5556-004 3.5552-004 0.01

1 125. 000 6.8762-003 6.7110-004 6.7093-004 0 .02

1 130.000 1.2752-002 1.1974-003 1 .197 0-003 0 .04

1 135.000 2.2468-002 2.0336-003 2.0323-003 0 .06

i 140. 000 3.7834-002 3.3064-003 3.3033-003 0 .09

1 145.000 6.1192-002 5.1721-003 5.1653-003 0.13

1 150. 000 9.5478-002 7.8184-003 7 .8043-003 0.18

1 155. 000 1.4426-001 1 .1464-002 1.1436-002 0.24

1 160.000 2.1176-001 1.6358-002 1.6308-002 0.31

1 165.000 3.0288-001 2.2781-002 2.2694-002 0.38

1 170.000 4.2317-001 3.1042-002 3.0899-002 0.46

1 175.000 5.7882-001 4.1479-002 4.1252-002 0.55

1 130.000 7.7662-001 5.4457-002 5 .411 1-002 0.64

1 135.000 1.0239+000 7.0359-002 6.9660-002 0,73

1 190.000 1.3287+000 8.9635-002 8.891 1-002 0 .81

1 195. 000 1.6991+000 1.1271-001 1 .1171-001 0 .89

1 200.000 2.1440+000 1.4006-001 1 .3872-001 0.97

1 205.000 2.6726+000 1.7222-001 1 .7047-001 1.03

1 210.000 3.2943+000 2.0973-001 2 .075 0- 001 1.03

1 215.003 4.0186+000 2.5321-001 2.5043-001 1.11

1 220.000 4.8561+000 3.0331-001 2.9993-001 1 .13

1 225.000 5.6165+000 3.6077-001 3.5674-001 1.13

1 230.000 6.9105+000 4.2642-001 4.2173-001 1.11

1 235.000 8.1487+000 5.0120-001 4.9585-001 1 .08

1 240. 000 9.5420+000 5.3616-001 5.6025-001 1.02

1 245. 000 1.1102+001 6.8262-001 6.7626-001 0.94

I 250. 000 1.2339+001 7.9203-001 7.8551-001 0.83

1 255.000 1.4766+001 9.1613-001 9.0997-001 0.68

1 250.000 1.6395+001 1.0572+000 1.0522+000 0.43

1 265.000 1.9238+001 1.2179+000 1.2154+000 0.21

1 270.000 2.1310+001 1.4016+000 1 .4041+000 -0.18

1 275.000 2.4624+001 1.6125+000 1 .6245+000 -0.74

i 230.000 2. 7697+ 001 1.8563+000 1 .886 1+ 00 0 -1.58

1 285. 00 0 3.1047+001 2.1404+000 ' 2.2047+000 -2.91

1 230.000 3.4693+001 2.4754+000 2.6108+000 -5.19

171
Table 5. Experimental and calculated saturated vapor densities

ID: (1) from Table 4; (10) Douslin

SATURATED VAPOR DENSITIES, E = 0.390

TTRP = 89.899, TCRT = 305.370, DCRT - 6.740, DGAT = 0.21587515 -0.08522342 -0.61523457 0.25452490

ID T,K KOL/L CALCO PCNT

1 90.000 1.3863-006 1.3863-006 0.00

1 100.000 1.3347-005 1.3356-005 -0.06

1 110.000 8.1612-005 8.1689-005 -0.09

1 120.000 3.5552-004 3.5564-004 -0.03

1 130.000 1.1970-003 1.1962-003 0.06

1 140.000 3.3033-003 3.2989-003 0.13

1 150.000 7.8043-003 7.7922-003 0.16

1 160.000 1.6308-002 1.6286-002 0.13

1 170.000 3.0899-002 3.U875-002 0.08

1 180.000 5.4111-002 5.4107-002 0.01

1 190.000 8.8911-002 8.8968-002 -0.06

1 200.000 1.3872-001 1.3888-001 -0.12

1 210.000 2.0750-001 2.0781-001 -0.15

1 220.000 2.9992-001 3.0040-001 -0.16

1 230.000 4.2172-001 4.2231-001 -0.14

1 240.000 5.8025-001 5.8083-001 -0.10

1 245.000 6.7626-001 6.7677-001 -0.07

10 248.150 7.4490-001 7.4384-001 0.14

1 250.000 7.8551-001 7.8586-001 -0.04

10 253.150 8.6310-001 8.6220-001 0.10

10 263.150 1. 1530+000 1.1516+000 0.12

10 273.150 1.5370+000 1.5357+000 0.09

10 283.150 2.0670+000 2.0669+000 0.00

10 293.150 2.8800+000 2.8748+000 0.18

10 298.150 3.5020+000 3.5051+000 -0.09

10 302.150 4.3070+000 4.3068+000 0.01

10 303.150 4.6040+000 4.6122+000 -0.18

10 304.150 5.0350+000 5.0298+000 0.10

NP = 28, RMSPCT = 0.107

1.35114-006

0.15177230

172
Table

6.

Experimental

and

calculated

liquid

saturation

temperatures

d

X!O

<Mw30Q

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rn

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173

OlMRHSPCT =

0.062,

TSRHSPCT =

0,127
Table

7.

Experimental

and

calculated

vapor

saturation

temperatures 4 CM 8

ro a.) • cr cr» vo 4 ro 8 a H (CK

cr ro

h- o 8

cr o ® o • • O n.

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cvi 4 CD B 4

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a cm 4

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in cm o cr oo ro 8 cm

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V- CM o 8 in 4 4 ro ro ro CM CM CM CM CM CM *4 *4

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HH 9 7 5 4 4 4 ro ro CM O' 8 ro CM t-4

1*- CD +4 CM CM 3 M CM CM

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H *4 o o o o o 8 o o 8 CD 8 o o CD 8 8 m o ro ro ro ro ro co CM ro cr o •H cm ro J- in l© K to 8 o tH CM ro J- J” in m V© 8 8 8 8 e o H *4 *4 w4 H CM CM CM CM CM CM CM CM CM CM CM CM CM CM ro ro ro

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aO CD CD o • i » 1 i 1 i i i I • 1 » 1 1 1 i 1 1 i 4 4 4 4 4 4 4 4

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H J- CM 8 •4- ro ro J- 8 ® 8 8 CM 8 8 CM ro CM

ro ro in CO ro iH 8 ao 8 ro

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v© CM 8 ro in ao V© in ro 8 8 J- ao r<H CM J- j- r^.

H 8 ao 8 J- CD 8

oo ro CM J- 8 CD CM ro 8 CD N- CO r^ 8 CM

K 8 CM 8 ro 8 N- CD CD CD ro ro CO m tH ro CD i© CD j- 8 ro o O' CM ao r- O’ ao 8 r4 8 O CO 8 ro 8 CD

*4 *4 oo ro *4 ro n- *4 ro 8 ao *4 CM CM J- 8 8 n- r^ CO n4 r4 CM CM ro J- 8 * -i 8 8 8 •4- ro ro ro CM CM CM CM ^4 H H *4 H H o o O CD O 8 CD CD 8 8 CD O o o a O O 8 8 8 8 8 8 8 8 o 8 o 8 8 8 8 o 8 CD O 8 8 8 _i G o o o o o o 8 O 8 8 O 8 8 8 a o 8 o 8 8 O 8 8 a CD o 8 ® r- 8 o i 1 1 1 | » i 1 1 • 1 1 1 1 1 i 1 1 » 1 4 4 4 4 4 4 4 4 t *H 8 X CM ro N. 4- 8 « a *4 K 8 4- •H a 8 8 8 CM 8 8 a 8 8 8 o a O 8 o 8 8 K ro N- CM 8 CM ro to ® •H CM o CM CM 4- 8 CD o o 8 o CD CD o 8 o CD ® 8 CM 8 J- wi 8 8 ro 4- 8 8 N- 8 8 r^ CM CM 8 8 w4 CO K- r^ o CM r- 4 8

*-l 8 « ro 8 8 8 CD 8 ro

® ^4 8 « N- 8 8 8 4- 8 ro 8 ro 8 ® e 8 8 ro

II® J- ro ro 8 ro

® 8 CD 4 ® ro CD 8 CM to 4-® 8 8 CD CD 8 ro 8 O 8 ro

a

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174

28,

DNRMSPCT =

0.162,

TSRMSPCT =

0.014
Table 8. Experimental and calculated second virial coefficients

ID: (3) Michels; (6) McGlashan; (10) Douslin

0. 552671 - 1. 106244 - 0.592947 -O.i041944 0.000000

ID T »K T/TC 9

4 CALC DIFF PCNT

6 150.000 0.4912 - 5.183 - 5.185 0 . 002 0.03

6 160.000 0 . 5240 -4 .48 9

- 4.487 - 0.001 - 0.03

6 170.000 0 . 5567 - 3.935 -3.933 - 0.002 -0.04

o 100.000 0.5894 - 3.485 - 3.483 - 0.001 - 0 .04

6 i ao . ooo 0 . 6222 - 3.112 - 3.112 - 0.001 - 0.02

o 20 G . 0 00 G . 65 4 9 - 2.600 - 2.800 0.000 0.01

6 210.000 0 . b 877 - 2.535 - 2.536 0.001 0.04

b 220 .000 0.7204 - 2.307 -2.309 0.002 0.07

6 230.000 0. 7532 - 2.110 - 2.111 0.002 0.09

D 2 4 C . 000 0 . 7859 - 1.937 - 1.939 0.002 0.10

b 2 5 G . 0 0 G 0-6187 - 1.765 - 1.766 0.002 0.10

o 260.000 0 . 6514 - 1.650 - 1.651 0 . 001 0.08

o 270.000 0.6842 - 1.529 - 1.530 0.001 0.05

o 260.300 0.9169 - 1.421 - 1.421 0.000 0.0 0 b 200.000 0 . 9497 - 1.323 - 1.323 - 0.001 - 0.06

6 300.000 0.9824 - 1. 235 - 1.233 - 0. 002 - 0.14

3 273 . 150 0 . 6943 - 1.493 - 1.494 0.002 0 .12

10 273.150 C • 6945 - 1.498 - 1.494 - 0.003 - 0.21

3 296.133 0 . 9763 - 1 .251 - 1.249 - 0. 002 - 0.14

13 2 96 . 15 0 0 . 9764 - 1.252 - 1.249 - 0.003 - 0.26

10 303.150 0 . 9927 - 1.209 - 1.207 - 0. 002 - 0.21

5 322 . 748 1.0569 - 1.058 - 1.058 - 0.000 - 0.01

10 . 323 . 150 1.0582 - 1.056 - 1.055 - 0.001 - 0.14

3 347. 652 1 . 1365 - 0 . 898 - 0.900 0 . 002 0.18

10 346 . 150 1 . 1401 - 0 . 896 - 0.897 0.001 0.07

3 372.522 1.2199 - 0.769 - 0.770 0.001 0.13

10 373.150 1 . 2220 - 0 .766 - 0 .767 0.001 0 .14

3 397 .644 1.3023 - 0.659 - 0.659 “ 0.000 - 0.02

10 396 . 150 1.3033 - 0.656 - 0.657 0 . 001 0.23

3 4 22 .0 0 1. 3642 - 0.566 - 0.566 0.000 0.02

10 423 . 1

C 1. 3657 - 0.563 - 0.564 0 . 001 0.12

10 446. 150 1 . 4676 - 0.463 - 0.484 0 . 001 0.13

10 473.150 1 . 5494 - 0.415 -0.414 - 0.000 - 0.09

1 0 4 9 c . 15 0 1.6313 - 0.353 - 0 . 353 - 0.000 - 0.07

10 523. 150 1. 7132 - 0.300 - 0.299 - 0.001 - 0.37

10 546.150 1.7950 - 0.251 - 0.251 - 0.001 - 0.30

10 573. 153 1. 6769 - 0 .208 - 0.208 - 0 . 001 - 0.36

10 590.150 1. 9563 - 0 . 168 - 0.169 0 . 000 0.10

10 623 .150 2 . 0 4 0 o

- 0 . 132 - 0.134 0.001 1.06

NP = 3 9. MEANPC T = 0.133

175
Table 8. Experimental and calculated second ririal coefficients (Continued)

ID: (1) Eucken; (2) Lambert; (4) Hoover; (5) Pope; (8) Gunn* Dymond / Smith

.

(9) Ham ann via

10 T »K T/TC 3

* CALC 0 IFF PCNT

1 230.039 0.6549 - 3 .053 - 2.800 - 0.253 - 9.03

2 2 013.

0

00 0.6549 — o . 060 - 2.800 - 0 . 260 - 9.27

5 2 09.

5

3 ** 0.6862 - 2.465 - 2.547 0.063 2.46

1 210.030 0.6877 - 2.763 - 2.536 - 0 . 227 - 8.97

2 210.000 0.6877 - 2.763 - 2.536 - 0. 227 - 8.97

4 215.030 0.7041 - 2.296 - 2.418 0.123 5.07

1 220 .030 0.7204 - 2.494 - 2.309 - 0 . 185 - 8.02

2 220 .000 0 . 720 +

- 2.528 - 2.309 - 0.219 - 9.48

1 230.000 0. 7532 - 2.244 - 2.111 - 0 . 133 - 6.30

2 230 . 00 G 0.7532 - 2.298 - 2.111 -0 . 187 - 8.85

5 236.759 0.7819 - 1.935 - 1.959 0 . 024 1.24

1 2 h 0 .000 0.7859 - 2.056 - 1.939 - 0.117 - 6.03

2 240.000 0 .785 9 - 2.076 - 1.939 - 0.137 -7 .07

4 240 .

0

30 0.7859 - 1.864 - 1.939 0 . 075 3.88

1 250.030 0.8187 - 1.887 - 1.786 - 0.101 - 5.64

2 250.000 0,8187 - 1.907 - 1.786 - 0.121 - 6.77

5 254.307 0.6344 - 1.700 - 1.719 0 . 019 1.11

1 260. 000 0 . 6514 - 1.725 - 1.651 - 0 . 074 - 4.51

2 2 o

C

. 030 0.8514 - 1.752 - 1.651 - 0 . 101 - 6.14

1 270 . 000 0.6842 - 1 .584 - 1.530 - 0.054 - 3.53

2 270 .030 0 . 6842 - 1.618 - 1.530 - 0.088 - 5.73

4 273. 150 0. 6945 - 1.506 - 1.494 - 0.011 - 0.76

h 273.150 0 . 6945 - 1.479 - 1.494 0 .016 1.06

3 273. 230 0 . 6947 - 1.498 - 1.494 - 0.004 -0 .25

i 260 . 030 0.9169 - 1.442 - 1.421 - 0.021 - 1.50

2 260 . 30 0.9169 - 1.483 - 1.421 - 0 . 062 - 4.35

2 2 30 . .30 , 0.9497 - 1.382 - 1.323 - 0.059 -4 •‘7

6

' 296.230 0. 9765 - 1.260 - 1.249 - 0.011 - 0.89

2 300.000 0 . 9824 - 1.281 - 1.233 - 0 . 047 - 3.85

5 306. 062 1.0023 - 1.181 - 1.163 0 . 002 0.13

0 310 . 940 1.0182 - 1.111 - 1.144 0 . 033 2.87

3 323.200 1.0584 - 1 .062 - 1.054 - 0.007 -0 .68

9 344.270 1.1274 - 0.913 - 0.920 0.006 0.68

9 377.630 1.2365 - 0.741 - 0.746 0 . 004 0.60

•3 377.600 1. 2365 - 0.737 - 0.746 0.009 1.14

6 410. 300 1 . 3456 - 0.604 - 0.608 0 .004 0.67

9 410 . 9+0 1.3457 - 0 .609 - 0.608 - 0.001 - 0.24

9 444.270 1.4549 - 0.500 - 0.496 - 0.004 -G .91

3 444.300 1.4553 - 0.499 - 0.496 - 0 . 003 - 0.65

9 477 . 63 G 1. 5640 - 0.404 - 0.403 - 0.001 - 0.27 < 3 4 7 7 .

6

3 0 1.5640 - 0.415 - 0.403 - 0.013 - 3.11

0 510 . 930 1.6731 - 0 . 344 - 0.325 - 0.019 - 5.92

9 510 . 940 1. 6732 - 0.319 - 0.324 0 .005 1.53

176
Table 9. Experimental and calculated third virial coefficients

ID: (7) Chueh; (10) Bouslin; (4) Hoover; (5) Pope

217 . 8 0 0 0 . 2 1* 42 26 G . 832S 29 0.534875 0.000000

10 r,K T/TC2T C* CALCD 01 FF

7 2 1 G .000 0 .6677 -0 .241 “0.237 -0.004

7 220.000 0 .7234 G .053 0.053 0.000

7 230.000 0 .7532 C . 239 0.233 0.002

7 240.000 0.7853 C . 353 0.352 0 .001

7 250.000 0.8137 0.419 0.421 -0.002

7 260.030 0 .8514 C.454 0.460 “0.005

10 273 .130 0.8945 C . 471 0.480 "0.010

10 296.150 0 . 9764 C . 482 0.471 0.011

10 303 . 150 0.3927 0.472 0.465 0.007

10 323 .150 1 . 0532 0.43 8 0.436 0.0 03

10 3 h6 . 15 3 1.1401 0 . 393 0.395 “0.001

10 373.150 1 .2220 C . 351 0.355 -0.004

10 336.150 1.3036 0.316 0.319 “0.003

10 423 . 150 1.3857 C .284 0.238 -0.004

1 0 448 . 130 1 .4676 C . 258 0.261 -0.003

10 473. 150 1.5494 C . 24 0 0.2 33 0.002

10 4 96. 15 C 1.6313 0 . 220 0.218 0.002

10 523 . 150 1.7132 C .204 0.201 0.003

10 546. 150 1 . 7950 0 .188 0.186 0.002

1 0 573.150 1 .67j9 C. 175 0.173 0.002

10 536.150 1.9536 0 . 161 0.162 -0.001

10 623 . 150 2.040c 0 .149 0.151 -0.003

NP = 22, HEANDIFF = 0.00 3

Iu T , K T / T C^T C* CALCD DIFF

5 209.534 0 .6862 -2.667 -0.254 -2.412

4 215.000 0 . 7041 -3.230 -0.076 -3.154

.> 236.769 0 .7ol9 0.168 0.341 “0.173

u 240.030 0 . 7659 -0.117 0.352 -0.469

5 254 . 307 0 .8344 0 . 386 0.443 -0.056

0 273.150 0.8945 C . 471 0.480 -0.010

4 273 . 150 0.6945 C . 482 0.480 0.002

4 273. 150 0 .8945 0.517 0

4 8 0 0.036

* 296 .136 0 .97o3 G . 488 0.471 0.017

5 306 . 062 1.0023 C .456 0.461 -0.006

4 322. 746 1 . 05o9 0 . 439 0.436 0.003

4 347. 652 1.1395 0 . 390 0.395 -0.006

*4 372 . 522 1.2199 G . 350 0.356 “0.006

4 3 97 . 8 4** 1 .3026 0 . 318 0.320 -0.002

4 422 . 7 .30 1 .3642 0 . 290 0.269 0.001

I 177
Table 11. Coefficients of the equation of state

DTRP = 21.6800, TTRP = 89.

OCRT = 6.7400, T CRT = 305.

AL = 2.00, BE = 1.00, EP = 1.848167996 1.569704511

-1.042842462 0.224978299

MOL/L TSAT THETA

0.5 235.219 203.322

1.0 258.239 230.548

1.5 272.349 249.833

2.0 282.050 264.599

2.5 289.067 276.149

3.0 294.268 285.179

3.5 298.122 292.103

4.0 300.905 297.215

4.5 302.825 300.790

5.0 304.083 303.124

5.5 304.868 304.520

6.0 305.290 305.215

6.5 305.370 305.367

7.0 305.370 305.367

7.5 305.339 305.258

8.0 305.101 304.735

8.5 304.546 303.552

9. 0 303.623 301.528

9.5 302.281 298.493

10.0 300.467 294.288

10.5 298.130 288.775

11. 0 295.227 281.851

11.5 291.719 273.446

12.0 287.576 263.540

12.5 282.779 252.156

13.0 277.314 239.372

13.5 271.175 225.313

14.0 264.365 210.151

14.5 256.890 194.102

15.0 248.763 177.416

15.5 240.000 160.367

16.0 230.619 143.243

16.5 220.643 126.336

17.0 210.093 109.923

17.5 198.992 94.264

18.0 187.364 79.584

18.5 175.236 66.069

19.0 162.640 53.856

19.5 149.619 43.037

20.0 136.230 33.650

20.5 122.556 25.688

21 .

0

108.713 19.098

21.5 94.854 13.788

22.0 81.182 9.635

22.5 67.940 6.494

23.0 55.403 4.205

PTRP = 0.000010099

PORT = 48.755014373

5.560186452

PSAT B C

.315 1.88 7 -1.754

.335 1.932 -1.540

.40 7 1.983 -1.340

.421 2.040 -1.152

.440 2.102 -0.978

.565 2.170 -0.817

.868 2.243 -0.668

.397 2.321 -0.532

.220 2.404 -0.408

.454 2.491 -0.296

.242 2.583 -0.197

.672 2.678 -0.109

.755 2.777 -0.832

.755 2.880 0.032

.723 2.985 0.686

.478 3.094 0.128

.916 3.204 0.159

.998 3.317 0.180

• 696 3.432 0.190

.990 3.548 0.189

.875 3.665 0.178

.366 3.783 0.157

.497 3.902 0.126

.323 4.021 0.886

.915 4.140 0.8 35

.358 4.260 -0.624

.746 4.379 -0.093

. 179 4.498 -0.171

.752 4.616 -0.258

.556 4.734 -0.354

.668 4. 851 -0.458

.149 4.967 -0.571

. 038 5.082 -0.692

. 351 5.196 -0.821

. 075 5.309 -0.958

.176 5.420 -1.102

.595 5.530 -1.254

.260 5.639 -1.414

.094 5.747 -1.580

. 026 5.853 -1.754

.005 5.957 -1.935

. 001 6.060 -2.122

• 000 6.162 -2.316

• 000 6.262 -2.516

. 000 6.361 -2.722

.000 6.458 -2.934

899,

370,

0.50

8

16

23

29

34

36

41

44

46

47

48

48

48

48

48

48

47

46

45

43

41

39

36

33

29

26

22

19

15

12

9

7

5

3

2

1

0

0

00

00

0

0

0

0

178
Table 12. Experimental and calculated P-p-T data

The following pages compare experimental P-p-T (compressibility)

data with densities and pressures computed by the equation of state (5).

The first column identifies sources of the data (as in Table 10):

ID Authors

2 Virial equation (4).

8 Reamer et al [57].

9 Michels et al [47].

10

Douslin and Harrison [14].

100+ A. K. Pal, via Pope [54].

The equation of state was adjusted only to data of ID = 2, 9, 10,

and 1300+

. Remaining data validate our extrapolation to higher pressures. Density deviations should be ignored near the critical point,

and pressure deviations should be ignored for compressed liquid at

low temperatures for reasons given in the text.

179
Table 12. Experimental and calculated P-p-T data

EQUATION OF STATE VS, PVT DATA

ID T , K MOL/t CAICO C ,PCT P, BAR CAUCD P, PCT

2 230.000 0.4000 0.4003 -0.07 6.693 6.689 0.06

2 240.000 0.4000 0.4003 -0. 07 7.070 7.066 0.06

2 250.000 0.4000 0.4002 -0.06 7.442 7.438 0.05

2 260.000 0.4000 0.4002 -0. 06 7.811 7.807 0.05

2 270.000 0.4000 0.4002 -0.06 8.177 8.173 0.05

2 200.000 0.4000 0.4002 -0. 05 8.541 8.537 0.05

2 290.000 0.4000 0.4002 -0.05 8.902 8.898 0.05

2 300.000 0.4000 0.4002 -0.05 9. 262 9.258 0.04

2 310.000 0.4000 0.4002 -0.04 9.621 9.617 0.04

2 320.000 0.4000 0.4002 -0, 04 9.978 9.974 0.04

2 330.000 0.4000 0.4002 -0. 04 10.334 10.330 0.04

2 340.000 0.4000 0.4002 -0.04 10.689 10.686 0.04

2 350.000 0.4000 0.4001 -0.04 11.044 11.140 0.03

2 360.000 0.4000 0.4001 -0.03 11.397 11.393 0.0 3 2 370.000 0.4000 0.4001 -0.03 11.750 11.746 0.03

2 380.000 0.4000 0.4001 -0.03 12.102 12.899 0.03

2 390.000 0.4000 0.4001 -0.03 12.454 12.451 0.0 3 2 400.000 0.4000 0.4001 -0.03 12.805 12.802 0.03

2 410.000 0.4000 0.4001 -0.02 13.156 13.153 0.02

2 420.000 0.4000 0.4001 -0.02 13.506 13.503 0.02

2 430.000 0.4000 0.4001 -0.02 13.856 13.853 0.02

2 440.000 0.4000 0.4001 -0.02 14.205 14.203 0.02

2 450.000 0.4000 0.4001 -0.02 14.555 14.552 0.02

2 460. 00 0 0.4000 0.4001 -0.02 14.904 14.901 0.02

2 470.000 0.4000 0.4001 -0.02 15.252 15.250 0.02

2 400.000 0.4000 0.4001 -0.02 15.601 15.598 0.02

2 490.000 0.4000 0.4001 -0. 01 15.949 15.947 0.01

2 500. 00 0 0.4000 0.4001 -0.01 16.297 16.295 0.0 1 2 510.000 0.4000 0.4001 -0.01 16.645 16.643 0.0 1 2 520.000 0.4000 0.4001 -0.01 16.993 16.990 0.01

2 530.000 0.4000 0.4001 -0.01 17.340 17.338 0.01

2 540.000 0.4000 0.4001 -0.01 17.687 17.685 0.01

2 550.000 0.4000 0.4001 -0.01 18. 035 18.032 0.01

2 560.000 0.4000 0 .4001 -0. 01 18. 382 18.379 0.0 1 2 570.000 0.4000 0.4001 -0.01 18.729 18.726 0.01

2 580.000 0.4000 0.4001 -0.01 19.076 19.073 0.01

2 590.000 0.4000 0.4001 -0.02 19.423 19.420 0.02

2 600.000 0.4000 0.4001 -0.02 19.769 19.766 0.02

NP = 38, ONRMSPCT = 0. 035, PMEANPC T = 0.028

180
Table 12. Experimental and calculated P-p-T data- - - (Continued)

EQUATION OF STATE VS. PVT DATA

ID T,K MOL/L CALCD C,PCT P,BAR CALCO P»PCT

8 310.928 3.5245 3.5650 -1.15 48.263 48.071 0.40

8 310.928 4.5021 4.5925 -2.01 51.711 51.498 0.41

8 310.928 5.5178 5.6358 -2.14 53.434 53.287 0.28

8 310.928 7.2697 7.2407 0.40 55. 158 55.192 -0.06

8 310.928 8.3632 8.1814 2.17 56.537 56.923 -0.68

8 310.928 8.8480 8.7333 1.30 57.916 58.294 -0 .65

8 310.928 9.1894 9.1054 0.91 59.295 59.673 -0.64

8 310.928 9.4447 9.3856 0.63 60.674 61.110 -0.55

8 310.928 9.6593 9.6110 0.50 62.053 62.385 -0.54

8 310.928 9.8423 9.8000 0.43 63.432 63.771 -0.54

8 310.928 9.9921 9.9633 0.29 64.811 65.074 -0.41

8 310.928 10.1321 10.1072 0.25 66.190 66.444 -0.38

8 310.928 10.2579 10.2362 0. 21 67.569 67.815 -0.36

8 344.261 4.9251 4.9626 -0.76 75.842 75.550 0.39

8 344.261 5.8407 5.8663 -0.44 82.737 82.542 0 .24

8 344.261 6.7517 6.7335 0.27 89.632 89.785 -0.17

8 344.261 7.5579 7.5011 0.75 96.527 97.880 -0.57

8 344.261 8.2287 8.1557 0.89 103.421 104.275 -0.82

8 344.261 8.7434 8.6969 0.51 110.316 110.943 -0.57

8 344.261 9.1754 9.1501 0.28 117.211 117.636 -0.36

8 344.261 9.5504 9.5302 0.21 124. 106 124.503 -0.32

8 344.261 9.8679 9.8559 0.12 131. 000 131.275 -0.21

8 310.928 0.5889 0.5911 -0.36 13.790 13.745 0.32

8 344.261 0.5165 0 .5173 -0.16 13.790 13.769 0.15

8 377.594 0.4620 0.4623 -0.07 13.790 13.780 0.07

8 410.928 0.4189 0.4190 -0.04 13.790 13.785 0.04

8 444.261 0.3838 0.3839 -0.03 13.790 13.785 0.02

8 477.594 0.3544 0.3546 -0.04 13.790 13.784 0.04

8 510.928 0.3295 0.3297 -0.07 13.790 13.780 0.07

8 310.928 1.3468 1.3519 -0.38 27.579 27.500 0.25

8 344.261 1.1212 1.1222 -0. 09 27.579 27.558 0.08

8 377.594 0.9762 0.9762 -0.00 27.579 27.578 0.00

8 410.928 0.8711 0.8708 0.03 27.579 27.587 -0.02

8 444.261 0.7892 0.7893 -0.02 27.579 27.574 0.02

8 477.594 0.7233 0.7238 -0.06 27.579 27.563 0.06

8 510.928 0.6684 0.6694 -0.15 27.579 27.540 0.14

8 310.928 2.4961 2.5158 -0.79 41.369 41.196 0.42

8 344.261 1.8567 1.8601 -0.18 41.369 41. 312 0.14

8 377.594 1.5546 1.5549 -0.02 41.369 41.363 0.01

8 410.928 1.3605 1.3589 0.12 41.369 41.411 -0.10

8 444.261 1.2172 1.2168 0.03 41.369 41.382 -0.0 3 8 477.594 1.1066 1.1068 -0.01 41.369 41.364 0.01

8 510.928 1.0165 1.0180 -0.14 41.369 41.312 0.14

8 310.928 7.2697 7.2407 0.40 55.158 55.192 -0.06

8 344.261 2.8018 2.8142 -0.44 55.158 55.802 0.28

8 377.594 2.2130 2.2174 -0.20 55.158 55.074 0.15

8 410.928 1.8902 1.8895 0. 04 55.158 55.175 -0.02

8 444. 261 1.6685 1.6684 0.00 55.158 55.159 -0.0 0 8 477.594 1.5040 1.5043 -0.03 55.158 55.145 0.02

8 510.928 1.3733 1.3755 -0.16 55.158 55.073 0.15

8 310.928 10.3736 10.3532 0. 20 68.948 69.201 -0.37

8 344.261 4.0959 4.1261 -0.74 68.948 68.679 0.39

181
Table 12. Experimental and calculate P-p-T data- (Continued) - - EQUATION OF STATE VS. ^VT DATA

ID T,K MOL/L CALCO C » FCT P $ BAR CALCO P,PCT

8 377,594 2.9702 2.9796 -0.32 68.948 68.789 0.23

8 410.928 2.4628 2.4656 -0.12 68.948 68.882 0.09

8 444.261 2.1426 2.1447 -0.10 68.948 68.887 0.05

8 477.594 1.9142 1.5163 - 0 . 11 68.948 68.876 0.10

8 510.928 1.7377 1.7417 -0.23 68.948 68.798 0.22

8 310.928 11.2820 11.3103 -0.25 86.184 85.486 0.81

8 344.261 6.3137 6.3109 0.05 86.164 86.a07 -0.03

8 377.594 4.0652 4.0858 -0.51 86.184 85.885 0.35

3 410.928 3.2373 3.2474 -0.31 86.184 85.970 0.25

8 444.261 2.7645 2.7714 -0. 25 86.184 86.801 0.21

8 477.594 2.4431 2.4490 -0.24 86.184 85.996 0.22

3 510.928 2.2028 2.2099 -0. 32 86.184 85.925 0.30

3 310.928 11.8116 11.8807 -0.59 103.421 100.977 2.36

8 344.261 8.2287 8.1557 0.89 103.421 104.275 -0.8 3 8 377.594 5.2776 5.3106 -0.63 103.421 102.959 0.45

8 410.928 4.0686 4.0863 -0.43 103.421 103.867 0.34

8 444.261 3.4145 3.4256 -0. 33 103.421 103.133 o. 2 e 8 477.594 2.9861 2.9963 -0. 34 103.421 103.105 0.31

8 510.928 2.6754 2.6862 -0.41 103.421 103.831 0.36

3 310.928 12.2182 12.2988 -0.66 120.658 116.984 3.05

8 344.261 9.3676 9.3479 0.21 120.658 121.018 -0.3 0 8 377.594 6.4713 6.4858 -0.22 120.658 120.431 0.19

8 410.928 4.9220 4.9488 -0.54 120.658 120.119 0.45

8 444.261 4.0781 4.0962 -0.44 120.658 120.194 0.36

8 477.594 3.5369 3.5520 -0.43 120.658 120.193 0.39

8 510.928 3.1538 3.1664 -0.40 120.658 120.207 0.37

8 310.928 12.5479 12.6333 -0.68 137.895 133.171 3.43

8 344.261 10.1360 10.1396 -0. 04 137.895 137.802 0.07

8 377.594 7.5147 7.4975 0.23 137.895 138.216 -0.23

8 410.928 5.7575 5.7831 -0.44 137.895 137.349 0.40

8 444.261 4.7394 4.7654 -0.55 137.895 137. ai7 0.49

8 477.594 4.0884 4.1085 -0.49 137.895 137.268 0.45

8 510.928 3.6322 3.6462 -0.39 137.895 137.389 0.37

8 310.928 12.8333 12.9143 -0.63 155.132 149.886 3.38

8 344.261 10.6669 10.7182 -0.48 155.132 153.407 1.11

8 377.594 8.3540 8.3367 0.21 155.132 155.527 -0.25

8 410.928 6.5294 6.5505 -0. 32 155.132 154.632 0.32

8 44^.261 5.3796 5.4124 -0.61 155.132 154.236 o.5e

8 477.594 4.6299 4.6564 -0.57 155.132 154.288 0.54

8 510.928 4.1041 4.1210 -0.41 155.132 154.516 0.40

8 310.928 13.0738 13.1579 -0.64 172.369 166.162 3.60

8 344.261 11.0985 11.1720 -0.66 172.369 169.320 1.77

8 377.594 9.0258 9.0201 0. 06 172.369 172.531 -0.09

8 410.928 7.2289 7.2381 -0.13 172.369 172.124 0.14

8 444.261 5.9919 6.0219 -0.50 172.369 171.493 0.51

8 477.594 5.1560 5.1860 -0.58 172.369 171.370 0.56

8 510.928 4.5658 4.5853 -0.43 172.369 171.633 0.43

8 310.928 13.2869 13.3736 -0.65 189.606 182.447 3.7 e 8 344.261 11.4646 11.5453 -0.70 189. 606 185.617 2. 1C

8 377.594 9.5652 9.5810 -0.17 189.606 189.074 0.28

8 410.928 7.8461 7 .8502 -0.05 189.606 189.482 0.07

8 444.261 6.5583 6.5860 -0.42 189.606 188.723 0.47

8 477.594 5.6568 5.6902 -0.59 189. 606 188.432 0.62

182
Table 12. Experimental and calculated P-p-T data- - - (Continued)

EQUATION OF STATE VS. PVT DATA

10 T > K MOL/L CALCD 0,PCT P, BAR CAICO P, PCT

8 510.928 5.0133 5.0344 **0.42 189.606 188.781 0.43

8 310.928 13.4768 13.5679 -0.68 206.843 198.548 4.01

8 344.261 11.7810 11.8628 -0.70 206.843 202.151 2.27

8 377.594 10.0144 10.0500 -0.35 206.843 205.433 0.68

8 410.928 8.3875 8.3906 -0.04 206.843 206.735 0.05

8 444.261 7.0812 7.1044 -0.33 206.843 206.939 0.39

8 477.594 6.1325 6.1653 -0.53 206.843 205.617 0.59

8 510.928 5.4446 5.4646 -0. 37 206.843 206.924 0.40

8 310.928 13.8169 13.9077 -0.66 241.316 231.536 4.05

8 344.261 12.3150 12.3850 -0,57 241.316 236.205 2.12

8 377.594 10.7385 10.7972 -0.55 241. 316 238.239 1.28

8 410.928 9.2546 9.2879 -0,36 241.316 239.874 0.60

8 444.261 8.0043 8.0164 -0.15 241.316 240.816 0 .21

8 477.594 6.9989 7.0249 -0.37 241.316 240.204 0.46

6 510.928 6.2432 6.2616 -0. 29 241.316 240.475 0.35

8 310.928 14.1021 14.1998 -0.69 275.790 263.723 4.38

8 344.261 12.7400 12.8070 -0.53 275.790 269.878 2.14

8 377.594 11.3044 11.3770 -0.64 275.790 271.638 1.72

8 410.928 9.9483 9.9983 -0.50 275.790 273.107 0.97

8 444.261 8.7521 8.7793 -0.31 275.790 274.453 0 .49

8 477.594 7.7541 7.7753 -0.27 275.790 274.748 0.38

8 510.928 6.9554 6.9734 -0.26 275.790 274.871 0.33

8 310.928 14.3527 14.4571 -0.73 310.264 295.792 4.66

8 344.261 13.0835 13.1626 -0.60 310.264 302.128 2.62

8 377.594 11.7680 11.8495 -0.69 310.264 303.853 2.07

8 410.928 10.5117 10.5772 -0.62 310.264 306.630 1.36

8 444.261 9.3799 9.4201 -0.43 310. 264 307.927 0.75

8 477.594 8.4052 8.4289 -0.28 310.264 308.925 0.43

8 510.928 7.5930 7.6094 -0.22 310.264 309.327 0.30

8 310.928 14.5677 14.6877 -0.82 344.738 326.363 5.33

8 344.261 13.3764 13.4709 -0.71 344.738 333.679 3.21

8 377.594 12.1604 12.2483 -0.72 344.738 336.676 2.34

8 410.928 10.9866 11.0620 -0.69 344.738 338.997 1.67

8 444.261 9.9098 9.9651 -0.56 344.738 340.967 1.09

8 477.594 8.9742 8,9992 -0.28 344.738 343.124 0,47

8 510.928 8.1552 8.1777 -0.28 344.738 343.297 0,42

8 310.928 14.9359 15.0894 -1.03 413,685 385.936 6.71

8 344.261 13.8663 13.9892 -0.89 413.685 395.994 4.28

8 377.594 12.3094 12.8982 -0.69 413.685 403.217 2.53

8 410.928 11.7577 11.8412 -0.71 413.685 405.383 2.01

8 444.261 10.7824 10.8474 -0.60 413.685 407.951 1.39

8 477.594 9.9049 9.9429 -0. 38 413.685 410,568 0.75

8 510.928 9.1371 9.1425 -0. 06 413.685 413.258 0.10

8 310.928 15.2790 15.4333 -1.01 482.633 450.484 6.66

8 344.261 14.2981 14.4173 -0.83 482.633 462.241 4.23

8 377.594 13.3124 13.4189 -0.80 482.633 467.419 3.15

8 410.928 12.3491 12.4538 -0.85 482.633 469.784 2.66

8 444.261 11.4576 11.5401 -0.72 482.633 473.608 1.87

8 477.594 10.6337 10.6943 -0.57 482.633 476.512 1.27

8 510.928 9.8992 9.9277 -0.29 482.633 479.885 0.57

8 31C.928 15.5877 15.7353 -0.95 551.581 516.844 6.30

6 344. 261 14.6722 14.7839 -0.76 551.581 529.535 4.0 0 8 377.594 13.7271 13.8549 -0.93 551.581 530.226 3.87

183
Table 12. Experimental and calculated

EQUATION OF STATE VS. PVT DATA

10 T,K MOL/L CALCD C,P

8 410.928 12.8373 12.9589 -0.

8 444.261 12.0126 12.1079 -0.

8 477.594 11.2338 11. 3126 -0.

8 510.928 10.5290 10.5812 -0.

8 310.928 15.8659 16.0055 -0.

8 344.261 14.9988 15.1058 -0.

8 377.594 14.1021 14.2311 -0 . 8 410.928 13.2590 13.3892 -0.

8 444.261 12.4801 12.5883 -0.

8 477.594 11.7416 11.8356 -0.

8 510.928 11.0763 11.1369 -0.

8 310.928 16.1346 16.2505 -0.

8 344.261 15.2747 15.3933 -0.

8 377.594 14.4380 14.5628 *0.

8 410.928 13.6362 13.7647 -0.

8 444.261 12.8838 13.0047 -0.

8 477.594 12.1848 12.2880 -0.

8 510.928 11.5520 11.6184 -0.

NP = 176, DNRMSPCT = 0.605, PMEANPCT =

p-T data- - - (Continued)

P,BAR CALCO P, PC T 551.581 533.862 3.21

551.581 539.119 2.26

551.581 542.088 1.72

551,581 545.625 1.08

620.528 584.101 5.89

620.528 596.696 3.84

620.528 595.836 3.98

620.528 598.584 3.54

620.528 604.863 2.65

620.528 607.339 2.13

620.528 612.496 1.29

689.476 656.075 4.84

689.476 660.150 4.25

689.476 662.597 3.90

689.476 664.891 3.57

689.476 668.504 3.04

689.476 672.912 2.40

689.476 679.400 1.46

.222

PCT

95

79

70

50

88

71

91

98

87

80

55

72

78

86

94

94

85

58

1 .

184
Table 12. Experimental and calculated P-p-T data- - - (Continued)

EQUATION OF STATE VS . PVT DATA

ID T * K MOL/L CALCD C,PCT P > BAR calco P » PC T 9 273.150 0.8538 0.8552 “ 0.16 15.874 15.854 0.13

9 296.142 0.8538 0.8545 - 0.08 17.978 17.967 0.06

9 323.140 0.8538 0.8540 - 0.02 20.036 20.032 0.02

9 348.143 0.8538 0.8538 0.00 22.065 22.065 - 0.00

9 373. 150 0.8538 0.8535 0. 04 24.066 24.875 - 0.04

9 396.160 0. 8538 0.8533 0 . 06 26.053 26.067 - 0.06

9 423.170 0.8538 0.8533 0.06 28.031 28.846 - 0.06

9 273.159 1.0672 1.0686 “ 0.13 18.802 18.784 0.10

9 258.142 1.0672 1.0675 - 0.03 21.539 21.534 0.02

9 323.140 1.0672 1.0669 0.03 24.201 24.206 - 0.02

9 348.143 1.0672 1.0665 0.06 26.812 26.826 - 0.05

9 373.150 1.0672 1.0662 0.10 29.385 29.410 - 0.08

9 398.160 1.0672 1.0660 0.12 31.933 31.967 - 0.11

9 423.170 1.0672 1.0661 0.11 34.468 34.502 - 0.10

9 273. 150 1.2812 1.2828 - 0.13 21.349 21.331 0.08

9 296.142 1.2812 1.2815 - 0.03 24.769 24.764 0.02

9 323.140 1.2812 1.2805 0.05 28.067 28.079 - 0.04

9 348.143 1.2812 1.2800 0.09 31.294 31.318 - 0.08

9 373.150 1.2812 1.2794 0.13 34.465 34.504 - 0.12

9 398.160 1.2812 1.2791 0.16 37.599 37.652 - 0.14

9 423.170 1.2812 1,2792 0.15 40.713 40.770 - 0.14

9 273.150 1.4870 1.4888 - 0.12 23.441 23.424 0.07

9 298.142 1.4870 1.4876 - 0.04 27.563 27.555 0.03

9 323.140 1.4870 1.4862 0.05 31.508 31.520 - 0.04

9 348.143 1.4870 1.4856 0.09 35.354 35.381 - 0.08

9 373.150 1.4870 1.4848 0.14 39.125 39.173 - 0.12

9 398.160 1.4870 1.4844 0.17 42. 848 42.912 - 0.15

9 423.170 1.4870 1.4845 0.17 46.543 46.612 - 0.15

9 298.142 1.6354 1.6366 - 0 . 07 29.397 29.384 O • o 9 323.140 1.6354 1.6351 0.02 33.830 33.836 - 0.02

9 348.143 1.6354 1.6343 0.07 38.142 38.163 - 0 .06

9 373.150 1.6354 1.6333 0.13 42.360 42.405 - 0.11

9 398.160 1.6354 1.6328 0.16 46.520 46.585 - 0.14

9 423.170 1.6354 1.6328 0.16 50.647 50.719 - 0.14

9 296. 142 1.7032 1.7050 - 0.11 30.189 30.169 0.07

9 323. 140 1.7032 1.7031 0.01 34.846 34.848 - 0.01

9 348.143 1.7032 1.7021 0.07 39.371 39.392 - 0.05

9 373. 150 1.7032 1.7010 0.13 43. 798 43.844 - 0.10

9 398.16 0 1.7032 1.7004 0 . 17 48.161 48.229 - 0.14

9 423. 170 1.7032 1.7005 0 . 16 52.490 52.564 - 0.14

9 296.142 1.9165 1.9202 - 0.19 32.483 32.446 0.11

9 323.140 1.9165 1.9174 - 0. 05 37.873 37.861 0.0 2 9 348.143 1.9165 1.9159 0.03 43. 093 43.104 - 0.0 2 9 373. 150 1.9165 1.9145 0. 10 48.192 48.232 - 0.0 8

r> 396*160 1.9165 1.9137 0.14 53.214 53.278 - 0.12

9 423.170 1.9165 1.9138 0.14 58.192 58.262 - 0.12

9 298.142 1.9754 1.9793 - 0. 20 33.063 33.025 0.11

9 323. 140 1.9754 1.9767 - 0 . 06 38.665 38.648 0.04

9 348.143 1.9754 1.9751 0.01 44. 084 44.888 - 0.01

9 373. 150 1.9754 1.9739 0 . 08 49.378 49.407 - 0.06

9 398.160 1.9754 1.9729 0.13 54.581 54.640 - 0.11

9 423.170 1.9754 1,9728 0.13 59. 738 59.807 - 0.12

185
Table 12. Experimental and calculated

EQUATION OF STATE VS. PVT DATA

ID T , K MOL/L CALCD C,F

9 298.142 2.1218 2.1279 -0.

9 323.140 2.1218 2.1243 -0.

9 348.143 2.1218 2.1222 -0.

9 373.150 2.1218 2.1204 0.

9 398.160 2.1218 2.1194 0.

9 423.170 2.1218 2.1195 0.

9 296.142 2.3339 2.3428 -0.

9 323.140 2.3339 2.3383 -0.

9 348.143 2.3339 2.3356 -0.

9 373.150 2.3339 2.3334 0.

9 398.160 2.3339 2.3321 0.

9 423.170 2.3339 2.3319 0.

9 298.142 2.4084 2.4175 -0.

9 323.140 2.4084 2.4130 -0.

9 348.143 2.4084 2.4103 -0.

9 373.150 2.4084 2.4081 0.

9 398.160 2.4084 2.4066 0.

9 423.170 2.4084 2.4063 0.

9 298.142 2.9393 2.9535 -0.

9 323.140 2.9393 2.9485 -0.

9 348.143 2.9393 2.9443 -0.

9 373.150 2.9393 2.9410 -0.

9 398. 160 2.9393 2.9390 0.

9 423.170 2.9393 2.9385 0.

9 323.140 3.5820 3.5966 -0.

9 348.143 3.5820 3.5907 -0.

9 373.150 3.5820 3.5867 -0.

9 398.160 3.5820 3.5841 -0.

9 423.170 3.5820 3.5836 -0.

9 323.140 4.4288 4.4544 -0.

9 346.143 4.4286 4.4450 -0.

9 373.150 4.4288 4.4392 -0.

9 398. 160 4.4288 4.4367 -0.

9 423. 170 4.4288 4.4361 -0.

9 323.140 5.4403 5.4572 -0.

9 348.143 5.4403 5.4494 -0.

9 373.150 5.4403 5.4478 -0.

9 398.160 5.4403 5.4476 -0.

9 423. 170 5.4403 5.4492 -0.

9 323. 140 6.6818 6.5878 1.

9 348. 143 6.6818 6.6341 0.

9 373.150 6.6818 6.6551 0.

9 358.160 6.6818 6.6654 0.

9 423.170 6.6818 6.6739 0.

9 323.140 8.2024 8.0128 2.

9 348.143 8.2024 8.1079 1.

9 373.150 8.2024 8.1498 0.

9 398.160 8.2024 8.1707 0 . 9 423.170 8.2024 8.1813 0.

NP = 101, ONRMSPCT = 0. 353, P MEANPCT =

T data - - (Continued)

P , BAR CALCO P, PC

T

34.428 34.374 0.16

40.556 40.524 o.oe

46.470 46.463 0.02

52.238 52.264 -0.05

57.913 57.967 -0.05

63.538 63.596 -0.0 9

36.183 36.115 0.19

43. 101 43.052 0.12

49.758 49.732 0.05

56.240 56.251 -0.02

62.614 62.655 -0.06

68.922 68.972 -0.07

36.734 36.668 0.18

43.938 43.887 0.12

50.862 50.834 0.06

57.603 57.609 -0.01

64.224 64.263 -0.06

70.776 70.828 -0.07

39.901 39.833 0.17

49.228 49.148 0.16

58.126 58.062 0.11

66.768 66.742 0.04

75.253 75.260 -0.01

83.640 83.659 -0.02

54.204 54.107 0.18

65.647 65.553 0.14

76.769 76.700 0.09

87.686 87.646 0.04

98.481 98.446 0.04

58.974 58.854 0.20

74.001 73.854 0 . 2 C 88.656 88.516 0.16

103.099 102.959 0.14

117.402 117.240 0.1<l

62.995 62.935 0.10

82.596 82.521 0.09

101.932 101.833 0.10

121.098 120.966 0.11

140.168 139.962 0.15

66.912 67.250 -0.51

92.790 93.230 -0.47

118.770 119.173 -0.34

144.726 145.073 -0.24

170.709 170.924 -0.13

72.785 73.780 -1.37

108.346 109.548 -1.11

144.605 145.681 -0.74

181. 105 182.004 -0.50

217.659 218.423 -0.35

135

P-P

CT

29

12

02

06

11

11

38

19

07

02

08

09

38

19

08

01

08

09

48

31

17

06

01

03

41

24

13

06

04

58

37

24

18

17

31

17

14

13

16

41

71

40

25

12

31

15

64

39

26

0 .

186
Table 12. Experimental and calculated P-p-T data- - - (Continued)

EQUATION OF STATE VS. PVT OATA

ID T f K MOL/L CALCD C,PCT P » BAR CALCO Ft PC T 10 248.150 0.7000 0.6999 0.02 11.763 11.764 -0.01

10 273.150 0.7500 0.7508 -0.11 14.298 14.285 0.09

10 298.150 0.7500 0.7506 -0.08 16.116 16.105 0.07

10 303.150 0.7500 0.7506 -0.08 16.475 16.464 0.07

10 323.150 0.7500 0.7504 -0.06 17.897 17.888 0.05

10 348.150 0.7500 0.7503 -0.03 19.652 19.646 0.03

10 373.150 0.7500 0.7502 -0.02 21.391 21.386 0,02

10 398.150 0.7500 0.7501 -0.01 23.116 23.113 0.01

10 423.150 0.7500 0.7500 -0.00 24.830 24.829 0.00

10 448.150 0.7500 0.7500 -0.00 26.538 26.537 0.0Q

10 473.150 0.7500 0 .7500 -0.00 28.239 28.238 0.0 0 10 498.150 0.7500 0.7500 0.00 29.934 29.934 -0.00

10 523.150 0.7500 0.7500 -0.00 31.627 31.626 0.00

10 548.150 0.7500 0 .7501 -0.01 33.315 33.313 0.01

10 573. 150 0.7500 0.7501 -0.02 35.003 34.997 0.02

10 598.150 0.7500 0.7502 -0.03 36.689 36,678 0.03

10 623.150 0.7500 0.7504 -0.05 38.375 38.357 0.05

10 273.150 1.0000 1.0003 -0.03 17.908 17.903 0.02

10 298.150 1.0000 1.0000 -0.00 20.450 20.449 0.0 0 10 303.150 1.0000 0.9999 0.01 20.948 20.949 - 0.01

10 323.150 1.0000 0.9996 0.04 22.919 22.926 - 0.03

10 348.150 1.0000 0.9994 0.06 25.344 25.358 - 0.05

10 373.150 1.0000 0.9992 0.08 27.738 27.757 - 0.07

10 398.150 1.0000 0.9991 0.09 30. 109 30.133 - 0.08

10 423.150 1.0000 0.9991 0.09 32.462 32.499 - 0.09

10 448.150 1.0000 0.9991 0.09 34.802 34.832 - 0.09

10 473.150 1.0000 0.9991 0.09 37. 130 37.162 -0.09

10 498.150 1.0000 0.9991 0.09 39,450 39.483 - 0.08

10 523. 150 1.0000 0.9992 0.08 41.763 41.796 - 0.08

10 548.150 1.0000 0.9993 0.07 44.071 44.102 - 0.07

10 573.150 1.0000 0.9994 0.06 46.375 46.402 -0.06

10 598.150 1.0000 0.9995 0.05 48.675 48.697 -0.05

10 623. 150 1.0000 0.9999 0.01 50.982 50.988 -Q.01

10 273.150 1.5000 1.4984 0.11 23.530 23.545 - 0.06

10 298.150 1.5000 1.4997 0.02 27.719 27.723 - 0,0 1 10 303.150 1.5000 1.4994 0.04 28.528 28.535 - 0.0 3 10 323.150 1.5000 1.4987 0 . 09 31.709 31.730 - 0.07

10 348.150 1.5000 1.4979 0.14 35.592 35.632 - 0.11

10 373.150 1.5000 1.4975 0. 16 39.407 39.461 -0.14

10 396.150 1.5000 1.4974 0.17 43.172 43.237 -0.15

10 423. 150 1.5000 1.4973 0. 18 46. 899 46.973 -0.16

10 448.150 1.5000 1.4975 0.17 50.600 50.678 -0.15

10 473. 150 1.5000 1.4975 0. 16 54.276 54.358 -0.15

10 498.150 1.5000 1.4977 0.15 57.934 58.017 -0.14

10 523. 150 1.5000 1.4979 0.14 61.578 61.659 -0.13

10 548.150 1.5000 1.4983 0.11 65.215 65.287 - 0.11

10 573.150 1.5000 1 .4983 0. 11 68.827 68.902 -0,11

10 598.150 1.5000 1.4987 0.09 72.443 72.506 - 0.09

10 623. 150 1.5000 1.4993 0.05 76.067 76.101 - 0.05

10 298.150 2.0000 2.0027 -0.14 33.289 33.263 o .o e 10 303.150 2.0000 2.0023 -0.12 34.448 34.425 0.07

10 323. 150 2.0000 2.0003 -0.02 38.978 38.974 0,0 1

187
Table 12. Experimental and calculated P-p-T data- (Continued) - - EQUATION OF STATE VS , PVT DATA

ID T,K MOL/l CALCD 0 ,PCT P 9 BAR CALCO P * PC T 10 348,150 2.0000 1.9986 0.07 44.474 44.496 - 0.05

10 373.150 2.0000 1.9978 0.11 49.850 49.094 - 0.09

10 398.150 2.0000 1.9972 0.14 55.139 55.203 - 0.12

10 423.150 2.0000 1.9969 0.15 60.365 60.445 - 0.13

10 448.150 2.0000 1.9971 0.15 65.550 65.635 - 0.13

10 473.150 2.0000 1.9973 0.13 70.697 70.783 - 0.12

10 498 . 150 2,0000 1.9975 0.13 75.809 75.898 - 0.12

10 523.150 2.0000 1.9977 0.11 80.898 80.984 - 0.11

10 548.150 2.0000 1.9979 0.11 85.959 86.847 - 0.10

10 573.150 2.0000 1.9982 0.09 91.008 91.889 - 0.09

10 598.150 2.0000 1.9987 0.06 96.054 96.114 - 0.06

10 623.150 2.0000 1.9997 0.02 101. 105 101.123 - 0.02

10 298.150 2.5000 2.5084 - 0.33 37. 369 37.313 0.15

10 303.150 2.5000 2.5077 - 0.31 38.918 38.860 0.15

10 323.150 2.5000 2.5042 - 0.17 44.928 44.883 0.10

10 348.150 2.5000 2.5007 - 0.03 52.169 52.159 0.02

10 373.150 2.5000 2.4989 0.04 59.233 59.252 - 0.02

10 398.150 2.5000 2.4981 0.07 66.177 66.216 - 0.06

10 423.150 2.5000 2.4977 0.09 73.029 73.085 - 0.08

10 448.150 2.5000 2.4978 0.09 79.818 79.880 - 0.0 8 10 473.150 2.5000 2.4977 0 . 09 86.544 86.616 - 0.08

10 498.150 2.5000 2.4979 0.09 93.231 93.305 - 0.08

10 523.150 2.5000 2.4984 0 . 06 99.892 99.953 - 0.06

10 548.150 2.5000 2.4989 0.04 106.522 106.568 - 0.04

10 573.150 2.5000 2.4993 0.03 113 . 120 113.153 - 0.02

10 598.150 2.5000 2.4998 0.01 119.704 119.713 - 0.01

10 623.150 2.5000 2.5013 - 0.05 126.314 126.251 0.05

10 298.150 3.0000 3.0121 - 0.40 40.172 40.118 0.12

10 303.150 3.0000 3.0125 - 0.42 42.149 42.082 0.16

10 323.150 3.0000 3.0080 - 0.27 49.750 49.681 0.14

10 348.150 3.0000 3.0029 - 0.10 58. 862 58.826 0.06

10 373.150 3.0000 3.0002 - 0.01 67.732 67.729 0.0 0 10 398.150 3.0000 2.9992 0.03 76.450 76.465 - 0.0 2 10 423.150 3.0000 2.9983 0.06 85.039 85 . C 79 - 0.05

10 448.150 3.0000 2.9986 0 . 05 93.560 93.599 - 0.04

10 473.150 3.0000 2.9988 0.04 102.007 102.044 - 0.0 4

10 498.150 3.0000 2.9990 0.03 110.392 110.427 - 0.0 2 10 523.150 3.0000 2.9995 0 . 02 118.741 118.759 - 0.02

10 548.150 3.0000 3.0002 - 0 . 01 127.056 127.848 0.01

10 573.150 3.0000 3.0007 - 0.02 135. 329 135.299 0.02

10 598.150 3.0000 3.0016 - 0.05 143.594 143.517 0.05

10 623.150 3.0000 3.0034 - 0.11 151.881 151.705 0.12

10 303.150 3.5000 3.5146 - 0. 42 44. 346 44.294 0.12

10 323.150 3.5000 3.5119 - 0.34 53.635 53.553 0.15

10 348.150 3.5000 3.5051 - 0 . 15 64.723 64.667 0.09

10 373. 150 3.5000 3.5017 - 0.05 75.512 75.486 0.03

10 398.150 3.5000 3.5007 - 0.02 86.122 86.108 0.02

10 423.150 3.5000 3.5000 0.00 96.586 96.586 - 0.00

10 448. 150 3.5000 3.5003 - 0.01 106.961 106.953 0.01

10 473.150 3.5000 3.5008 - 0.02 117.256 117.232 0.02

10 498.150 3.5000 3.5010 - 0 . 03 127.471 127.438 0.02

10 523.150 3.5000 3.5015 - 0.04 137.642 137.583 0.04

10 548.150 3.5000 3.5021 - 0.06 147.765 147.676 0.06

188
Table 12. Experimental and calculated P-p-T data- - - (Continued)

EQUATION OF STATE VS. PVT DATA

ID Tf K MOL/L CALCD C,PCT P,BAR CALCO P» PC T 10 573.150 3.5000 3.5029 “0.08 157.853 157.724 0.08

10 598.150 3.5000 3.5039 “0.11 167.924 167.731 0.11

10 623. 150 3.5000 3.5061 -0.17 178.025 177.702 0.18

10 303.150 4.0000 4.0149 -0.37 45.714 45.684 0.07

10 323.150 4.0000 4.0182 -0.45 56.768 56.667 0.18

10 348.150 4.0000 4.0086 -0.21 69.920 69.836 0.12

10 373.150 4.0000 4.0044 -0.11 82.737 82.675 0.07

10 398.150 4.0000 4.0030 -0.07 95.353 95.299 0.06

10 423.150 4.0000 4.0025 -0.06 107.820 107.764 0.05

10 448.150 4.0000 4.0031 -0.08 120.189 120.108 0.07

10 473.150 4.0000 4.0035 -0.09 132.460 132.355 0.06

10 498. 150 4.0000 4.0038 -0.10 144.652 144.521 0.05

10 523.150 4.0000 4.0046 -0.11 156.793 156.618 0.11

10 548.150 4.0000 4.0046 -0. 12 168.860 168.656 0.12

10 573.150 4.0000 4.0055 -0.14 180.897 180.643 0.14

10 598.150 4.0000 4.0067 -0.17 192.920 192.583 0.17

10 623.150 4.0000 4.0093 -0.23 204.991 204.481 0.25

10 303.150 4.5000 4.5112 -0.25 46.448 46.437 0.02

10 323.150 4.5000 4.5245 -0.54 59.302 59.191 0.19

10 348.150 4.5000 4.5115 -0.25 74.601 74.498 0.14

10 373.150 4.5000 4.5068 -0.15 89.556 89.466 0.10

10 398.150 4.5000 4.5058 -0.13 104.316 104. ai3 0.10

10 423.150 4.5000 4.5055 -0.12 118.922 118.800 0.1G

10 448.150 4.5000 4.5065 -0.15 133.434 133. 261 0.13

10 473.150 4.500P 4.5065 -0. 15 147.823 147.621 0.14

10 498.150 4.5000 4.5072 -0.16 162.148 161.896 0.16

10 523. 150 4.5000 4.5076 -0.17 176.399 176.898 0.17

10 548.150 4.5000 4.5076 -0.17 190.571 190.336 0.18

10 573.150 4.5000 4.5080 -0.18 204.706 204.318 0.15

10 598.150 4.5000 4.5093 -0. 21 218.837 218.348 0.22

10 623.150 4.5000 4.5123 -0.27 233.031 232.331 0.30

10 323.150 5.0000 5.0242 -0.48 61. 395 61.300 0.16

10 348.150 5.0000 5.0099 -0.20 78.919 78.835 0.11

10 373. 150 5.0000 5.0065 -0.13 96. 135 96.850 0.05

10 398.150 5.0000 5.0068 -0.14 113.178 113.057 0.11

10 423.150 5.0000 5.0073 -0. 15 130.076 129.91? 0.13

10 448.150 5.0000 5.0083 -0.17 146.871 146. 646 0.15

10 473.150 5.0000 5.0086 -0.17 163.555 163.281 0.17

10 498.150 5.0000 5.0089 -0.18 180.155 179.830 0.18

10 523.150 5.0000 5.0087 “0 . 17 196.667 196.306 0.18

10 548.150 5.0000 5.0088 -0.18 213.119 212.715 0 .19

10 573.150 5.0000 5.0094 “0.19 229.543 229.063 tH •

CD 10 598.150 5.0000 5.0107 -0.21 245.951 245.357 0.24

10 623. 150 5.0000 5.0140 -0.28 262.444 261.600 0.32

10 323.150 5.5000 5.5078 -0.14 63.184 63.156 0.04

10 348.150 5.5000 5.4995 0. 01 83. 020 83.024 -0.01

10 373.150 5.5000 5.5009 -0.02 102.635 102.623 0.01

1 0 398.150 5.5000 5.5036 -0. 06 122.111 122.046 0.05

10 423.150 5.5000 5.5056 -0. 10 141.466 141.335 0.05

10 448.150 5.5000 5.5070 -0.13 160.716 160.516 0.12

10 473.150 5.5000 5.5075 -0.14 179.857 179.604 0.14

10 498.150 5.5000 5.5083 -0.15 198.931 198.612 0.16

10 523.150 5.5000 5.5081 -0.15 217.90

217.547 0.16

189
Table 12. Experimental and calculated P-P-T data- - - (Continued)

EQUATION OF STATE VS . PVT DATA

10 T,K MOL/L CALCD 0 ,PCT P » BAR CALCO Pf PC T 10 548.150 5.5000 5.5080 - 0.15 236.807 236.415 0.17

10 573.150 5.5000 5.5087 - 0.16 255.693 255.221 0.18

10 598.150 5.5000 5.5099 - 0.18 274.554 273.970 0.21

10 623.150 5.5000 5.5135 - 0.25 293.532 292.665 0.30

10 323.150 6.0000 5.9723 0.46 64.792 64.887 - 0.15

10 348.150 6.0000 5.9798 0.34 87.049 87.221 -0.2 0 10 373.150 6,0000 5.9890 0.18 109.215 109.367 - 0.14

10 398.150 6.0000 5.9962 0.06 131.309 131.383 - 0.06

10 423.150 6.0000 5.9999 0.00 153.294 153.295 -o.oc

10 448.150 6.0000 6.0026 - 0.04 175.196 175.118 0.04

10 473.150 6.0000 6.0042 - 0.07 197.010 196.861 0.08

10 498.150 6.0000 6.0053 - 0.09 218.751 218.531 0.10

10 523.150 6.0000 6.0049 - 0.08 240.359 240.132 0.09

10 548.150 6.0000 6.0051 - 0.09 261.935 261.668 0.10

10 573.150 6.0000 6.0056 - 0.09 283.465 283.143 0.11

10 598.150 6.0000 6.0070 - 0.12 304.998 304.557 0.14

10 623.150 6.0000 6.0109 - 0 . 18 326.668 325.914 0.23

10 323.150 6.5000 6.4217 1. 20 66.335 66.610 - 0.41

10 348.150 6.5000 6.4533 0.72 91.161 91.579 - 0.46

10 373.150 6.5000 6.4720 0.43 116.055 116.465 - 0.35

10 398. 150 6.5000 6.4843 0.24 140.958 141.281 - 0.23

10 423.150 6.5000 6.4913 0.13 165.80 0 166.031 - 0.14

10 448.150 6.5000 6.4957 0.07 190.579 190.717 - 0.07

10 473.150 6.5000 6.4981 0.03 215.266 215.340 -0.03

10 498.150 6.5000 6.4997 0.00 239.886 239.900 - 0.01

10 523.150 6.5000 6.4995 0 . 01 264. 373 264.398 - 0.01

10 548.150 6.5000 6.5003 - 0.00 288.851 288.833 0.01

10 573.150 6.5000 6.5005 - 0.01 313.236 313.207 0.01

10 598.150 6.5000 6.5023 - 0 . 04 337.677 337.520 0.05

10 623.150 6.5000 6.5059 - 0.09 362.215 361.772 0.12

10 323.150 7.0000 6.8616 1.98 67.920 68.441 - 0.77

10 348.150 7. 0000 6.9238 1.09 95.515 96.251 - 0.77

10 373.150 7.0000 6.9537 0.66 123.367 124.100 - 0.59

10 398.150 7.0000 6.9727 0. 39 151.344 151.950 - 0.40

10 423.150 7.0000 6.9822 0.25 179.269 179.778 - 0.28

10 448.150 7.0000 6.9890 0 . 16 207. 185 207.572 - 0.15

10 473.150 7.0000 6.9918 0.12 234.982 235.323 - 0.15

10 498.150 7.0000 6.9933 0 . 10 262.698 263.022 - 0.12

10 523.150 7.0000 6.9939 0.09 290.334 290.667 - 0.11

10 548.150 7.0000 6.9943 0.08 317.906 318.353 - 0.11

10 573.150 7.0000 6.9948 0 . 07 345.424 345.778 - 0.10

10 598.150 7.0000 6.9967 0 . 05 372.994 373.241 - 0.07

10 623.150 7.0000 7.0011 - 0.02 400.729 400.640 0.02

10 323.150 7.5000 7.3181 2.43 69.687 70.439 - 1.08

10 348.150 7.5000 7.4020 1.31 100.302 101.338 - 1.03

10 373.150 7.5000 7.4407 0.79 131.381 132.409 - 0.78

10 398.150 7.5000 7.4644 0.48 162.693 163.557 - 0.53

10 423.150 7.5000 7.4762 0 . 32 193.990 194.733 - 0.38

10 448.150 7.5000 7.4843 0.21 225.305 225.906 - 0.27

10 473.150 7.5000 7.4879 0.16 256.509 257.056 - 0.21

10 498.150 7.5000 7.4900 0.13 287. 646 288.170 - 0.18

10 523.150 7.5000 7.4901 0.13 318.646 319.235 - 0.18

10 548.150 7.5000 7.4899 0.14 349.569 350.246 - 0.16

190
Table 12. Experimental and calculated P-p-T data- - - (Continued)

EQUATION OF STATE VS. PVT DATA

ID T* K MOL/L CALCD D,PCT P » BAR CALCD F,PCT

10 573.150 7.5000 7.4900 0.13 380.454 381.196 -0.20

10 323.150 8.0000 7.8017 2.48 71.775 72.734 -1.34

10 348.150 8.0000 7.8935 1.33 1 05.750 107.024 -1.2C

1 0 373.150 8.0000 7.9379 0.78 140.417 141.621 -0.86

1 0 398.150 8.0000 7.9617 0.48 175.341 176.373 -0 .59

10 423.150 8,0000 7.9749 0.31 210.334 211.202 -0.41

10 448.150 8.0000 7.9832 0.21 245.348 246.061 -0.29

10 473.150 8.0000 7.9884 0.14 280.338 280.917 -0.21

10 498.150 8.0000 7.9888 0.14 315.099 315.748 -0.21

10 523.150 8.0000 7.9884 0 . 14 349.779 350.538 -0.22

10 548.150 8.0000 7.9882 0.15 384.407 385.276 -0.23

10 323.150 8.5000 8.3116 2.22 74.407 75.542 -1.52

10 348.150 8.5000 8.3967 1.22 112.147 113.592 -1.29

10 373.150 8.5000 8.4411 0.69 150.763 152.072 -0.87

10 398.150 8.5000 8.4648 0.41 189. 705 190.779 -0.57

10 423.150 8.5000 8.4774 0.27 228.728 229.609 -0.39

10 448.150 8.5000 8.4858 0.17 267.823 268.497 -0.25

10 473.150 8.5000 8.4903 0.11 306.859 307.399 -0.18

10 498.150 8.5000 8.4898 0.12 345.630 346.287 -0.19

10 523.150 8.5000 8.4886 0 . 13 384. 306 385.139 -0.22

10 323.150 9.0000 8.8361 1. 82 77.856 79.144 -1.65

10 348,150 9.0000 8.9087 1.01 119.857 121.393 -1.28

10 373.150 9.0000 8.9493 0.56 162.857 164.171 -0.81

10 398.150 9.0000 8.9723 0.31 206.258 207.234 -0.47

10 423.150 9.0000 8.9836 0.18 249.728 250.455 -0.29

10 448.150 9.0000 8.9901 0. 11 293.226 293.756 -0.18

10 473.150 9.0000 8.9943 0 . 06 336.726 337.085 -0.11

10 498.150 9.0000 8.9924 0.08 379. 850 380.403 -0.15

10 323. 150 9.5000 9.3667 1.40 82.499 83.907 -1.71

10 348.150 9.5000 9.4253 0.79 129.325 130.868 -1.19

10 373. 150 9.5000 9.4606 0.41 177.203 178.418 -0.69

10 398.150 9.5000 9.4811 0.20 225.515 226.290 -0.34

10 423.150 9.5000 9.4913 0.09 273.897 274. 343 -0 .16

10 448. 150 9.5000 9.4975 0 .03 322.334 322.486 -0.05

10 473.150 9.5000 9.4993 0 . 01 370.609 370.659 -0.0 1 10 323. 150 10.0000 9.8976 1.02 88.838 90.311 -1.66

1 0 348.150 10.0000 9.9423 0.58 141.085 142.568 -1.05

10 373. 150 10.0000 9.9730 0.27 154.424 195.427 -0.5 2 10 398. 15 0 10.0000 9.9915 0.08 248.207 248.618 -0.17

1 0 423.150 10.0000 9.9996 0. 00 301.977 301.991 -0.0 0 10 448.150 10.0000 10.0037 -0 . 04 355.71

355.450 0.07

10 323. 150 10.5000 10.4239 0 . 73 57.478 98.972 -1.53

10 348.150 10.5000 10.4587 0.39 155.840 157. 176 -0,86

1 0 373.150 10.5000 10.4843 0.15 215.238 215.943 -0.33

1 0 398.150 10.5000 10 . 4999 0.00 275.014 275.018 -0,00

10 423. 150 10.5000 10 . 5069 -0. 07 334.734 334,252 0.14

1 0 448.150 10.5000 10.5097 -0 . 09 394.346 393.551 0 .20

1 0 296.150 11.0000 10.9727 0 . 25 46.397 46.734 -0.73

10 323.150 1 1 .000 0 10.9450 0.50 1 09. 20 1 110.664 -1.34

10 348.150 11.0000 10.9729 0.25 174.42 0 175.525 -0.6 3 1 0 373.150 11.0000 10.9952 0 . 04 240.596 240.858 -0.11

10 398.150 11.0000 11.0079 -0.07 306.980 306.438 0 . 18

10 423.150 11.0000 11.0133 -0.12 373.226 372.128 0.29

191
Table 12. Experimental and calculated P-P-T data- - - (Continued)

EQUATION OF STATE VS. PVT DATA

ID T » K MOL/L CALCD 0,FCT P, BAR CALCD P,PCT

10 298.150 11.5000 11.4689 0. 27 54.120 54.730 -1.13

10 323.150 11.5000 11.4619 0.33 124.979 126.340 -1.0 9

10 348.150 11.5000 11.4841 0.14 197.803 198.620 -0.41

10 373.150 11.5000 11.5036 -0.03 271.474 271.232 0.09

10 398.150 11.5000 11.5151 -0.13 345.236 343.992 0.36

10 298.150 12.0000 11.9705 0. 25 66.139 67.006 -1.31

10 323.150 12.0000 11.9763 0.20 146.022 147. 141 -0.77

10 348.150 12.0000 11.9934 0. 05 227.224 227.651 -0.19

10 373.150 12.0000 12.0104 -0.09 309. 160 308.307 0.28

10 398.150 12.0000 12.0220 -0. 18 391.141 388.973 0.55

10 298.150 12.5000 12.4738 0.21 83.768 84.868 -1.31

10 323.150 12.5000 12.4854 0.12 173.516 174.419 -0.52

10 348.150 12.5000 12.5006 -0.01 264. 063 264.011 0.02

10 373.150 12.5000 12.5155 -0.12 355.074 353.521 0.44

10 298.150 13.0000 12.9782 0.17 108.587 109.845 -1.16

10 323.150 13.0000 12.9890 0.08 208.863 209.738 -0.42

10 348.150 13.0000 13.0057 -0.04 309.878 309.305 0.18

10 273.150 13.5000 13.4989 0. 01 31.583 31.642 -0.19

10 298.150 13.5000 13.4821 0.13 142.310 143.698 -o.9e

10 323.150 13.5000 13.4926 0. 05 254.146 254.893 -0.29

10 348.150 13.5000 13.5083 -0. 06 366.398 365.364 o.2e

10 273. 150 14.0000 13.9904 0. 07 62,783 63.504 -1.15

10 298.150 14.0000 13.9863 0. 10 187.036 188.425 -0.74

10 323.150 14.0000 13.9986 0 . 01 311.735 311.915 -0.06

10 273. 150 14.5000 14.4880 0.08 106.237 107.449 -1.14

10 298.150 14.5000 14.4911 0.06 245.114 246.273 -0.47

10 323.150 14.5000 14.5033 -0.02 383. 607 383.080 0.14

10 273.150 15.0000 14.9872 0.09 164.251 165.958 -1.04

10 298.150 15.0000 14.9928 0. 05 318.560 319.750 -0 .37

10 248.150 15.5000 15.4982 0.01 67.393 67.644 -0.37

10 273.150 15.5000 15.4916 0. 05 240.347 241.786 -0.60

10 298.150 15.5000 15.4932 0.04 410.257 411.635 -0.34

10 248.150 16.0000 15.9930 0.04 144. 656 145.900 -0.86

10 273.150 16.0000 15.9950 0 . 03 336.908 337.977 -0.32

NP = 298 , DNRMSPCT = 0.401, PMEANPCT = 0.256

192
Table 12. Experimental and calculated P-p-T data- - - (Continued)

EQUATION OF STATE VS. PVT DATA

ID T » K MOL/L CALCD D,PCT P , BAR CALCQ P,PCT

101 2 63 . ft 4 7 1.1061 1. Q9Q1 1.45 1 7.993 18.174 - 1 - 01

102 267.267 1. 1058 1.0955 0.92 18.458 1 8. 578 -0.65

103 270.457 1. 1054 1.0970 Q.76 1 8 . 8 49 18.951 -0. 54

104 273.094 1. 1054 1.0977 0.69 19.165 19.261 -0.50

105 276.946 1.1051 1 .0987 0.58 19.623 1 9.706 -0. 42

106 261.362 1. 1048 1.0995 0.48 20.142 20.213 -0. 35

107 283.868 1. 1044 1.1000 0.40 21.006 21.069 -0. 30

108 293.954 1. 1038 1.0998 0.36 22.139 22.202 -0.28

109 306.232 1.1034 1.0999 0.32 22.953 23.012 -0.25

110 315.923 1.102b 1.0994 0.31 24.016 24.077 ”0. 25

1 1326.1 85 1.1021 1 .0990 0 .28 25.1 35 25.192 -0. 23

1 112 332.655 1.1018 1.0989 0.26 25.836 25.892 - 0. 22

113 343.612 1. 1011 1. 0 96.4 0.25 27.010 27.067 -0.21

211 29Q..3L3-5 2.5966 2. 5 S2.1 Q.56 3-5. .4 79 3 5,55 3 -Q.21

202 292.700 2.5963 2.5957 0.02 36.139 36.142 -0.01

203 294.967 2.5959 2.5983 -0.09 36.907 36.894 n. 04

204 297.293 2.5956 2.5988 -0.12 37.678 37.658 0.05

205 299.402 2.5953 2.6006 -0.20 38.380 38.346 0. 09

206 300.717 2.5953 2.5987 -0.13 38.797 38.773 0.06

207 306.169 2.5943 2.5983 -0.16 40.554 40.524 0.08

i 208 311.528 2.5936 2.5974 -0.14 42.255 42.223 0.07

209 317.621 2.5926 2.5557 -0.12 44.159 44.130 0. 07

210 325.244 2. 5916 2.5535 -0.07 46.507 46.487 0.04

211 333.158 2.5903 2.591

-0.03 48.909 48.900 Q. 02

212 343.446 2.5890 2.5883 0 • C 3 51.991 52.000 -0.02

301 305.270 4.5943 4.519 0 1.64 47.863 47.962 -0.21

30 2 306.575 4.5939 4.536B 1 .24 48.748 43.836 -0. 18

303 3C6.998 4.5939 4.5454 1.06 49.040 49.118 -0.16

3Q4 308.355 4.5936 4.5483 0.99 49.934 50.018 -0. 17

305 309.475 4.5933 4.5514 0.91 50.671 50.757 -0. 17

306 310.226 4 .5929 4.5 54 7 0.83 51.168 51.251 ”0.16

307 311.461 4.5926 4.5562 0.79 51.973 52.060 -0.17

3Q8_ 314.528 4.5920 4.5585 0.73 53.959 54.053 -0. 16 ... 309 316.957 4. 5913 4.5537 0.71 55.518 55.628 -0. 20

. 3J-CL 326.208 4. 5890 4.5558 0.72 61.371 61.537 _ ~Ha_2J _ 311 329.514 4.5880 4.5471 0.89 63.647 63. 878 -0. 36

112 3 33. 690 4.5670 4.5821 0.11 66.220 66 , 251 ... -G_^_Q5,

401 305.232 5 .3595 4.9727 7.22 48.302 48.507 -0,42

402 306.165 5.3595 5.1961 3.05 49.168 49.266 ”0. 20

.. 4Q3 307.343 5.3588 5.2688 1.68 50.145 50.216 -Q.T4

404 308.378 5.3585 5.2844 1.38 50.973 51.045 -0. 14

405 310.753 5.3576 5.3268 0.58 52.892 52.935 -0. 08

406 315.523 5.3565 5.3429 0.25 56.662 56.693 -0.05

407 320.133 5.3552 5.3418 0.25 60.250 60.291 -0. 07

406 324.789 5.3535 5.3397 0.26 63.845 63.90 0 -0. 09

. 489 329.529 5.3522 5.3387 0.25 67.488 67.553 _ 410 334.774 5 . 3505 5.3379 0.24 71.501 71.574 -0.10

411 342.584 5.3482 5,3379 0.19 77.45Q 77.525

1 93
Table 12. Experimental and calculated P-p-T data- - - (Continued)

EQUATION OF STATE VS. PVT DATA

ID T,K MOL/L CALCD D,PCT P,BAR CALCD P,PCT

501 304.721 6. 1373 5.2442 14.55 48.051 48.166 -0.24

502 305.360 6.1370 5.5227 10.01 48.682 48.763 -0.17

503 305.932 6,1367 5.6833 7.39 49.202 49.289 -0.18

504 306.528 6.1367 5.7928 5.60 49.760 49.854 -0.19

505 307.927 6. 1360 5.9612 2.85 51.087 51.173 -0.17

506 309.803 6.1354 6.0301 1.71 52.846 52.933 -0.16

507 314.618 6.1337 6.0789 0.89 57.330 57.425 -0. 17

508 320.295 6. 1317 6.0814 0.82 62.550 62.692 -0.23

509 325.427 6.1300 6.0801 0.82 67.241 67.434 -0.29

510 330.799 6.1280 6.0821 0.75 72.153 72.381 -0. 32

511 336.699 6. 1260 6.0860 0.65 77.549 77.797 -0.32

512 343.543 6. 1237 6.0873 0.59 83.782 84.059 -0. 33

601 305.423 6.7892 5.9149 12.88 48.790 48.811 -0. 04

602 305.743 6.7888 5.6716 16.46 49.034 49.151 -0.24

603 306.184 6.7888 5.8169 14.32 49.461 49.619 -0.32

604 306.693 6.7885 6.0142 11.41 49.978 50.159 -0.36

605 307.189 6.7885 6.2012 8.65 50.499 50.685 -0. 37

606 309.162 6.7875 6.4936 4.33 52.576 52.781 -0. 39

607 312.231 6.7865 6.5013 4.20 55.667 56.040 -0.67

608 317.552 6.7845 6.5778 3.05 61.188 61.688 -0.82

609 322.347 6.7825 6.6161 2.45 66.200 66.775 -0.87

610 327.148 6.7805 6.6398 2.08 71.229 71.864 -0.89

611 333.270 6.7782 6.6639 1.69 77.676 78.349 -0. 87

612 343.351 6.7745 6.6836 1.34 38.268 89.013 -0.84

701 305.633 8.1021 5.9810 26.18 48.991 49.211 -0.45

702 306.319 8.1016 7.1329 11.96 49.819 50.129 -0.62

703 307.031 8.1014 7.6433 5.65 50.808 51.087 -0.55

704 309.123 8. 1008 7.6411 5.67 52.160 52.564 -0.77

705 311.913 8.0991 7.6884 5.07 56.966 57.728 -1.34

706 316.998 9. 0968 7.7679 4.06 63.649 64.713 -1. 67

707 322.404 8.0941 7.8239 3.34 70.899 72.181 -1.81

708 327.708 9.0918 7.8583 2.89 78.080 79.537 -1.87

709 333.451 8.0891 7.8875 2.49 85.935 87.525 -1.85

710 339.014 8. 0865 7.9157 2.11 93.653 95.278 -1.73

711 343.093 8 . 0845 7.9315 1.89 99.332 100.969 -1.65

801 305.015 6. 8104 8.2090 6.83 48.426 48.920 -1.02

802 306.220 8.8098 8.2922 5.87 50.132 50.785 -1. 3C

803 • 307.783 8.8088 6.3015 5.76 52.332 53.219 -1.70

804 309.310 8. 8081 8.4607 3.94 54.784 55.611 -1.51

805 310 .839 9 . 8 074 P .4754 3.77 57. 061 58.016 -1. 67

806 314.681 8.8055 8.4776 3.72 62.751 64.091 -2. 14

807 319.840 8. 8028 8.5218 3.19 70.675 72.302 -2.30

808 325.591 8.7998 8.5685 2.63 79.720 81.50 7 -2. 24

809 331.302 8.7971 e .6010 2.23 8 8.7 9** 90.690 -2. 13

810 337.309 6. 7938 8.6277 1.89 98.429 100.374 -1.98

811 342.720 8.7912 8.6448 1.67 107.138 109.122 -1.85

901 303.430 9.6887 5.5875 1.04 48.035 48.413 -0. 79

902 303.752 9.6887 9.585 0 1 . 07 48.615 49.016 -o. e 2 903 303.962 9.6887 9.5803 1.12 48.982 49.410 -0.87

194 _
Table 12. Experimental and calculated P-P-T data- - - (Continued)

EQUATION OF STATE VS. PVT DATA

ID T,K MOL/L CALCD D,PCT P» BAR CALCD P,PCT

904 3 0 4.336 9.6884 9.5310 1 .62 49.484 5 0.110 -1 . ?7

905 305.899 9.6874 9.5180 1.75 52.267 53.046 -1. 49

906 303-437 9.6861 9.5031 1.89 56.812 57.339 -1 .81

907 313.081 9.6834 9.5096 1.80 65.354 66.663 -2. 00

908 S') ft „ n u ft 9. 6fl07 9.531 8 1.54 74.730 76.163 -1 - 9?

909 322.924 9. 6781 9.5421 1.40 83.951 85.534 -1.89

910 S ? 7 . 9 9

9 . 6751 9.5515 1.28 93. 6ns 95.306 -1 .81

* 911 334.413 9. 6714 9.5540 1.21 105.611 107.733 -1.82

912 342.647 9.6668 9.5814 0.88 122.022 123. 717 -1.39

1001 293.336 11 .3761 11.3655 0.09 38.979 39.135 -0.40

1002 293.674 11.3761 11.3634 0.11 39.876 40.064 -0.47

inns 294.1 03 11. 3758 11 .3587 0.15 4 0.9R1 41 .23 ft -fi.63

1004 294.883 11.3751 11.3534 0.19 43.036 43.374 -0.78

ions 295.416 11 . 3748 11. 3495 0.22 44.436 44.835 -n. 90

1006 295.792 11.3745 11.3470 0.24 45.424 45.865 -0.97

i nn7 296.034 1 1 . 3745 11.3452 0.26 46.058 46.53? -1.03

1006 298.624 11.3728 11.3334 0.35 52.946 53.646 -1. 32

1009 301.993 -11. 3705 11 .3220 0 .43 61.951 62.91

-1.55

1010 304.995 11. 3685 11.3180 0.44 70.089 71.18 3 -1. 56

1011 309.657 11.3651 11.3151 0.44 82.812 84.041 -1.40

1012 314.468 11.3622 11.3130 0.43 95.989 97.341 -1.41

_ 1013 11 . 3588 11.3170 0.37 109.329 110.604 -1. 17 .. 1014 324.667 11.3552 11.3213 0.30 124.415 125.561 -0.92

1015 325.535 11 . 3525 11.3216 0.27 135.300 136.420 -0, 83

1016 335.200 11. 3482 11.3225 0.23 153.711 154.743 -0.67

1017 341.335 11.3442 11.3099 0.30 170.251 171.747 -0.88

1101 277.504 12. 9867 13.0057 -0.13 27.349 26.677 2.46

1102 277.925 12. 9884 13.0037 -0.12 28.958 28.348 2. 11

1103 273.136 12.9884 13.0006 -0.09 29.682 29.192 1. 65

1104 278.777 12.9877 12.9994 -0.09 32.203 31.730 1.47

1105 279.387 12.9874 12.9966 -0.07 34.536 34.156 1.10

1106 279.902 12. 9670 12.9955 -0.07 36.554 36.202 0.96

1107 282.317 12.9850 12.9836 Q .01 45.716 45.770 -0.12

1103 284.543 12. 9834 12.9823 0.01 54.539 54.588 -0. 09

1109 286.727 12.9614 12.9784 0.02 63.074 63.214 -0.22

1110 290.613 12. 9784 12.9727 0.04 78.298 73.585 -0. 37

1111 297.190 12.9734 12.9664 0 . 05 104.097 104.490 -0.38

1112 304.683 12.9674 12.9640 0.03 133.702 133.914 -0.16

1113 312*£Z5_ 12.9614 12.9601 0.01 164.925 165.016 -0.06

1114 320.632 12.9548 12 .9581 -0.03 197.261 197.007 0.13

1115 329.753 12.9476 12.9589 -0.09 232.594 231.663 . 0 * 4 C _ 1116 339.939 12.9401 12.9531 -0.10 272.480 271.290 0.44

1201 263.389 13. 7157 13.7212 -0.04 21.840 21.525 1. 44

1202 263.613 13. 7153 13.7206 -0.04 22.869 22.567 1. 32

1203 263.944 13 . 7150 13.7198 -0.04 24.394 24.115 I. 14

1204 269.313 13. 7150 13.7180 -0.02 26.037 25.862 0.67

1205 269.861 13.7143 13.7169 -0.02 28.565 28.418 0.52

1206 270.539 13. 7137 13.7146 -0.01 31.644 31.586 0, 18

1207 271.359 13. 7130 13.7128 0.00 35.412 35.424 -0.03

12 08 272.788 13.7120 13.7094 0.02 41.957 42.115 -3.38

195
Table 12. Experimental and calculated P-p-T data- - - (Continued)

EQUATION OF STUE VST PVT OATA

ID T * K MOL/L CALCD D,PCT P» BAR CALCO P» PCT

1209 277.605 13. 7060 13.7001 0.06 64.048 64.572 -0.82

1210 281.789 13. 7044 13.6957 0.06 83.378 33.991 -0.74

1211 266.317 13.7007 13.6911 0.07 104.232 104.953 -0.69

1212 290.328 13.6974 13.6879 0.07 122.712 123.454 -0.61

1213 296.212 13.6924 13.6851 0 . 05 149.868 150.484 -0. 41

1214 302.145 13. 6874 13.6819 0.04 177.132 177.624 -0.28

1215 310.715 13.6604 13.6790 0.01 216.504 216.647 -0. 07

1216 313.093 13.6734 13.6783 -0.04 255.083 254.561 0.20

1217 334.225 13.6606 13.6723 -0.08 323.892 322.512 0 • 43

1301 256.613 14 . 5544 1 4 .5 58 4 -0.03 19.044 13.702 1.80

1,30 2 257.326 14.5537 14.5556 -0.01 22.901 22.743 0. 69

1303 257.911 14.5534 14.5538 -0.00 26.113 26.073 0. 15

1304 259.065 14.5524 14.5519 0.00 32.560 32.60 7 -0.15

1305 263.450 14 . 5484 14.5440 0.03 56.915 57.324 -0.72

1306 266.631 14.5437 14.5353 0 . 06 85.525 86.354 -0. 97

1307 273.496 14. 5391 14.5321 0.05 112.695 113.417 • -0.64

1306 283.116 14.5304 14.5247 0.04 165.879 166.542 -0.40

1309 291.287 14.5231 14.5194 0.03 210.784 211.238 -0. 22

1310 298.372 14.5168 14.5160 0.01 249.591 249.70 0 -0. 04

1311 307.254 14. 5088 14.5117 -0.02 297.945 297.542 0.14

1312 319.529 14.4978 14.5045 -0.05 364.059 363.039 0.28

1401 248.290 15 .0496 15.0457 0.03 14.224 14.625 -2. 82

1402 249.192 15. 0486 15.0456 0.02 20.022 20. 331 -1.54

1403 250.248 15. 0476 15.0433 0.03 26.564 27.018 -1. 71

1404 253.374 15 . 0446 15.0378 0.05 45.992 46.742 -1. 63

1405 258.654 15. 0396 15. 0 30 0 0.06 78.728 79.845 -1. 42

1*06 265.858 15. 0329 15.0229 0.07 123.345 124.612 -1.03

1407 272.972 15.0263 15.0163 0.07 167. 038 168.374 -0. 80

1403 279.035 15. 0206 15.0116 0.06 204.080 205.354 -0.62

1409 285.189 15. 0146 15.0074 0.05 241.489 242.571 -0.45

1410 29*. 840 15. 0057 15 .0025 0.02 299.962 300.461 -0. 17

1411 30*. 470 14. 9967 14.9963 0.00 357.549 357.617 -0. 02

1412 316.744 14.9850 14.9999 -0.10 432.383 429.618 0. 64

1501 240.739 15 . 4546 15.4609 -0.04 10.100 9.335 7.57

1502 240.885 15. 4546 15.4603 -0.04 11.065 10.369 6.28

1503 241.249 15.4543 15.4602 -0.04 13.638 12.90 5 5. 37

150 4 241.891 15. 4536 15 . 4590 -0.03 18.027 17.364 3.68

1505 243.148 15.4523 15.4565 -0.03 26.600 26.074 i.9e

1506 246.601 15.4490 15.4481 0.01 49.622 49.938 -0.23

1507 251.930 15.4436 15.4423 C. 01 86.273 86.453 -0.21

1508 257.186 15.4386 15.4375 0.01 122.011 122.182 -0. 14

1509 261.7*5 15. 4343 15.4335 0.01 152.813 152.930 -0. 08

1510 267.242 15.4287 15.430 0 -0.01 189.660 139.655 0.11

1511 273.834 15. 4223 15.4245 -0.01 233.736 233.380 0.15

1512 282.799 15 . 4137 15.4187 -0.03 293.088 292.212 0. 30

1513 290.022 15. 4067 15.4131 -0.04 340.314 339.120 0.35

1514 296.219 15.3987 15.4081 -0.06 393.682 391.85 0 0.47

1515 309.559 15. 3378 15.4010 -0.09 466.789 464.006 0.60

1601 230.051 16. 0366 16.0361 0.00 8.0 60 8.126 -0.82

196
Table 12. Experimental and calculated P-p-T data- (Continued)

EQUATION OF STATE VS. FVT DATA

ID T t K MOL/L CALCD D,PCT P,BAR CALCD P,PCT

1_qT2 16. 0362 16.0357 n - nn 9.965 1 fl.043 -0.78

1603 230.307 16. 0359 16.0348 0.01 13.973 14.142 -1.21

1 604 232.572 16. 0339 16.0324 0.01 27. 840 28.078 -0.85

1605 2 3h . 16 0 16. 0323 16.0286 0.02 40.005 4 0.59 0 -1.46

1606 9 7 u O C ~ 16.0268 0.03 48.499 49.21

-1 . 48

1607 242.791 16. 0236 16.0158 0.05 106.582 107.928 -1. 26

1 608 249.107 16. 0170 16.0093 0.05 155.042 156.422 -0.89

T 1609 254.888 16. 0110 16.0029 0.05 198.800 200.331 -0.77

1610 262.164 16. 0037 15.9976 0 . 04 253.808 255.01

-0. 46

1611 271.236 15.9943 15.9880 0.04 320.920 322.271 -0. 42

1612 279.282 15.9860 15.9829 0.02 3 B 0.442 381.144 -0.18

1613 286.940 15.9781 15.9779 0.00 436.516 436.544 -0.01

1 614 2 94 . 5 1+3 15.9704 15.9734 -0.02 491.788 491.055 0.15

1615 301.025 15.9638 15.5651 -0.01 537.420 537.087 0.06

1701 222.875 15.4230 16.4030 0.12 7.625 11.158 -46. 34

1702 223.264 16. 4227 16.4017 0.13 10.831 14.539 -34. 24

1703 223.573 16.4223 16.4012 0.13 13.464 17.210 -27. 83

170 4 225.014 16. 421

16.3994 0.13 25.785 29.680 -15. 10

1705 230.291 16 . 4154 16.3902 0.15 70.101 74.832 -6. 75

1736 237.396 16. 4077 16.3812 Q.16 129.495 134.758 -4.06

1707 252.785 16. 3911 16.5647 0.16 255.712 261.545 -2. 28

1708 253.848 16. 3838 16 .3580 0.16 312.610 318.592 -1. 91

1709 2b7.6Q2 16. 3755 16.3512 0.15 374.481 380.373 -1. 57

1710 275.649 16.3668 16.3460 0.11 438.898 443.679 -1. 09

1711 282.466 16. 3598 16.3429 0.10 492.335 496.803 -0.91

17. 1.2 293.185 16 . 3485 16.3360 0®08 575.740 579.231 -0. 61

.14 Hi. 215 .247 16.7539 16.7727 -0.11 6.823 3 .Q84 54. 8Q

1802 215.504 16.7536 16.7728 -0.11 9.325 5.477 41.27

1 3 Q 3 215.892 16.7532 16.7715 -0.11 12.777 9.119 28.62 . 1804 216.369 16.7526 16.7710 -0.11 17.256 13.541 21.53

1805 216.832 16.7522 16.7702 -0.11 21.511 17.890 16.83

1306 217.058 16.7519 16.7692 -0.10 23.470 19.977 14. 88

1807 220.809 16. 7476 16.7629 -0.09 57.842 54.663 5. 50

1808 22o.802 16.7409 16.7551 -0.08 112.523 109.436 2. 74

1809 2 3 -f . 9 1 7 16. 7323 16.7456 -0.08 185.542 132.440 1_. 67

1810 243.045 16 .7233 16.7365 -0 .08 257.383 254.185 1. 24

18UL 250.885 16.7147 16.7300 -0.09 326.185 322.276 1 . 20

1812 260.378 16 .7044 16.7226 -0.11 408.366 403.433 1.21

1313 2.oJ±3lZ7 16. 6937 16.7176 -0.14 490.451 433.674 1. 38

1314 273. 13 0 16 . 6847 16.7118 -0.16 559.695 551.671 1. 43

1315 2 8-4.744 16.6778 16.7078 -0.18 615.144 605.967 1. 49

1816 293.608 16.6681 16.7025 -0.21 686.810 677.857 1.59

1901 206.953 17. 1250 17. 0977 0.16 8.116 14.30 0 -76. 19

1902 209.053 17. 1244 17.0967 0 .16 14.067 20.385 -44. 71

1903 213.403 17. 1194 17.0891 0.18 57. 037 64.142 -12.46

1904 213.5_6Sl 0.19 107.538 115.363 -7,. 2.8 1905 227. 034 17. 1038 17.0713 0.19 189.571 197.916 -4, 40

1906 233.700 17. 0961 17.0636 0.19 252.998 261.697 -i. 44 _ 1907 241.770 17. 0871 17.0560 0.18 328.989 337.725 -2.66

1908 251.549 17.0762 17.0496 _ 0.16 4.2 0.2 78 428.155 -1.87

197
(

Table 12. Experimental and calculated P-p-T data- - - (Continued)

EQUATION OF STATE VS. PVT OATA

ID T,K MOL/L CALC D D,PCT P, BAR CALCO P,PCT

1909 260.957 17.0655 17.0446 0.12 507.048 513.568 -1. 29

1910 268.486 17.0569 17.0368 0.12 574.398 580.876 -1.13

1911 280.494 17. 0436 17.0328 0.06 683.038 686.701 -0.54

2001 193.356 17.5291 17.5476 -0.11 7.130 2.315 67.53

2002 199.230 17.5281 17.5454 -0.10 16.592 12.067 27.27

2003 200.946 17.5261 17.5424 -0.09 35.439 31.123 12.18

2004 2 0 h . 75 6 17.5214 17.5355 -0.08 76.814 72.991 4.98

2005 210.931 17, 5141 17.5267 -0.07 143.419 139.863 2.48

2006 220.998 17.5022 17.5152 -0.07 250.280 246.369 1.56

2007 227.537 17. 4945 17.5071 -0.07 318.013 314.102 1. 23

2008 235.067 17.4859 17.5015 -0.09 395.918 390.856 1.28

2009 242.758 17.4769 17.4948 -0.10 473.940 467.90

1

1.27

2010 249.071 17.4692 17.4903 -0.12 537.459 530.140 1. 36

2011 256.389 17.4609 17.4875 -0.15 611.081 601.535 1.56

2012 263.603 17. 4523 17.4829 -0.18 682.214 670.834 1.67

2101 183.907 17.9415 17.9532 -0.07 6.728 3.226 52.05

2102 189.331 17.9411 17.9521 -0.06 11.762 8.484 27. 87

2103 169.746 17.9405 17.9515 -0.06 16.843 13.521 19.72

210^ 192.590 17.9368 17.9459 -0.05 50.874 48.097 5.46

2105 198.660 17.9295 17.9362 -0.04 123.000 120.883 1.72

2106 205.509 17.9209 17.5254 -0.03 202.640 201.149 0.74

2107 213.217 17. 9115 17.9159 -0.02 291.132 289.643 0.51

2108 220.733 17.9022 17.9096 -0.04 376.667 374.052 0.69

2109 228.543 17.8929 17.9040 -0.06 464.311 460.202 0.89

2110 233.949 17.3799 17.9001 -0.11 580.193 572.381 1.35

2201 176.719 18 . 4456 18.4480 -0.01 3.471 2.652 23. 59

2202 177.382 18. 4450 18.4462 -0.01 12.310 11.869 3. 58

2203 173.429 18.4433 ie .4445 -0.01 26.585 26.156 1. 61

2204 179.691 18 . 4416 ie .4416 -0.00 43.417 43.41

3

0.01

2205 182.793 18. 4376 18.4358 0.01 84.808 35.485 -0.60

2206 188.263 18.4307 18.4260 0.03 156.732 158.461 -1.10

2207 195*143 18 . 4217 18.4155 0 .03 245.802 248.198 -0.97

2208 201.949 18. 4130 18.4077 0.03 332.786 334.917 -0.64

2209 203.686 16. 4044 16.4024 0.01 418.212 419.023 -0.19

2210 215.452 18.3957 18 . 3979 -0.01 502.825 501.907 0.18

2211 222.008 18. 3871 18.3956 -0.05 584.427 580.711 0.64

2212 2 2 7 . 0 3 0 18. 3808 ie.3942 -0.07 646.312 640.353 0.92

2213 229.121 18. 3781 18.3946 -0.09 672.368 664.967 1. 10

2301 163. C32 18.8234 18.8126 0.06 10.003 14.303 -42.99

2302 163.479 18 .6227 18.8117 0.06 16.593 21.008 -26.61

2303 169.437 16. 8214 16.6093 0 .06 30.514 35.366 -15.90

2304 171.067 18. 8194 16.8057 0.07 54.233 59.759 -10.19

2305 1 73.679 16. 8158 18.8008 0.08 92. 210 98.292 -6.60

2306 177.673 18.8104 18.7931 0.09 149.285 156.488 -4. 83

2307 183.136 18.8031 18.7831 0.11 226.036 234.559 -3. 77

2308 163.344 18. 7955 18.7749 0.11 305.443 314.423 -2.94

2309 195.448 18 . 7665 18.763 8 0.09 396.636 404.799 -2. 01

2310 201.251 18.7788 18.7661 0.07 476.851 482.746 -1.24

2311 206.784 18.7715 18.7606 0.06 55 0.626 555.305 -0.94

198
Table 12» Experimental and calculated P-p-T data- - - (Continued

EQUATION OF STATE VS. PVT DATA

ID T,K MOL/L CALC D D,PCT P , BAR CALC D P,PCT

2 31 2 212.460 , 16 .7-613 16.7616 T.J11 628.513 629.515

2313 217.337 18.7576 16.7591 -0.01 692.835 692.094 0.11

2401 157.201 19.2261 19.222 0 0.02 5.219 7. 098 -36. 01

240? 1 6 4 - 4 9 F, 19. 224

19.2189 0.03 26. 1 62 28.51-9. on .

2403 159.577 19.2225 19.2149 0.04 42.627 46.284 -8. 07

2404 1 9 . 2208 19.2138 0.04 62.930 66.128 -5. 08

2405 163.656 19. 2168 19.2080 0.05 108.664 112.741 -3.75

2406 167.103 19. 2122 19.1981 0.07 161.353 167.949 -4. Q9

2407 172.270 19 . 2049 19.1897 0.08 241.688 248.95 8 -3. 01

2J±M 1 77. 321 19.1 970 1 9.1 81 5 0.09 31 8.533 326.541 .. -2. 51

2409 183.160 19. 1896 19.1764 0.07 407.622 414.225 -1. 62

2410 1 88 .69? 19.1819 1 9 . 1 72 6 0 . 05 490.353 495.107 - -0.97

2411 194.552 19.1739 19. 1703 0.02 578.543 580.48 0 -0. 33

241 2 199.115 19.1673 19.1720 -0.02 647.704 645.181 fl. 39

2413 202.417 19. 1630 19.1682 -0.03 694.537 691.718 0.41

2501 134.069 20.4330 20.1037 1.60 14.291 221.481 -1449.79

25 02 20.4293 20.1019 1.60 25.882 234.170 -308. 77

2503 1 36.071 20. 4270 20.0975 1.61 53.739 264.078 -391.41

2504 1 37.536 20 . 4247 20. 0931 1.62 82.345 294,824 -258. 04

2505 140.791 20 . 4194 20.0642 1.64 145.396 362.087 -149. 04

25Q6 144.763 20 ^ 41,3 4 2G.H763 1 . 66 221.796 442.862 -99.67

2507 149.679 20 . 4054 20.0673 1.66 315.714 540.141 -71.09

2508 154.382 20 . 3981 2C. 0628 1.64 405.313 631.278 -55. 75

2509 159.399 20. 3904 20.0607 1.62 500.568 726.521 -45. 14

2510 164.174 20 . 3828 20.059b 1.58 590.104 815.074 -38. 12

2511 168.954 20 .3755 20.0614 1.54 679.933 902.343 -32. 71

NP = 321, DNRMSPCT = 2.853, PMEANPCT =14.092

199
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200
Table 14. Interpolated ideal gas functions

ETHA N F IHEflL GAS FUNCTIONS;. JOULES .MOLES. 1KFl VT KS

T ,K H7 - S7 O \I7 r p 7

9 C 2 2 7 3.7 3027.0 If 0.150 26.66 35.17 _ i an 2550.1 -3381.5 IP 3.8,84 27.42 35 .73

lie 2827. 0 3741.6 . 187.316 27.98 36.29

i ?n 31 03.4 1 07.4 190.458 28.54 3 6 .66

.150 3 3 3 7. E 4478.3 193.471 29.12 3 7.43

140 345?.

4856.0 19 6 .2 66 29.71 3 8.0?

15 0 3 <392. 1 5239.3 198.910 3 0 . 32 38.64

16 J 4 2 9 b . fa 5628.9 \ 20 1.424 3 0.97 39.28

170 4 611. t 6025.1 2C 3. 826 31.65 39.96

1 3t 4931.7 b 4 2 8 .206.131 32.37 4 0.69

190 5 259.

6338.9 208.351 33.14 41.45

2 0 0 5594.6 7257.4 210. 467 33.95 42.26

2 10 5 9 3 3.2 7684.3 21 2 .579 34.80 43.12

22 4 6 2 9 0. 7 8116.9 21 4.6 06 35.70 4 4.92

2 30 o 65 2. 5 6564.3 216.583 36.65 44.97

2 4 U 7 0 23. 9 C Q1°.4 213.513 37.64 45.96

2 5 C 7 4 0 5.5 5484.1 22 0 . 415 3 6.66 46.99

2 EC- 7 79 ?. c 9959.

222 . 279 3 9.75 46.07

2 70 6 2 0 0.6 1 li 44 c. 5 224.113 4 0 .86 49.18

2 50 3614.5 10943.0 226.9?? 42.01 30.32

2 5 C 9 040. « 11452.0 227.708 43.18 51.49

3 0 0 9 h 75.1 1 972.9 229.474 44.38 52.69

3 1C 9 92 8. 5 12506.0 231.222 4 5.61 53 . 92

3 2 0 1 0 39 0. £ 13051.4 232.654 48.65 55.17

3 50 1 0 8 6 5.6 13609.

234.670 46.11 56.43

3 hO 1 1 353. 1 14160.0 236.374 49.39 57.70

3 50 1 1853. 4 14763.4 23 8 . C65 5 G .68 5 6.99

3 o0 12 3 6 6.6 15359.3 239.745 51.97 6 0 . 2 3 . . 3 70 12 392. c 15 96 c .l 24

. 4 14 53.27 61.58

.3 . n 1 3 43?. n 16691.4 24 7 . 074 5^.57 62.83

3 50 1 3 934.

17226.3 244.724 55 .67 6 4.13

4 : g 1 4 5 49. 4 17875.1 246.366 57.17 6 6.48

4 10 15 127. 5 18536.4 247.993 5 0.46 66.78

•+ 7 0 15 718.6- 192in.o 246 . 6 ?3 59.75 6 8 . 07

4 3 0 16 322. = 16867.7 251.240 61.03 6 9.35

u ^ n 1 6 936. ? 2 0 ^ Cj 7 .

252.849 62.30 70.6?

4 50 1 7 5bo. 6 21310.0 254.450 .6 3.56 7.1 .88

4 AH 1.-21 0. 5 ? 2 0 3 e- . n 26 fi . 0 43 6 4.81 73.13

4 7 0 1 6 6 b 4 . tr 22772.5 257.629 6 6.05 74.37

4 a.-s 1 « 6 ?, ; .

- ? 5 6 ? 2 . .3 269.208 67 .26 75.59 - .

-+ 5 0 2 0 210. 3 29284.4 260 . 773 6 8.49 76 .31

u n n 20401.

?9n5P.4 26 2.343 6 9 .69 . 7 8 . 0 0 . . ... 5 1 0 2 1 6 0 4. 1 2 6 8 9 4 .

263. 699 70.67 7 9.19

5 2 n 2 2 31 26642.1 265.443 7?.05 8 0.36

5 3 r 2 3 0 4 5.

27451.5 266.660 7 3.20 81.5?

5 401 2 3 76 2.7 28 272.4 266.524 74.35 3 2.66

w

-3 !

«\ 2 4 5 31. 2

C 104.7 27 0 . 051 76.47 6 3.29

5 c 0 25 262. 2 ? c 448.2 27 1 .571 76.59 6 4.90

5 70 2 6 3 6 3.6 3 C 6 0 2 .

273 . C 84 77.69 66.01

5 30 2 6 8-. 5. 9 31666.2 274.569 78 .78 p 7 . 0 9

5 5 0 27639.

32544.5 276. 0 87 79.65 68.17

o 00 2 8 44 3. 0 33431.5 277.578 60 .92 89.23

201
Table 15. Experimental and calculated heats of vaporization

ID; (10) Douslin; (11) Wiebe; (13) Riedel via Furtado; (20) Furtado

“ 17 21027302+001 1.11655879+001 1 .65392652+9(9

-7 . L 6546945 +0 01 6.21662337+001 -3 .26105136+001

10 T * K K J/ MOL Cf LCD PCNT nr 246 . 15 11.299 11.235 0.57

10 253.15 10.925 10 . 862 0.53 nr ZbTTXT 10. 072 10.039 0*33

10 273.15 9.073 9.072 0.01

10 269. T5 7. 8 + 4 7 .878 -0.44

10 293.15 6.17 0 6.253 -1.34 nr 293.15 5.034 5.090 -1.09

10 302.15 3.677 3.708 -0.85 nr 303 .13 —37337 37238 -0732

10 304.15 2.546 2.547 0.04

13 10 J . 00 17.154 17.312 -T.9X

13 111.11 16.926 17.068 -0.82

TT 1 5 5 • 53 16.455 16.492 -3722

13 155.56 15.853 15.797 0.35

l3~ lfc o . O

7

'15 .433 15.403 0.50

13 160 . 00 14.957 It- .886 0.48

I Z 164.10 1 4 .“73c 93 . 7X7 -T.T7

13 164 . 11 14.802 lc .716 0.58

IT 190.00 14.526 in • 4bb 07773 13 200.00 14.049 14.012 0.26

13 21 u .xnr 1 5 • b 5 0 13.525 9737

13 220 . 00 12.999 12.998 0.01

1

3

2td . od T2.338 127725 -0*30

13 240.00 11.743 11 . 797 -0.46

13" 2X77X3 11.044 11.099 -0.50

13 260.00 10.237 10.311 -0.24

13 ““2T7 . TO 9.416 ? • 3 9 6 “0722

13 260.00 8.353 8.287 0.80

13 293 . rr 6 . 8o 3 67 83 6 0.70

13 300.00 4.557 4.531 0.57

2X 1 0 U . 03 1/ .54 4 17.312 1794

20 111.11 17.117 17.068 0.28

23 133. 3r XT'. 4 37 IF. 492 0.03

20 155 • 5o 15.761 15.797 -0.23

20 1 c b • 6 ( 15.351 9577439 -0.34

20 160.00 14.832 14.886 -0.36 nr 184.11 14.677 14.716 -0."27 20 190.00 14.422 14 .465 -0.30

20 23F. 00 X 3 .3c 3 17 . TXT -0.42

20 210.00 13.438 13.525 -0.27

20 225. TO 12.939 127 998 0.01

20 230.00 12.434 12.425 0.07 nr 240 . 00 11.314 11.797 0.15

20 250.00 11.065 11.099 -0.31

20 2cT0 . m 13723 7 1379X1 -0.24

20 27 0 . 00 9.416 9.396 0.22

20 26 0 . TT 3. 279 F. 287" -0.46

20 290.00 6*663 6.836 0.40 nr 333733 4 • b 1 2 4.531 1.78

li 190 .00 13.777 14 ,465 -4.75

li 135.30“ 13. 639 17.24

n

-4.27

n 200.00 13.501 14 .012 -3.65

n 205.30

' 13.338 17.773 -3.16

n 210.00 13.179 13.525 -2.56

li 215 . 30 12.939 13.266 -2.02

li 220.00 12.806 12.998 -1.47

n 225. 03 12.334 127718 -1.03

n 230.00 12.362 12.425 -0.50

n '“233.33 12.11 X 12.119 -0.06

n 240.00 11.844 11.797 0.40 rr 235733 11. 55 1' ' 11.458 078X

ii 250.00 11.233 11.099 1.20 xn “255730 13789X7“ X0759 0 1.52

n 260.00 10.492 10.311 1.75 “m 265. 00 13. 0Tb 97372 1 . 63

n 270.00 9.534 9.396 2.00 rr 275733 973X2 5 .872 " 1.4/

n 260.00 6.429 8 . 287 1.71

n “'265733 7.70 0 77329 r. T3

n 290.00 6.834 6.836 -0.03

n 23:7.03 57 779 3.865 -1 • 4o n 300.00 4.294 4.531 -5.24

NP = 49, R9SPCT = 0.56

202
Table 16. Experimental and calculated specific heats for saturated liquid

ID: (11) Wiebe; (12) Witt Tc

- 3 ^. 3 7

6.73153+001 -1.65876+001 1. 63526+001 r c t - 0-5

ID T.K J/ f'OL/K CflLCD PCNT

-jg Q fl - 0 0 6ft- ?? 6 a r 17 0,07

11 96.77 68. 42 68.33 0 . 14 it 96.82 68.22 68.33 0*57

11 98.06 68.51 68.36 0.21

12 1 o o „00 68. 55 68 „ 4-1 0*-20 ii 101.54 68. 68 68.46 0.32

i n 7 . n ft 6 ft. 69 6 ft .. 6

-0,03

ii 108.65 68.51 68.66 -0.22

12 1 1 Q-fll) 6ft. 93 6ft .7f) 8*32

u 115.74 68. 63 68.89 -0 .38

- ii 116.19 68.42 68.91 ^8.70

12 120.00 69. 26 69.04 0.31

1 1 1 ?? . 7 Q 69.5 1 A 9 _ \ 9 0,6?

ii 123.60 69. 14 69.18 -0 .06

- 11 128.08 69.51 69.36 (U22

11 128.49 69. 47 69.38 0 .14

- 12 130.00 69.-51 6 9.44 0-10

11 132.65 69. 81 69.55 0 . 36

1 3 ft . 0 5 A Q, AA 6 9 . * 0 0,06

11 138.18 69. 97 69.81 0 .23

_ 11 138.31 69. 81 69.82 -0.01

12 140.00 69. 85 69.90 -0.07

- 11 162 .63 70.06 —70,02 8.05-

11 143.36 70.02 70.07 -0.08

115 0 .00 7 0.27 7 0 i 4 3 -0,23

ii 151.75 69. 93 70.53 -0 . 85

ii 152.60 7 0.10 70.58 -8,68

ii 154.99 70. 22 70.72 -0 .71

- ii 156.98 - 70.22 70.8-5 0 .88

ii 157.42 70. 06 70.88 -1.15

12 160-00 7 0.86 71.04 -0,27

ii 160.10 71.06 71.05 0.02

- ii 162.65 71. 14 71.22 -0.11

ii 164.49 71. 69 71.35 0.48

ii 71- 56 7 1 . A1 - q , 06

12 170.00 71.48 71.75 -0 .38

1 1 17 0 - 1

7ii 73 71-77 -0,05

11 172.05 71.73 71.91 -0 .25

- 11 172.69 72.11 71.96 0.2-0 11 178.17 72. 78 72.42 0 .49

12 1 ft 0*0 0 7?, 23 72-+ 5 A - a * 48

ii 181.50 73. 03 72.72 0.43

1 8 2 i 0 3 7 3.28 72-77 0 , 7

ii 190.00 73. 49 73.55 -0 .08

11 1 99 ,ft 6 * 3 \ 7-4 -67 ~ Q ,46

ii 208.88 75.62 75.87 -0 . 32 11 ?12* ft Q 7 5* 92 76*45 -0*70

ii 220.48 77. 76 77.73 0.03

77 ft . 7F, an. rf, 7Q. 75 1 .53

ii 236.21 82.2 8 81.06 1 .50

11 244*6

a 3. 9i 83.19 0.62

ii 252.53 87. 09 86.11 1.14

11 25 A „?2 ft B. 39 aa ,4ft -0*10

ii 265.25 92. 28 92.09 0 .20

ii 273.06 98.05 97.44 0.63

ii 278.07 1 01.28 102.01 -0 .72

1

284, o 7 10 QT Q A 1 QQ T UR -0*39

ii 291.27 122. 62 124.08 -1.18

11 294.85 13 a, 72 1 36*37 -o *47

NP- ~ 59. KHSPCT = 0,-54

203
T able 1

7

• Experimental and calculated specific heats C„(T)

ir on isobar P,b

TM * 354.0, CM = 117.333

89154 -0 .15442 -0. 14149 -0. 50644

T,K J/MOL/K CALC PCT

110. 928 68.19 68.45 -0.39

118.372 68.45 68.55 -0.15

122. 039 68.56 68.62 -0.08

133. 150 68.94 68.87 0.10

144. 261 69.44 69.23 0.31

155. 372 70. 08 69.70 0.55

166. 483 70.59 70.29 0.42

177.594 71. 09 71.03 0.09

186. 872 71.58 71.75 -0.24

188. 706 71.71 71.91 -0.27

199. 817 72. 72 72.94 -0.30

210.928 73. 98 74.15 -0.23

222. 039 75. 37 75.54 -0.23

233. 150 77.13 77.14 -0.01

241. 761 78.63 78.53 0.13

244. 261 79. 0 0 78.96 0.06

255. 372 81.14 81.03 0.13

266.483 83. 41 83.42 -0.01

277.594 86.31 86.17 0.17

282. 706 87.70 87.58 0.13

288. 706 89.71 89.39 0.36

299. 817 92.97 93.22 -0.27

305. 261 94.86 95.38 -0.55

310.928 97. 8 8 97.88 0.00

322. 039 103.80 103.63 0.17

324. 817 105. 43 105.26 0 .16

333. 150 110.45 110.54 -0.08

344.261 116.62 116.62 0.00

NP = 28, RMS = 0.25

204
Table 18. Calculated P(p) critical isotherm

The following page gives a high-resolution examination of the

critical isotherm of ethane as computed by equation of state (5). Column

headings have the following interpretations -

D/DC = d/dc , density reduced at the critical point.

P/PC = P/Pc , pressure reduced at the critical point.

DP/DD = c'P/cid, slope of the critical isotherm, bar/(mol/X).

The last five columns give the density-dependence of functions

used in the equation of state, where R = p = d/d^ is density reduced at the liquid triple point-

DTS/DR = dT a

(p)/dp, K.

DTH/DR = d0(p)/dp, K.

DPS/DR = dPr7 (p)/dp, bar.

DXB/DR = B$(p, T)/9p.

DXC/DR h 3Y( P , T) /Bp.

205
Table 18. Calculated P(p) critical isotherm

TC = 305 . 370 , DC = 6 . 740 , PC = 48.7550

0 /DC P/PC OP/DD CTS/OR

0.75 0 .993995341 0 . 658819307 40.90712

0 . 76 0.994858823 0. 591217592 38.34226

0.77 0.995632133 0. 528321099 35.89818

0 . 78 0.996321595 0. 469866251 33.56442

0.79 0.996933166 0. 415589108 31.32866

0 .80 0.997472439 0. 365229997 29.17651

0.81 0 . 997944660 0. 318539129 27.09132

0.82 0 . 998354733 0. 275283463 25.05409

0 . 83 0 . 998707261 0. 235255248 23.04356

0 . 84 0. 999006584 0. 198282488 21.03666

0.85 0 . 999256832 0. 164241474 19 .

0

0951

0.86 0 . 999462008 0. 133071105 16.93942

0 .87 0.999626082 0. 104787529 14 . e 0834

0.88 0. 999753105 0. 079495860 12.60834

0.89 0 . 999847343 0. 057392249 10.34968

0.90 0.999913379 0 . 038744754 8 .07130

0.91 0 . 999956191 0. 0238 36 181 5.65191

0.92 0.999981094 0. 012651315 3.61596

0.93 0 . 999993499 0. 005707396 2.12263

0 . 94 0 . 999998411 0. 001681248 0.92089

0 . 95 0. 999999775 0 . 0 C 0380 131 0.26456

0.96 0 . 999999987 0. 000031585 0.03611

0 . 97 0 . 999999999 0 . 0 0 0 0 00 362 0.00107

0.98 1.000000000 0.000000001 0.00000

0.99 1. 000000000 0. 000000000 0.00000

1.00 1. 000000000 0. 000000001 0.00000

1.01 1 . 000000000 0. 000000001 - 0.00000

1.02 1. 000000000 0.000000000 - 0.00000

1.03 0 . 999999999 0. 000000307 - 0.00017

1 . 04 1. 000000006 0. 000015499 - 0 .0 0658

1.05 1 . 00 00 0 0 099 0 . C 00163143 - 0.05510

1 .06 1 . 000000673 0. 000790788 - 0.21774

1.07 1. 000002769 0. 002471622 -0 .566 0 1 1.08 1. 000008306 0 . 0 0 5884 665 - 1.1 3956

1.09 1.000020147 0 . Cl 1698 168 - 1.9430 3 1.10 1 . 000042032 0 . 0 20506538 - 2.95766

1.11 l . 000078458 0. 032614787 - 4 . 15409 -

1 . 12 1 . 0001 34569 0. 049048904 -5 .5 0116 - 1.13 1 . 000216050 0 . 069575 997 - 6.97053 -

1 . 14 1 . 000329066 0. 054724915 - 8 .53860 - 1.15 1. 000480221 0 . 124803633 - 10.1 8679 -

1 . 16 1 . 000676539 0 . 1601 12464 - 11.90101 - 1.17 1 . 000925457 0.200953526 - 13.67097 - 1.18 1 . 001234836 0. 247637223 - 15 .48936 - 1.19 1 . 00 1612976 0. 300486478 - 17.35121 -

1 .20 1 . 002068631 0. 359839428 - 19.25328 - 1.21 l . 002611035 0. 426051033 -21 . 1 9357 - 1.22 1 . 00 3249928 0. 499493948 - 23.17105 - 1.23 1 . 00 3995570 0. 560558929 - 25 .

1

8528 -

1 . 24 1. 004858783 0. 669654959 - 27.23630 -

1 .25 1. 005850959 0. 767209159 - 29.32441 -

DTH/OR OPS/DR DXB/DR CXC/CR , .38357 40.77208 - 0.13448 0.40412

.22775 38.32854 - 0.12600 0 .38616

.29211 35.98713 - 0. 11792 0.36888 ( .56723 33.73933 - 0. 11021 0.35219

.04173 31.57456 - 0.10284 0.33599

.70206 29.47982 - 0.09575 0.32014

.53235 27.43963 - 0.08888 0.30447

.51428 25.43582 - 0.08217 0.28875

.62722 23.44768 - 0 . 07556 0.27271

.84865 21.45237 - 0 . 06896 0.25603

.15516 19.42597 - 0. 06230 0.23833

.52453 17.34554 - 0.05551 0.21919

.93907 15.19272 - 0 . 04 e 52 0.19819

. 39122 12.95942 - 0. 04130 0.17498

.89154 10.65629 - 0.03390 0.14936

.47924 8.32377 - 0. 02644 0.12153

.23329 6.04377 - 0.01517 0.09228

.27835 3.94613 - 0.0125 0 0.06328

.77383 2.19740 - 0.00695 0.03716

.86884 0 .95413 - 0.00202 0.01707

,61736 0.27427 - 0.00087 0.00521

.90191 0.03745 - 0. 00 Cl 2 0.00076

.48808 0.00111 - 0.00000 0.00002

.21645 0.08000 - 0.00000 O.OOOCO

.05411 0.00000 - 0.00000 0.00000

.00000 0.00000 0.00000 0.00000

.05411 - 0.00000 0.00000 - 0.00000

.21645 - 0.00000 0.00000 - 0.00000

.48719 - 0.00018 0.00000 - 0.00000

.87239 - 0.00683 0 . 0 0 0 0 2 - 0.00014

.40790 - 0.05714 0.00018 - 0.00109

.16574 - 0.22573 0 . 00 C 71 - 0.00408

.21735 - 0.58651 C . 00 185 - 0.01010

.60234 - 1.18018 0 . 00 37 3 - 0.01943

.32524 - 2.01086 0 . 00 6 35 - 0.03171

.36717 - 3.05834 0.00669 - 0.04633

.69861 - 4.29137 0 . 01 36 0 - 0.06259

.28819 - 5.6768 2 0.01602 - 0 . 079 c l .10734 - 7.18454 0 . 02 28 3 - 0.09782

.13220 - 8.78935 0.02797 - 0 . 115 c 8 .34387 - 10.47126 0.03337 - 0.13414 „ .72791 - 12.21500 0.03699 - 0.15216

.27363 - 14.00923 0 . 0448 0 - 0 . 169°5

.97332 - 15.84571 0 . 05 076 - 0.18744

.82149 - 17.71 862 0.05687 - 0 . 20463 ' .81437 - 19.62388 0.06212 -C .22150

.94941 - 21.55873 0 . 0695 0 - 0.23807

.22492 - 23.52133 0 . 0 7 6 0 0 - 0.25436

.63980 - 25.51048 0.08262 - 0 .270 39

.19332 - 27.52539 C . 0 8 9 3 8 - 0.26618

.88500 - 29.56554 0.09626 - 0.30175

74

69

64

59

55

50

4 6 42

38

34

31

27

23

20

16

1 3 10

74

2

10

0

00

0 -0

-0

-0

-0

-1

-2

-3

-4

-6

-e

1 o 13

16

19

22

2 5 29

32

36

40

44 . 49

5 3 58

62 .

206
Table 19. Loop closure computations for saturated liquid.

FNTHALPY, H, \/IA FURTADC CP(T). HC \/IA ClAPEYPCN FQN.

T,K H HC PC T S SC PCI

9 Q 5306 5 38 ? 1.45 76.57 77.16 0.77

95 5648 5677 0.51 80 . 28 80.44 0.21

1 00 5991 5 978 - 0.22 83.8 0 83.55 - 0.29

105 6335 6296 - 0.61 87. 15 66.65 - 0.57

110 6678 6633 - 0.68 90 . 35 69.79 - 0.62

1 15 7023 6987 - 0.52 93.41 92.93 - 0 . 51

120 7368 7352 - 0.21 96.

5 ° 6 .05 - 0.31

125 7714 7724 0.13 99.17 99.09 - 0 . c s 130 8061 8058 0.46 101.89 102.04 0,14

135 8409 8470 0.73 104. 52 104.86 0.32

140 8758 8837 0.90 107. 06 107.54 0.45

1 45 31 C 8 915 7 0.98 109.51 110.03 0.52

1 5 C 9460 9552 0.97 111.90 112.50 0.54

155 9814 9901 0.89 1 14. 22 114.80 0.51

1 6 0 10169 10 246 0.76 116. 47 117.00 0.45

165 10527 10 589 0.60 1 18. 67 119.11 0 . 36

170 10886 10 532 0.42 120. 81 121 .16 0 . 29

175 11248 11277 0.26 122. 91 123.16 0.20

1 3 0 11513 11626 0.11 124. 96 125.11 0.13

185 11981 11579 - 0.02 126.96 127.04 0 . C 6

190 1 2 352 12 340 - 0.10 128.93 128.95 0 . 02

195 12727 12707 - 0.15 130 . 87 130.35 - 0.01

200 13106 13 0 8 3 - 0.17 132. 77 132.73 - 0.03

205 1 3468 13466 -0 . 16 134.65 134.61 -0.03

2 1 C 1 38 76 1385 7

- 0.14 136.

0 136.47 -0.02

215 14268 14255 - 0.09 138. 32 138.32 -0.00

220 14666 14 66 0 - 0.04 140 . 1

140.15 0»0?

225 15070 15 071 C. 00 141. 92 141.97 C , 04

233 15480 15486 0.04 143. 69 143.77 0 . 05

2 35 15898 15 90 8 0.06 145. 45 145.54 0.06

240 16323 16 336 0.06 147. 21 147.30 0 , 06

245 16758 1676 8 0. 07 148. 96 149.04 C . 06

250 1720 2 17210 0.05 150.70 150.77 0.05

2 55 17657 17660 0.02 152. 45 152.50 0.03

260 16125 18 123 - 0.01 154 .

1 154.24 0.02

265 18607 186 C 1 - 0.03 155. 99 156 .00 0.01

270 1910 7 19 0 98 - 0.05 157,78 157.78 0.00

2 75 19628 19619 - 0.04 159. 62 159.62 0.0 0 2 30 2 017 5 20 169 -0.03 161 . 50 161.51 0.01

265 20756 20 784 - 0.01 163.46 163.46 0 . 0 1 29 3 213 8 6 21 36 3 - 0.02 165.55 165 .56 0.01

2 9 5 22093 22 06 0 - 0.06 167. 84 167.82 -0.01

3 00 2295 0 2293 5

- 0.16 170. 58 170.49 -0.06

207
Table 20. Experimental and calculated specific heats, Cp(p,T).

THE CP ISOBAR AT P = 0.000 BAR

T *K MOL/L J/MOL/K CA LCD PCNT 99.817 0.000 35.86 35.72 0.37

110.928 0 . 000 36.49 36.34 0.41

118.372 0 . 000 36. 98 36.76 0.59

122.039 0.000 37.24 36.97 0.73

133.150 0.000 37.99 37.61 1.00

144.261 0.000 38.74 33.28 1.19

155.372 0.000 39. 25 38 . 98 0.69

166.483 0 . 000 40.02 39.72 0.74

177.594 0.000 40.77 40.51 0.64

186.872 0.000 41.39 41.21 0.43

188.706 0.000 41.65 41.35 0.72

199.617 0.000 42.53 42.24 0.67

210.928 0.000 43.52 43.20 0.74

222.039 0 . 000 4 4.53 44.21 0.73

233.150 0.000 45.55 45.27 0.60

241.761 0 . 000 46. 43 46.14 0.62

244.261 0.000 46.67 46.39 0.59

255.372 0.000 47.93 47.56 0.76

266.483 0 . 000 49. 20 48 . 78 0.85

277.594 0.000 5 0.46 50.04 0.82

282.706 0.000 50.96 50 .63 0.65

288.706 0.000 51.71 51.34 0.72

299.817 0.000 52.84 52 .67 0.31

305.261 0.000 53. 21 53.34 -0.23

310.928 0 . 000 53. 85 54.03 -0.34

322 .039 0.000 55.24 55.42 -0.33

324.817 0.000 55.61 55.77 -0.29

333.150 0.000 56.62 56.83 -0.36

344.261 0.000 58.12 58.25 -0.22

355.372 0.000 60.15 59.68 0.77

366.483 0.000 61.65 61.12 0.85

366.817 0.000 61.78 61.17 0.99

377.594 0.000 63.17 62 . 57 0.94

388.706 0.000 64.53 64 . 02 0.80

399.817 0.000 . 65.81 65.46 0.53

410.928 0.000 66.56 66.90 -0.51

422 .039 0.000 67.81 68.33 -0.76

THE CP ISOBAR AT 'P = 17.237 BAR

T * K MOL/L J/MOL/K CALCD PCNT 99.817 21 .340 6 8. 45 68.59 -0.21

110.928 20.943 66.69 63.80 -0.15

118.372 20.676 68.83 63.98 -0.23

122.039 20.544 6 8.94 69 .09 -0.22

133.150

20 . 1*2 6 9. 20 6

9' .'50 -0.43

144.261 19.734 69. 82 70.03 -0.30

155 . 372 19.318 70.70 70.70 -0.00

166.483 18.891 71.47 71 .55 -0.11

177T594

18.452 72.46 72.59 -0.18

186.872 18 . 073 73. 34 73.63 -0.39

188.706 17.996 73. t*7 73.86 -0.53

199.817 17.522 74.99 75.41 -0.55

210.928 17.025 76.75 77.31 -0.72

222.039 16.498 78. 89 7 9.66 -0.98

233.150 15.933 82.02 82.67 -0.80

’241 . 761 15.460 8 5 • 3to 85.68 -0.44

244.261 15.315 85.94 86.70 -0.89

249.817 14.980 8 9.33 8 9.31 0.02

252.594 14.804 91. 34 90 .84 0.55

255 . 372 14'. 621 94.11 92.54 1.67

258.150 14.431 98.76 94.48 4.33

260.928 1. 05 3 7 4.35 71.68 3. 59

262.594 1 . 037 72.72 70.51 3. 04 265.372 1.012 70.21 68.68 1.90

266.483 1.002 69.44 68.32 1.62

277.594 0.921 6 5.17 64.56 0.94

282.706 0.890 64. 05 63.57 0.75

288.706 0.558 6 3.28 62.77 0*80

299.817 0.605 62.40 62.01 0.62

305.261 0.783 "' 62715 61 . 87 0.45

310.928 0.761 62. 02 61.86 0.27

3 22.039

0.723 62.28 62.10 OTTO 324.817 0.714 62.40 62.20 0.31

333.150 0.689 62.77 62 • 6i 0.26

344.261 0.659 63.65 63.31 0.53

355.372 0.632 64.53 64 . 17 0.57

366.463 0.608 65. 30 65.12 0.27

TF5T8T7 O'." 607 65.41 65.15 0T4TJ 377.594 0.536 66.16 66.17 0.03
Table 20. Experimental and calculated specific heats, C (P,T), (continued).

THE CP ISOBAR AT P = 28.269 BAR T7K~ MOL/L J/MOL/K CA LCD punt

277 .594 13.020 115.37 113.73 1.42

278 . 706 12 #90 6 116.13 116.21

279.017 12.788 118.65 119.01 -0.31 THE CP ISOBAR AT P = 34.474 BAR

T »MOL/L J/MOL/K CALCO PUNT 233.150 16.045 81.78 81.55 0.28

241.761 15 '.'594 84.42 84.13 07T5

244.261 15.457 85. 30 84.99 0.37

255.372 14.807 89. 20 89.67 -0.53

266.483 14.066 96.86 96.69 0.20

277 .594 13.165 109.70 109.28 07T5

282.706 12.652 119. 26 119.93 -0.56

285.928 12.27? 128.8? ““130 i 62 -1.40

~ 287.594 12.049 136.68 138.50 -1.18

288.706 11.886 142.81 145,26 -1.72

290.372 2.432 131.60 132.60 -0.77

291.483 ? . i 7 7 122.28 124.59 -1.89

292.594 2.327 115.63 118.25 \ -2.27

294.261 2 . 261 107.19 1 111 . 84 -3~.4 0 297.039 2.166 98.52 101.99 -3.53

299.817 2 • U 6 7 98.38 y 5 .// 2.66

305.261 1.359 87.06 37.69 -0.72

310.928 1.853 82. 28 82.43 -0.18

322.039 1.691 76.25 76.54 -0.39

324.817 1 .658 75.61 75.60 0.02

333 . 150 1 . 569 73.72 73.53 0.26

344.261 1.47 0 72. 22 71.96 0.36

355.372 1.338 71.47 71.23 0.33

366 .483 1.318 71.47 71.04 0.60

366.817 1.316 71.47 71 . 04 0.60 THE CP ISOBAR AT P = 41.369 BAR

T.k MOL/L J/MOL/K C A LCD PCNT 282.706 12.642 111.60 113.45 -1.66

288.706 12.131 129.59 129.39 0.16

294.261 11 . 356 161.66 163.98 -1.43

295 .928 11.021 179. 26 187.10 -4.36

297.039 10.752 195.01 212.72 -9.08

298.706 3.25 2 220.60 203,18 5.71

299 . 817 3 . 131 189.98 179.61 5.46

299.817 3 . 131 189. e5 179.61 5.39

300.650 3.055 168.60 165.17 2.03

301.206 3 . 009 157.76 157.51 0.16

302.594 2.909 137.89 142.85 -3.59

305.261 2.754 122.41 124.78 -1.94

310.928 2.516 104.66 104.74 -0.06

322.039 2.214 89.20 83 . 19 1.13

324.817 2.157 86. 93 85 . 89 1.20 THE CP ISOBAR AT P = 46.678 BAR

T,K MOL/L J/MOL/K CALCD PCNT

298.428 10 . 938 174.88 180.66 -3.31

299.817 10 1 619 198.79 206.55 -3.90

300 .650 10.392 221.43 230 . 76 -4.21

301.206 10.219 240. 31 253.87 -5.64

302.039 9.906 279.31 310 . 02 -10.99

302.594 9.639 320.83 381.40 -18.88

302 . 872 9.47 4 352.28 443 . 36 -25.85

303.150 9.270 401.35 549.78 -36.98

303.983 4.273 425.25 457.03 -7.47

304.261 4.176 352. 28 394.11 -11.87

305.261 3.922 299. 44 281.47 6.00

305.372 3.900 293.15 274.01 6.53

305.928 3.799 261.69 243.90 6.80

306.761 3.673 223.95 213.18 4.81

308.150 3.505 184. 94 181.23 2.00

309.539 3.371 162. 30 161.11 0.73

310.928 3.259 146.47 147.11 0.92

310 . 926 3.25 9 148.84 147.11 1.17

313.706 3.073 130.05 128.66 1.67

316.483 2.934 120.28 116.93 27T3

322.039 2.712 119.02 102.71 13.71

324 .817 2.623 97.88 93 . 06 -0.18

209
Table 20. Experimental and calculated specific heats, C (P,T), (continued).

P

' THE CP ISOBAR A T'P = 49. 160 TO

T * K MOL/l J/MOL/K CALCD PC NT 232.706 13.026 106.07 108.18 -1.99

283.150 12.986 106.69 103.82 -2.0 0 288.706 12.443 119. 15 119.03 0.10

294.261 11.778 135.50 ' 136.93 -1.06

297.039 11.366 149. 08 152.75 -2.46

298.261 11 . 158 156.64 162.78 -3.92

299.817 10 . 858 177.89 180.52 -1.47

300.928 10,610 193. 13 199.02 -3.05

302.039 10 . 320 217.40 226.77 -4.31

302.594 10.152 231.24 246.82 -6.74

3 0 3 .150 9.963 246.48 274.21 -11.25

303.706 9.743 274.40 314.24 -14.52

304.261 9.476 566.16 379.44 32.98

304.817 9.125 691.97 510.24 26.26

305.261 8.70 7 1006.50 795.16 21.00

305.261 8 . 707 1132. 32 795 .16 29.73

306.483 4.904 553.58 709.02 -28.08

307.039 4.60 3 488. 15 474.72 2.75

307.594 4.401 375.56 “371778 1.01

308.150 4.247 332.39 312.59 5.96

309.261 4.016 261. 83 246.21 5797

310.928 3.769 200.05 196.12 1.96

313.706 3.435 158.14 155.87 1.44

316.483 3.281 135.50 134.78 0.53

T~2'2“.''d39 2.937 108.82 112.55 -3.42

324.817 2.375 101.91 105.91 -3.92

327.594 2.777 102.54 100.83 i .6? 333.150 2.613 95.37 93.61 1.84

THE CP ISOBAR AT P = 51.711 BAR

T7TT“ MOL/L J/MOL/K CALCD PCT7

322.039 3.310 125.81 126.12 -0.25

324.817 3.164 116.88 116.22 0.57

333.150 2.841 99.26 99.23 0.04

344 . 2bl 2.549 88. 82 88.60 0.26

355.372 2.339 83.03 83.19 -0.19

366.483 2.17 6 79.27 80.19 -1.16

366.817 2.171 79. 13 80.12 -1.25

377.594 2.043 76.75 78.50 -2.28

THE CP ISOBAR AT P

=

b fc . 4 fc 8 BAR

T,K MOL/L J/MOL/K CALCD PCNT

3 107 372 8 .'515 406.89442.02 -8.10

310 .650 8 . 338 444. 12 479.25 -7.91

310.928 8.146 467712

—519.80 -7.59

311.206 7.938 530.92 560.87 -5.64

3 1 1 .483 7.718 577.48 596.74 •3 • 3 3 311.761 7.438 626.55 619.71 1.09

3T2V0 39 7.256 666TF1 623 # 91 6.43

312.150 7.165 680. 65 620.86 8.78

312.261 7.076 689.46 616.16 10 • 63 312 .428 6.944 693. 22 607.65 12.34

312.594 6.817 694746

—598.49 1 3 • 8 2 312.706 6.733 693.22 598.20 13.71

317.817 6.632“ ET9T797 591.75 14.48

312.928 6.572 679. 39 585.18 13.87

313.150“ 6.413 644.15 —571.49 11.28

313.428 6.235 595.10 549.95 7.59

313.706 6.064 552.21

520.95 5.68

313.983 5.90 9 514.58 489.20 4.93

314.261 5.766 485.64 438.85 5.61

210
1

Table 20. Experimental and calculated specific heats, C (p,T), (continued). P

THE- CP ISOBAR AT P = 63.948 TAR

T,K MOL/L J/MOL/K C A LCD PC NT 110 .928 21. 009 b 8 • 5 b b 3 . 64 -O'. 11 118.37? 20 .748 68.69 63.79 -0.13

12?; 03? 20 .61? 6 6.83 68*67 -0.07

133.150 20.227 69.07 69.21 -0.20

144 . 2bl 19.830 69.71 69 • 66 0TTT7 155 . 372 19.426 70.46 70.23 0.32

166.483 19.015 71.21 70 .96 0.35

177 .594 16.593 71.84 71.84 -0.00

186.872 18 . 232 72.46 72.73 -0.36

188.705 16 . 159 73. 23 72 . 92 0.43

199.817 17.711 73.98 74.20 -0.29

210.928 17 .24 6 75.37 75.72 -0.47

222.039 16.760 77.00 77. 54 -0.70

233.150 16 .25 0 79.27 79.71 -0.57

241.761 15.633 81.14 81.72 -0.72

244.261 15 . 708 82.41 82.37 0.06

255.372 15.126 8 5.68 85.68 -0.01

266.483 14.439 89. 46 90.00 -0.60

277.594 13. 773 95.74 95 .01 -0.23

282.706 13.407 98. 89 99.72 -0.83

238.706 12.937 104.93 105.30 -0.36

299.817 11 . 886 111.84 122.47 -9.50

305.261 11.228 137.15 133.02 -0.64

310 . 928 10.35 3 156.53 165.91 -5.2 9 314.261 9.68 7 176.39 196.21 -11.23

316.483 9. 14 8 200.16 223.37 -11.59

317.594 8.644 222.69 238 . 79 -7.23

319.261 8. 349 254. 27 260 . 98 -2.64

320.372 7.998 270.62 271.62 -0.37

320.928 7.320 277.80 27*+ .61 1.15

322.039 7 . 46 8 284.97 274.66 3.62

322.706 7 .264 285.59 271 .01 5.11

323.706 6 . 972 265.22 262.63 7.92

324.817 6.670 281.83 256.13 9.12

324.817 6.670 282.20 256.13 9.24

325 .372 6.528 277.16 251 .11 9.40

326.433 6.261 258.30 240.78 6.73

327.594 b . 01240.93 223.87 5.01

330.372 5.503 200.55 199.26 0.64

333.150 5.103 176.51 175.40 0.62

335.928 4.784 158. 91 157 .02 1.19

338.706 4.525 143.69 142.97 0.50

344 . 261 4.126 123.29 123.74 -0.36

355.372 3.594 104.42 103.65 0.73

366.483 3.241 94.49 93.94 0.58

366 .317 3.232 94. 24 93.73 0.55

THE CP ISOBAR AT P = 36.184 BAR

T t K MOL/L J/MOL/K CALCD PCNT

282 .706 13.675 94. 86 95.17 -0.33

283.706 13.260 98. 89 93.94 -0.05

299.817 12.389 106.21 108.67 -0.42

305.261 11 . 694 114.62 115 .53 -0.80

310 .923 11.310 123. 42 125.07 -1.33

316.483 10.647 134.61 137.82 -2.33

322. Q39 9.867 149.97 154.63 -3.11

324.817 9.428 160.16 164.03 -2.41

327.594 6.957 168.20 172.82 -2.75

330 .372 6.467 176.13 179.23 -1.76

333.150 7.973 180.54 181.35 -0.45

334.817 “ 7.634

' 181.17 180.18 0.55

337.039 7.317 180.29 176.04 2.36

338*706 7.060 177.65 171.68 3.3b

341.483 6.665 170.23 165.13 2.99

344.261 6.311 1 6 1 157 . 81 2.46

349.817 5. 713 146.47 142.89 3.75

355.372 5 . 24 1 134.00 130.08 27T2

366.483 4.557 114. 24 112.09 1.88

T66'.'B'i 7 4.540 113.96 111.68 27TH

377.594 4.036 101.66 101.36 0.30

211
Table 20. Experimental and calculated specific heats, C (p,T), (continued).

THE CP TSOBAR AT P = 103.421 BAR

T »K MOL/t J/MOL/K CALCD PCNT

241.761 16.045 79.64 79.93 -0.36

244.261 15.929 80. 15 80 .44 -0. 37 255.372 15.394 82.79 82.99 -0.25

266.433 14.824 85.94 86 . 07 -0.15

277 .594 14.207 89. 84 89.86 -0.03

282.706 13.903 91.84 91.94 -0.11

283.706 13.528 94.73 94.74 -0.01

299.817 12.765 101.66 101.29 D7T7 305.261 12.349 105.68 105 .41 0.25

310 .928 11.881 110.34 110.57 -0.21

316.483 11.378 115.63 116.70 -0.92

322.039 10 .625 122.17 124.00 -1.50

324.817 10.528 126.44 128.06 -1.28

327.594 10 . 217 129.97 132.29 -1.79

333.150 9.555 137. 89 140.60 -1.96

3 3 8 • 7 0 6 8.855 144.81 146.68 -1.29

344.261 8.156 150.85 148.60 1.49

344.928 8 . 074 151.73 148 • 33 2724

345.928 7.953 151.48 147.78 2.44

348 .150 7.691 151.11 146 • 01 3# 3? 349.817 7.501 149.22 144.25 3.33

352.594 7.202 144.81 140.73 2.82

355.372 6.923 140. 91 136.97 2.80 A* 360.928 6.425 132. 35 130 .00 1777

366.483 5 . 396 126.82 123.53 2.60

366 *817 5 .972 126. 44 123.14 2 • 6

1

377.594 5.311 116.75 112.23 3.87 THE CP ISOBAR AT P = 120.658 BAR

T7K MOL/L J/MOL/K CALCD PUNT 324.817 11.192 113.73 113.36 0.33

33 3 . 15 0 10 . 439 120.28 120.95 -0.56

338.706 9. 903 124.68 125.75 -0.86

344.261 9.348 129.70 13 0 • 0 3 -0.25

347.039 9.06 8 131.60 130.98 0.47

349 . 81

7

8.790 132.74 131.44 0793

351.761 6.598 133.12 131.44 1.26

352.317 6.543 13 3* £3 131 • 39 1*38

355.372 6 . 2*+ 8 132.35 130.74 1.21

358.150 7.938 130.34 129.64 0.54

360.928 7.738 128.34 128.13 0.16

3bb . 483 7.274 124. 04 124.21 • 0 • 1

3

366.817 7.247 123.80 123.95 -0.12

377.594 67936 IT7726 115.09 TT99

THE CP ISOBAR AT P = 137. 895 9'AR T,K MOL/L J/MOL/K CALCO PCNT

110 .928 21.095 6 8.19 68.45 -0*39

118.372 20.341 68.45 68.55 -0.15

122.039

—20.716 68.56 6 8 .62 -3738

133 . 150 20.335 68.94 68.87 0.10

144.261 19.952 69.44 69 .23 0731

155.372 19.564 70.08 69.70 0.55

lbb .483 197773 73759

79729 U .41 177.594 18.768 71. 09 71.03 0.09

1367872 18.427

71158 71.75 -9". 24 188.706 18.358 71.71 71.91 -0.27

T99T3T7 177978 7 2.72 72 .94 • 0 • 3 13 210 . 928 17.507 73.98 74.15 -0.23

7727979

177967

f 5 . 3 ( 75759 • DT73

233.150 16.603 77.13 77.14 -0.01

241 .761 lb • <?35 fS.bJ f 3 • 53 0*13

244.261 16.126 79. 00 79.96 0.06

255.372 15.628

81.14 8 1 • O 3 0*13

266.483 15.105 83.41 83.42 -0.01

277.594 14.552 86.31 86.17 • 0.17

282.706 14.285 87. 70 87.58 0.13

288.706 13.961 89.71 89.39 0.36

299.817 13.325 92.97 93.22 -0.27

305.261 12.994 94. 86 95 .38 -0.55

310.928 12.633 97.88 97.88 0.00

322.039 iTTeT? —nnrreo 103.63 5717

324.817 11.673 105. 43 105.26 0.16

333.150 11 . 041 110.45 110.54 -0.08

344.261 10.140 116.62 117.70 -0.93

355.372 9.204 120.28 120 . 81 -0.44

366.483 6.302 120.65 120.01 0.53

366.817 8 .276 118. 38 119.93 -1.30

377 .594 7.497 112.61 115 . 84 -2.87

212
Table 21. Comparison of Enthalpies for Saturated Liquid, J/mol

T, K Tester [70] This Report Difference

100 6 075 5 991 84

120 7 447 7 368 79

140 8 833 8 758 75

160 10 243 10 169 74

180 11 682 11 613 69

200 13 156 13 106 50

220 14 678 14 666 12

240 16 281 16 32 3 -42

260 18 006 18 125 -119

280 19 940 20 175 -235

300 22 720 22 950 -230

213
Table 22. Comparison of Enthalpies, J/mol

P = 20 atm P = 100 atm

T, K H° HT TE RG" HT TE RG

280 31 228 29 493 29 457 29 535 --

3 20 33 348 32 169 32 169 32 137 24 122 23 774 24 019

360 35 666 34 781 34 799 34 708 29 715 29 733 29 72 0

400 38 188 37 493 37 515 37 391 34 185 34 270 34 134

460 42 353 41 837 41 862 41 718 39 680 39 771 39 564

HT = Tester [70], TE = Eubank et al. [18], RG = This Report,

Pressure of 20 bar; ** Pressure of 100 bar.

214
Table 23. Calculated P(T) isochores

The following pages give P(T) along isochores, as computed by

the equation of state. The third column DP/DD is the isotherm slope

(ciP/Bp) in units of the bar and mol/X. The last two columns give the

2 2

isochore slopes and curvatures cP /BT, S P/dT , in units of the

bar and K.

These tables show that the isochore curvatures are qualitatively

consistent with a maximum in the specific heat C v

(p, T) at the critical

point.

215
Table 23. Calculated P(T) isochores.

THE ISOCHORE AT 1.00 MOL/L

T * K P»BAR DP/DO DP/OT 02P/DT2

266.0 17.157 12.481 0.1051 -0.00021

274. 0 17.992 13.495 0.1035 -0.00017

282.0 18.815 14.482 0.1023 -0.00015

29 0.0 19.628 15.448 0.1012 -0.00012

298.0 20.434 16.395 0.1003 -0.00011

306.0 21.233 17.328 0.0995 -0.00009

314.0 22.026 18.248 0.0988 -0.00008

322.0 22.814 19.156 0.0982 -0.00007

330.0 23.597 20.055 0.0976 -0.00007

338 ,

0

24.375 20.946 0.0971 -0.00006

346. 0 25.150 21.828 0.0967 -0.00005

354.0 25.922 22.704 0.0963 -0.00005

362.0 26.691 23.574 0.0959 -0.00004

370.0 27.457 24.438 0.0956 -0.000 04

378.0 28.220 25.298 0.0953 -0.00004

386.0 28.981 26.152 0.0950 -0.00003

394.0 29.740 27.003 0.0947 -0.00003

402.0 30.497 27.849 0.0945 -0.00003

410.0 31.252 28.692 0.0943 -0.00003

418.0 32.005 29.532 0.0941 -0.00002

426.0 32.757 30.369 0.0939 -0.00002

434. 0 33.508 31.203 0.0937 -0.00002

442.0 34.257 32.034 0.0936 -0.00002

450.0 35.004 32.863 0.0934 -0.00002

458.0 35.751 33.690 0.0933 -0.00002

466.

0

36.497 34.514 0.0931 -0.00002

474.0 37.241 35.337 0.0930 -0.00002

482.0 37.985 36.157 0.0929 -0.00001

490.0 38.727 36.976 0.0928 -0.00001

498.0 39.469 37.793 0.0927 -0.00001

506.0 40.210 38.609 0.0926 -0.00001

514.0 40.950 39.423 0.0925 -0.00001

522.0 41.690 40.235 0.0924 -0.00001

530.0 42.428 41.047 0.0923 -0.00001

538.0 43.166 41.857 0.0922 -0.00001

546.0 43.904 42.666 0.0921 -0.00001

554. 0 44.641 43.473 0.0921 -0.00001

562.0 45.377 44.280 0.0920 -0.00001

570.0 46.113 45.085 0.0919 -0.00001

578.0 46.848 45.890 0.0919 -0.00001

586.0 47.583 46.694 0.0918 -0.00001

594.0 48.317 47.496 0.0917 -0.00001

216
Table 23. Calculated P(T) isochoresTHE ISOCHORE AT 2.00 HOL/L

- (Continued)

T * K P,BAR DP/DD OP/DT D2P/DT2

290.0 31.339 8.269 0.2384 -0. 00066

298.0 33.227 9.482 0.2338 -0.00051

306. 0 35.082 10.654 0.2301 -0.00042

314.0 36.910 11.796 0.2270 -0.00035

322.0 38.716 12.915 0.2244 -0.00030

330.0 40.502 14.015 0.2222 -0.00026

330. 0 42.272 15.099 0.2202 -0.00023

346.0 44.027 16.169 0.2185 -0.00020

354. 0 45.769 17.228 0.2170 -0.00018

362.0 47.499 18.276 0.2156 -0.00016

370 .

49.219 19.315 0.2144 -0.00015

378.0 50.930 20.346 0.2133 -0.00013

386.52.632 21.370 0.2123 -0.00012

394.0 54.327 22.387 0.2113 -0.00011

402.0 56.014 23.399 0.2105 -0.00010

410.0 57.695 24.404 0.2097 - 0.0 00 09

418 .

59.369 25.405 0.2090 -0.00009

426.61.039 26.401 0.2083 -0.00008

434. 0 62.703 27.393 0.2077 -0.00007

44 2.0 64.362 28.380 0.2071 -0.00007

450.0 66.017 29.365 0.2066 -0.00006

458.0 67.668 30.345 0.2061 -0.00006

466.69.314 31.323 0.2056 -0.00006

474.0 70.958 32.297 0.2052 -0.00005

482.0 72.597 33.269 0.2048 -0.00005

49 0.0 74.234 34.238 0.2044 -0.00005

498 .

75.867 35.204 0.2040 -0.00004

506.0 77.498 36.168 0.2036 -0. 00004

514.0 79.126 37.130 0.2033 -0.00004

522. 0 80.751 38.090 0.2030 -0.00004

530.

82.374 39.047 0.2027 -0.00004

538. 0 83.994 40.003 0.2024 -0.00003

546.0 85.613 40.957 0.2021 -0.00003

554. 0 87.229 41.909 0.2019 -0.00003

562.0 88.843 42.860 0.2016 -0.00003

570.0 90. 455 43.808 0.2014 -0.00003

578 .

92.065 44.756 0.2012 -0.00003

586.93.674 45.701 0.2010 -0.00003

594.0 95.281 46.646 0.2008 -0.00003

217
Table 23. Calculated P(T) isochores- - - THE ISOCHORE AT 3.00 MOL/l

T * K P,BAR DP/ DO DP/OT

298.0 40.058 4.460 0.3967

306.0 43.187 5.8 49 0.3862

314.0 46.246 7.159 0.3788

322.

0

49.252 8.432 0.3731

330.0 52.218 9.682 0.3684

338.0 55.149 10.913 0.3645

346. 0 58.051 12.131 0.3611

354.

0

60.928 13.336 0.3582

362.0 63.782 14.532 0.3556

370.0 66.617 15.719 0.3532

378.0 69.435 16.898 0.3512

386.0 72.237 18.071 0.3493

394. 0 75.024 19.239 0.3476

402.0 77.799 20.401 0.3460

410.0 80.561 21.558 0.3446

418.0 83.313 22.710 0.3433

426.0 86.054 23.859 0.3421

434.0 88.787 25.004 0.3410

442. 0 91.510 26.146 0.3399

450.0 94.226 27.284 0.3390

458.0 96.934 28.419 0.3381

466.0 99.635 29.552 0.3372

474. 0 102.330 30.681 0.3364

482.0 105.018 31.808 0.3357

490.0 107.700 32.933 0.3349

498.0 110.377 34.056 0.3343

506.0 113.049 35.176 0.3336

514. 0 115.715 36.294 0.3330

522. 0 118.377 37.410 0.3325

530.

0

121.034 38.524 0.3319

538.0 123.688 39.637 0.3314

546.0 126.337 40.748 0.3309

554.0 128.982 41.856 0.3304

562.0 131.623 42.964 0.3300

570.0 134.261 44.070 0.3295

578.0 136.895 45.174 0.3291

586.0 139.527 46.276 0.3287

594.

0

142.155 47.378 0.3283

(Continued)

02P/DT2

-0.00163

-0.00107

-0.00080

-0.00064

-0.00053

-0.00045

-0.00039

-0.00034

-0.00031

-0.00027

-0. 00025

- 0.00022

- 0.00020

-0.00019

-0.00017

-0.00016

-0.00015

-0.00014

-0. 00013

- 0.00012

- 0.00011

- 0.00010

- 0.00010

-0.00009

-0.00009

-0.00008

-0.00008

-0.00007

-0.00007

-0.00007

-0.00006

-0.00006

-0.00006

-0.00006

-0.00005

-0.00005

-0.00005 Tj

-0.00005

218
Table 23. Calculated P(T) isochores- - - (Continued)

THE ISOCHORE AT 4.00 MOL/L

T » K P > BAR DP/DD DP/OT D2P/0T2

306.0 47.293 2.606 0.5608 -0.00241

314.0 51.716 4.014 0.5465 -0.00137

322.56.049 5.384 0.5373 -0.00098

330.0 60.319 6.736 0.5304 -0.00076

338.0 64.539 8.079 0.5248 -0.00063

346.0 68.719 9.415 0.5202 -0.00053

354.0 72.864 10.746 0.5163 -0.00046

362. 0 76.981 12.074 0.5129 -0.00040

370.0 81.071 13.398 0.5098 -0.00036

378. 0 85.139 14.720 0.5072 -0.00032

386. 0 89.186 16.040 0.5047 -0.00029

394.93.215 17.358 0.5025 -0.00026

402.0 97.228 18.674 0.5005 -0.00024

410.

101.224 19.988 0.4987 -0.00022

418.

105.207 21.301 0.4970 -0.00020

426. 0 109.177 22.612 0.4955 -0.00019

434.0 113.135 23.922 0.4940 -0.00017

442.

117.082 25.230 0.4927 -0.00016

450.0 121.018 26.537 0.4914 -0.00015

458.0 124.944 27.843 C . 4902 -0.00014

466.0 128.861 29.147 0.4891 -0.00014

474. 0 132.770 30.450 0.4880 -0. 000 13

482.0 136.670 31.752 0.4870 -0.00012

490.0 140.563 33.052 0.4861 -0.00011

498.0 144.448 34.351 0.4852 -0.00011

506.0 148.326 35.649 0.4844 -0.00010

514. 0 152.198 36.946 0.4835 -0.00010

522.

156.063 38.242 0.4828 -0.00009

530.0 159.922 39.536 0.4820 -0.00009

538.0 163.775 40.829 0.4813 -0.00009

546. 0 167.623 42.121 0.4806 -0.00008

554.0 171.466 43.412 0.4800 -0.00008

562. 0 175.303 44.702 0.4793 -0.00008

570.0 179.135 45.990 0.4787 -0.00007

578.0 182.962 47.278 0.4781 -0.00007

586.0 186.785 46.564 0.4776 -0.00007

594. 0 190.604 49.849 0.4770 -0.00007

219
Table 23. Calculated P(T) isochores- (Continued) - - THE ISOCHORE AT 5,00 MOL/L

T * K P,BAR DP/DD DF/DT D2P/DT2

306* 0 48.895 0.835 0.7449 -0.00551

314. 0 54.747 2.274 0.7225 -0.00167

322.

0

60.482 3.709 0.7120 -0.00104

330.0 66.148 5.155 0 .7049 -0.00077

338.0 71.765 6.610 0.6994 -0.00061

346. 0 77.342 8.074 0.6950 -0.00051

354.

0

82.886 9.546 0.6912 -0.00044

362.0 88.402 11.024 0.6879 -0.00038

370.0 93.894 12.508 0.6850 -0.00034

378.0 99.363 13.996 0.6824 -0.00031

386.0 104.813 15.489 0.6801 -0.00028

394. 0 110.246 16.985 0.6780 -0.00025

402. 0 115.662 18.484 0.6761 -0.00023

410.0 121.063 19.985 0 .6743 -0.00022

418.0 126.451 21.489 0.6726 -0.00020

426.0 131.826 22.994 0.6711 -0.00019

434. 0 137.188 24.502 0.6696 -0. 00018

442.0 142.540 26.010 0.6683 -0.00017

450.0 147.881 27.520 0.6670 -0.00016

458.0 153.211 29.030 0.6657 -0.00015

466.0 158.533 30.542 0.6646 -0. 00014

474.0 163.845 32.053 0.6635 -0.00013

482. 0 169.149 33.565 0.6624 -0.00013

490.0 174.444 35.078 0.6614 -0.00012

498.0 179.731 36.590 0 .6605 -0.00012

506.0 185.011 38.103 0.6595 -0. 00011

514.0 190.284 39.615 0.6586 -0.00011

522.0 195.549 41.128 0.6578 -0.00011

530.0 200.808 42.640 0.6569 -0.00010

538.0 206.060 44.151 0.6561 -0.00010

546.0 211.306 45.663 0.6553 -0.00010

554.0 216.545 47.173 0.6546 -0.00009

562.0 221.779 48.684 0.6538 -0.00009

570.0 227.007 50.193 0.6531 -0.00009

578.0 232.229 51.702 0.6524 -0.00009

586.0 237.445 53.211 0.6517 -0.00008

594.0 242.656 54.718 0.6510 -0.00008
1

Table 23. Calculated P(T) isochores- - - (Continued)

THE ISOCHORE AT 6.00 MQl/L

T,K P»8AR DP/DD OP/DT D2P/DT2

306.0 49.334 0.167 0.9259 -0.00990

314.0 56.633 1.634 0.9058 -0.00105

322. 0 63.853 3.183 0.8995 - 0. 00061

330.0 71.031 4.777 0 .8954 -0.00044

338.0 78.182 6.402 0.8922 -0.00036

346.0 ©5.309 8.052 0.8896 -0.00030

354. 0 92.417 9.720 0.8874 -0.00026

36 2.

99.508 11.404 0.8854 -0.00023

370.0 106.584 13.102 0.8837 -0.00021

378.0 113.647 14.811 0.8820 -0.00019

386. 0 120.697 16.530 0.8805 -0.00018

394.0 127.736 18.257 0.8791 -0.00017

402. 0 134.763 19.992 0.8778 -0.00016

410.0 141.781 21.734 0.8766 -0.00015

418.0 148.789 23.481 0.6754 -0.000 15

426.0 155.787 25.233 0.8742 -0.00014

434.0 162.776 26.989 0.8731 -0.00013

442.0 169.757 28.750 Q.8721 -0.00013

450.0 176.729 30.513 0.8710 -0.00013

458.0 183.694 32.280 0.8700 -0. 00012

466.0 190.650 34.048 0.8691 -0.00012

474.0 197.599 35.819 0.8681 -0.00012

482.0 204.540 37.592 0.8672 -0.00011

490.211.474 39.367 0.8663 -0. 00011

498.0 218.401 41.142 0.8654 -0.00011

506.0 225.321 42.919 0.6645 -0.00011

514. Q 232.234 44.697 0.8637 -0.00011

522.0 239.140 46.475 0.8628 -0.00010

53 Q . 0 246.039 48.254 0.8620 -0.00010

538.

252.932 50.033 0.8612 -0.00010

546 .

259.819 51.812 0.6604 -0.00010

554.0 266.699 53.591 0.8596 -0.00010

562.0 273.573 55.371 0.8588 -0.00010

570.0 280.440 57.150 0.8581 -0.00010

578.

287.302 58.928 0.8573 - 0. 000 09

586. 0 294.157 60.707 0.8565 -0,00009

594.0 3Q1.006 62.485 0.8558 -0.00009

221
Table 23. Calculated P(T) isochores- - - (Continued)

THE ISOCHORE AT 6.74 MOL/L

T,K P,BAR DP/DD DP/DT D2P/DT2

306.0 49.418 0.104 1.0528 -0.00000

314. 0 57.840 1.691 1.0527 -0.00001

322.0 66.261 3.401 1.0526 -0.00002

330.0 74.681 5.171 1.0524 -0.00003

338.

0

83.100 6.981 1.0521 -0.00004

346.0 91.515 8.823 1.0518 -0.00004

354.0 99.929 10.690 1.0515 -0.00005

362.0 108.339 12.578 1.0511 -0.00005

370.0 116.746 14.483 1.0506 -0.00006

378.0 125.149 16.403 1.0501 -0. 00006

386.0 133.548 18.336 1.0496 -0.00007

394.0 141.943 20.279 1.0491 -0.00007

402.0 150.333 22.233 1.0485 -0.00007

410.0 158.719 24.195 1.0479 -0.00008

418.0 167.100 26.165 1.0473 -0.00008

426. 0 175.476 28.141 1.0466 -0.00008

434.0 183.846 30.122 1.0460 -0.00008

442.0 192.211 32.109 1.0453 -0.000 09

450.0 200.571 34.100 1.0446 -0.00009

458.0 208.925 36.095 1.0439 -0.00009

466.0 217.273 38.093 1.0432 -0.00009

474.0 225.616 40.094 1.0425 -0.0 00 09

48 2.0 233.953 42.098 1.0417 -0.00009

490.0 242.284 44.103 1.0410 -0.00009

498.0 250.609 46.111 1.0402 -0.00009

506.0 258.927 48.119 1.0395 -0.00010

514.0 267.240 50.130 1.0387 -0.00010

522.0 275.547 52.141 1.0379 -0.00010

530.

0

283.847 54.152 1 .0372 -0.00010

538.

0

292.141 56.165 1.0364 -0.00010

546.

0

300.429 58.178 1.0356 -0.00010

554. 0 308.710 60.191 1.0348 -0. 00010

562.0 316.986 62.204 1.0340 -0.00010

570.0 325.255 64.216 1.0332 -0.00010

578.0 333.517 66.229 1.0324 -0.00010

586.0 341.774 68.241 1.0317 -0.00010

594.0 350.024 70.253 1.0309 -0.00010

222
Table 23. Calculated P(T) isochores- - - (Continued)

THE ISOCHORE AT 8.00 HOL/L

T,K P,BAR DP/DD DF/OT C2P/DT2

306.0 49.651 0.447 1.3126 0.01309

314.0 60.333 2.529 1.3477 0.00208

322.0 71.169 4.704 1.3601 0.00119

330.0 82.083 6.937 1.3680 0.00083

338.93.051 9.214 1.3738 0.00063

346.0 104.060 11.524 1.3782 0.00049

354.0 115.100 13.861 1.3817 0.00039

362.0 126.165 16.221 1.3846 0.00032

370.0 137.251 18.600 1.3869 0.00026

378.0 148.354 20.994 1.3887 0.00021

386.0 159.470 23.403 1.3903 0.00017

394.0 170.597 25.824 1.3915 0.00014

402.0 181.733 28.255 1.3924 0.00011

410.0 192.876 30.696 1.3932 0.00008

418.0 204.024 33.144 1.3937 0.00006

426.0 215.175 35.599 1.3941 0.00004

434.0 226.329 36.060 1.3944 0.00002

442.0 237.485 40.526 1.3945 0. 00001

450.0 248.640 42.997 1.3945 -0.00001

458.0 259.796 45.471 1.3943 -0.00002

466.0 270.950 47.949 1.3941 -0.00003

474.

282.101 50.429 1.3938 -0.00004

482.

293.251 52.911 1.3935 -0,00005

49 0.0 304.397 55.396 1.3930 -0.00006

493.0 315.539 57.882 1.3925 -0.00007

506.0 326.677 60.369 1.3920 -0.00007

514. 0 337.811 62.857 1.3914 -0.00008

522.0 348.939 65.345 1.3907 -0.00008

530.0 360.062 67.834 1.3900 -0.00009

538.0 371.180 70.323 1.3893 -0.00009

546.0 382.291 72.812 1.3886 -0.00010

554. 0 393.397 75.301 1.3878 -0.00010

562.0 404.495 77.789 1.3869 -0.00010

570.0 415.588 80.276 1 .3 861 -0.00011

578.0 426.673 82.763 1.3852 -0.00011

586 .437.751 85.249 1.3843 -0.00011

594.0 448.823 87.733 1.3834 -0.00011

223
Table 23. Calculated P(T) isochores- - - (Continued)

THE ISOCHORE AT 9.00 MOL/L

T,K P,8AR DP/00 OF/DT C2P/OT2

306.0 50.818 2.236 1.6175 0.00728

314.0 63.920 5.028 1.6527 0.00291

322.0 77.221 7.822 1.6712 0.00186

330.0 90.644 10.640 1.6839 0.00136

338.0 104.155 13.480 1.6935 0.00106

346. 0 117.734 16.341 1.7011 0.00085

354.0 131.368 19.218 1.7072 0.00069

362. 0 145.046 22.110 1.7123 0.00057

370 .

0

158.762 25.014 1.7164 0.00048

378.

0

172.508 27.929 1.7199 0.00040

386.0 186.279 30.853 1.7228 0.00033

394.0 200.072 33.784 1.7252 0.00027

402. 0 213.882 36.723 1.7272 0. 00023

410.0 227.707 39.666 1.7289 0.00018

418.0 241.543 42.614 1.7302 0.00015

426.0 255.389 45.566 1.7312 0.00011

434. 0 269,242 48.522 1 .7320 0.00008

442.0 283.100 51.479 1.7326 0.00006

450.0 296.962 54.439 1.7330 0.00004

458.0 310.827 57.400 1,7332 0.00002

466.0 324.692 60.363 1.7332 -0.00000

474.0 338.558 63.326 1.7331 -0. 00002

4e2.

0

352.422 66.289 1.7329 - 0. 0 00 03

490.0 366.284 69.252 1 .7326 -0.00005

498.0 380.143 72.215 1.7322 -0.00006

506.0 393.998 75.178 1 .7316 -0.00007

514. 0 407.849 78.139 1.7310 -0.00008

522.0 421.695 81.100 1.7304 -0.00009

530.0 435.535 84.059 1.7296 -0.00010

538.0 449.369 87.017 1.7288 -0.00010

546.0 463.196 89.973 1.7279 -0.00011

554. 0 477.015 92.928 1.7270 -0. 00012

562.0 490.828 95.880 1 .7261 -0.00012

570.0 504.632 98.831 1.7250 -0.00013

578.0 518.428 101.779 1.7240 -0.00013

586.0 532.216 104.725 1.7229 -0. 00014

594.0 545.995 107.669 1.7218 -0.00014

224
Table 23. Calculated P(T) isochores- - - (Continued)

THE ISOCHORE AT 10.00 MOL/L

T,K Pf BAR DP/ CD DF/DT D2P/DT2

306. 0 55.121 7.041 2 . C 254 0. 00422

314.0 71.438 10.701 2.0519 0.00265

322.0 87.929 14.316 2.0699 0.00192

330.0 104.545 17.915 2.0834 0.00149

338.0 121.257 21.505 2.0941 0.00119

346.0 138.045 25.092 2.1027 0.00097

354.154.896 28.677 2.1098 0.00080

362.0 171.799 32.261 2.1157 0.00067

370.0 188.745 35.843 2.1206 0.00056

378.0 205.726 39.424 2.1246 0.00046

386. 0 222.737 43.004 2.1280 0.00038

394.0 239.772 46.582 2.1308 0.00032

402. 0 256.828 50.158 2.1331 0.00026

410.0 273.901 53.732 2.1349 0.00021

418.0 290.986 57.304 2.1364 0.00016

426. 0 308.082 60.873 2.1375 0. 00012

434.0 325.186 64.440 2.1383 0.00009

442.0 342.295 68.004 2.1389 0.00005

450.0 359.407 71.564 2.1392 0.00003

45 8.376.522 75.122 2. 139 3 0.00000

466 • 0 393.636 78.676 2.1392 -0.00002

474.0 410.749 82.226 2.1390 -0. 00004

482.0 427.859 85.773 2.1386 -0.00006

49 0.0 444.966 89.316 2.1380 -0.00008

498.0 462.067 92.856 2.1373 -0.00009

506.0 479.162 96.391 2.1365 -0.00011

514.0 496.251 99.922 2.1356 -0.00012

522.0 513.332 103.449 2.1346 -0.00013

530.

530.405 106.972 2.1335 -0.00014

538. 0 547.469 110.491 2.1324 -0.00015

546. 0 564.523 114.005 2.1312 -0.00016

554.0 581.567 117.515 2.1299 -0.00017

562.0 598.600 121.021 2.1285 -0.00017

570.0 615.623 124.522 2.1271 -0.00018

578.0 632.634 128.018 2.1256 -0.00018

586.0 649.633 131.510 2.1241 -0.00019

594.0 666.620 134.998 2.1226 -0. 00020

225
Table 23. Calculated P(T) isochores- - - (Continued)

THE ISOCHORE AT 11.00 MOL/L

T,K P ,8 AR DP/DD DF/DT C 2 P /0 T 2

298.0 46.355 12.389 2.5254 0.00353

306 . 0 66.658 17.137 2.5488 0.00244

314.0 87.118 21.783 2.5657 0.00184

322 . 0 107.698 26.365 2.5787 0.00144

330.

0

128.370 30.903 2,5890 0.00116

338 . 0 149.117 35.406 2.5974 0.00094

346.

0

169.924 39.881 2.6042 0.00077

354 . 0 190.781 44.332 2.6098 0.00063

362.0 211.678 48.763 2.6144 0.00052

370.

0

232.609 53.175 2.6181 0.00042

378.

0

253.567 57.570 2.6211 0.00033

386.0 274.546 61.950 2.6235 0.00026

394.0 295.541 66.316 2.6254 0. 00020

402.0 316.550 70.668 2.6267 0.00014

410.

0

337.568 75.007 2.6277 0.00010

418.0 358.592 79.334 2.6283 0.00005

426.

0

379.620 83.650 2.6286 0. 00002

434.0 400.648 87.954 2.6285 - 0.00002

442.

0

421.675 92.248 2.6283 - 0.00005

45 0.0 442.700 96.531 2.6278 - 0.00008

458.

0

463.719 100.804 2.6270 - 0.00010

466 . 0 484.732 105.067 2 .6261 - 0.00012

474.

0

505.737 109.320 2.6251 - 0.00014

482 . 0 526.733 113.564 2.6239 - 0.00016

49 0.0 547.718 117.798 2.6225 - 0.00018

498 .

0

568.693 122.024 2.6210 - 0.00019

506.0 589.655 126.240 2.6194 - 0.00020

514.

0

610.603 130 . 44 e 2.6178 - 0. 00022

522.0 631.538 134.647 2.6160 - 0.00023

530.0 652.459 138.838 2.6141 - 0.00024

538.0 673.364 143.020 2.6 122 - 0.00025

546 . 0 694.254 147.194 2.6102 - 0.00025

226
Table 23. Calculated P(T) isochores- - - (Continued)

THE ISOCHORE AT 12.00 MOL/L

T,K P , BAR DP/DD OP/DT 02P/DT2

290 .

41.028 23.606 3.1812 0.00170

294. 0 53.766 26.598 3.1875 0. 00146

298.0 66.527 29.555 3.1929 0.00127

302. 0 79.308 32.483 3.1977 0.00112

306.0 92.108 35.385 3.2019 0.00098

310.0 104.923 36.264 3.2056 0.00087

314. 0 117.751 41.123 3.2068 0.00076

318.0 130.593 43.963 3.2117 0.00067

322.0 143.445 46.785 3.2142 0.00059

326. 0 156.306 49.592 3.2165 0.00052

330.0 169.176 52.384 3.2184 0.00046

334.0 182.053 55.162 3.2201 0.00040

338.0 194.937 57.928 3.2216 0.00034

342. 0 207.826 60.681 3.2229 0.00029

346. 0 220.719 63.423 3.2239 0.00025

350.0 233.617 66.154 3.2248 0.00020

354.

246.518 68.875 3.2256 0.00016

358.0 259.421 71.587 3.2261 0.00013

362.0 272.327 74.289 3.2266 0.00009

366.0 285.234 76.982 3.2269 0.00006

370.0 298.142 79.666 3.2271 0.00003

374.0 311.050 82.342 3.2271 0. 0 00 0 0 378.

323.959 85.011 3.2271 -0.00002

382.0 336.867 87.672 3.2270 -0.00005

38 6.349.774 90.325 3.2267 -0.00007

390 .362.681 92.972 3.2264 -0.00009

394.0 375.586 95.612 3.2260 -0.00011

398.388.489 98.245 3.2255 -0.00013

402. 0 401.390 100.872 3.2250 -0.00015

406.0 414.288 103.492 3.2243 -0.00017

410.427.184 106.107 3.2237 -0.00018

414.0 440.077 106.715 3.2229 -0.00020

418.

452.967 111.318 3.2221 -0.00021

422.0 465.854 113.915 3.2212 -0. 00022

426.0 478.737 116.507 3.2203 -0.00024

430.0 491.616 119.094 3.2193 -0.00025

434.0 504.492 121 .676 3.2183 -0.00026

438.0 517.363 124.252 3.2172 -0.00027

442.

530.229 126.823 3.2161 -0.00028

446.0 543.092 129.390 3.2150 -0.00029

450.

555.949 131.952 3.2138 -0.00030

454.0 568.802 134.509 3.2126 -0.00031

458.

581.650 137.062 3.2113 -0.00032

462.594.493 139.610 3.2101 -0.00032

466.0 607.331 142.154 3.2087 -0.00033

470.0 620.163 144.694 3.2074 -0.00034

474.0 632.990 147.229 3.2060 -0.00035

478.0 645.811 149.761 3.2046 - 0. 0 00 35

482. 0 658.627 152.288 3.2032 -0.00036

486.

671.437 154.811 3.2018 -0.00036

490.0 684.241 157.330 3.2003 -0.00037

494 .

697.039 159.846 3.1988 -0.00037

227
Table 23. Calculated P(T) isochores- - - (Continued)

THE ISOCHORE AT 13.00 MOL/L

T,K P r BAR DP/DD DP/DT D2P/OT2

278.0 29.111 39.986 4.0115 -0.00049

282.0 45.153 43.672 4.0095 -0.00048

286.0 61.188 47.321 4.0076 -0.00048

290.

0

77.215 50.936 4.0057 -0.00048

294.0 93.234 54.518 4.0038 -0.00048

298.0 109.245 58.072 4.0019 -0.00048

302. 0 125.249 61.597 4.0000 -0.00048

306.0 141.245 65.096 3.9980 -0.00049

310.0 157.233 68.571 3.9961 -0.00050

314. 0 173.213 72.022 3.9941 -0.00050

318.0 189.186 75.452 3.9920 -0.00051

322.0 205.150 78.861 3.9900 -0.00052

326. 0 221.105 82.251 3.9879 -0.00052

330.0 237.053 85.621 3.9858 -0.00053

334.0 252.992 86.974 3.9836 -0.00054

338.

0

268.922 92.310 3.9815 -0.00055

342.0 284.843 95.630 3.9793 -0.00055

346. 0 300.756 98.935 3.9771 -0,00056

350.0 316.660 102.224 3.9748 -0.00057

354. 0 332.554 105.499 3.9725 -0.00057

358.

0

348.440 108.761 3.9702 -0.00058

362.0 364.316 112.009 3.9679 -0.00058

366.0 38 0.183 115.245 3.9655 -0.00059

370.0 396.041 118.468 3.9632 -0.00060

374.0 411.889 121.680 3.9608 -0. 00060

378.0 427.727 124.880 3.9584 -0.00061

382.0 443.556 128.070 3.9559 -0.00061

386.0 459.374 131.248 3.9535 -0.00061

390.

0

475.183 134.417 3.9510 -0.00062

394.0 490.983 137.575 3.9486 -0.00062

398.0 506.772 140 .724 3.9461 -0. 00063

402.0 522.551 143.863 3.9435 -0.00063

406.0 538.320 146.993 3.9410 -0. 00063

410 .

0

554.079 150.114 3.9385 -0. 00064

414.0 569.828 153.227 3.9359 -0.00064

418.0 585.567 156.331 3.9334 -0.00064

422.0 601.295 159.427 3.9308 -0.00064

426.0 617.013 162.514 3.9282 -0.00065

430.0 632.721 165.594 3.9256 -0.00065

434.0 648.418 168.667 3.9230 -0.00065

438 .

0

664.105 171.732 3.9204 -0.00065

442.0 679.781 174.790 3.9178 -0.00065

446.0 695.447 177.840 3.9152 -0.00066

228
Table 23. Calculated P(T) isochoresTHE ISOCHORE AT 14.00 HOL/L

(Continued)

T,K P,OAR

266.0 27.449

270.0 47.640

274.0 67.779

278.0 87.870

282.0 107.915

286. 0 127.916

290 .147.876

294. 0 167.797

298.0 187.680

302. 0 207.526

306. 0 227.338

310.0 247.116

314.0 266.862

318.0 286.577

322.

306.261

326. 325.916

330.0 345.541

334.0 365.139

338.0 384.710

342.0 404.254

346.0 423.772

35 0.

443.265

354.0 462.733

358.0 482.176

362.0 501.595

366. 0 520.990

370.0 540.362

374.0 559.712

378.0 579.039

382.0 598.343

386.0 617.626

39 0.0 636.888

394.0 656.128

398.

675.347

402. 0 694.545

DP/DD

67.107 5

71.553 5

75.957 5 80.323 5

84.651 5

88.944 4

93.204 4

97.431 4

101.627 4

105.794 4

109.932 4

114.044 4

118.130 4

122.191 4

126.229 4

130.244 4

134.238 4

138.210 4

142.162 4

146.095 4

150.009 4

153.905 4

157.783 4

161.645 4

165.491 4

169.320 4

173.135 4

176.935 4

180.720 4

184.492 4

188.250 4

191.995 4

195.727 4

199.448 4

203.156 4

DF/DT D2P/0T2

.0 545 “0.00345

.0412 “0.00323

. 0286 “0.00304

.0168 -0.00287

. 0 057 -0.00272

.9951 -0.00258

.9850 -0.00246

.9754 -0.00236

.9661 -0.00226

.9572 -0.00217

.9487 -0.00210

.9405 -0.00202

.9325 -0.00196

.9248 -0.00190

.9173 -0.00184

.9100 -0.00179

.9030 -0.00175

.8961 -0.00170

.8893 -0.00166

.8827 -0.00163

.8763 -0.00159

. 8700 -0.00156

.8638 -0.00153

.8578 -0.00150

.8518 -0.00148

.8460 -0.00145

.8402 -0.00143

.8345 -0.00141

.8289 -0.00139

. 8234 -0.00137

.8180 -0.00135

.8126 -0.00133

.8074 -0.00131

.8 021 -0.00130

.7970 -0.00128

229
Table 23. Calculated P(T) isochores- - - (Continued)

THE ISOCHORE AT 15,00 MOl/L

T,K P,BAR

250.0 20.439

254.0 45.843

258.0 71.129

262.0 96.306

266.0 121.379

270.0 146.355

274.0 171.238

278.0 196.034

282.0 220.746

286. 0 245.379

290.0 269.936

294.0 294.421

298.0 318.836

302.0 343.185

306.0 367.471

310.0 391.694

314.0 415.839

318.0 439.967

322. 0 464.020

32 6.

0

488.019

330.

0

511.967

334. 0 535.865

338.0 559.714

342.

0

583.516

346. 607.272

35 0.0 630.983

354. 0 654.651

358.

0

678.276

OP/OD D

103.276 6.

108.584 6.

113.846 6.

119.061 6.

124.232 6.

129.361 6.

134.449 6.

139.498 6.

144.509 6.

149.484 6.

154.425 6.

159.331 6.

164.206 6.

169.050 6.

173.865 6.

178.650 6.

183.408 6.

188.140 6.

192.846 6.

197.528 5.

202.185 5.

206.820 5.

211.432 5.

216.023 5.

220.593 5.

225.143 5.

229.674 5.

234.185 5.

P/DT 02P/0T2

3663 -0.00782

3360 -0.00732

3077 -0.00687

2810 -0.00647

2559 -0.00610

2321 -0.00578

2096 -0.00548

1883 -0.00520

1680 -0.00496

1486 -0.00473

1301 -0.00452

1124 -0.00433

0955 -0.00415

0792 -0.00399

0636 -0.00384

0485 -0.00369

0340 -0.00356

0200 -0.00344

0064 -0.00333

9933 -0.00323

9806 -0.00313

9683 -0.00304

9563 -0.00295

9447 -0.00287

9334 -0.00279

9224 -0.00272

9116 -0.00265

9011 -0.00259

230
Table 23. Calculated P(T) isochores- - - (Continued)

THE ISOCHORE AT 16.00 WQL/L

T* K P,8AR

232.0 18.224

234.0 34.221

236.0 50.161

238.0 66,04®

24 0.0 81.882

242.97.666

244. 0 113,400

246. 0 129.087

248.0 144.728

25 0.0 160.325

252.0 175.877

254.0 191.388

256. 0 206.858

258.222.287

26 0.0 237.678

262.0 253.031

264.0 268.348

266.0 283.628

268.0 298.874

270.0 314.085

272. 0 329.264

274.0 344.410

276.0 359.524

278.

374.608

280.

389.661

282.0 404.665

284.

419.680

286.0 434.647

288.0 449.586

290 .

464 .499

292.0 479.385

294.494.245

296.0 509.080

298. 523.890

30 0. 0 538.675

302.0 553.437

304.0 568.175

306.0 582.891

308.597.584

310.0 612.255

312. 0 626.904

314.0 641.532

316.0 656.139

318.0 670.725

320.0 685.291

322.0 699.837

DP/OD D

153.066 8.

156.194 7.

159.307 7.

162.407 7.

165.494 7.

160.568 7.

171.629 7.

174.677 7.

177.713 7.

180.737 7.

183.750 7.

186.750 7.

189.739 7.

192.717 7.

195.683 7.

198.639 7.

201.585 7.

204.519 7.

207.444 7.

210.359 7.

213.263 7.

216.158 7.

219.044 7.

221.920 7.

224.787 7.

227.645 7.

230.494 7.

233.335 7.

236.167 7.

238.991 7.

241.806 7.

244.614 7.

247.413 7.

250.205 7.

252.989 7.

255.766 7.

258.535 7.

261.298 7.

264.052 7.

266.800 7.

269.541 7.

272.276 7.

275.003 7.

277.724 7.

280.439 7.

283.147 7.

P/DT D2P/0T2

0124 -0.01443

9840 -0.01395

9566 -0.01349

9301 -0.01306

9043 -0.01265

8794 -0.01226

8553 -0.01188

8319 -0.01153

8092 -0.01119

7872 -0.01086

7657 -0.01055

7449 -0.01025

7247 -0.00997

7050 -0.00970

6859 -0.00944

6673 -0.00919

6491 -0.00895

6315 -0.00873

6142 -0.00851

5974 -0.00830

5810 -0.00810

5650 -0.00790

5494 -0.00772

5342 -0.00754

5193 -0.00737

5047 -0.00720

4904 -0.00704

4765 -0.00689

4629 -0.00674

4495 -0.00660

4365 -0.00646

4237 -0.00633

4112 -0.00620

3989 -0.00608

3868 -0.00596

3750 -0.00585

3634 -0.00574

3521 -0.00563

3409 -0.00553

3300 -0.00543

3192 -0.00533

3086 -0.00524

2983 -0.00515

2880 -0.00506

2780 -0.00498

2681 -0.00489

231
Table 23. Calculated P(T) isochores- - - THE ISOCHORE AT 17.00 HOL/L

T * K P , BAR

212. 0 22.625

214. 0 42.745

216.0 62.771

210.0 82.704

220.

0

102.548

222.0 122.307

224. 0 141.982

226.0 161.577

228.0 181.094

230.0 200.535

232.0 219.904

234. 0 239.202

236.0 258.431

238.0 277.593

240.0 296.691

242.

0

315.726

244.0 334.699

246.0 353.614

248.0 372.471

250.0 391.271

252. 0 410.017

254.0 428.710

256.

0

447.351

258.0 465.942

260.0 484.483

262.0 502.977

264. 0 521.423

266. 0 539.824

268.0 558.181

27 0.

0

576.493

272.0 594.764

274. 0 612.992

276.0 631.181

278.

0

649.329

28 0.

0

667.438

282.0 605.510

DP/DD CP/OT

219.957 10.0847

223.563 10.0362

227.155 9.9893

230.735 9.9441

234.300 9.9004

237.853 9.8582

241.393 9.8173

244.920 9.7777

248.434 9.7394

251.936 9.7023

255.426 9.6664

258.904 9.6315

262.370 9.5977

265.825 9.5649

269.268 9.5330

272.700 9.5020

276.121 9.4719

279.532 9.4427

282.931 9.4142

286.321 9.3866

289.700 9.3596

293.069 9.3334

296.428 9.3070

299.77

7

9.2029

303.117 9.2586

306.448 9.2349

309.769 9.2110

313.081 9.1892

316.384 9.1672

319.679 9.1457

322.964 9.1247

326.242 9.1041

329.510 9.0841

332.771 9.0644

336.024 9.0452

339.268 9.0264

(Continued)

02P/DT2

-0.02469

-0.02303

-0.02301

-0.02223

-0.02140

-0.02077

- 0.02010

-0.01946

-0.01004

-0.01026

-0.01770

-0.01717

-0.01666

-0.01617

-0.01571

-0.01526

-0.01403

-0.01442

-0.01403

-0.01366

-0.01330

-0.01295

-0.01262

-0.01230

-0.01199

-0.01170

-0.01142

-0.01114

-0.0108e

-0. 01063

-0.01039

-0.01015

-0.00993

-0.00971

-0.00950

-0.00930

232
Table 23. Calculated P(T) isochores- - - (Continued)

THE ISOCHORE AT 18.00 HOL/L

T K P , BAR DP/DD OP/DT D2P/0T2

188.0 9.323 304.719 12,8014 - 0.04276

190.0 34.841 308.783 12.7175 - 0. 04110

192.0 60.195 312.839 12.6369 - 0.03953

194 . 0 85.391 316.885 12.5594 - 0.03804

196 . 0 110.435 320.923 12.4847 - 0.03662

198.0 135.332 324.952 12.4128 - 0.03528

200.0 160.088 328.972 12.3436 - 0.03401

202 . 0 184.708 332.983 12.2768 - 0.03280

204.0 209.196 336.985 12.2123 - 0.03165

206 . 0 233.558 340.977 12.1501 - 0.03056

208.0 257.798 344.961 12.0900 - 0.02952

210.

281.920 348.936 12.0320 - 0.02853

212 . 0 305.928 352.903 11.9759 - 0.02759

214.0 329.825 356.860 11.9216 - 0.02669

216.0 353.615 360.809 11.8691 - 0.02584

218.0 377.302 364.749 11.8182 - 0.02502

220.0 40 o.eag 368.680 11.7690 - 0.02424

222.0 424.379 372.603 11.7213 - 0.02349

224 . 0 447.775 376.517 11.6750 - 0 . 0227 e 226.0 471.080 380.423 11.6301 - 0.02210

228.0 494.297 384.321 11.5866 - 0.02145

230.0 517.427 388.211 11.5443 - 0. 02083

232.0 540.474 392.092 11.5032 - 0.02024

234 . 0 563.441 395.965 11.4633 - 0.01967

236 . 0 586.328 399.831 11.4245 - 0.01912

238.0 609.140 403.688 11.3868 - 0.01860

240.0 631.876 407.537 11.3501 - 0.01810

242.0 654.541 411.379 11.3144 - 0.01762

244.0 677.135 415.213 11.2797 -0.01715

246 . 0 699.660 419.040 11.2458 - 0.01671

233
Table 23. Calculated P(T) isochores- - - (Continued)

THE ISOCHORE AT 19.00 MQt/L

T » K P ,BAR OP/CD DF/DT D2P/DT2

163. 0 6.143 419.883 16.3415 -0.07340

164. 0 22.448 422.072 16.2689 -0.07174

165.0 38.681 424.264 16.1980 -0.07014

166.0 54.844 426.458 16.1286 -0.06858

167.0 70.939 428.655 16.0608 -0.06707

168.

0

86.966 430.854 15.9945 -0.06560

169.0 102.928 433.056 15.9296 -0.06418

170.0 118.826 435.259 15.8661 -0.06280

171.0 134.661 437.465 15.8040 -0.06146

172.0 150.434 439.672 15.7432 -0.06016

173.0 166.148 441.881 15.6836 -0.05889

174.0 181.802 444.092 15 .6254 -0.05767

175.0 197.399 446.304 15.5683 -0.05647

176.0 212.939 448.517 15.5124 -0.05531

177.0 228.424 450.732 15.4576 -0.05419

178.0 243.855 452.949 15.4040 -0.05309

179.0 259.232 455.166 15.3515 -0.05203

180.0 274.558 457.385 15.2999 -0.05099

181.0 289.833 459.604 15.2495 -0.04999

182. 0 305.057 461.825 15.2000 -0.04901

183.0 320.233 464.046 15.1514 -0.04806

184.

0

335.360 466.268 15.1038 -0.04713

185.0 350.441 466.491 15.0572 -0.04623

186.0 365.475 470.715 15.0114 -0.04535

187.

0

380.464 472.939 14.9665 -0.04450

188.0 395.408 475.164 14.9224 -0.04367

189.0 410.309 477.389 14.8791 -0.04286

190 .

0

425.167 479.615 14.8367 -0.04207

191.0 439.982 481.840 14.7950 -0.04130

192.0 454.757 484.067 14.7541 -0.04055

193.0 469.491 486.293 14.7139 -0.03982

194.0 484.185 488.520 14.6744 -0.03911

195.0 498.840 490.747 14.6356 -0.03842

196.

0

513.456 492.974 14.5976 -0.03774

197.0 528.035 495.201 14.5602 -0.03708

198.0 542.577 497.428 14.5234 -0.03644

199.0 557.082 499.655 14.4873 -0.03582

20 0.

0

571.552 501.882 14.4518 -0.03521

201.

0

585.986 504.109 14.4168 -0.03461

202.

0

600.385 506.336 14.3825 -0.03403

203.0 614.751 508.562 14.3488 -0.03346

204.0 629.083 510.789 14.3156 -0.03291

205.0 643.382 513.015 14.2830 - 0. 03237

206. 0 657.649 515.241 14.2508 -0.03184

207.0 671.884 517.466 14.2193 -0.03133

208 .

0

686.088 519.692 14.1882 -0.03083

234
Table 23. Calculated P(T) isochores- - - (Continued)

THE ISOCHORE AT 20.00 MOL/L

T,K P,BAR OP/DD DP/OT D2P/OT2

137.0 16.308 575.795 21.0926 -0.12851

138. 0 37.337 577.966 20.9658 -0.12506

139.0 58.241 580.153 20.8424 -0.12174

140.0 79.023 582.356 20.7223 -0.11853

141.0 99.687 584.579 20.6053 -0.11543

142. 0 120.235 586.816 20.4914 -0.11245

143.0 140.670 589.068 20.3804 -0.10956

144. 0 160.997 591.335 20.2722 -0.10678

145.0 181.216 593.616 20.1668 -0.10408

146. 0 201.331 595.911 20.0640 -0.10148

147.0 221.345 598.219 19.9638 -0.09897

148.0 241.260 600.540 19.8661 -0.09654

149.0 261.078 602.873 19.7707 -0.09419

150.0 280.802 605.219 19.6777 -0.09192

151.0 300.434 607.575 19.5869 -0.08972

152.

319.976 609.943 19.4982 -0.08760

153. 0 339.431 612.322 19.4116 -0.08554

154.0 358.800 614.711 19.3271 -0.08354

155. 0 378.086 617.110 19.2445 -0.08162

156.0 397.290 619.519 19.1639 -0.07975

157. 0 416.414 621.937 19.0850 -0.07794

158.0 435.460 624.364 19.0080 -0.07618

159. 0 454.431 626.800 18.9326 -0.07448

160.0 473.326 629.245 18.8590 -0.07284

161.0 492.149 631.697 18.7869 -0.07124

162.0 510.901 634.158 18.7165 -0.06969

163.0 529.583 636.626 18.6475 -0.06819

164. 0 548.196 639.101 18.5801 -0.06673

165.0 566.743 641.584 18.5141 -0.06532

166.0 585.225 644.073 18.4494 -0.06395

167.

603.643 646.569 18.3862 -0.06262

168.0 621.998 649.072 18.3242 -C. 06132

169.0 640.291 651.581 18.2635 -0.06007

170.0 658.525 654.095 18.2040 -0.05885

171.0 676.700 656.615 18.1458 -0.05767

172.0 694.817 659.141 18.0887 -0.05652

235
Table 23. Calculated P(T) isochores- - - (Continued)

THE ISOCHORE AT 21.00 HOL/L

T » K P,BAR DP/DD DP/OT 02P/0T2

109.0 8.092 782.786 28.1089 *0.24813

110.0 36.078 784.450 27.6650 -0.23973

111.0 63.825 786.177 27.6294 *0.23170

112.0 91.340 787.964 27.4015 *0.22402

113. 0 118.631 789.810 27.1812 -0.21668

114. 0 145.705 791.713 26.9681 -0.20965

115.0 172.569 793.669 26.7618 -0.20292

116.0 199.230 795.677 26.5621 *0.19647

117.0 225.695 797.735 26.3688 -0.19030

118.0 251.970 799.841 26.1814 -0.18438

119.0 278.060 601.994 25.9999 -0.17871

120.0 303.972 604.191 25.8240 -0.17326

121.0 329.710 606.431 25.6533 -C.168C4

122.0 355.280 808.712 25.4878 -0.16303

123. 0 380.687 611.034 25.3272 -0.15822

124. 0 405.936 613.394 25.1713 -0.15359

125.0 431.031 615.790 25.0200 -0.14915

126.0 455.977 618.223 24.8730 *0.14488

127.0 480.779 620.690 24.7301 -0.14078

128.0 505.439 623.190 24.5913 -0.13683

129.0 529.962 825.722 24.4564 -0.13303

130.

0

554.353 628.285 2 A . 3 252 -0.12938

131.0 578.614 830.878 24.1976 -0.12586

132.0 602.749 833.500 24.0735 -0.12247

133.0 626.762 836.149 23.9526 -0.11921

134. 0 650.656 838.825 23.8350 -0.11606

135.0 674.433 641.526 23.7205 -0.11303

136.0 698.098 844.253 23.6089 -0.11011

THE ISOCHORE AT 22.00 HOL/L

T t K P,BAR DP/OD OP/DT C2P/0T2

96.0 533.498 1074.777 33.3642 -0.28865

97.0 566.720 1076.862 33.0810 -0.27785

98 .

0

599.663 1079.053 32.8083 -0.26758

99.0 632.339 1081.344 32.5456 -0.25782

100.0 664.750 1083.732 32.2925 -0.24854

101.0 696.927 1086.211 32.0484 -0.23971

236
Table 24. Calculated P(o) isotherms

The following pages give P(p) isotherms, as computed by

the equation of state (5). The third column DP/DD is the isotherm slope

(3P/Bp) in units of the bar and mol/j£. The last two columns give the

isochore slopes and curvatures, DP/DT = (3P/3T), D2P/DT2 =

2 . 2

(B P/BT ) in units of the bar and Kelvins.

These tables show that 3P/Bp is non-negative, and that it increases

monotonically with density to pressures about twice those for adjusting

the equation of state.

237
Table 24. Calculated P

THE ISOTHERM AT

MOL/L P> BAR DP

21.50 4.806 911.

21.55 50.760 926.

21.60 97.480 942.

21.65 144.974 957.

21.70 193.253 973.

21.75 242.326 989.

21.80 292.204 1005.

21.85 342.897 1022.

21.90 394.418 1038.

21.95 446.777 1055.

THE ISOTHERM AT 1

MOL/L P , BAR DP

21.35 31.210 871.

21.40 75.180 886.

21.45 119.908 902.

21.50 165.402 917.

21.55 211.671 933.

21.60 258.726 949.

21.65 306.577 965.

21.70 355.234 981.

21.75 404.708 997.

21.80 455.011 1014.

21.85 506.155 1031.

21.90 558.152 1048.

21.95 611.015 1066.

22.00 664.758 1083.

22.05 719.393 1101.

THE ISOTHERM AT 1

MOL/L P,BAR DP

21.00 36.078 784.

21.05 75.660 798.

21.10 115.964 813.

21.15 157.000 828.

21.20 198.777 843.

21.25 241.305 858.

21.30 284.592 873.

21.35 328.649 888.

21.40 373.486 904.

21.45 419.114 920.

21.50 465.543 936.

21.55 512.785 953.

21.60 560.851 969.

21.65 609.754 986.

21.70 659.506 10 03.

21.75 710.120 1020.

isotherms.

00 CEG • K

DP/DT D2P/DT2

32.9615 -0.359363

33.0105 -0.353331

33. 0636 -0.347309

33.1208 -0.341302

33.1826 -0.335313

33.2489 -0.329348

33.3202 -0.323411

33.3966 -0.317505

33.4782 -0.311636

33.5655 -0.305809

DEG. K

DP/OT D2P/DT2

31.1230 -0.310639

31.1884 -0.305784

31.2572 -0.300928

31.3296 -0.296076

31.4057 -0.291231

31.4858 -0.286396

31.5700 -0.281575

31.6586 -0.276773

31.7517 -0.271991

31.8495 -0.267236

31.9523 -0.262509

32.0603 -0.257815

32.1736 -0.253157

32.2925 -0.248540

32.4171 -0.243968

DEG. K

OP/DT D2P/CT2

27.8650 -0.239728

27.9509 -0.236564

28.0391 -0.233386

28.1297 -0.230198

28.2230 -0.227000

28.3189 -0.223795

28.4177 -0.220586

28.5196 -0.217375

28.6247 -0.214164

28.7332 -0.210957

28.8451 -0.207755

28.9608 -0.204561

29. 0803 -0.201377

29.2038 -0 .198208

29. 3315 -0.195054

29.4635 -0.191920

(P)

95.

'/DO

484

705

107

697

484

475

6 79

104

760

656

00 . VCD

909

956

184

599

208

019

038

274

736

432

370

559

010

732

735

10 .

/CD

450

827

376

104

014

114

409

906

610

530

672

043

652

506

613

982

238
Table 24. Calculated P(P) isotherms (Continued)

THE ISOTHERM AT 120.00 OEG • K

MOL/L P*8AR DP/DD DP/DT 02P/DT2

20.60 5.090 692. 070 24. 9991 -0.190010

20.65 40.029 705. 492 25.0963 -0.187977

20.70 75.642 719. 075 25.1949 -0.185923

20.75 111.939 732. 823 25.2952 -0.183852

20.80 148.927 746.739 25.3971 -0.181763

20.85 186.616 760.830 25.5008 -0.179658

20.90 225.013 775. 099 25.6065 -0.177539

20.95 264.129 789. 550 25.7141 -0.175407

21.00 303.972 804. 191 25.8240 -0.173264

21.05 344.551 819. 025 25.9361 -0.171111

21.10 385.877 834. C58 26.0506 -0 .168951

21.15 427.960 849. 296 26.1676 -0.166784

21.20 470.811 864. 746 26.2873 -0.164612

21.25 514.439 880. 413 26.4097 -0.162438

21.30 558.856 896. 303 26.5351 -0.160263

21.35 604.073 912. 424 26.6636 -0.158089

21.40 650.102 928. 783 26.7952 -0.155918

21.45 696.955 945. 386 26.9301 -0.153751

21.50 744.645 962. 241 27.0685 -0.151592

THE ISOTHERM AT 140.00 OEG. K

MOL/L P f BAR OP/OD DP/DT D2P/DT2

19.90 21.970 558. 809 20.5026 -0.120130

19.95 50.202 570. 510 20.6121 -0 .119339

20.00 79.023 582. 358 20.7223 -0 .118529

20.05 108.440 594. 355 20.8334 -0.117703

20.10 138.461 606. 504 20.9453 -0.116859

20.15 169.093 618. 808 21.0582 -0.115998

20.20 200.345 631. 271 21 . 1721 -0.115121

20.25 232.223 643. 894 21.2870 -0.114229

20.30 264.737 656. 683 21.4031 -0.113321

20.35 297.894 669. 641 21.5204 -0.112399

20.40 331.704 682. 771 21.6390 -0.111463

20.45 366.174 696. 078 21.7589 -0.110514

20.50 401.315 709. 565 21.8802 -0.109552

20.55 437.134 723. 237 22.0031 -0.108579

20.60 473.641 737. 098 22.1275 -0.107594

20.65 510.847 751. 153 22.2536 -0.106600

20.70 548.760 765. 407 22. 3815 -0.105595

20.75 587.391 779. 864 22.5112 -0.104583

20.80 626.750 794. 530 22.6428 -0.103563

20.85 666.848 809. 410 22.7764 -0.102536

20.90 707.695 824.510 22.9122 -0.101504

20.95 749.302 839. 835 23.0501 -0.10 0 466

239
Table 24. Calculated P(p) isotherms (Continued)

THE ISOTHERM AT 160.00 DEG. K

MOL/L P * BAR OP/DD DP/DT D2P/0T2

19.15 20.934 442. 231 16.8979 -0.078123

19.20 43.292 452.114 17.0083 *‘0 .077910

19.25 66.148 462. 126 17.1191 -0.077685

19.30 89.507 472. 268 17.2304 -0.077447

19.35 113. 377 482. 543 17.3422 -0 .077196

19.40 137.763 492. 952 17.4545 -0.076933

19.45 162.674 503. 498 17.5675 -0.076657

19.50 188.115 514. 182 17.6810 -0 .076369

19.55 214.095 525. 008 17.7953 -0 .076068

19.60 240.619 535. 978 17.9102 -0.075755

19.65 267.695 547. 094 18.0258 -0.075431

19.70 295.331 558. 359 18.1422 -0.075094

19.75 323.533 569. 776 18.2594 -0.074746

19.80 352.311 581. 348 18.3774 -0.074386

19.85 381.671 593. 078 18.4963 -0.074015

19.90 411.621 604. 568 18.6162 -0.073633

19.95 442.170 617. 023 18.7371 -0.073240

20.00 473.326 629. 245 18.8590 -0.072837

20.05 505.098 641. 638 18.9820 -0.072424

20. 10 537.493 654. 205 19.1061 -0.072001

20.15 570.521 666. 952 19.2314 -0.071568

20.20 604.191 679. 880 19.3579 -0.071127

20.25 638.512 692. 995 19.4858 -0 .070677

20.30 673.494 706. 301 19.6150 -0.070219

20.35 709.146 719. 8C1 19.7456 -0 .069753

20.40 745.477 733. 501 19.8778 -0.069281

*

240
Table 24. Calculated P(p) isotherms (Continued)

THE ISOTHERM AT 100.00 OEG • K

MOL/L P > BAR DP/DD DP/OT D2P/DT2

0.05 0.729 14. 231 0.0043 -0.000002

10.35 15.706 342. 424 13.8992 -0.050964

18.40 33.031 350. 573 14.0043 -0.051014

10.45 50.765 358. 831 14.1099 -0.051056

18.50 68.916 367. 202 14.2158 -0.051090

10.55 87.487 375. 685 14. 3222 -0.051117

18.60 106.486 384. 263 14.4290 -0.051136

18.65 125.918 392.998 14.5362 -0.051147

18.70 145.788 401. 829 14.6438 -0.051149

18.75 166.103 410. 760 14.7519 -0.051144

18.80 186.868 419. 852 14.8605 -0.051131

18.85 208.090 429. C 47 14.9696 -0.051109

18.90 229.775 438. 366 15.0792 -0.051079

18.95 251.929 447. 811 15.1893 -0.051041

19.00 274.558 457. 365 15.2999 -0.050994

19.05 297.669 467. 069 15.4112 -0.050939

19. 10 321.269 476.925 15.5230 -0.050876

19. 15 345.364 486. 896 15.6355 -0.050804

19.20 369.961 497. 003 15.7486 -0.050724

19.25 395.067 507. 250 15.8624 -0.050636

19. 30 420.688 517. 638 15.9768 -0.050539

19.35 446.833 528. 170 16.0920 -0.050435

19.40 473.508 538. 849 16.2080 -0.050322

19.45 500.720 549. 678 16.3247 -0.050202

19.50 528.478 560.658 16.4422 -0.050074

19.55 556.789 571. 794 16.5606 -0.049938

19.60 585.660 563. 088 16.6799 -0.049795

19.65 615.100 594. 542 16.8001 -0.049644

19.70 645.117 606. 162 16.9212 -0.049486

19.75 675.719 617. 949 17 .0434 -0 .049321

19.80 706.915 629. 907 17.1665 -0.049149

19.85 738.713 642. 041 17.2908 -0.048971

241
Table 24. Calculated P(P) isotherms (Continued)

THE ISOTHERM AT 200.00 DEG. K

MOL/L P,9AR DP

0.05 0.814 15.

0.10 1.596 15.

17.50 13.541 258.

17.55 26.647 265,

17.60 40.085 272.

17.65 53.859 278.

17.70 67.973 285.

17.75 82.433 292.

17.80 97.243 299.

17.85 112.409 306.

17.90 127.935 314.

17.95 143.826 321.

18.00 160.088 328.

18.05 176.725 336.

18.10 193.743 344.

18.15 211.147 351.

18.20 228.943 359.

18.25 247.135 367.

18.30 265.729 375.

18.35 284.732 384.

18.40 304.147 392.

18.45 323.982 400.

18.50 344.242 409.

18.55 364.933 418.

18.60 386.061 426.

18.65 407.631 435.

18.70 429.650 444.

18.75 452.125 454.

18.80 475.061 463.

18.85 498.465 472.

18.90 522.344 482.

18.95 546.704 492.

19.00 571.552 501.

19.05 596.894 511.

19.10 622.739 521.

19.15 649.092 532.

19.20 675.962 542.

19.25 703.356 553.

19. 30 731.280 563.

DP/OT D2P/DT2

0.0042 -0.000001

0.0087 -0.000005

11.3605 -0.032662

11.4570 -0.032ei5

11.5539 -0.032964

11.6512 -0.033110

11.7489 -0.033251

11.8469 -0.033389

11.9454 -0.033522

12.0443 -0.033651

12.1437 -0.033775

12.2434 -0.033895

12.3436 -0.034009

12.4442 -0.034120

12.5452 -0.034225

12.6467 -0.034325

12.7486 -0.034420

12.8511 -0.034510

12.9540 -0.034595

13.0573 -0.034674

13.1612 -0.034748

13.2656 -0.034817

13.3705 -0.034880

13.4760 -0.034938

13.5820 -0.034990

13.6886 -0.035036

13.7957 -0.035077

13.9035 -0.035113

14.0118 -0.035143

14.1208 -0.035167

14. 2304 -0.035186

14.3408 -0.035199

14.4518 -0.035207

14.5635 -0.035209

14.6759 -0.035205

14.7091 -0.035197

14.9031 -0.035183

15.0178 -0.035163

15.1334 -0 .035139

'/DO

975

285

847

425

097

864

727

686

743

899

155

512

972

535

203

977

859

849

950

163

489

930

487

163

959

877

919

086

381

806

363

054

882

849

957

209

608

156

856

242
Table 24. Calculated P(p) isotherms (Continued)

THE ISOTHERM AT 220. 00 DEG. K

MOL/L P* BAR DP/DD OP/DT D2P/DT2

0.10 1.768 17. 082 0.0086 -0.000003

0.20 3.411 15. 770 0.0178 -0.000014

16.60 17.768 190.467 9.2021 -0.020109

16.70 37.336 200. 940 9.3742 -0.020462

16.80 57.967 211. 733 9.5479 -0.020809

16. SO 7S.693 222. 851 9.7233 -0.021149

17.00 102.548 234. 300 9.9004 -0.021482

17.10 126.565 246. C88 10.0792 -0.021806

17.20 151.777 258. 222 10.2598 -0.022121

17.30 178.221 270. 708 10.4420 -0.022427

17.40 205.931 283. 554 10.6260 -0.022722

17.50 234.944 296. 769 10.8119 -0.023005

17.60 265.297 310. 360 10.9995 -0.023278

17.70 2S7.029 324. 337 11.1890 -0.023537

17.80 330.178 338. 710 11.3803 -0.023785

17. SO 364.784 353. 487 11.5737 -0.024018

18.00 400.889 368.680 11.7690 -0.024239

18.10 438.535 384. 300 11.9664 -0.024445

18.20 477.764 400. 359 12.1659 -0.024637

18.30 518.621 416. 870 12.3677 -0.024814

18.40 561.153 433. 846 12.5718 -0 .024976

18.50 605.407 451. 302 12.7783 -0.025124

18.60 651.430 469. 253 12.9873 -0.025256

18.70 699.274 487. 716 13.1989 -0.025373

18.80 748.991 506. 709 13.4133 -0.025475

243
Table 24. Calculated P(p) isotherms (Continued)

THE ISOTHERM AT 240.00 OEG. K

MOL/L P t BAR OP/DD DP/DT 02P/CT2

0.10 1.940 18. 652 0.0085 -0.000002

0.20 3.766 17. 661 0.0176 -0.000009

0.30 5.473 16. 494 0.0272 -0.000022

0.40 7.066 15. 364 0.0374 -0.000044

0.50 8.547 14. 263 0.0483 -0.000076

15.50 9.671 124. 461 7.1561 -0.011002

15.60 22.499 132. 140 7.3023 -0.011333

15.70 36.108 140. 077 7.4502 -0.011664

15.80 50.523 148. 278 7.5998 -0.011994

15.90 65.772 156.749 7.7512 -0.012322

16.00 81.882 165. 494 7.9043 -0.012648

16.10 98.880 174.519 8.0592 -0.012972

16.20 116.795 183. 828 8.2159 -0.013293

16.30 135.656 193. 428 8.3743 -0.01 3611

16.40 155.491 203. 325 8.5345 -0.013925

16.50 176.331 213. 524 8.6964 -0.014235

16.60 198.206 224. 030 8.8601 -0 .014540

16.70 221.147 234. 852 9.0256 -0.014840

16.60 245.187 245.994 9.1929 -0.015135

16.90 270.357 257. 463 9.3620 -0.015423

17.00 296.691 269. 268 9.5330 -0.015706

17.10 324.222 281. 414 9.7058 J 0 .015981

17.20 352.985 293. 910 9.8805 -0.016250

17.30 383.016 306. 764 10.0571 -0.016511

17,40 414.350 319. 985 10.2357 -0.016764

17.50 447.025 333. 5e0 10.4162 -0.017008

17.60 481.079 347.560 10.5987 -0.017244

17.70 516.551 361. 935 10.7834 -0 .017471

17.80 553.480 376. 715 10.9701 -0 .01 7689

17.90 591.908 391.912 11.1590 -0.017897

18.00 631.876 407.537 11.3501 -0.018096

18.10 673.430 423. 604 11.5436 -0.018285

18.20 716.612 440. 125 11.7394 -0.018464

244
Table 24. Calculated P(p ) isotherms (Continued)

THE ISOTHERM AT 260.00 DEG. K

MOL/L P,BAR DP/DD DP/DT D2P/CT2

0.10 2.110 20.604 0.0085 -0.000001

0.20 4.116 19.511 0.0175 -0.000006

0.30 6.014 18. 446 0.0269 -0.000015

0.40 7.807 17. 423 0.0367 -0.000028

0.50 9.499 16. 433 0.0471 -0.000047

0.60 11.094 15. 465 0.0579 -0.000071

0.70 12.593 14.511 0.0693 -0.000103

0.80 13.997 13. 566 0 . 0811 -0.000143

0.90 15.306 12. 629 0.0935 -0.000193

1.00 16.523 11.698 0. 1065 -0.000255

14.30 17.323 75. 033 5.4238 -0.004694

14.40 25.089 80. 318 5.5430 -0.004975

14.50 33.393 85. 806 5.6639 -0.005257

14.60 42.257 91. 502 5.7865 -0.005538

14.70 51.701 97. 411 5.9108 -0.005819

14.80 61.747 103. 537 6.0368 -0,006101

14.90 72.416 109. 885 6.1646 -0.006382

15.00 83.731 116. 459 6.2941 -0.006663

15.10 95.715 123.264 6.4254 -0.006944

15.20 108. 392 130. 304 6.5584 -0.007225

15.30 121.784 137.585 6.6932 -0.007506

15.40 135.917 145. 110 6.8297 -0.007786

15.50 150.814 152. 885 6.9679 -0.008065

15.60 166.502 160. 915 7.1080 -0.008343

15.70 183.006 169. 205 7.2498 -0.008620

15.80 200.352 177. 759 7.3934 -0.008895

15.90 218.567 186.584 7.5387 -0.009169

16.00 237.678 195. 663 7.6859 -0 .009441

16.10 257.713 205. 064 7.8349 -0.009710

16.20 278.700 214. 731 7.9856 -0.009978

16.30 300.669 224. 690 8.1382 -0.010242

16.40 323.648 234. 947 8.2927 -0 .010 504

16.50 347.669 245. 509 8.4489 -0.010762

16.60 372.761 256. 381 8.6071 -0.011016

16.70 398.956 267. 571 6.7671 -0.011267

16.80 426.286 279. 086 8.9290 -0.011514

16.90 454.784 290. 932 9.0928 -0.011756

17.00 484.483 303. 117 9.2586 -0.011993

17. 10 515.419 315. 650 9.4263 -0.012226

17.20 547.625 328. 538 9.5961 -0.012453

17.30 581.139 341. 791 9.7679 -0.012675

17.40 615.996 355. 418 9.9418 -0.012891

17.50 652.235 369. 428 10.1177 -0.013101

17.60 689.895 383. 833 10.2959 -0.013305

17.70 729.015 398, 642 10.4763 -0.013503

245
Table 24. Calculated P(P) isotherms (Continued)

THE ISOTHERM AT 280.00 DEG. K

MOL/L P» 8 AR OP/DO DP/DT D2P/0T2

0.20 4.464 21. 334 0.0174 -0.000004

0.40 8.537 19. 416 0.0363 -0.000020

0.60 12.240 17. €35 0.0568 -0.000048

0.80 15.595 15. 518 0.0789 -0.000091

1.00 18.610 14.238 0.1026 -0.000152

1.20 21.292 12.596 0.1279 -0.000235

1.40 23.651 11. 005 0.1549 -0.00 0346

1.60 25.699 9. 482 0.1836 -0.000496

1.80 27.449 8. 034 0.2141 -0.000706

12.80 29.399 35.601 3.8292 0.000011

13.00 37.133 41. 834 4.0105 -0.000486

13.20 46.172 48.656 4.1979 -0.000961

13.40 56.637 56. 100 4.3915 -0.001425

13.60 68.656 64.199 4.5916 -0.001882

13.80 82.363 72. 985 4.7981 -0.002336

14.00 97.898 82. 492 5.0112 -0.002789

14.20 115.410 92. 751 5.2310 -0.003244

14.40 135.051 103. 798 5.4575 -0.0C3700

14.60 156.984 115.667 5.6908 -0.004157

14.80 181.375 128. 392 5.9309 -0.004617

15.00 208.400 142. 008 6.1780 -0 .005 078

15.20 238.240 156. 553 6.4320 -0.005539

15.40 271.085 172. 064 6.6931 -0.006000

15.60 307.133 188. 579 6.9613 -0.006459

15.80 346.587 206. 139 7.2367 -0.006915

16.00 389.661 224. 787 7.5193 -0.007366

16.20 436.577 244. 567 7.8092 -0.007812

16.40 487.566 265.527 8.1066 -0.008250

16.60 542.870 287. 718 8.4116 -0.008679

16.80 602.739 311. 197 8.7244 -0.009097

17.00 667.438 336.024 9.0452 -0.009502

17.20 737.243 362. 265 9.3742 -0.009894

246
Table 24. Calculated P(P) isotherms (Continued)

THE ISOTHERM AT 290.00 DEG. K

MOL/L P » 8 AR DP/DO OP/DT D2P/DT2

0.20 4.638 22. 237 0.0173 -0.000004

0.40 8.898 20. 396 0 . 0361 -0.000017

0.60 12.805 18. 691 0.0563 -0.000040

0.80 16.379 17. 052 0 . 0780 -0.000076

1.00 19.628 15. 448 0.1012 -0.000124

1.20 22.561 13.862 0 . 1258 -0.000187

1.40 25.185 12. 368 0.1519 -0.000268

1.60 27.512 10.922 0.1793 -0.000369

1.80 29.559 9. 554 0.2082 -0.000496

2.00 31.339 8. 269 0.2384 -0.000659

2.20 32.872 7. 068 0.2701 -0.000872

2.40 34.172 5. 945 0.3033 -0.001165

11.80 36.715 19. 597 3.0333 0.002241

12.00 41.028 23.606 3. 1812 0.001695

12.20 46.187 28. 061 3.3345 0.001209

12.40 52.284 32. 991 3.4934 0.000760

12.60 59.417 38. 427 3.6582 0.000336

12.80 67.691 44. 398 3.8289 -0.000074

13.00 77.215 50.936 4.0057 -0 .00 0 476

13.20 88.105 58. 070 4.1888 -0.000873

13.40 100.484 65. 832 4.3781 -0 .00 1268

13.60 114.482 74. 253 4.5739 -0.001665

13.80 130.232 83. 366 4.7762 -0.002063

14.00 147.876 93. 204 4.9850 -0.002465

14.20 167.564 103. 798 5.2005 -0.002869

14.40 189.448 115. 183 5.4227 -0.00 3278

14.60 213.692 127. 392 5.6516 -0 .003689

14.80 240.462 140. 461 5.8874 -0.004103

15.00 269.936 154. 425 6 . 1 30

-0.004520

15.20 302.294 169. 319 6.3798 -0.004937

15.40 337. 728 185. 183 6.6365 -0.005355

15.60 376.435 202. 056 6.9003 -0.005772

15. 8Q 418.620 219. 977 7.1713 -0.006187

16.00 464.499 238. 991 7.4495 -0 .006599

16.20 514.293 259. 142 7.7352 -0.007007

16.40 568.235 280 . 4ei 8.0285 -0.007408

16.60 626.567 303. 059 8.3294 -0.007802

16.80 689.545 326. 934 8.6381 -0.008187

247
Table 24. Calculated P(p) isotherms (Continued)

THE ISOTHERM AT 300.00 DEG. K

MOL/L P,BAR DP/CD CP/DT 02P/CT2

0.20 4.811 23. 137 0.0173 -0.000003

0.40 9.258 21. 366 0.0355 -0.000014

0.60 13.367 19. 733 0.0559 -0.000034

0.00 17.156 18. 164 0.0773 -0.000064

1.00 20.634 16.630 0 . 1001 -0.000103

1.20 23.810 15. 132 0.1241 -0.000154

1.40 26.691 13. 685 0.1495 -0.000216

1.60 29.289 12. 304 0.1760 -0.000 291

1.80 31.618 11. 000 0.2038 -0.000380

2.00 33.694 9. 778 0.2328 -0.000486

2.20 35.534 8. 6 39 0.2628 -0.000611

2.40 37.155 7. 580 0.2940 -0.000760

2.60 38.572 6. 596 0 . 3262 -0.000940

2.80 39.798 5.681 0.3594 -0.001160

3.00 40.848 4. 630 0.3936 -0.001439

3.20 41.734 4. 040 0.4289 -0.001803

3.40 42.468 3. 308 0.4653 -0.002303

3.60 43.062 2.633 0. 5028 -0.003045

3.80 43.525 2. 015 0.5420 -0.004278

18.20 44.034 5.581 2.0913 0.006320

10.40 45.307 7.188 2.1950 0.005196

10.60 46.926 9. 043 2.3028 0.004369

10.80 48.942 11.169 2.4150 0.003717

11.00 51.413 13. 590 2.5321 0.003176

11.20 54.399 16. 331 2.6541 0.00 2708

11.40 57.968 19. 419 2.7813 0.002289

11.60 62.192 22. 879 2.9139 0.001903

11. 80 67.147 26.737 3.0518 0.001540

12.00 72.915 31. 022 3.1954 0.001191

12.20 79.586 35. 762 3.3446 0.000852

12.40 87.252 40. 963 3.4997 0.000517

12.60 96.013 46. 717 3.6607 0.000185

12.80 105.975 52. 992 3.8278 -0.000148

13.00 117.248 59. 838 4.0010 -0.000482

13.20 129.950 67. 285 4.1803 -0.000820

13.40 144.204 75. 365 4.3660 -0.001162

13.60 160.140 84. 108 4.5581 -0.001509

13.80 177.894 93. 547 4.7566 -0.001860

14.00 197.607 103. 714 4.9616 -0.002217

14.20 219.430 114. 641 5.1733 -0.002579

14.40 243.517 126. 362 5.3916 -0.002945

14.60 270.030 138. 911 5.6167 -0.00 3316

14.80 299.139 152. 322 5.8485 -0.003690

15.00 331.019 166. 632 6.0873 -0.004067

15.20 365.854 181. 877 6.3329 -0.004446

15.40 403.834 198. 094 6.5856 -0 .00 4826

15.60 445.159 215. 324 6.8455 -0.005206

15.80 490.034 233. 608 7.1125 -0.005585

16.00 538.675 252. 589 7.3868 -0.005962

16.20 591.306 273.515 7.6686 -0.006335

16.40 648.161 295. 236 7.9580 -0 .006704

16.60 709.484 318. 205 8.2551 -0.007067

248
Table 24. Calculated P(p) isotherms (Continued)

THE ISOTHERM AT 305.37 DEG. K

MOL/l P,BAR DP/DD DP/DT 02P/DT2

0.40 9.451 21. 864 0.0358 -0.000013

0.80 17.570 18. 754 0.0770 -0.000059

1.20 24.474 15. 792 0.1233 -0.000140

1.60 30.230 13. 029 0.1746 -0.000260

2.00 34.937 10. 563 0.2303 -0.000424

2.40 38.723 8. 420 0.2902 -0.000641

2.80 41.713 6. 571 0.3539 -0.000925

3.20 44.014 4. 977 0.4207 -0 .00 1304

3.60 45.725 3.616 0.4904 -0.001823

4.00 46.939 2. 491 0.5623 -0.00 2567

4.40 47.751 1.609 0.6361 -0.00 3696

4.80 48.257 0.962 0.7110 -0 .005536

5.20 48.547 0.519 0.7866 -0.008912

5.60 48.693 0.232 0.8625 -0.016770

6.00 48.748 0. 057 0.9383 -0.049009

6.40 48.755 0.000 1.0104 -0.480413

6.80 48.755 -0. 000 1.0567 17.287460

7.20 48.755 0. 002 1.1174 0.285379

7.60 48.764 0. 064 1.2016 0.061370

8.00 48.828 0. 264 1.3013 0.025533

8.40 49.022 0. 730 1.4149 0.014647

8.80 49.453 1. 486 1.5429 0.009849

9.20 50.265 2. 655 1.6862 0.007230

9.60 51.649 4. 362 1.8458 0.005584

10.00 53.846 6. 749 2.0227 0.004434

10.40 57.159 9.974 2.2179 0.00 3554

10.80 61.960 14. 212 2.4324 0.002828

11.20 68.688 19. 649 2.6672 0.002185

11.60 77.865 26.485 2.9232 0.001586

12.00 90.091 34.930 3.2012 0.001002

12.40 106.052 45. 204 3.5022 0.000416

12.80 126.528 57. 535 3.8269 -0.000183

13.20 152.387 72. 162 4.1760 -0.000801

13.60 184.596 89. 327 4.5502 -0.001443

14.00 224.220 109. 262 4.9500 -0.002108

14.40 272.428 132.288 5.3762 -0.002795

14.80 330.493 158. 613 5.8292 -0.003500

15.20 399.799 188. 540 6.3097 -0.004219

15.60 481.845 222. 370 6.8182 -0 .004942

16.00 578.258 260. 428 7.3556 -0 .00 5664

16.40 690.800 3 0 3. 0 83 7.9229 -3.006373

249
Table 24. Calculated P(d) isotherms (Continued)

THE ISOTHERM AT 310.00 DEG. K

MOL/L P » BAR DP/OD OP/DT 02P/DT2

0.40 9.617 22. 329 0.0358 -0.000013

0.80 17.926 19. 259 0.0767 -0.000055

1.20 25.044 16. 354 0.1227 -0.000129

1.60 31.035 13. 645 0.1734 -0.000237

2.00 35.999 11. 228 0.2285 -0.000382

2.40 40.061 9. 130 0.2875 -0.000564

2.80 43.342 7. 320 0 . 3499 -0.000789

3.20 45.949 5. 758 0.4153 -0.001059

3.60 47.978 4. 424 0.4831 -0.001378

4.00 49.519 3. 318 0.5526 -0.001736

4.40 50.664 2. 447 0.6234 -0 .00 2101

4. 80 51.507 1. 804 0.6948 -0.002402

5.20 52.133 1. 359 0.7664 -0.002528

5.60 52.614 1. 066 0.8384 -0.002353

6.00 53. COO 0.885 0.9112 -0.001801

6.40 53.339 0. 837 0.9862 -0.000910

6.80 53.682 0. 879 1.0648 0.000162

7.20 54.045 0. 945 1.1483 0.001334

7.60 54.451 1. 113 1.2383 0.002503

8.00 54.961 1. 474 1.3372 0.003449

8.40 55.664 2. 084 1.4474 0.004001

8.80 56.672 3. 018 1.5713 0.004148

9. 20 58.134 4. 377 1.7106 0.003995

9.60 60.246 6. 283 1.8665 0.00 3667

10.00 63.253 8. 880 2.0402 0.003253

10.40 67.463 12. 326 2.2325 0.002803

10.80 73.250 16. 794 2.4443 0.002337

11.20 81.060 22. 472 2.6765 0.001860

11.60 91.416 29.559 2.9300 0.001371

12.00 104.923 38. 264 3.2056 0.000866

12.40 122.272 48. 808 3.5040 0.000340

12.80 144.244 61.417 3.8260 -0.000211

13.20 171.713 76. 330 4.1723 -0.000789

13.60 205.647 93. 788 4.5436 -0.001393

14.00 247.116 114. 044 4.9405 -0.002024

14.40 297.290 137. 357 5.3635 -0,002679

14.80 357.445 163.996 5.8134 -0.00 3352

15.20 428.968 194.244 6.2906 -0 .004040

15.60 513.361 228. 402 6.7958 -0.004734

16.00 612.255 266. 800 7.3300 -0.005427

16.40 727.416 309. 808 7.8940 -0.006111

250
Table 24. Calculated P(p) isotherms (Continued)

THE ISOTHERM AT 320.00 DEG. K

MOL/L P j BAR DP/DD DP/DT 02P/DT2

0.40 9.974 23. 285 0.0357 *0.000011

0.80 18.691 20. 340 0 . 0762 -0.000047

1.20 26.265 17. 554 0.1215 -0.000110

1.60 32.758 14. 954 0.1712 -0.000198

2.00 38.266 12.637 0.2250 -0.000311

2.40 42.909 10. 627 0.2825 -0.000445

2.80 46.805 8. 893 0. 3431 -0.000597

3.20 50.055 7. 395 0.4064 -0.000758

3.60 52.749 6. Ill 0.4719 -0.000916

4.00 54.973 5. 043 0.5393 -0.001054

4.40 56.814 4.201 0.6082 -0.001 146

4.80 58.363 3. 581 0.6785 -0.001168

5.20 59.706 3. 164 0.7504 -0.001100

5,60 60.916 2. 911 0.8243 -0.000934

6.00 62.052 2. 791 0.90D8 -0.000677

6.40 63.171 2. 834 0.9810 -0.000343

6.80 64.335 2.994 1.0657 0.000043

7.20 65.572 3. 205 1.1558 0.000466

7.60 66.918 3. 557 1.2526 0.000906

8.00 68.451 4. 153 1.3576 0.001327

8.40 70.281 5. 050 1.4725 0.001689

8.80 72.541 6. 319 1.5990 0.001956

9.20 75.398 8. 055 1.7391 0.002108

9.60 79.062 10. 374 1.8942 0 .00 2142

10. 00 83.793 13.415 2.0659 0.002069

10.40 89.910 17. 330 2.2555 0.001906

10.80 97.797 22. 293 2.4640 0.001669

11.20 107.909 28. 488 2.6925 0.001372

11.60 120.778 36. 112 2.9419 Q. 00 1 025

12.00 137,017 45. 376 3.2130 0.000633

12.4 0 157.326 56. 497 3.5067 0.000202

12.80 182.493 69. 702 3.8236 -0.000266

13.20 213.397 85. 226 4.1645 -0 .00 0770

13.60 251.015 103. 313 4.5301 -0.001305

14.00 296.423 124.213 4.9210 -0.001871

14.40 350.795 148. 185 5.3379 -0.002462

14.80 415.416 175. 499 5.7813 -0.003074

15.20 491.678 206. 438 6.2519 -0.003701

15.60 581.090 241. 306 6.7505 -0.004338

16.00 685.291 280. 439 7.2780 -0.004976

251
Table 24. Calculated P(o) isotherms (Continued)

THE ISOTHERM AT 330,00 OEG • K

MOL/L P f B AR DP/DD DP/DT 02P/0T2

0.40 10.330 24.236 0.0356 -0.000010

0.80 19.451 21. 408 0.0758 -0.000041

1.20 27.475 18. 734 0.1205 -0.000094

1.60 34.461 16. 238 0.1694 -0.000168

2. 00 40.502 14. 015 0.2222 -0.000260

2.40 45.713 12. 088 0.2784 -0.00 0365

2.60 50.208 10. 426 0.3377 -0.000477

3.20 54.084 8. 990 0.3997 -0.000589

3.60 57.427 7. 759 0.4640 -0.000689

4.00 60.319 6. 736 0.5304 -0.000765

4.40 62.846 5. 936 0.5987 -0.000804

4.60 65.097 5. 361 0.6690 -0.00 0794

5.20 67.163 4.997 0.7415 -0.000731

5.60 69.119 4. 811 0.8168 -0.000612

6.00 71.031 4. 777 0.8954 -0.000444

6.40 72.966 4. 929 0.9782 -0.000232

6.80 74.993 5.218 1.0659 0.000010

7.20 77.150 5. 583 1.1594 0.000276

7.60 79.482 6. 119 1.2597 0.000555

6.00 82.083 6. 937 1.3680 0.000829

8.40 85.077 8. 096 1.4859 0.001078

8.80 88.615 9.669 1.6148 0.001283

9.20 92.880 11. 751 1.7563 0.001426

9.60 98.099 14. 455 1.9121 0.001496

10.00 104.545 17.915 2.0834 0.001489

10.40 112.551 22.281 2.2719 0 .00 1408

10.80 122.513 27. 722 2.4785 0.001258

11.20 134.897 34. 421 2.7045 0.001045

11.60 150.244 42. 572 2.9508 0.000776

12.00 169.176 52. 364 3.2184 0.000456

12.40 192.401 64. 073 3.5081 0.000092

12.80 220.714 77. 864 3.8207 -0.000314

13.20 255.004 93. 993 4.1569 -0.000758

13.60 296.252 112. 701 4.5174 -0.001237

14.00 345.541 134.238 4. 9030 -0.001747

14.40 404.054 158. 863 5.3142 -0.002283

14.80 473.079 186. 846 5.7517 -0 .002841

15.20 554.017 218. 473 6.2164 -0.003416

15.60 648.384 254. 051 6.7089 -0.004002

252
>

Table 24. Calculated P (P ) isotherms (Continued)

THE ISOTHERM AT 3^0.00 DEG, K

MOL/L P * BAR OP/OD OP/OT 02P/CT2

0.40 10.686 25. 181 0.0355 -0.000009

0.80 20.207 22. 465 0 . 0754 -0.000036

1.20 28.675 19. 898 0 .1196 -0.000082

1.60 36.148 17. 501 0.1679 -0.000145

2.00 42.712 15. 368 0.2198 -0.000221

2.40 48.480 13. 521 0.2751 -0.00 0 306

2.80 53.563 11. 931 0.3334 -0.000394

3? 20 58.054 10. 558 0.3944 -0.000478

3.60 62.035 9. 383 0.4579 -0.000550

4.00 65.587 8. 413 0.5236 -0.000600

4.40 S8.795 7. 666 0.5916 -0.000621

4.80 71.751 7. 150 0,6620 -0.000606

5.20 74.545 6. 853 0.7352 -0.000553

5.60 77.259 6. 748 0.8115 -0.000463

6.00 79.965 6. 813 0.8915 -0.000339

6.40 82.737 7. 083 0.9761 -0.000 185

6.80 85.652 7. 508 1.0659 -0.000009

7.20 88.756 8. 030 1.1616 0.000134

7.60 92.103 8. 752 1.2643 0.000386

8.00 95.800 9. 788 1.3750 0.000588

8.40 99.984 11. 201 1.4950 0.000775

8.80 104.820 13. 064 1.6257 0.000934

9.20 110.508 15. 473 1.7686 0.0G1053

9.60 117.287 18. 543 1.9250 0.001121

10.00 125.447 22. 402 2.0964 0.001132

10.40 135.334 27. 2C2 2.2842 0.001082

10.80 147.356 33. 105 2.4896 0.000973

11.20 161.990 40. 293 2.7137 0.000806

11.60 179.787 48. 958 2.9576 0.000586

12.00 201.380 59. 306 3.2223 0.000317

12.40 227.485 71. 552 3.5086 0.000001

12.80 258.905 85.920 3.8173 -0.000356

13.20 296.535 102. 643 4.1493 -0.000752

13,60 341.366 121. 964 4.5053 -0.001183

14.00 394.485 144. 131 4.8860 -0 .00 1645

14.40 457,084 169. 403 5.2921 -0.002134

14.80 530.458 198. 051 5.7243 -0.002645

15.20 616.014 230. 363 6.1834 -0.003174

15.60 715.278 266. 648 6.6703 -0.003715

253
Table 24. Calculated P(d) isotherms (Continued)

THE ISOTHERM AT 360.00 OEG . K

MOL/L P » BAR OP/DD DP/DT D2P/0T2

0.40 11.393 27. 058 0 .0353 -0.000007

0.80 21.708 24. 554 0.0748 -0.000028

1.20 31.053 22. 187 0.1182 -0.000064

1.60 39.478 19.977 0.1653 -0.000111

2.00 47.068 18. 015 0.2160 -0.000166

2.40 53.927 16. 325 0.2698 -0.000226

2.80 60.160 14. 878 0.3267 -0.000286

3.20 65.857 13. 637 0 . 3863 -0.000341

3.6-0 71.095 12. 588 0.4487 -0.00 0 385

4.00 75.954 11. 742 0.5137 -0.000414

4.40 80.519 11. 124 0.5814 -0.000423

4. 60 84.866 10. 750 0.6521 -0.000410

5.20 89.152 10. 616 0.7261 -0.000375

5.60 93.408 10. 698 0.8039 -0.000317

6.00 97.737 10.982 0.8859 -0.000239

6.40 102.226 11. 507 0.9729 -0.000144

6.80 106.966 12. 219 1.0654 -0.000035

7.20 112.018 13. 065 1.1642 0.000085

7.60 117.452 14. 162 1.2700 0.000211

8.00 123.397 15.629 1.3839 0.000336

8.40 130.013 17.533 1.5069 0.000455

8.80 137.492 19.953 1.6402 0.000558

9.20 146.057 22. 986 1.7850 0.000638

9.60 155.978 26. 747 1.9426 0.000687

10.00 167.569 31. 365 2.1143 0.000699

10.40 181.203 36. 987 2.3013 0.000670

10.80 197.314 43. 773 2.5050 0.000597

11.20 216.400 51. 899 2.7263 0.000479

11.60 239.036 61. 554 2.9664 0.000316

12.00 265.874 72. 939 3.2264 0.000110

12.40 297.646 86. 266 3.5071 -0.000138

12.80 335.175 101. 758 3.8095 -0.000424

13.20 379.372 119. 644 4.1344 -0.000747

13.60 431.242 140. 165 4.4825 -0.001103

14.00 491.888 163. 570 4.8548 -0.001489

14.40 562.516 190. 118 5.2519 -0.001901

14.80 644.438 220. 081 5.6747 -0.002336

15.20 739.075 253. 751 6.1240 -0.002788

254
Table 24. Calculated P(P) isotherms (Continued)

THE ISOTHERM AT 360.00 DEG. K

MOL/L P t BAR DP/DD DP/OT D2P/CT2

0.40 12.099 28. 922 0 .0352 -0.000006

0.80 23.198 26. 613 0.0743 -0.000023

1.20 33.404 24. 434 0.1170 -0.000051

1.60 42.764 22. 400 0.1634 -0.00 0 087

2. 00 51.356 20. 603 0.2130 -0.000130

2.40 59.282 19. 068 0.2659 -0.000175

2.60 66.642 17. 766 0 . 3217 -0.000219

3.20 73.522 16. 665 0.3804 -0.000259

3.60 79.999 15. 754 0.4420 -0.000290

4.00 86.153 15. 0 51 0.5065 -0.000310

4.40 92.071 14. 584 0.5741 -0.000317

4.80 97.854 14. 375 0.6450 -0.000308

5.20 103.606 14. 426 0.7196 -0.000283

5.60 109.427 14. 718 0.7983 -0 .00 0244

6.00 115.411 15. 240 0.8817 -0.000 191

6.40 121.656 16. 035 0.9702 -0.000126

6.80 128.267 17. 046 1.0646 -0.000052

7.20 135.315 18.227 1 . 1653 0.000030

7.60 142.888 19. 701 1.2732 0.00 0 115

8.00 151.132 21. 595 1.3692 0.000200

8.40 160.229 23. 980 1.5141 0.000280

8.80 170.392 26. 936 1.6491 0.000350

9.20 181.868 30. 565 1.7952 0.000404

9.60 194.949 34.982 1.9537 0.000436

10.00 209.976 40. 319 2.1255 0.000442

10.40 227.346 46. 719 2.3120 0.000417

10.80 247.515 54. 343 2.5144 0 .00 0 359

11.20 271.006 63. 362 2.7336 0.000264

11.60 298.415 73.962 2.9708 0.000133

12.00 330.413 86. 342 3.2271 -0.000035

12.40 367.754 100. 711 3.5033 -0.000238

12.80 411.276 117.289 3.8005 -0.00 0 476

13.20 461.909 136. 303 4.1194 -0.000747

13.60 520.675 157. 993 4,4610 -0 .00 1048

14.00 588.694 182. 608 4.8262 -0.001376

14.40 667.186 210. 407 5.2157 -0.001730

255
Table 24. Calculated P (p ) isotherms (Continued)

THE ISOTHERM AT 400.00 DEG. K

MOL/L P,BAR DP /DO DP/DT 02P/DT2

0.40 12.802 30. 774 0.0351 -0.000005

0.80 24.679 28. 650 0.0738 -0.000019

1.20 35.736 26. 648 0.1161 -0.000041

1.60 46.015 24. 783 0.1618 -0.000070

2.00 55.593 23. 146 0.2107 -0.000104

2.40 64.567 21. 764 0.2627 -0.000139

2.80 73.035 20.611 0.3176 -0.000174

3.20 81.082 19.657 0.3758 -0.000204

3.60 88.786 18. 894 0.4369 -0.000229

4.00 96.226 18. 345 0.5010 -0,000244

4.40 103.495 18. 044 0.5685 -0.000250

4.80 110.698 18. 017 0.6396 -0.000244

5.20 117.946 18. 269 0.7146 -0.000228

5.60 125.348 18. 784 0.7939 -0.000200

6.00 133.008 19. 558 0.8781 -0.000163

6.40 141.036 20. 635 0.9678 -0.000117

6.80 149.547 21. 954 1.0634 -0.000064

7.20 158.625 23. 473 1.1655 -0.000007

7.60 168.370 25. 327 1.2749 0.000053

8.00 178.948 27. 647 1.3922 0.000113

8.40 190.559 30. 503 1.5185 0.000169

8.80 203.434 33. 983 1.6547 0 .00 0217

9.20 217.842 38. 188 1.8017 0.000253

9.60 234. 097 43.238 1.9606 0.000272

10.00 252.563 49. 264 2.1326 0.000271

10.40 273.658 56. 410 2.3186 0.000246

10.80 297.861 64. 836 2.5198 0.000194

11.20 325.719 74. 711 2.7373 0.000114

11.60 357.848 86. 220 2.9721 0.000003

12.00 394.939 99. 559 3.2253 -0.000140

12.40 437.767 114. 934 3.4978 -0.000312

12.80 487.187 132. 564 3.7905 -0.000515

13.20 544.149 152. 675 4.1045 -0.000747

13.60 609.690 175. 505 4.4405 -0.001007

14.00 684.948 201. 303 4.7995 -0.001291

256
Table 24. Calculated P(P) isotherms (Continued)

THE ISOTHERM AT 420.00 DEG. K

MOL/L P* BAR DP/DD DP/DT D2P/DT2

0.40 13.503 32. 616 0.0350 -0.000004

0.60 26.153 30. 668 0.0735 -0.000015

1.20 38.051 28. 835 0.1154 -0.000034

1.60 49.238 27. 133 0.1605 -0.000058

2.00 59.787 25. 654 0.2088 -0.00 0 085

2.40 69.795 24. 425 0.2602 -0.000114

2.80 79.358 23. 423 0.3146 -0.000141

3.20 83.560 22. 621 0.3721 -0.000 166

3.60 97.480 22. 014 0.4327 -0.000186

4.00 106.201 21. 629 0.4966 -0.000199

4.40 114.818 21. 505 0.5640 -0.000204

4.80 123.443 21. 670 0.6351 -0.000201

5.20 132.194 22. 134 0.7104 -0.000190

5.60 141.189 22. 884 0.7902 -0.000171

6.00 150.539 23. 919 0.8751 -0.00 0 144

6.40 160.368 25. 285 0.9655 -0.000111

6.80 170.801 26.917 1.0620 -0.000074

7.20 181.932 28. 780 1.1651 -0.000032

7.60 193.875 31. 014 1.2755 0.000011

8.00 206.811 33. 757 1.3939 0.000053

8.40 220.958 37. 060 1.5211 0.000092

8.80 236.564 41. 072 1.6580 0.000124

9.20 253.919 45. 840 1.8057 0.000 147

9.60 273.356 51. 504 1.9649 0 .00 0 157

10.00 295.259 58. 196 2.1367 0.000150

10.40 320.070 66.063 2.3222 0.000 124

10.80 343.287 75. 262 2.5224 0.000076

11.20 380.480 85. 964 2.7384 0.000004

11.60 417.283 98. 351 2.9711 -0.000093

12.00 459.411 112. 6 18 3.2217 -0.000217

12.40 507.655 128.969 3.4909 -0 .00 0 368

12.80 562.893 147. 620 3.7799 -0.000545

13.20 626.089 168. 800 4.0895 -0.000747

13.60 698.301 192. 744 4.4207 -0.000975

257
Table 24. Calculated P(p) isotherms (Continued)

THE ISOTHERM AT 450.00 DEG. K

MOL/L P,BAR DP/DD DP/DT 02P/CT2

0.40 14.552 35. 366 0.0345 -0.000003

0.80 28.352 33.667 0. 0731 -0.000012

1.20 41.498 32. 077 0.1145 -0.000026

1.60 54.030 30. 612 0. 1590 -0.00 0 044

2.00 66.017 29. 365 0.2066 -0.000065

2.40 77.555 28. 365 0.2572 -0.000087

2.80 88.739 27. 593 0.3109 -0.000108

3.20 99.656 27. 025 0.3678 -0.000127

3.60 110. 3e6 26. 663 0.4279 -0.000142

4.00 121.018 26. 537 0.4914 -0.000153

4.40 131.654 26. 692 0.5586 -0.000159

4.60 142.414 27. 162 0.6298 -0.000159

5.20 153.427 27. 959 0.7053 -0.000153

5.60 164.823 29. 075 0.7856 -0.000142

6.00 176.729 30. 513 0.8710 -0.000126

6.40 189.284 32.323 0.9622 -0.000107

6.80 202.627 34. 433 1.0596 -0.000084

7.20 216.866 36. 816 1.1637 -0.00 0 059

7.60 232.136 39. 623 1.2751 -0.000033

8.00 248.640 42. 997 1.3945 -0.000008

8.40 266.619 47. 010 1.5226 0.000014

8.80 286.346 51. 757 1.6603 0.000030

9.20 308.137 57. 347 1.8083 0.00 0 040

9.60 332.353 63. 9C4 1 . 9677 0.000039

10.00 359.407 71. 564 2.1392 0.000026

10.40 389.771 80. 474 2.3239 -0.000002

10.80 423.974 90.791 2.5227 -0.000047

11.20 462.614 102. 687 2.7367 -0.000111

11.60 506.359 116. 343 2.9667 -0.000195

12.00 555.949 131. 952 3.2138 -0.000300

12.40 612.208 149. 718 3.4789 -0.000427

12.80 676.040 169. 855 3.7631 -0.000575

13.20 748.439 192. 591 4.0671 -0.000745

258
Table 24. Calculated P(p) isotherms (Continued)

THE ISOTHERM AT 5C0.00 DEG, K

MOL/L P» BAR DP/DO DF/DT D2P/CT2

0,40 16.295 39. 920 0 . 0348 -0.000002

0.80 31.994 38. 610 0.0726 -0,000008

1.20 47.194 37. 402 0.1134 -0.000018

1.60 61.931 36. 315 0.1572 -0.000030

2.00 76.275 35. 445 0.2039 -0.000044

2.40 90.321 34. 827 0.2537 -0.000059

2.80 104.168 34. 445 0.3065 -0.000074

3.20 117.906 34. 281 0. 3625 -0.00 0 087

3.60 131.623 34. 346 0.4220 -0.000099

4.00 145.418 34. 676 0.4850 -0.000108

4.40 159.407 35. 323 0.5519 -0.000114

4.60 173.724 36. 327 0.6230 -0.000117

5.20 188.518 37. 704 0.6986 -0.000117

5.60 203.937 39. 454 0 .7792 -0.000114

6.00 220.132 41. 586 0 . 8652 -0.000109

6.40 237.265 44. 153 0.9570 -0.000102

6.80 255.499 47. 071 1.0552 -0.000094

7.20 274.966 50. 327 1.1601 -0.000084

7.60 295.829 54. 088 1.2723 -0.000075

6.00 318.324 58. 503 1.3924 -0.000067

8.40 342.729 63. 649 1.5212 -0.000062

8.60 369.354 69. 623 1.6593 -0.000061

9.20 398.553 76. 541 1.8074 -0.000065

9.60 430.730 84. 534 1.9664 -0.000076

10.00 466.341 93. 740 2.1371 -0.000096

10.40 505.903 104. 310 2.3204 -0.000127

10.80 549.993 116. 406 2.5170 -0.00 0 169

11.20 599.254 130. 198 2.7280 -0.000225

11.60 654.402 145. ee9 2.9542 -0.000295

12.00 716.226 163. 612 3.1966 -0 .00 0 380

259
Table 24. Calculated P (P ) isotherms (Continued)

THE ISOTHERM AT 550.00 DEG. K

MOL/L P,9AR DP/DD DP/OT 02P/0T2

0.40 18.032 44. 448 0 . 0347 -0.00 Q002

0.80 35.616 43. 5C1 0 . 0723 -0.000006

1.20 52.844 42. 655 0.1127 -0.000013

1.60 69.756 41. 933 0 . 1559 -0.00 0 022

2.00 86.421 41. 433 0.2020 -0.000032

2.40 102.938 41. 194 0.2511 -0.000043

2.80 119.410 41. 207 0.3033 -0.00 0 054

3.20 135.935 41. 458 0 . 3588 -0.000065

3.60 152.610 41. 963 0.4177 -0.000074

4.00 169.545 42. 767 0.4803 -0.000082

4.40 186.871 43. 925 0.5469 -0.000089

4.80 204.738 45. 482 0.6178 -0.000093

5.20 223.312 47. 460 0.6933 -0.00 0 097

5.60 242.763 49. 861 0.7739 -0.00 0 098

6.00 263.260 52. 702 0.6600 -0.000099

6.40 284.991 56. 035 0.9520 -0.000099

6.80 308.139 59. 768 1.0504 -0.00 0 098

7.20 332.858 63. 900 1.1555 -0.00 0 097

7.60 359.337 68. 611 1.2679 -0.000097

8.00 387.845 74. 057 1.3882 -0.000099

8.40 418.690 80. 313 1.5169 -0.000103

8.80 452.217 87. 485 1.6549 -0.000110

9. 20 488.816 95. 692 1.8026 -0.000121

9.60 528.927 105, 069 1.9609 -0.000138

10. 00 573.046 115. 761 2.1305 -0.000 162

10 . 40 621.731 127. 921 2.3122 -0.000 194

10.80 675.601 141. 715 2. 5C68 -0.000234

11.20 735. 343 157. 315 2.7151 -0.000285

260
^able 24. Calculated P(0) isotherms (Continued)

THE ISOTHERM AT 600.00 DEG. K

MOL/L P BAR DP/DD DP/DT D2P/DT2

0.40 19.766 48.957 0.0346 -0.000001

0.80 39.222 48.356 0.0720 -0.000005

1.20 58.462 47. 858 0.1121 -0.000010

1.60 77.525 47. 469 0.1549 -0.000017

2.00 96.485 47. 353 0.2006 -0.000025

2.40 115.445 47. 492 0.2492 -0.000033

2.00 134.514 47. 900 0 . 3009 -0.000042

3.20 153. 800 48. 572 0.3559 -0.000051

3.60 173.409 49. 526 0.4144 -0 .0 0 0 059

4.00 193.465 50. 812 0.4766 -0.00 0 066

4.40 214.111 52. 491 0.5429 -0.000073

4.80 235.517 54. 613 0.6135 -0.000079

5.20 257.864 57. 202 0.6888 -0.000084

5.60 281.341 60. 262 0.7693 -0.000088

6. 00 306.139 63. 818 0.8552 -0.000092

6.40 332.470 67. 922 Q .9472 -0.000096

6.80 360.534 72. 472 1.0454 -0.000099

7.20 390.507 77. 477 1.1504 -0.000104

7.60 422.604 83. 132 1.2627 -0.000109

8.00 457.121 09. 596 1 . 3827 -0.000116

8.40 494.398 96. 947 1.5112 -0.000125

8.80 534.811 105. 291 1.6486 -0.000137

9. 20 578.781 114. 756 1.7957 -0.000153

9.60 626.783 125. 479 1.9531 -0.000173

10.00 679.352 137. €10 2.1214 -0.000198

10.40 737.081 151, 308 2.3015 -0.000230

261
I

I

Table 25. The Joule-Thomson inversion locus.

T » K P,BAR MCl/L TfK P,BAR MOL/L

425 467. 3 11.93

25 0 26.3 15.06 430 474.2 11 .85

255 47.2 14.95 435 481.0 11.77

260 67.3 14.85 440 487.6 11.70

265 86.7 14.75 445 493.9 11.62

2 7 0 105.3 14.65 450 50 0.1 11.55

275 123.4 14.55 455 506.0 11.47

28 0 140.6 14.45 460 511. 7 11.40

285 157.6 14.36 465 517. 3 11.32

29 0 173.8 14.26 470 522.6 11.25

295 189.5 14.16 475 527.8 11.17

300 204.7 14. 07 480 532.7 11.10

30 5 219.5 13.97 48 5 537.5 11.03

310 233.7 13 .ee 49 0 542.

1

10.95

315 247.5 13. 7 C 495 546.5 10 . 88

320 260.9 1 3. 69 500 550.

7

10.81

325 273.9 13.60 505 554.8 10.73

33 0 296.5 13.51 510 558.6 10.66

335 296.7 13.42 515 562.3 10.59

340 310 .

6

13.33 520 565. 8 10.52

345 322.1 13.24 525 569.1 10.44

35 0 333.3 13.16 530 572.3 10.37

355 344.1 13.07 535 575.2 10.30

36 0 354.7 12.96 540 578. 0 10.23

365 364.9 12.90 545 58 0.7 10.16

370 374.9 12.81 550 563.2 10.09

375 384.6 12.73 555 585.5 10.01

330 393.9 12.65 560 587.6 9.94

38 5 403.1 12.57 565 569.6 9.87

390 411.9 12.48 570 591.4 9.80

395 420.6 12.40 575 593.0 9.73

40 0 428.9 12.32 580 594. 5 9.66

40 5 4 37.1 12.24 585 595.9 9.59

4 10 445.0 12.16 590 597. 1 9.52

4 15 452.6 12.08 595 596. 1 Q. 44

42 0 4 6 0.0 12.01 600 599. 0 9.37

262
Table 26. Thermophysical properties of the saturated liquid

This table was computed by integrating first along isotherm

of Figure 9> then along isobar P^, and finally along each isotherm down to the saturated liquid boundary <> Column headings have the following interpretations --

DPS/DT = dP^ /dT, vapor pressure,

DDL/DT = dp^/dT, saturated liquid,

DP/DT = (dP/ST), single phase,

DP/DD = (dP/6p), single phase,

Q, VAP = AH , heat of vaporization

vap

CV C (P , T)

V

CS = C (T)

cr CP = C (P , T)

P

W = speed of sound

263
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Table 27. Thermophysical properties along isobars

The following pages give physical and thermodynamic properties

along selected isobars, as computed by methods of section 3 of the

text.

The first line of each table refers to freezing liquid on the P(T)

melting line.

Each table P<PC contains a blank line for the transition from

saturated liquid to vapor, as seen by the abrupt decrease of density.

Table headings for partial derivatives have the following interpretations - - DP/DT s dP/6 T,

DP/DD = d P /d p . The specific heat interpretations are -

CV = C (P , T), v CP - C (P , T)

.

P

*These tables are extrapolated beyond the range of P-p-T data used for

adjusting the equation of state (P~350 bar).

266
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268

427
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27.

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276
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2 X rH rH CD CD CD O' O' O' 0 0 P- P- P~ 0 0 0 0 p^ P- 0 0 0 0 0 0 4 4 4 4 4 4 0 0 0 0 0 0 0 0 0 0 0 (VJ OJ (VJ (VJ OJ 0J CVJ <1 (VI (VJ (VI CVJ (VI rH rH rH rH rH rH rH rH rH rH T

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rH rH rH rH rH rH rH rH rH rH (VI (VJ (VI (VJ OJ 0J 0J 0J OJ CVJ 0J OJ 0 0 0 0 0 0 0 0 0 0 4 4 4 4 4 4 4 4 4 4 0 0 0 0 0 0

280
Table

27.

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281

439
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27.

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289
Table

27.

Thermophysical

properties

along

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(Continued)

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27.

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properties

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293
Table

27.

Thermophysical

properties

along

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(Continued)

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2: vO vO vO vD vO vO P P P p p P P P ao CD ao CP CP O ro 0 CM y 0 ao ao p P p p P p p p p p P P p P P co ao ao CD ao ao CP V“5

vi vi CM CM rl vi

D* CD vD vO vO CM p CP 0 «=> (P p in CM CD CM CM CM CP in H ro P vO CP CP CD P v£> 0 ao 0 y CP a) ro vi CD in CM co ro 0 ro CM r^ v£) O \ ro CM C3 ao in ro O CP CO CP 0 O y CD ro ao in CM 0 (P 0 ro vO ao O GO H P in y y in in p CD CP vi ro in \£> ® O ro vO ao O CM O y y y ro ro ro ro CM CM CM ro ro ro ro y y in vi) p P IT 0 a> ro CM vi CM CM 10 -y in sL> p 0D CP 0 CM ro y in vD ao CP 0 CM y P^ CP 2: y J- y y y y y y y y y y y y y y y J" y y y in in in in in in in in in in in in in in vO vD vO vO vO vO sD sD P- pw r^ p- p* 00 \

in 2»- CM CM CM 0 CP in P- U) a- in CM CD P- vd Vi) y in ao CM r^ CD y CP in y y y CO v£> y O' ro in vO y ao vi in O O y y y in O y CD V v£> ao CM H ro ao O in vD ao ro ro CM CM y CM ao vD CM ao CM ro 0 in <P y H vO vO vD CO ro y 0 ro CM CP ro vO vO in CM P vi in y <p a> in

_J vD y 0 CD in Vi) in 0 ro y y CM CP in CD in CP y CD fs. CD ro vi y cm CM CO vi ro y y y ro CM 0 ao in ro O p y vi p y vO ao O' CD vi X vD ro CD vO vD t4 vD 0 y ao CM in CP ro vO CP ro P* 0 in co r^ CP ro vO CO vi ro in p CP v4 ro in vO CO CD CM ro in P CO 0 ro vO O' ro vD

v. P- CD CP CP CD O H CM CM CM ro ro ro y y y in in vO vD vD co ao CP CP CP CD 0 0 CD 0 vi ri vi v4 CM CM CM CM CM CM ro ro ro ro y y 1 ri T • vi vi 0 vi H i-i vi CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM VVI CM OJ CM CM CM X _J CP H y in y ao CD in CM CM ro ro y ro CM in y y ro ao ro vO <D vi ao vi CO <P ro O CO vO CM in CM in P CM vi .6 .5 .6 vi ao V0 in y O'

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in Vi) vD r^. co ao CP CD TH CM ro PO y in VD r^ OD O' CD vi CM p ao O’ CD vi CM CM ro y in in VD p CO ao O' CD vi vi CM ro y vD p O' vi ro

*H *-4 •H •H •H CM (M CM CM CM CM ro ro ro ro ro ro ro ro ro ro ro ro ro y y y y y y y y y in in

LU _J vO CP O' ao ro ro I in ro - y CP CD rH CP CP y vO CO CD co P in CM CP w vi in vO ao O' ro 0 vD p in CM p CM CP cp CM ao CM O' in in X ro O' CM r^ in vD CM CP in 0 p- ro CP CP p- y in CP vi P- y y CM y CD vi) Vi) ao CP Vi p CD CP in CD in O' CM vO CP ro CD co O CM vD CD

v. in y !M O 0 O 0 CM in ao ro 0 ao CP ro y in y P- y CO CP CM CP CM y in vO CD O' CM y CD ro ao y CM a CP CD vi p •O fVJ CD

ro 0 Vi) ro CJ P y H CD U I CM CP p» in CM 0 CP CD r^ p- O' ao in 0 <p P ro CD vi) CM co y 0 P ro O' VD CM CP vD ro O' p y au ro O' US vi in in vO P- co CD a- O O H CM CM ro y in vD v£» CD a« 0 vi vi) p p» CO <P CD 0 vi vi CM ro ro y y in vi) vD P co CO CP CD vi ro y vO ao

'rH H vd r4 v-l iH CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro y y y y y y

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1 Vi) p- ao CD ro vD 0 in O us wi P- ro 0 y CP vD y CM vi vi •i vi vi CM CM CM CM CM CM CM ro ro ro ro ro ro ro y y y y y

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0 O CD y y in CM 0 ao vD in y CM v-t 0 CP CD r^- vO in y y ro CM 0 0 CD CD O CD O CD O O CD CD CD O O CD CD CD CD CD O CD CD O O O CD

ro ro CM CM CM CM tH r-i tH vd iH

11 a O' CM vi ro ao P vi CD vD CP CD CM in ro CP GO CO vi cd ro y vi in vi CM CP V0 ro vO ro ro 0 V0 CP ro p 0 ao ao ro ao in ao ao vi vO in vD in O 0 CD co Vi) y CM vi vi vi vi CM in co CM ao in in CO vO cd in v£> O' CM vO ao O' O CP O' cp ro in v£> O' v£> vi) CM CM O' ro ro vi vi) O' CD ro vi y ro

i— D» X vi) vi) P ao CP CD vi CM ro y in vD co CP vi ro in ao CM vO ro vi CM CM P vO CP vi) vi y vD vi) in ro vi co in vi vi) CM P CM vi) CD O' vi) ro CP in

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in Z _j CP 0 in O ro CM vO ro vi CD P 0 vD ro vO ao CP in O' P vO vi ro V0 ro vi y ao CO vi) P <0 P CM ro ao P CP ro vi CD vi y CP CM vi CM ao vO Hi UJ V O' vO 0 in O' ro vO cr vi CM vi 0 vD vi ro CM P p CO vO in <X) 0 ro O' y vD CM vi cm y P vi vO vi vO CM CD in CM CP v£> ro CD vO CM ao y vi LJ _J <0 ro CD vD CM CP in vi ao y CD v£> vi P CM P vi in ao CD cn CO CM ao ro vi CP ao P v£> in y y ro ro CM CM vi vi O O CD CD CP O' co co CO Z X Vi vi vi CD CD CP CP CP ao co <D P P vD vO in in y ro ro vi CD ro CM CM CM vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi vi CD CD CD CD CD

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r- sc CM CD 0 CD CD CD O CD O CD CD CD O O O O CD CD CD 0 CD y y CD O CD CD CD CD CD O CD CD CD CD O CD O O CD CD O O CD CD O 0 CD O

CM CD 0 CD CD CD CD O CD O O O O CD CD CD O CD CD O O p p CD CD O O CD CD CD O O CD O CD O CD CD CD O O O CD CD CD CD CD O CD 0 in O 0 CD O CD O O O CD O O O O CD CD O CD CD O O O' O' CD O O O O CD CD O CD CD a O CD CD CD O O CD CD O CD CD O CD CD CD 0 CD O 0 CD O CD O O CD CD O CD 0 CD O O O CD CD CD O in in CD CD O CD CD O O CD O CD 0 O O CD O CD O CD O CD O CD CD CD O O

CP O vi CM ro y in vD P ao O' CD vi CM ro y in vD P ao O' CP O' CD vi CM ro y in vD P CO O' CD vi CM ro y in vO P CO CP CD CM y Vi) CO CD

vi vi vi vi vi vi vi vi vi vi CM CM CM CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro ro y y y y y y y y y y in in in in in vO

•

1

294

S

2

*i
Table

27.

Thermophysical

properties

along

isobars

(Continued)

ETHANE

ISOBAR

ATP=

44.0

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296

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299
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302
Table

27.

Thermophysical

properties

along

isobars

(Continued)

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303
Table

27.

Thermophysical

properties

along

isobars

(Continued)

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307
Table

27.

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properties

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(Continued)

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308
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27.

Thermophysical

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309 -
Table

27.

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properties

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O —1 vA CO GO ro -X O O' ro tH OJ O ro P- LA LA LA ro 4 O vA 4 P OJ ao LA vA CD 4 P O' CM vA <P OJ P 4 O' CD CD vA vA CM O' o 4 CM <P O o vA oo CP -J J- LA ro O' CM LA vA P- 00 CD ro vU CP ro vA P t-4 ro 4 CD 4 in CD t-4 CP CM 4 LA ro 0J P ao t-4 LA CD LA o o t-4 in tH P X vA ro LA ^4 CP t-4 CD t-4 oo vA ro ro 4 ro 00 vA LA 4 OJ (P ro LA vA LA 4 4 4 4 0J ro ro CD OO ao CD ro vA o LA O' 4 ao p IA CM ao 4 o -1 vA 00 LA p LA t-4 0J CO oo ro CM 4 CP r- O LA 0J t-4 t-4 4 CO 4 OJ OJ 4 ao 4 0J t-4 t4 OJ OJ ro LA vA P O' CD t-4 ro 4 p CD ro in ao

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LJ \ rt J- 4 CD CD OO Ut CD CM vU 4 t—4 LA p- p. CD CD CD P aj O' P OJ LA P 0J 4 ao vu ro ro CO O' CD VU 4 t-4 vU p ro ro VU t4 4 ro P 4 o \ CL OJ o t-4 CD LA OO LA t-4 OJ vA 0J ao 0J 4 ro <P O vA vA t-4 CD ro CD O 4 ro vU 4 co p o vO LA P O' ro ao ro O' vA ro CD vA CM CP vA 4

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o O CP LA ro CD OO A- LA -J- 4 4 LA vA ao t-4 LA o p IA LA P ro OJ LA LA CM O' P P O' OD t-4 VU O ro 4 ro <P 4 vU vU 4 CD P 03 4 LA ro

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CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD o CJ CD O CD CD t-4 t-4 t-4 t-4 T-4 t-4 tH t-4 t-4 t-4 CM CM CM CM CM CM CM CM ro ro

CD CD O CD CD CD CD CD O CD CD O O O o CD CD CD CD O a o CD CD O O CD O CD O o CD CD CD CD CD O CD O CD CD CD CD CD CD CD CD O

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LU V LA OC 4 CD vA H P 0J X tH 4 vA 00 CP CO p- 4 <P CM ro CM P O' vA <P P 0J vA 0J 4- J- CVJ vA P ro ro P 4 ro in GO ro vA ro 4 P CM

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CP CD tH OJ ro 4 LA VA ao CP CD T-4 CM m 4 LA vD P CO O' CD H OJ ro 4 LA VU P a? CP CD t-4 CM m 4 LA vD P ao O' CD OJ -y vD OO CD

t-4 H H t-4 t-4 t-4 t-4 t-4 t-4 OJ OJ OJ 0J 00 00 00 0J CM OJ ro ro ro ro ro ro ro ro ro ro 4 4 4 4 4 4 4 4 4 4 IA in LA in LA vA

312
Table

27.

Thermophysical

properties

along

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313
Table

27.

Thermophysical

properties

along

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1

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O'dCP CP CD X V0 vD in in 3 3 ro ro CM CM CM CM tH

— CD vD 3 LT. CD 3 CM 3 in X vD CD in X CM CD H UJ ro ao i-4 a> CM CD vD CD in UJ X CD V0 3 X UJ X O’ CP CO vD

LJ X ri X ao in u\ H X CD LJ CM CO ro vD vD in X X CO X -1 vu CD CM H CP vD vD ao U> 3 i-4 X CM 3 3 X CM vD X U' X 3 X 1-4 X 3 X Ql CM ro in in H VD ro CD CM X ro CD in CO ao 3 vD ro in Pj CM X in X CM CM vD 3 X 3 in CP vD in vD ao CM vD H X X CD 3 CD vD X CD

LL d T-1 ro »H 3 »H CD CM VD T~1 X in 3 ro ro 3 vD aj tH 3 CO CM VD i-4 vD CM co 3 1-4 aj vD 3 CM i-4 CD O' co CD X X vD vD UJ in U> 3 3 3

O CD 3 t—

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cc in ro CP P 'D 3 ro CM CD CP ac X X vD in in 3 3 ro X) CM CM CM i-4 i-4 i—4 CD CD O CD CD CD CD CD CD CD CD CD CD

ro ro CM CM CM C\J -r-i H -I H tH

_J _j in CD in rH CD CM ao ac CM rH in V0 3 rH UJ CM O' rH O CO rH CM CP CP CM CD i-4 3 CO CM CD X CD rH X in CM X X CM X CD 3 X X i-4 CD O o O' in CM CD CO UJ 3 ro X X X 3 UJ O' CM X CM CD O' CP X O' X CM CM X rH CM 1-4 X CD 3 rH X CM X rH X 3 3 CM O' X CM CM X CM

r> i- in vD X GO ao O' CD rH CM X 3 in UJ X CP CD CM 3 in X CD CM in O' X X X O' UJ X CM CD O' X UJ 3 X rH O' X X CM X CM X X X

X 3 3 3 3 3 3 in in in in in in in in in UJ UJ UJ U) V0 X X X X X X O' O' CD rH CM X X 3 in X X X X O' CD rH CM 3 X X X

_J CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD o CD r-i i-4 i-4 rH **-* *“• 'H CM CM CM CM CM CM CM

CD CD O CD CD CD o O CD CD O CD CD O CD CD CD O o o CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD z -J in vD ao CD rH CD in in O' <o CD 3 CP in CD X CM in CP X 3 X CM UJ O CP V0 CO in x 3 O' O O' CD X 3 X X X X X X CM X rH

UJ X UJ CD vD CM O' in i-4 UJ rH in CP X in UJ X X in CM X o CM rH X rH i-4 O' X X rH X O' UJ X X O' X X rH X X X X X CM O CD X

_J X in ao 3 ’rH CD 3 X X CD UJ CM CO 3 CD UJ rH X CM X UJ CD X X CD 3 X i-4 U> rH X X CD X X CM CD X X X X X X

X i-4 CD CD CD CP CP CP co CO CC X X UJ UJ UJ in in 3 3 X X CM (M i-4 CD CD CP X X X X V0 X X in X X X 3 3 3 3 X X X

CM CM CM CM CM CM rH rH rH rH rH rH rH rH rH rH rH rH ** rH rH rH rH rH rH rH rH

v0 CD CD CD CD CD CD CD CD CD CD CD CD O CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD o CD CD CD CD CD CD

^-4 O O CD CD CD CD CD CD CD O CD CD CD O CD O CD CD O CD CD CD CD CD CD CD CD CD O CD CD CD CD CD CD O CD CD CD CD CD CD CD CD CD CD

DEG in CD O CD CD CD CD CD O CD o CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD O CD CD CD CD CD CD O CD

CM CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD O CD CD CD CD CD O CD CD CD CD CD CD CD CD CD CD CD CD O CD CD CD CD

O’ CD rH fM X 3 in UJ r^- co CP CD rH CM X 3 in UJ X X CP CD i-4 CM X 3 in *0 X X O' CD rH CM X 3 in X X X X CD CM 3 X X CD

i-4 rH rH rH rH rH rH rH rH rH CM CM CM CM CM CM CM CM CM CM X X X X X X X X X X 3 J- 3 3 3 3 3 3 3 3 X X X X X X

I

I

314
Table

27,

Thermophysical

properties

along

isobars

(Continued)

ip4 3 o p 3 ro

p ID P p ID ID

p o 3 CD UJ 3 PD 3 ID CP ro CD CP CP r*-' Jf ro ao an CM CP ao CO CP CD ro u> CD r^ tr> CP r^ UJ

UJ C\J LT> ID UJ

pC3 UJ CT CM ID CP CM U> CP ro

p

H ID (P j- CP ro ao -3- CD P- -3- CM CD CP CP CO CO CO CC CP CP CP CD CD CM CM ro -3- in CM 1 O CP oo P P UJ ID 3 3 ro OJ CM' •»-< CD o CP O' 3D r^ i^- UJ vD LD ID ID J" •s J- ro ro ro ro ro ro ro ro ro J" -3- J- -3 -3- -3 -3 \

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LL * ID ID CMpO CM 3 vOO 3 Cj CO CP ro o UJ P -3- CM UJ O' r^ ID ID -3 CM -3 o ID CM CP ao ao ro p- CD CM CD CM CM

O UJ O'

(J

V ro ro ro 3 UJ CC CM U)p ID ro ro ro LD CP 3 O

p vO r- o ID J- CP

O CD ro UJ o UJ CP' CD >3-

H CM UJ CO U> UJ O' UJ U> ID o CD CD CD 00 00 OO O' O' O o CM ro 3 ID vO ao o ro ID CO CD ro vD ^-1 J- U) r^ K r^ ID ro CM o <P CD P» U) UJ ID ID ID ID U) CD X U5 vD UJ U> vO vO vD VO P p- P p p P p r<- oo OO ao CO ao CP CP CP CD CD CD CD CD CD CD o CD CD CP CP <P CP CP CP CP CP CP CP CP CP \

~>

wH T-l v-4 > * i-4 CP UJ o ro ac OO ro UJ p p UJ 3 CM CP ro 3 o i-4 ID CM ro ro N- vD ID CO CO CT- ID CM O CD CD CM ID ao LD CP K. ro CD CD CP o 'v 3 CM o CO LD CNJ o (P CO OO CD H 3 ao CM ao -3" ao ID ro o H r^ UJ CM o CP CP CP CP CP CP CP CP a' CP CP CD O CD CM CM ro CM O in LP in 3 3 3 3 ro ro ro ro 3 3 ID ID. UJ p P 0D O' CD tH CM ro UJ r- OO ac IP CD CM ro J' ID UJ rv. ao CD CM J- UJ CO CD CM X\ 3 3 3 3 3 3 3 3 3 *3

3 3 3 3 3 -3" -3" 3 3 -3- <3- ID ID ID ID LD ID ID LD ID U) UJ UJ UJ U) U) UJ U) UJ r^ P- P» P- P- P- 00 00

in CM ro ID U> IDp VD aj ro ro CO

O ID ID CM CD v£> ro ro CM ro U) UJ CD CP CM

O CM ID CD UJ ro CO UJ ID ao P^ •r-l -3- CD JV ru CM ro CO P U> CM O 3 UJ i-4 O ID CO CM U> ro 3 CP CD N- vO CP -3 CM CD CO U) vD ID ro 'H CM ID CD U) (P -T UJ U> K <p

—1 C\J 3 O' CO ro 3 CM P CP CD CO ID CD 3 ao CD CM ro ro 3 ro ro CM o o CD (P CP r^ ID CM OO ro rO CM ro j- -3 ro tH P- CM UJ CP £ p c\j ao 3 o ID CD 3 CD CM vO cd 3 h- C3 <3- p CD ro UJ CP CM ID CO ( J- P- CP CM ID CO ro UJ ao ro ID r^ CP •J-! ro N- CD p- CD \ p CD CO CP cd CD i-4 CM CM ro ro ro -3- 3 -3- ID LD IT LD vD UJ UJ r-~ P'- N- CO oo ao CT CP CP CD CD CD o CD tH CM CM CM ro -< i~4 1 1—4 H *-« 1-4 H 1 *-* ^ri n •*-1 H •*-* ^—1 *-» »-« »-» tH -* CM CM CM i\j VM CM t\J LM CM VM VM CM

X -1 ID ro ID -3” -t -3- UJ OO <o .9 .3 CD ID (P U) U) ID CM GO N- ID CM 3 ro r^ ro CM CP CP CP ID 3 ao UJ O' ro ao r^ ao CO 3 ID

2- ro -T UJ -3 J- ®u p- CM CP co ao CD ao r^. 3 CD CM CM 3 ro CM ro CD UJ CD ro C-t 3 CM GD U' 3 CO 1^- 3 UJ O' CD \ CP CP UJ J- ro CM H CM ro ID Pw <?—

UJ ro CD CP o ro CO ID 3 UJ CD ro GO ID CM CD U> *—

3 ID ID ro ao 3 o UJ N. CP ID fM

~J UJ ro CD p- -3 ao ID CM CP UJ ro co UJ 3 CD co UJ LD 3 m ro ro ro ro 3 ID UJ UJ Pw rv. P^ p- N- UJ UJ UJ U' 3 ro ro CM CM

UJ u> p- CO CO CP CD o i CM CM ro -3 LT LD UJ CO CP CP CD «-H (M ro 3 IX' UJ CO CP CD CM ro 3 ID UJ ao CP CD •rH ro ID p- O' y~* *H vi c=J t •H •H •H CM CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro ro 3 3 3 3 3 3 ID

UJ _J LD p- ID ao CP vO ID UJ ID ro CO < ro CM

O ao ID ao ID CM CP CD ID ao CD 3 U> CO ID CD CM LD O' CM co UJ ID CP ao CM UJ - X UJ r^ r^ P- CD UJ -3 UJ ro ID ID CM ao -3 CD CP vO P^ 3 r^ CD CM ao CM 3 r^- ro U> ao 3 «H CO CO 3 CP CD 3 CD CP UJ 3 ao V UJ ID CM CP UJ ~3 O' K vO ID LD UJ P^ O •3 ao ID fM v) CM 3 CP ID ro ID CP 3 CD ID CP CM ro CO 3 O' CM UJ CP 3 CD UJ ID UJ CP “J ro CO U'v CU LD CM CO LD CM (P UJ ro CD ao ID CM LD VO UJ 3 CM CD O' ao UJ UJ UJ ID <3 3 ro CM CD O' p- UJ 3 CM O' vL CM O' UJ ro LD ID UJ r^- P- ao CP CP O CM ro J- -3 LD U> P^ N- CO CP CD CM ro 3 ID UJ CO CP o CM CM ro 3 ID U) N- P- O' CM 3 U)

r-lH -1 n 'H CM OJ CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro ro ro 3 3 3 3 o CP ro ro CD CD -3 ro ro CD vD ao CD ro CD UJ 1^- UJ 3 CO CD O' P- LD ID UJ CD ro CP ID LD ro p- CM tj CD LD co LD CM

CJ o ao to CM UJ CP UJ CM GO

a UJ ro ( N- -3 ID CD CD CD CP CD 3 CO UJ ID ao 3 ID O' O' ro 3 CO CM ID UJ UJ o N- N- CD ro 3 \

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X r^ ID ro ro ID S p- CO N- o ro ID CM ro LD r^ UJ ro U> U) 3 ao o <P 3 LD (P 3 ao CP 3 v*4 CD CP CD ro UJ CD 3 Pw ro CP

CJ _J CM UJ CO N- ro 3 CD i-i UJ ID co ro i-4 CM LD CD P- UJ N- CD 3 CD CD P- O'

H UJ CM CP CO P- ao CP CD o CM ro 3 LD UJ CP CM 3 P- O' 1 0 CM ro ID Ou CM UJ UJ P- ro CD P- 3 i-4 O' UJ 3 CM i-4 O' CO UJ ID 3 3 ro ro CM CM CM CM CM CM ro ro ro ro ro ro ro ro 3 3 3 3

or CP CP co P- UJ U> ID LD 3 3 ro ro ro CM CM CM i-4

or

•a CD

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— ao ro CP UJ UJ P~ CD r^ ao r- ao rl P- ro

H ro GO CO P- CM O' CD O' 3 UJ 3 CD O' (D CO O' CM CM CD P- CM au LD CO p- CM au UJ

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N ro CD CM P- CD P- ID CD 3 3 ro CD 3 P^ 3 CD 3 CD P- CD CP p~ 3 P- CD CM lit O' 1-4 ro ro P- CP UJ 3 ro CP CM i-4 3 CM CM CD 3 3

CD \ CL P- ID CD CO 3 O' P- 3 U) CM O' UJ CM LD LD CM 3 CM 3 H CM P- UJ CP ID UJ

O CO o N P- CD vO 3 3 UJ CP ro p^ ro O' ID O' 3 O UJ ro • LL <X CD ro ^—1 3 i-i CD CM UJ au U' 3 3 3 U' P- O' CM U' CP ro P~ CM P- ro CP UJ CM CD p*. LD 3 CM CD CP au CD r^ p- UJ UJ LT* ID ID 3 3

CD Cj CU

ao 3 *-« CO lro i~\ O' UJ 3 ro C\J T-t CD O' co P~ P^ UJ ID ID 3 3 ro ro CM CM CM CM y-4 1-4 i-4 o CD CD CD CD CD CD

O CDO CD CD ro ro CM CM CM CM H i-4 i-i

II

CL -J —I 3 CO CM 00 r^ ao ro CM UJ 3 p- P- 3 GO 1 3 O' P- CD CM ID ID vO LD O' p. ao UJ ro ro 3 P CD P UJ U) U) 3 CD in CP CD "H

p o o O' 3 CU O' p- ID 3 ro CU CM CM ro li'r P~ i-< ID CD P UJ UJ aj ro ro CP i-4 O' 3 UJ 3 P 3 OU ru O' P 3 o in O' 1-4 0J CD ro CM CP

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X ID UJ r^ p- 0O O'

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H a' Uj ro i-4 U' O' OJ in

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V 3 3 3 3 3 3 LD LD ID ID ID ID ID ID ID UJ UJ UJ UJ UJ UJ P P- ao ao O' O' o CD 0J ro 3 3 in UJ P p co CP CD i-4 0J 3 in UJ -J o CD CD CD CD CD CD O CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD -r4 ,H i-4 H (M CM (M 0J OJ CM

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inX -1 UJ UJ CO ID OJ CO 3 UJ 3 LD

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p CM in P P P ro

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V UJ iH P- 3 CD UJ CM CO ro 03 ru UJ aoO <sD CD ao 3 ao i-4 CM

O U) O' CD O' u> 3 ro UJ ro U> ro in 'tH o ro CO LD in P 3 UJ CM ro

CD -J P- LD ao ID tH CO 3 P- 3 CD UJ ro CP ID UJ CM P- ro ao ro P- UJ O' ro P- in CD in

p 3 ao in ro t O' UJ ro CP

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X i-4 v-r CD CD CD CP CP CP ao CD CO p- p. UJ U) UJ ID ID 3 3 ro ro CM CM CD CD <P O' ao CO

p P UJ UJ UJ in in in in 3 3 3 3 ro ro <LX

CM CM CM CM CM CM -< i-4 i°4

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ao CD CD CD CD CD CD CD CD CD CD o CD CD CD CD

O CD CD CD CD CD CDO CD CD CD CD CD CD CD CD CD CD CD CD o CD CD CD CD

O o CD CD CD CD

vD CD CD CD CD CD CD CD CD CD CD CD CD CD CD

O CD CD CD CD CD CD

O CD CD CD CD CD CD CD CD CD CD CD CD CD o CD CD CD CD CD CD CD CD CD CD LD UJ o CD CD CD O CD CD CD CD CD o CD O O CD CD O CD CD CD CD CD O CD CD CD CD CD O CD CD CD O CT CD CD CD CD CD CD CD CD CD CD CD CD o CM o CJ O CD CD CD CD CD CD CD CD CD CD CD CD CD CD O CD CD CD CD CD CD O CD O CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD O CD CD CD CP CD 1-4 CM m 3 IP aj P- au CP CD i-1 CM m 3 LD UJ P- ao O' CD tH CU ro 3 U' UJ P- au CP CD i-4 OJ ro 3 in UJ P- OJ CP CD OJ 3 UJ ao CD

i-4 i-4

H i-4 tH 1-4 i-4 i-4 CM CM CM CM CM CM CM CM CM CM ro ro P) ro ro ro ro ro ro ro 3 3 3 3 3 3 3 3 3 3 in in in in in UJ

315
Table

27.

Thermophysical

properties

along

isobars

(Continued)

cl

CL

CD

II

CL

LUx

»—UJ

X o p ro p U> CP t-4 in CM t—

4

CM J- P CM CO UJ in in UJ (P ro CP P P CP CM in CM -3 CVJ in ro UJ ~4 CP CD CO O' 4 ro UJ O P in ro CD

UJ c\j in in UJ CD CP CM 3 p CD ro UJ CP ro U) CD -3 ao CM UJ ^—4 in CD in CD UJ CM CP UJ >3 CM yi o CD CP CP CP O' O o O CM ro 3 in

l/J CM 7-4 o CP CO p P UJ in IT* 3 ro CM CM y4 o CP CP ao ac- p P UJ UJ in in -3 3 -3 3 3 3 3 ro ro ro ro 3 3 3 3 3 3 3 3 3 \

X

cm CM CM tH H t-4 y-i H r4 tH 7- -4 t-4 H yi

LL o O' ro CM CO CM 3 in UJ p ao yi -3" CD P u> CD CM CD co CM ro UJ -3 ro UJ CM O' 3- o O' 3 CD UJ ro in O' O' ro ro in in CD ro ao O' O p IO CM ro 3 in CO -4 in O UJ ro CM tH CM ro UJ CD UJ CM o CD i -3 ro aj co P CD P UJ P in UJ 3 3 UJ o UJ ro yi in O' O' o CD CD OD ao CO CD CP CP CD o yi CM ro J- in UJ CD CP H ro in p IP CM in CP yi ro in in in 3 ro CM o O' CO P p UJ UJ UJ UJ UJ P p ao x iD U> kD UJ UJ U> U) UJ p p P P p P p p P p CD 0D cn or CD CP CP CP CD CD CD CD CD CD CD fD> CP CP O' O' CP CP CP CP CP CP CP CP V

“> H rH *-4 H tH yi > <D UJ ro UJ CP in 3 CP CM ro ro CM tH UJ in CP CP vT UJ O U) UJ in P in CM -3 ro ro O' <D CO CP CD (M 3 p o ro P T-l in ro O' ro in 3 o J- ro 7-4 CD in ro tH CP CP CP o CM Ift CO ro rO 3 ao UJ ro vl o H p UJ CM CD CP ao CO CO <P O' CP O' CD CD o yi CM CM ro ro ro o li' in in J- 3 J- -3 ro ro ro J- 3 -S’ -3- in in UJ P P CO CP CD "4 CM ro U) P ao co O' CD yi CM ro 3 in UJ ao O' CD CM 3 UJ ao CD CM X

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J- -a- 3 J- 3 J- -

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J- •3 J- J- 3 3 3 j- 3 3 -3 3 -3 *3 in in in in in in in in in UJ UJ UJ UJ UJ UJ UJ UJ UJ P P P P P P CD 00

(/) yi o CD CO CM CD in UJ p p CP 3 CD -3- CD U> CD ro CD CD CM ro UJ j- p ro in CO 3 O' CM o in 3 p ro p UJ in O' CP ro ro UJ 3

V UJ in UJ O CP CD 3 tH J- U) o aj ro UJ ao y* P UJ o <P .3 in in ro y* yi ro ro CP o in T-l <P P in in p ro CM UJ in CP UJ o CM 3 ao

-J CM ro CO CO CM ro U CO CD p ro CP ro U> <P o CM o (P CO P UJ in CM co in CD in O' CM 3 UJ P p p UJ 3 «-4 u> CD ro r P CM ao 3 CD in o 3 CO CM UJ CD ro p o ro P O ro UJ CP CM -3 P O ro UJ CP CM in p CD ro in p CD CM 3 u> CD CD CM UJ O ro P CD V p CD 00 CP CD CD t-4 7-4 t-4 CM CM ro ro ro J- 3 -3 in in in in U> UJ UJ P P p p CO co CO O' CP O' CP CD CD CD CD o y-i *-4 CM CM CM ro

** t-4 ** *"* T-* y-i ** yi H yi tH "4 ’rH yi H -4 CM CM CM CM CM CM CM CM CM CM CM CM X o 3 3 t-4 t-4 tH CD CM CM P CO P ro <P UJ P ro UJ CD p y-4 CO in tH CD ao H ro CP P O 3 CM in CM 3 in ao CM CO yi 3 CM CM CD 3

£ ro ro UJ CD in CM in ro UJ UJ J- yi P in in CP p CM ro 3 J- p in CM CM O' ro CD UJ <x> CD ao CM CM "H CM in 3 CO yi ro O' in UJ in V 3 ro tH CD CO p UJ in in in U) CO y* -3- CP in CM y-i CM 3 CO CM ro P <3 in p CM P ro CO ro in P P UJ 3 yi CO 3 yi ro in CP 3 yi “5 CM p 3 7~i p 3 t-4 CD in CM CP UJ ~T CD UJ -3 CM CD <D UJ in -3 ro CM CM CM CM ro ro 3 3 in in in in in in in 3 3 3 ro CM *-*4 y-i yi

UJ UJ p ao CD CP CD CD 7-4 CM CM ro -T in in UJ P cc O' CP CD y4 CM ro -3 in U) P co O' CD yi CM ro 3 in UJ p CU O' CD yi r*"» in p O' yi

yi ^4 •H yi •H ^4 y* wi rH v4 CM CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro ro 3 3 3 3 3 3 in

LU -J ro ao ao tH CM p J- CD -3- in y4 ro r4 J- CM in 3 UJ P TH ro ro co o in •3 <3 in CM ro in CO *-4 3 CO O' p CD p 3 UJ ro P 3 O' X CD CD CP CP CP CD J- yi H UJ P -3* O' CM in <D ro CD in in CD CM CM in CM P CD O' *-4 yi UJ UJ CD CM UJ in CP CM 3 CM CD UJ CM CM P in 7-4 CO in ro CD CO UJ 3 ro ro ro in p CD in CD U) UJ <r UJ ro ro in O' ro UJ CD ru CM •H CP in o 3 CD yi in OD in ro CM 3 CD

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ro y4 O ao p UJ in 3 -3 ro ro CM CD CD p UJ 3 CM yi o» P 3 *-4 ac in CM

LT> in UJ P p CD <P CP CD tH 7-4 cm ro J- -3- in UJ P P co <P CD y-i CM ro j- in UJ p co O' CD yi CM ro 3 in UJ UJ P O' yi CM 3 UJ ’* t-4 ** rt H "H H CM CM CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro ro ro 3 3 3 3

O -J CO U) CO tH p in P CD p CD CM CD P P ro y* ro UJ CO in UJ CM P P UJ O' ro CM UJ O' CP UJ 3 ro ro 3 in UJ O' CD H P P ro UJ o O t-4 CD CD CP in in 7-4 p yi 7—

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UJ CM UJ CP CD CP p ro CO UJ CM in ro ao P O' p CM CO U) in 3 in ro O' ro m ao O' in u> 3 co in CM UJ P X in O' CO o -4- tH in CP o CM t-4 in CP H CP H ro UJ co P -3 ao ao in co <XJ >3 UJ ro CM ro ro o CM CO in 3 ro ro 3 UJ ao ro CO 3 CD in o _J ro in CP CM t—

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p CD 3 UJ 7~

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1 O' CM ro UJ CP CM UJ -4 UJ CM CD 3 CD p -3" CM CP P in ro <P CD p UJ in -3 «3 ro ro ro ro ro ro ro ro ro ro ro ro ro ro 3 3 3 3 in a

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(_J p ro CP ro CD CP 3 co LP UJ UJ o ro ro t—4 CD CP p CD p aj <3 ao CD O' UJ LT UJ 3 p CM 3 O' 3 3 p CD CM yi UJ UJ CD ro p <D UJ \ O' CM UJ o tH p ro 7—4 CO 7-4 P in CM ao CM CM CP CM o ro »—

4

CM tD P yi p CO ro <-4 ro O' CO yi UJ ro ro 3 UJ CD 3 O' 3 o ro ao ro O' UJ

LL <1 CD ro CM U> 7-4 7“4 ro UJ CM ao UJ U' JT in UJ p CD ro UJ CD -3 OD ro U' 3 CD p J- ao UJ in ro CM *-4 CD O' O' ao p P p UJ U' in 3 3

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J- 7—I ao in ro 7-4 CP p UJ -3- ro CM CD CP ao ao P UJ UJ in -3 -3 ro ro ro CM CM CM i ^—4 T—

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^—4 yi ^—4 CD CD CD CD CD CD CD CD o CD o

ro ro CM CM CM CM tH t-4 t-H t-4 t-4 t-4 H

_J 3 ro in O' in ro in O' P CD P CD CO ro UJ P co CP ro P CM ao O' CP in 3 o in UJ u> 4 CD tH 3 in 7-4 t-4 3 CO CM P P O' in <P in o O O' 3 r-4 O' P in ro (M CM t—

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CM CM 3 UJ O' ro CO in ro CM 3 CO 3 3 CD p yi *-4 UJ p ro ro in <D yi 3 P O' CD CD CD CU CM CM O' CM ro > X in UJ P p CO O' CD -4 CM ro 3 U> UJ p CD CD yi ro in P O' yi 3 P CD 3 O' 3 O' in CM O' UJ ro yi co in CM CD P 3 CD 3 P O' CM 3

p 3 3 3 3 3 3 in in in in in in in in in u> UJ u> UJ UJ UJ P P P CO CD CO O' CP CD H rH CM ro 3 3 in UJ P P CO O' CD t-4 CM 3 in

_J CD CD CD c_> CD CD CD CJ CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD 'rH 7—4 H *"• ** t-4 7-4 7-4 t-4 7-4 t-4 CM CM CM CM CM O CD CD CD CD O CD CD CD O CD CD CD CD CD CD CD O CD CD O O O O O CD CD CD O CD CD CD CD o CD CD CD CD CD O O CD 0. 0.

CD CD CD z -J H P CD 3 O 3 in 3 CO P O' CD ro <t) ro CO -4 UJ in in UJ in CM CP CD P in m O CM in ro in UJ CM ao 7-4 P 7* CP U> CM O' P CM

LU p P CM O' in CM co 3 CD in o in CO CM 3 in UJ in 3 *-4 U> CD CM CM a UJ O' yi CM ro in o CO CD P CO ro CM ro CO ro ro O' CD 3 CM ro o -J P in t—

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CD in CD in CO 3 O P ro O' in «H P ro <o 3 CP 3 CP ro p CM UJ CD 3 O' ro O' 3 CD p 3 t—4 CD UJ 3 CM CO UJ ro CP X ^—4 y-i CD CD CD CP CP CP OD CO CO P P UJ UJ u> in in 3 3 ro ro CM CM CD CD O' CD co p P P UJ UJ UJ in in in in 3 3 3 3 ro

CM CM CM CM CM CM *-4 yi yi yi yi »-4 yi yi yi yi yi yi yi yi yi yi

— *: CP CD CD CD O CD CD CD CD CD CD CD O CD CD CD CD CD CD CD O o O CD CD CD o CD CD CD o CD CD o o CD o CD CD o CD CD CD CD o CD CD

y-i O CD CD CD CD CD o CD CD O CD CD CD CD CD CD CD CD CD o CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD o CD CD

UJ OD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD o CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD O CD CD CD CD CD CD CD o CM O CD O CD CD CD O CD CD CD CD O O CD CD CD CD CD CD CD CD CD CD CD CD O CD CD CD O CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD

CP CD y-i (VJ m 3 in UJ P au O' CD >•—4 CM ro 3 in UJ P CD CP CD yi CM ro 3 in UJ P OD O' CD t—4 CM ro 3 in UJ P CO CP CD CM 3 UJ ao CD

yi yi y-i y-i y-i yi y—i yi yi CM CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro ro 3 3 3 3 3 3 3 3 3 3 in in in in in UJ 316
Table

27.

Thermophysical

properties

along

isobars

(Continued)

.T

-X o X

XX cr 3 ro in. CDK n- ro in o K inm

X ro CM N- in 3 in CO CM in CM 3 ^4 ro cr CD 3 CD cCO cr

O —4 3 ro CD ao vD 3

LlJ cm in in

x CO CD CM in n- CD ro o -3 »—

in cr ro CO CM r^ CM CM CO 3 H CO vD 3 CM CM *—CD CD CD ^—4 ( CM ro ro 3 in

in CM i—

O cr CO CO NX in in 3 ro ro CM i-l o O' CP CD CO r^- r- X) vX) in in in 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 VX

CM CM CM i—rH iH i—

^4 i—

iH 1-4 i—

iH

LLx CC O' in CO cr QU oo n- N- cr CM in n- in 3 in r- ro

X UD ^—4

m o ro ro CO O' “4 ao cn ro cn CO 3 3 vD CD CD in O' rX N C\J (\J ro ro in o 3 cr in CM o O' CD i-4 3- r^ CM CO in ro ro 3 cr cr -4 CD cr H CO cr CD n- vU vX) cr 3 CD n- X) X) cr in ro ro O GO GO CO CO CO CO cr cr cr o CM CM 3- in X Pw cr CD CM 3 X CO o ro CO CD ro ro 3 ro fM CD cr CO r^- n- n- X) X) X) vX> n- ao cr

TX

X

X

X

XX

X

X

x r^ N- N- N- N- n- ao CD CO CO GOmm cr CD o CD CD CD CD CD

O CD cn cr cn cr cr cn cn cn cr cr cr cn

V

"5

T-l t—

*-4

H

IT, CM cr CM

X i-4 CDX CO cr cr CO N- 3- CD 3 in 1-4 i—3 o cr 00 O' in ^-4 CO CO 3 ro ir< r^»

O ro vD CD 3 CO CM o ao 3 ao CD <r o V x 3 iH O' X 3- CM CD cr <r a CM in cr 3- cr in CM cn X 3 iH CD h n- v£) CM cr CO ao CO CO CO cr cn cr CD O o tH CM CM ro ro 3 ro O x in in 3 3 3 3 3 ro ro 3 3 -3 3 in in X QJ O' O 1-4 CM ro vO r- eo O' o t-4 CM ro 3 lf‘ a. O' CD CM 3 x> 00 CD CM XV 3 3 -3* 3 -3- 3 3 3 3 3 3 -3 3 -3 -3 3 3 3 3 3 3 in in in m in in in in in vO vX) vX) i£ v£ vL X) vX) X) h- h- N- ao CO

if) CO n- in CM CM

X -3 in CM CO CM r*»X 3 a' 3 CD O' cr o GO iH

X ro vO CO CD CM cr CM r^ t-4 in 3 CO

O CO O' CD in CO in r- ro vH CM o K- CO ro X in CM in X CD N- 1-4 ro 3- CM cr 1-4 cr iH n- CM v£) O' ro ro CD CD 3 cn vX) 3 in r^ ro 3 © 00 ro CM r^ tH in CD

_J ro C\J r- CM CM CD in r^ nX CM CO CM in n- cr cr CD cr cr 00X in ro CM CD cr n- in CM CO ro CO CM in n- O' CD o CD CD CO 3 o 3 CO 3: n- CVJ CO 3 O in CD -5- CO CM X CD ro r^ CD ro x cr ro in CO 1-4 3 n- o ro vT 00 3 N- cr CM 3 O' »—4 ro vX) CO O Lf O' ro X) cr

v. n- CO CO cr o CD iH

H CM CM ro ro ro 3 3 3 3 in in in

X vX)X r- n- n- f- CO CO CO CD cn cn cr cr CD CD CD CD «rd ^—4 CM CM CM

iH 1-1 i-4 i-4

H i-i i-4 1-4 1-1 1—4 i-4 iH iH i-4 iH i-l 1-4 1-4 i-4 <r-1 ^-4 t-4 ^-4H 1-* T-4 •*-4 r4 ^—4 IM CM CM CM CM CM CM CM CM CM CM

X -J X) in 3 cr in o ro o ro .9 .1 r^» cr cn

X ro CMX 3 cr ro CM CD .9 .3 CD cr

X

X cr ro 3 CD CDX O' cr CD CM iHX CM iHX ro

X CM CM in ao ro CD cr CM or* *-4 n- CM r^ ro CM n- r- 3 X CM

X ro

X CM roX CM ro -TX ro

X r*.

X IH O' CDX

X ro r- n- 3

cr r^ in ro CM (T cr ao cn o ^-4 3 n- CM CO

X ro ro

XX 3 iH i-4 ro O'X O' iHX

X ro

X O' o CD crX

X ro

O

XX ro n- ro i-^ “5 CM n- 3 a. in ^—4 CO in CM o 3 iH cn X 3 CM o X X X 3 ro CM iH 1-4 i-4 CM CM CM ro ro ro 3 3 ro ro ro ro ro CM 1-4 i—4 o CD CD

ViJ vo n- 40 a.' cn CD CD CM ro 3 in in a.^ n- <Xj O' O' CD 1-4 CM

X 3 X

X rX cn o iH CM ro 3 XX nX

X

X iH ro

X nX iH r4 iH CM CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro ro 3 3 3 3 3 3 X

LU

—

J (T - 3 in O' 3 X) in cn 00 ro CD CD ^-4 CM CM

X PX CD cr

X

X 3 CM ro i—4 3 X i-^ CO

X

X 1-4 roX CM CD CM

X

X

X CM 3 X 3 ro CM CD cn O' CM r^ X) O' <3? ro X r^ r^ r^ X H X X X X X X X CM CM CD 3 cr 1-4 3 r- X ro X 3 CM X X ro CD r^ 3 CD CM O' V 3 SO 3 *-4 cn X) 3 CM •H CM 3 r^ K ro ^4 CD i-4 ro ro CM ro X n- cr CM ro ro CM o X CM X X ro o X X CM X “> ro ao in co in CO m CM O' XI ro O n- 3 CM X U* ro i-4 O' X X 3 ro CM i—

1—4 CD O'

X r- u* 3 CM 1-4

X Is- X ro U'

X 3 iH in in x> r- n- CO O' cn O t—

CM ro 3 3 X

XX N»

X cr CD CD i-4 CM ro 3 X

X nX O' cn o iH CM ro 3 X

XX nX o CM 3 X

d-4 wH iH 1—4 iH *-* CM CM CM CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro ro 3 3 3 3 O 3 lO n- CD 3 r- 3 o in O' X in 3 X X X X X X X X O' i—4 o X fO ro O ro X <T 3 3 X X i-4 CM X X CD CM a X X 3 o O in N- in *-4 ro CD 3 n- in r- o CM X X ro X iH CM 3 CM 3 N- CM X ro i-4 O' x CM CM X r- CD ro CD X X X 3 X 3 X X X CD

LL

X

V. CM CM 3 CD ro ^-4 X) CM in in CD in CO

XX CM

X

X

X

X cn crX

X

X CD cn i-4 S- 3 o ro CM

X CM CD

X n- N»

X

X ro r- CM N- ro

O -1X

X ro

X

X i—4 CM

X

O

X 3 K- CM CD i—4 3 CD r*-X n- CD 3 CD

X NX i—4 3 CD

X 3 ro CM CM CM ro 3 3 X

X

X i-4 toXX 1—4 1 X CM 3 X X ro r^- i-4 N- CM X 3 i-i X X CM CD r- X ro CJ CD X r^ X X X 3 3 ro ro ro ro ro ro ro ro ro ro ro ro ro 3 3 3 3 X

c* O'X

X r>wX

X

X

X 3 3 ro ro ro CM CM CM CM i—

iH 1-4 iH i-4

Ctl

*3. CD X 1— CD CM nX

X

XX

X r^ CM

X

X n- CM

X ro

X

X CM iH roX CM i—4

X CM 3 ro

XX

X

X r- r^- ro CM 3 nX n- O'X

X

X CD i-4 3 X U^ X X r^ 1-4 CD X ro 3 X X 1—4 u> r-w X ro U^ CD 3 ro 3 X X CM X X ro n- n- CM CD X ro 1—4 O' ro o X X CD 1-4 X 3 3 X ro nCD \ Or n- X CM ro iH X ro X CM CD X 3 X X n- a O' CM CD CM X X CM X CD X ro X 1—4 CD iH X ro 1—4 CM 3 X a X O X X CM r- ro X • X <L O' ro CM X CM i—4 ro r^ CM O' n- X uv X X X 1-4 ro n- iH X X 3 CD X CM X X CM CD X X 3 ro CM 1-4 CD in O' X X n- X u_; X X 3

CD o Oj

CDX i—4

X

X ro i—4

X

X 3 ro CM i—4 o XX

X rX

XX 3 3 3 ro ro CM CM CM CM i-4 i-i i—

iH i-l i—4 o CD CD CD CD CD CD

X CD CD

CM ro ro CM CM CM CM i—4 i-4 i—4 i-4 i—4 i—4 iH 1-4

ii

CL

—1 -J CM ro CM CD iH

X CM 3 CD (\J

X ro 3 ro i-4 CD CD 3 ro CM i-4

X rH CD CD 3 X CMX 3 XK 1—4 ro

X 3 X n- CD

X ro ro i-4 n- 3 X o <_> o 3 1-4 X n- X ro CM 1-4 i-H i-4 i-4 ro X X CM r^ ro CD X CD ro X X X X CD i-4 X X X X ro i—4 X n- 3 i-4 X ro X X X X r-» no

b~ T>

X

X r^ nX

X CD i—4 OJ ro 3 XX r^

X CD i—4 ro IX)

XX 1-4 ro

X

X ro r^ CM r^ no

X 3 i—4XX i-4XX CM

X

X i—4 3 XX CD CM 3 3 3 3 3 3 X X X X X X X X X X X X X X X n- r- r- n- X X X X CD CD i—4 ro CM ro 3 3 X X X r^ X X CD 1—4 ro 3

CD CD o CD CD CD o CD CD o a CD CD CD o CD CD CD CD CD CD CD CD CD o CD CD CD CD 1—4 i-l i—4 i—4 i“4 i-4 i—4 ** i-4 1-4 i—4 CM CM CM CM

CD

CD CD o CD

O

O o CD

a CD CD CDO CD CD

O CD o o CD o CD CD o CD CD CD CD CD CD CDO CD

O

O

O CD CD o o O CDa CD

O CD

a

O

in Z -J

X iH

X 3 X ro ro

X iH

X

X CM

X

X

X

X

X

X o a ro

X

X

X n- ro iHX iH

X nX 3 CD

X ro CMX 3 ro

O iH PO 3 X

—4 UJ n- ro CD

X ro

X

X CM ro N, »-4X

X CD o X 3 X CM ro ro 1-4 r- no

X

X 3 CD

X CM

X

a 3 CM ro

X CM CD o 3 ro

X ro CM 3 n- X CM X X i—4 X X i—< X 3 i—4 r^ ro O' X OJ n- to X 3 o X CD X X 3 X CM n- CM X CM N- 3 CD n- 3 ’ rH O' N. X i—4 X X ro i—4

t: i—4 i—4 i—4 CD o a

XXX

XXX N- hX

X

XX

X 3 3 3 ro ro CM 1—4 i-4 CD o X

X

X

X n- r^X

X

X

X

X

X

X 3 3 3 3

«3T

CM CM CM CM CM CM iH iH ^•4 iH iH i-4 iH iH i-4 iO •f*4 1^ iH iH

X

h- i—4

O CD CD CD CD CD CD

O

C

O CD CD

O CD CD o O CD CD CD o CD CD CD CD

OO CD CD CD o CD CD o o CD o o o CD o a CD CD CDO

r*> CD CD CD CD o CD CD CD CD CD CD

O CD CD CD CD CD CD CDO CD CD CD CD CD o CDO CD CD CD CD CD CD CD CD o CD CDO o o CD CD CD CD o X CD CD CD O CD CD CD CD O CD O CD CD CD CD CD O O CD CD CD CD CD CD CD CD CD o CD CD CD CD CD CD CD CD CD CD o o CD o CD CD O CD o CM CD CD CD CD CD CD CD CD O CD CD CD CD CD CD CD CD CD O CD CD CD O CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD o CD o O CD CD CD X CD i-4 no ro 3 X X N- X X CD 1-4 no ro 3 X X r«w X X CD i-4 CM ro 3 X X N- X X CD i-4 CM ro 3 X X n. X X CD no 3 X X CD

i—4 i-4 i—4 iH iH i—4 i—4 i—4 i—4 1—4 CM CM CM CM no CM 00 00 00 CM ro ro ro ro ro ro ro ro ro ro 3 3 3 3 3 3 3 3 3 3 X

XX

XXX

317
Table

27.

Thermophysical

properties

along

isobars

(Continued)

ETHANE

ISOBAR

AT

P

=

220.0

eAR

I

I

IT o CO <P 3 in t4 t-4 -S’ CP CO CO CD 3 cp vO 3 3 in p. ^—4 P- 3 3 in SC ro ao CM o *—4 P p 4 CP CD 3 C CO ao CO eo CD vi CM ao in ro

UJ CM LA vi p (P t-4 ro in CD t-4 in CO t-4 in CP ro r^ -—4 vO CD in CD in CD vi 4 00 in CM CP p Vi 3 3 ro ro CM CM CM CM ro ro ro 3 3 in vi

(/) CM t-4 CD CP CD CO p Vi) in IX> 3 ro ro CM *“"4 i CD o CP CP © ao p P vi vi in in in 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 p

r

CM CM CM t-4 t4 "H t4 t-4 -1 t-4 t-4 t—

4

^—4 -—4

CL P in p 3 P CP ao in CM CP Vi) ro CD ao LTv 3 <P in O' ro vi ro ao O' P O' -4 p 3 3 in vi O CP P CD ao CD ao 3 O CD O' 3

CJ p (M CM CM ro 3 Vi) <P ro ao ro CD CO P- vi> r^ cr CM in CD in CM CP <c O' in 3 CP in co CP in P m CD 3 p CP ro CP in ro CM ro P ro CD CD o CO CO CO ao 00 CO ao CP CP o t-4 CM ro 3 in P* ao O ro 3 vi CO *“4 in vi ao CP o -4 •H «H CD CP CD ao P P p P p P ao CP CD X vD vi vi vi vi vi vi vO vD p p P P- p. P- r^ r^ r^ CO er> eo CO cn ao CP CT' <P (P CP CD CD CD CD CD CD CP CP CP CP CP CP CP CP CP CP CP CD \

“5

4 H 4 r4 t4 O CD vi CM in ao ro ro CD CD t4 t-4 CD ao vO CM in vi) H ro CD vi ro CM in cr vi CM CD in vi aO ro CO ro ao ro CP 3 CP 3 O' p 3 ao CP ao o V vD in ro CD P in ro T—

4

tH t-4 CM 3 vi) o in CD vD ro O 3 CM t-4 CM p in H (P ao p p P ao ao CP (P o CD wH CVJ CM ro 3 3 3 3 o in in in in *3- -S' -3 -3 3 -3 3 3 3 in u> vi) vi) r- ao co CP CD CM ro vi P p co CP CD y-< CM ro 3 in p CO O' CD *-4 CM 3 vi ao CD CM X

p

3 3 3 3 -3- -S’ -3 -3 -3 -3 3 3 3 3 3 3 3 3 3 3 3 in in in in in in in in in Vi Vi vi vi vi vi vi vi vi P P P P P P ao 00

l/J CL CM p CP -3- Vi -3 p in CM in (P 3 ao fP ro ao ro vi in vi p- CM CM CP vi in CP p in Vi CD CD CM ro ro in 3 3 CM *-4 CO ro ro vi O' 3

V P ro ro p in ro CO -3 vi P CP in ao cc CO CP v-4 p. vD CD CP 3 vi in CM o cr 3 vi 3 P in vi CD P p o P ao 3 in ro P ro t-4 —1 ro t-4 Vi) in CD t4 CO ro in in p) CD in CP CM 3 vi) vi) vi Vi 3 ro »-4 O' p in CM CD p 3 CD vi *-4 Vi CP CM in vi P 0D ao ao vi ro ao ro P

X p CM 00 3 CD in CP -3 ao CM vO O ro vi) CD ro vO CP CM in ao 3 vi CP CM in CD CD ro vi CO *—4 ro in CO o CM 3 vi ao CD 3 CD in CO p p CO CO CP CD CD CD t-4 t-4 CM CM ro ro ro 3 3 3 3 in in in Vi vi vi vi P p P OD co ao ao <P CP CP O' o CD CD CD CD «rH -4 CM CM CM

t-4 T~1 *"* t-4 rH t-4 r_1 *-4 4 *"* ^—4 1 ** t 4 H ‘rH l\) CM CM CM i\j CM CM CM CM CM CM X -1 vO CP 3 3 -3" ro <T p P (P CM vO vO CD vO vO P- CO CO P- 3 CM vi CD ro <c o wM co in CM in CD 3 in Vi to in CP 3 ro CP 3 in X CD ro Vi) CD Vi) -3 in CM (P 3 vi) CO CD 3 CP ao O' ro 3 ro CM 3 in p 3 p ro CD P CD ao CO *-4 CO O' Vi 3 o CD CP ro 3

p CT in ro t-4 CD CO p vi vi vO vO CO CD ro ao ro <P r- P- p- CD 3 CD <o ao *—4 p in 3 in vi ao CP H CP P in ro CD in CD in ro CM

“5 ro CO in CM CP in CM CP Vi) ro CD p in CM CP P. 3 CM CD CO in 3 CM tH -—4 CD CD CD CD CD CD CD -H H tH CD CD CD CD CD CP O' CD ao co

Vi. vi p 03 or CP CD CD t-4 CM fO ro 3 in in viJ au O' CP CD o CM ro 3 u> VO P CD CP CD -< CM ro 3 in Vi P ao CP CD *-4 CM 3 vi ao CD •4 t-4 t-4 tH -4 •H ^1 v-4 CM Csj CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro ro 3 3 3 3 3 3 in

UJ _J 03 3 cp 3 in vi P CM CM ro vi ao CP P- CM CM 3 vi) ro O’ o CP H vi ro ro in vi ro 3 p CM ro CP CD p CD in CP P ro CO CD ro in CM

2- t4 <D vi ro CD ao 00 P p CM ro P- CM vD CD in CM CD CM in ro in 3 in CD CM CD CM 3 ro P ro CD CD P p 3 CD vi O' ro t-4 <XD ao V CO ro CP vi ro CP vO -3 t-4 CP CO P P- P- CP -4 in cr in ro CD CP CD CM vi CM o CD CD CD CD CP co Vi ro CP 3 CP 3 CP ro CM ro in ao 3 ~) ro cc 3 t4 cc -3 t-4 aj in t-4 CL in CM CP vi) 3 CO vi 3 CM O' CO VD 3 ro IM 4 CD cr ao P in 3 ro CM CD cr P vi 3 ro CD p 3 t-4 CP

LT> in vi P P CO (P CP CD t-4 ro ro 3 IT io vi 00 CP CP CD CM ro 3 in vi vi P co (P CD *-4 CM ro ro 3 in vi P (P CD CM 3 in

t-4 t—

1

t-4 tH H r-4 'H CM CM CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro ro 3 3 3 3

Q —1 CM H CT t-4 3 CP ro CO CD in 3 vi CP H in vD P- CM ro cr CO ro P O CM CD ^-4 in H CP vi CM vi vi 3 vi vi CO CD vi -4 co O' P in ro P

o o vi t-4 in 3 t-4 vi ro in in p 3 CD 3 CP CO tH CP H -( o CM vi CM P Vi ro H ao 3 3 CM 3 vi vi vi vi Vi CD CD vi P CM in ro ro \ X P CD in CM CD CD p -3 p t-4 ro CP in CP CP ro r^ CM vi p. in CP CP 3 in CD CD 3 CP CP <X> in <X> vi CO ro CD CO P vi in vi CP CM vi CD o _J CO vO o ro ro CP CD P ao 3- ro in ,H CP o 3 CP r^ vi r^ CD 3 CD CO p CO CD ro CO ro o CO p vi vi vi p CO <o CP CD t—

4

ro in ao CD ro

1 <P ro U' P CD ro CO CM P- ro CP in CM CO vi) ro O ao vi 3 ro t-4 CD ao p Vi vi in 3 3 3 ro ro ro ro ro ro ro ro ro 3 3 3 3 3 in in

(X

<1 cp cp 00 p P v0 in in 3 3 ro ro ro (M CM CM CM -4 ^—4 4 H *—

4

»- o r^ P p CP T-4 in CD 3- CD ro vi) 3 CD in in CM CD P- CP r- vi CP CM vi p o 3 P CD CM p vi CD CM vi -—4 vi in in in 3 CP CM vi

LJ p O' CD CM in ro CO t-4 CP O 3 p- ao in p- P- CD tH aj CO aj vi CM ro O' CD vi 3 3 in ro vi CM CO CD VD U' ro CD 3 3 O' O' CM ro CM

V. Q: CO t-4 P CP p -3 ro CM in ro t-4 cr vi) ro -H in in cr P- CD P- CO ro *“4 CM <o vi CC ro CM in H <X) ao CO CD ro p vi P CD in CD vi

LL <i CO 3 CM in CM CM -3 CO ro CD CO vi) vi) p- aj CD CM in CU CM P- ^-4 vi CM CO 3 CD p 3 CM CD CO vi UV ro CM *-4 -—4 CD CP cr CO P r- vi VD in O CL ro t4 CO in ro t-4 cr P- vi in ro CM *-( CD CP CP ao r^ vi vi in in 3 3 ro ro ro CM CM CM CM -—4 *-4 4 -H T-» t—

4

-—4 CD CD CD o CD CD CD o

ro ro CM CM CM CM t-4 t4 H t-4 t-4 -4 •H

-J -1 CD CO t-4 vi ro ro vi CM ro P p CM ro t-4 Vi CD ro vi CM t—

4

vi CD 3 CM ao in vi 3 CM co CD 3 ro CM CM CP CO in CP <P in in t4 CM O' ro in o o cr ro H CO vi 3 CM tH CD CP CP CD «-4 ro in a' ro ao in ro CM 3 P ro t-4 ro ao P CD vi p CD vi 3 ro CM CM CM t-4 o CP p CM 3 ro t-4 vi

r> X in vi P P CC CP CD t-4 CM CM ro in VD P co CP t-4 (M 3 vi CO CD CM in ao t-4 3 aj ro p IM ao ro CP in t—

4

P ro CP in CD vi ao CP CD t4 t-4 p 3 3 3 3 3 3 in in in in in in in in in in vi vi vi vi vi P P p P ao CO ao CP CP CD o t-4 t-4 CM ro ro 3 3 in vi vi P CO CD t-4 CM

_J O CD o CD CD CD CD CD CD o CD CD CD CD CD CD CD o a O CD CD O CD CD CD CD CD CD CD *"* t-4 *"• t-4 t-4 t-4 t-4 t-4 t-4 t—

4

t-4 CM CM CM

CD CD CD CD CD CD CD o CD CD CD CD CD CD O CD CD CD CD O O O o CD CD O CD O o CD CD CD CD CD CD CD CD CD CD O O O O CD CD CD CD Z -J vi CP in 3 ro t-4 P tH 00 CP in in CP vi in vi CO CP o <P in p vi t4 ro 3 <o t-4 CO P vi CD 3 O P 3 t-4 ro ao ro P t-4 CP CD Vi CM UJ p CC in CM CP vi ro (P vi CM P CM p t-4 3 p CP a CD CP 3 CD 3 P CP O' <c vi in ro ro in CD P CO t-4 CO CO o 3 t-4 <P t-4 p CP ro tH

-J p in CM ao in CM ao in (M ao in T—

4

ao 3 CD vi ro CP 3 o vi CM P CM p CM p CM p CM p CM CD ro CP vi CM (P p 3 CM (P Vi CM CP P in X T—

4

t-4 CD CD O CP CP cr co ao ao P P P vi vi in in in 3 3 ro ro CM CM t-4 tH CD CD CP CP CO ao p P P vi vi vi vi in in in 3 3 3

CM <\| CM CM CM T-4 t-4 T^ tH tH t-4 T—

4

T^ t-4 t-4 t-4 tH tH t-4 tH t-4 T-4 t-4 t-4 tH t-4 t*4 T-4 t-4

4— * CM CD CD o CD CD o CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD o CD CD CD O o CD CD o CD CD CD CD CD CD o CD o CD O CD o

P CD CD CD CD O CD CD CD CD CD CD CD CD CD CD CD CD O CD CD CD O O CD CD O CD O CD CD CD CD CD CD CD CD O CD CD o O o O o o CD o CM CD CD CD CD CD CD CD CD CD O O CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD O o CD CD O CD CD CD CD O CD CD CD CD CD CD CD CD CD O

a ro CD O CD O CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD O O CD O O CD CD CD CD CD CD CD CD CD o CD CD CD O CD CD CD o o CD CP CD tH CVJ ro 3 in 'JJ P CO cr CD tH CM ro 3 in vi P CD CP CD r4 CM ro 3 in vi P CD O' O t-4 CM ro 3 in vi P ao cr CD CM 3 vi ao CD

t-4 t-4 t—

4

t-4 t-4 t-4 t-4 t-4 t-4 t-4 CM CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro ro 3 3 3 3 3 3 3 3 3 3 in in in in in vi

318
Table

27.

Thermophysical

properties

along

isobars

(Continued)

.,T X

%

3 o or & p rH r^ CD (VJ O' ao CT (VJ PO o rH y ao ro rH CD rH -3 CT* in rH r- in p rH CD ro co CD <P -y o K~ vD *X) n. P^ CD in CD kD ro LU (VI P P <XD p rH -3 P CT (VJ p CP ro rH in CP PO CD PO ao ro CO ro CP in rH CO in PO rH CP P- 'X) in in in y y y y y in in \£> kO p- U? (VJ rH o p CD CD P in in y ro ro (VJ OJ rH CD O CP CP CO CD n- P P P in in in in y J- -y -y y y y y y y y y y y y y V

x

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T-1 -1 tH tH T^ iH

— tH -1 T-l T-4 T-l T-l CM CM CM CM CM CM CM <M CM CM CM ro ro ro ro ro ro ro ro ro ro 7 7 7 7 7 P

UJ 7 CP CDX

a ro CM 7 p ro P CP 7 X

X cr CM cr P P CD O' ro P P ro P cr- 7 7 P 7 X ro - - 7 O' CM

p 7 CM 7 CM CD P 7 CM 2 7 tH rj 7 p X CD. p r»j 7 O' CD P cr cr CO 7 CD P CD ro X CD 7 CM X ro P CM 7 t-1 Tl 7 CO CM P N O' CP cr O' CP 7 cr CO P P X O CP P tH X ro CD p no CD X P 7 ro ro 7 P CP CM X CM co P 7 7 P O' ro CO ro O' P T-l X 7 O P CM an 7 o P O' CM X 7 ro

“> 7 X 7 T-l

X 7 T-l

X 7 t-1

X 7 co

p CM O' P or T-4 O' P 7 CM CD CL

p

p ro <M CD CP CO

p P 7 CM tH o co

X P CM CD

X P ro P p P X X CO CP cr CD tH tH CM ro ro 7 P P vL X CC co O' CD t-4 CM CM ro 7 p P X X <o O' CD T-l CM io ro 7 p P CO CD tH ro P

tH T-1 tH tH T-1 tH T-1 T-4 T-1 T-4 T-4 T-l CM CM CM CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro 7 7 7 7 o CM CO CD CM 7 CO CD ro P 7 7 O' P ro O' CD p CM p ro P iH CO t-4 P p X p P tH O' ro 7 CD p P CM CD p P ro X P P ac O' a o T-1 7 CP O' 7 P O' CM p X tH CM CP P X CD CO CM CD CP' CD 7 P P T-1 P ro CO 7 ro CO CP CD CD T-l ro O' T-l CM p CD CD CD X 7 P X X X P T-l X ro CP P <o T-l ac P CM tH CD CO T-1 co P ro O' T-l T-1 P 7 X 7 ro p CO ro CO CM p X P O' CO T-1 O' O' T-l P CM X ro T-l CD CD

Q_X

a _J O' P T-1

p P CM 7 CM ro CP O' CM CO P ao T-1X P 7 p O' ro CP P P p

p CO CM P CM ao

p ro t-4 CD CD CP CP CD

O T-1 CM 7 P cc CD » CD P X O' CM P o P CD p tH OJ 7 T-l aj p ro T-4 O' X p 7 C\, t-4 CD O' p X X p P P p P P P P 7 7 P P P P P P p P

CL CD CP CO

XX P p P P 7 7 ro ro ro CM CM CM CM T-l tH T-l T-l T-l t-1 T-l <z tH

cr7

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CU i— tH CP CM CP P ro

p CO CM ro P ao i-< T-l CD ro P CO CM t-4 P X P CP CM CO ro 7 P p ro P ro cc 7 T-l ro 7 CP ro 7 CM <J T-1 T-1 7 X

CJX 7 CMX

X P X 7 X

p O' T-1 tH CO P p ro 7 P t-1 O'X ro 7 CD

X

p 7 CD ro tH CM

pX aj P p CD P T-l U'

X O' ro CM ro 7

CD

X LL T-l CM CD

p P p

X

X ro CM CM ro CM CC CM CM co O' P p CD O' CM ao CU o p P X tH CO

X 30 T-l P ro T-1 T-1 T-l ro P CC P X O' CM P • LL <a P P 7 X 7 7 P CD p ro T-1 CD CD CD CM 7 p O’ ro X CM p CM X ro CD p ro CD <X> P ro T-1 CD OJ X P UN 7 ro CM T-t CD O' an co X

CD CJ CJ

ao ro tH CD

p ro T-| CP COp LT 7 ro CM t4 CD O' co

XX

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p 7 7 7 ro ro ro CM CM CM CM CM T-1 t-4 T-1 T-l t“4 T-1 T-1 tH T-1 CD CD CD CD CM

II a

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i— D>

X P P pX co LP CD CD T-1 CM ro 7 p

p

X cr CD tH ro 7 P CO CD CM 7 p O' CM P CO tH P CO CM

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<xX 7 7 7 7 7 7 P P P P P P p

p

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p P P p P P P XXXXX aj co CO O' O' O' o CD t-4 tH T-1 CM CM ro ro 7 P P X

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CD

CD CD CD C3 CD CD CD CD CD CD CD CD CO CD CD CD CD CD o CD

a CD CD CD CD CD CD o CD CD CD CD o tH *“•

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CD CD CD CD CD

O CD CD CD o O CD o CD

O CD CD

O CD CD o a CD

O CDO CD CD

O CD CD CD o o CD CD CD CD

O CD CD CD CD CD CD CD CD

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(/)

X _J P CM P CDX ro CP CM 7 CM

X P 7 X Lf.

X 7 P CM T-l 7 tH CD 7 T-1 ro P T-4 CO CD

O

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H-l Ll

X CM O'X 7 CM O'

X 7 X ro O' 7 O' ro

X CD ro P P X

X P P ro T-1 ao P ro CM T-1 T-4 CM P O

X P X O' ro O' P cc 7 7 X c _J CO P CM CP P ro cr P ro CD p ro CP P CM cr P CM an 7 o p CM co 7 CD P T-l X ro O' P tH X ro CD p ro o X P CM CO 7 T-1 CO P

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O O' CP O' co CO COXX

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<1X

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LU

T-1 o CD o o CD CD CD CD o CD CD CD CD CD CD CDO CD CD CD CD

O CD CDO CD CD CD o O

O CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD

X o CD CD CD CD CD CD

O CD CD CD CDO CD CD CD CD CD CD CD CD CD CD CDO CD CD CD CD CD CD CD CD CD CD CD CD CD

O CD CD CDO CD

O CD

OEG •H CD CD CD CD CD

O CD CD CD CD CD CD CD CD CD CDO CD CD CDO CD CD CD o CD CD CDO CD

a CD CD CD CD

a CD CD CD o CD CD CD CD CD

O 7 CD CD CD CD CD CD CD CD CD O CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD O o CD CD CD CD CD CD CD CD CD O CD CD CD CD CD CD CD CD CD

CP CD T-f CM

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X GO CP CD t-4 CM ro 7 P P X CD O' CD CM 7 P CD CD

H T-| TH T-| tH TH T-1 i-i TH CM CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro ro 7 7 7 7 7 7 7 7 7 7 P P P P P P

321
Table

27.

Thermophysical

properties

along

isobars

(Continued)

i

j

I

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x

CM CM CM rH rH 'r" H rH rH tH rH rH rH rH rH rH rH rH

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X vO vD vf> vD vO vD vO vO VP vD p- P- p P p P p p P p CO CO <r> co ao co CP CP CP (P CP CP CP CP CP CP CP CP CP CP CP CP CP CP CP CD O

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V. 3 J- 3 3 -3* J- -j- -3- 3 J- J- -3- -3- -3 j* •3 3 3 3 3 3 in in in in in in in in in vO vO sD vO vO sD vO sO \D r^ r^ r^ P- r- N* ao ao

tfi * 3 ro P- j- rH rH in CO rH p- CD rH vP CD vp in vi) vP CM O 3 CP ro ao ® a; r^ CO o 3 CD 3 o ro 3 ^-4 vi) o 3 CP 3 o ro r^ V CO vP in CO 3 O CM vP 3 CM o ro rH vP rH in rH (P o in 3 p in CD kO in CO ro in ro vO in O CD N» CP r^ 3 CD O CM in -J vi) in CD CP J- in CVJ vD CO <o vO CM P CD ro -3 in 3 3 CM CD p 3 rH r^ ro CP 3 CP 3 CO CM vO CP CM 3 v£> CD CP O' CP CP CD in CM X rH CO ro CP 3 CP ro rH in CP CM vD CP CM in ao rH 3 p CP CM in r^ a CM in pw CD CM in r*^ CP CM 3 vO CO CD CM 3 vO O 3 ao H in

P- aj 00 CP CP CD CD H rH CM CM CM ro ro ro 3 3 3 in in m in vD vP vX) r^ r^ r^ N- CD CD CO CO CP <P CP CP CD CD O o CM CM

“) *-* rH rH rH rH *-* *-* rH *-* H ri »-» v-* 1 CM IM IM CM CM IM CM CM CM

oX r^ 3 in VO ao Vi) ro 3 CP CT' Vi) CP O CD CP CP o» CD ro ro CM UN UN Vi) CM to 3 rH OD UN CP rH CD CD 3 rH CD O CM UN VP in 3 o

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Vi) r- r^. ao O' O' CD rH CM ro 3 3 in Vi' vO r-. OD O' CD CD rH CM ro 3 3 UN vD P- ao CP CD rH CM ro 3 UN so P- 0D CP CD CM 3 VP ao CD

rH rH rH rH rH rH •H rH rH rH rH CM CM CM CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro ro 3 3 3 3 3 in

UJ _J r^ CM 3 CD in in in r*D in CD 3 P- UN vO P- 3 r 3 3 ro CD vP CM CD ao 3 vO UN r^ ro CP ao CM ro CM CM K p- CP CO 3 CM 3 3 CM CM CM X CM <3D co CO r^ r*- ac vD in r- 3 P- vO CM vD <D CO r- in CM P» CM r^ 3 CP 3 3 C

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rH rH rH rH rH rH rH "H rH CM CM CM CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro ro 3 3 3

-J o o vO in vD ro o in rH ro r^ vD ro UN vD ao CP CP CP 3 UN ro CO CP CP vD 3 vO CP CP CD CP ro ro rH CP rH o CD rH rH vP CO rH K

o o N- 3 ro ro ro v£> ao in CM vD CD rH ao ro CM ro ao ao rH 3 p- rH CO CM vP UN ro 3 rH P- in ao CD r- ao CM CM CD CM CD CD CO r^ r-H ao 3 CD V X CO GO in 3 co CM rH o r^ P* r^ vD CD P- UN ro O ro CM P- in ao ro rH rH CM 3 UN vP UN CM vP vP CM CM vP ro ro UN ao CD vP CM CD CP o _l ro CM ao CM ro CD CM o CM CO r*- CD vD in P- o vD 3 3 u. CO CM ao UN 3 3 in r^ CD 3 CP in CM CP P- vC in 3 3 3 3 3 vP p- CP CM

1 U> r- CD ro r^ vO rH vO CM CP in CM CP r^ 3 CM CD a

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CD r— * CM CM CM CD ao CD r^ ro ro 3 CM CD 3 Vi) rH 3 r^ O' Vi) vO CM CD CD ro CM ro CP P- CD ro CD 3 CP CO UN vP 3 vP CD ro vi) ro CP 3 ro CP

LJ CD au ro ro O' CM rH Vi) CM rH O' 3 Vi) ao 3 P- ro a) O' CM UN UN CD CO <D co vi) CM 3 O' P- UN CM p- CO ro rH CD CD co 3 p- rH ro au ro o \ Cl ro in in H CM CM UN sD CM CM ro ro ro CD 3 in rH ro CP CD vO UN CO UN 3 P- ro CM 3 CO 3 ro 3 r^ rH r- UN 3 3 UN vP CP vP vP O' ro

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CD ro tH CO in ro CT' CO vD IT 3 ro CM rH CD CT 00 CD P- vO vD UN UN 3 3 3 ro ro ro CM CM CM CM CM CM rH rH rH rH rH rH «-H rH rH o CD CD

ro ro ro CM CM CM CM rH rH rH rH rH rH

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i— D> X in vO vO r- ao CP CP a rH CM ro 3 UN vO P- CO o rH CM 3 UN P- CP rH ro UN P- CD ro vO (P CM in CP CM vi) O 3 ao CM vP CD a> vP 3 rH CP < N, 3 3 3 3 3 3 3 m UN in in UN UN UN UN UN vD vO vD vD v£) Vi) vP P- P- P- P- CO ao CO CO (P CP CP CD CD rH rH rH CM CM ro ro 3 in vP vP

-J CD CD CD CD CD C_D CD CD CD CD CD CD CD CD O CD CD UD O CD o CD O CD CD o CD CD o CD CD CD CD CD rH rH TH rH rH rH rH rH rH rH

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CO z -J in ro CO in 3 ro CM X> ro in 3 CP rH CP ro CM r^ CM CM vP vP o CP ro 3 rH r^ ro rH 3 ro rH O ro rH UN vO 3 CP O P- ro rH ro CM ro

»-H UJ CM 3 CP N» in ro CD ao in CM <o UN CD Vi) rH in CP ro vO ao CD CM CM ro ro ro CM CM CM CM ro UN ao CM CO UN 3 UN P> CM N. ro 3 CP CD o -J CO JD ro O' vD ro CD r^ ro CD r^ ro CD ro CD vD CM CP UN rH <D 3 CD vP CM co 3 CD vP CM co 3 CD p~ ro CD P- 3 rH CP vO CM CO 3 rH O'

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h- CP CD o o CD o CD CD CD o CD CD CD CD CD CD CD O CD o CD CD CD CD O O CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD o o o CD CD o

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D 3 CD O CD CD CD CD CD CD CD CD CD CD CD O CD O o O CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD O O O CD CD CD O CD O o O CD

O' CD r-4 CM ro 3 in vD r^ an CP CD rH CM ro 3 UN vD P- CO CP CD rH CM ro 3 UN VP P- co CP CD rH CM ro 3 UN VL) P- X) CP CD CM 3 vi) ao CD r4 rH y-i T—

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tH rH rH rH CM CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro ro 3 3 3 3 3 3 3 3 3 3 in in in in UN vP

322
Table

27.

Thermophysical

properties

along

isobars

(Continued) t * i 1

or

IT o 1-4 i-4 CD If 3 CO in in P i-4 CO

X vO CO i—P ro CM ro in CP vO ~3 ro 3- -3 CM ro in CD P P CP roO CP CD CM vO i—l CO in r»- PD 3 CD

LU ro CO CO CD cv 3 P CD ro P CD 3 CO CM P i—X iH vD i-4

X CM CD -3" o vD ro CD p- in CM CD ao

p vO 3 3 ro CM CM iH iH v~i iH iH iH CM

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O CO CO co CO cc CO CO CO CP CP

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iH i-t i—4 i-4 i-4 i—4 iH 1-4 i—4 iH 1-4 CM cm CM CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro ro 3 3 3 O vO CM O' O' in P *rH CD 3 OO i-4 CD iH CD 3 3 ao O' CM i-4 ao CM 3 CO CM vX P ro CO 3 ro in i-4 O' i—4 ip ao vX CD o vX CD i—4 ro P in

CD o vO CM vX in CD ro ro in 3 O' 3 3 O' CM CO vX vX CM CD vX CD CM vX ro P ro ro CM 3 1-4 CO P 1—4 3 P MJ 1-4 co

a CM CO 3 vX vX ro CD 3 P X\

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ao in CO CD i-4 CM ao ro ro ro v-4 CM ro ro P in 3 ro

O ro rop inp iH CO iX in 3 ro CD vX CD CD vX CO in in CD P vX CO vX O' in CM O'

vO O' in CD i-4 co CD ao CD vX vO O' in 3 in O' in ro ro 3 p i—4

p 3 ro pj ro in CC CM P CM O' vX ro i—i o CP O' CO CD CO CP o CM 3 in 1 i-4 v£> ao iH 3 P CM vX CM P ro O' vX ro CD p in ro w-i O p vX 3 ro CM i—4 o O' CO oo P P VX vX *x vX vX in in in in in in vX vX vX X

01 CD O' cc CO P vX vX in in 3 3 ro ro ro ro CM CM CM CM iH iH i-4 iH iH i—4 1—4 i-i <1 T-l CD

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X i-4

X CM O'

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X ao ro i—4 P ao ao CM 3 p

X

X CD CD 3 X

X 3 roXX co ao CD P X P X

X 1—4 3 i—4 i-4 iH roX P X

X

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p co 3 O' CO CM OJ co 3 X P i—4 3 3 CM

X O' P au au ro CD

X

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p au CD i—( CDX U)

X ro CO iH i—4 P P O' ro P CD i—4 3 o 3 ro ro

CD P CL 3 O' O'

X O'X CM 3 i—4 1-4 ro 3 3 CM

Xp 3 X ro

X i—4 CD ro CD o 3 CD

X CD 3 o O'

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X P CD • t-L 3 3 in 3 CO X in co CM CO X ro CM CM ro 3 X O’ CM X CD X CD in 1—4 p ro CD vu 3 1—4 O' X 3 ro i-4 CD co P X in 3 3 CM iH CD O' X

CD CL

CM ro it CC

X ro 1-4X CO

X

X 3 ro CM i-4 CD

X ao ao

p P X

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X 3 3 3 ro ro ro CM CM CM CM CM CM i-« i—4 i—4 i—4 i—4 1-4 i—4 i-4

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li

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X ro

X ro

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p CO

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X CD CO P X P CO P ro 3 X

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X CD 3 O O aj i-4 CO X ro CD ao X 3 ro CM CM CM CM ro X P CD ro co ro O' X X 3 X P CD X CM X X X 1—4 3 CD ro X X i-4 CO X X ro X ao X

1— .> z in

XXp oo O'X CD i-4 CM ro 3 X

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p a0

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X CO CD CM 3 X O' i—4 3 XX CMXX CM

X O’ ro P CD 3 iH O'X ro o 3 p 3 3 3 3 3 3 3 X X X X X X X X X X X X X X X X P P P p p ao OD CO ao X X X CD CD CD i—4 1-4 CM CM ro ro 3 X X 3 CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD o CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD 1-4 i—4 i—4 iH *"• i-4 3

CD

CD CD CD CD CD CD CDO CD CD CD CD CD CD CD o CD o O CD CD CD CD CD

O CD CD

O CD CD CD CD CD CD CD

O CD CD CD CD CD CD CD o CD CD CD

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in z 3 in 3 CD CD i-4 ro 3 3 CM

p CD CD P CD

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X P 3 CO P CM ro

X CM i—4 CO CM

X

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XX ro CD iH P CO ro 3 X

XX CM CM 3

4-4 UJ P ro

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X 3 CM

X P 3 CD P CM CO ro GO CMX CD ro

X ao

a iH fO 3 X P X PM

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X CM CD

X CD ro P CM P P CM CD i-4

Q 3 COX ro CD P ro CD P 3 CD P 3 i—4 P 3 CD

p ro o X ro

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p ro CD P 3 CO COX CM CDX i—4 COX CM

LU o Z z i—4 i—4 i—4 i—4 CD CD CD

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XX CO 00 0O P P P XXX

XX 3 3 3 ro ro ro CM CM i—4 i-4 •r-4 CD o CDXX

X CO ao ao ao

p P XXX 3X

CM CM CM Pd CM CM CM iH 3 i-4 iH i-4 iH iH iH i-4 iH iH i-4 i-( 1-4 iH i-4 i"4

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iH cU i—4 i-4

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X CD CD o O CDO CD CD CDO CD CD

O CD CD CD

O CD CD CD o CD CD CD CD CD CD CD CD CD CD CD CD CD CD

O CD CD CD CD CD o CD CD o CD

X CD CD CDO CD CD CD CD CD CD CD CD CD CD CD CD CD CD

O CD CD CD CD CD

O CD CD CD CD

O CD CD CD CD CD CD CDO CD CD CD o CD CD CD CD L? P CD CD o CD O CD o CD CD CD CD CD CD CD CD CD CD CD CD CD O CD CD CD CD CD CD CD O O O CD CD O O CD CD o CD CD CD CD CD O CD CD Q 3 CD CD CD O CD CD CD CD CD CD CD CD CD O CD CD CD CD CD CD O CD CD CD CD CD O CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD O

O' CD i—4 CM ro 3 in VO P OD O' CD CM ro 3 X

X P ao

X CD i-4 CM ro 3 X

X P ao

X CD i—4 CM 40 3 X

X P an O' CD CM 3 X au CD

i-4 i-4 i-4 i-4 i-4 i-4 i—t iH i—4 i-4 CM CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro ro 3 3 3 3 3 3 3 3 3 3 X

X

X

X

X

X

323
Table

27.

Thermophysical

properties

along

isobars

(Continued)

it

3 o CM IP LP O t-4 LP ro ro vD CM (P ao CP vO CM CD CP t-4 CP N- vO vO ai CP P- co t-4 vO ro ro d ao d CM CM ro P- T-4 r^ ro O' CO CO O ro

LU ro CD CP t-4 ro IP CO t-4 d CO *-1 CP d ao ro co CM ao ro CO d CD vO CM CD IP CM CD P- lp ro t-4 O' CO P- vO LP d d ro ro CM CM CM ro ro

l/) cm t-4 o CD CP 00 p p vD IP IP d ro ro CM CM T-4 •-4 CD CD CP CP CP co CO r^ r^ h- r^ vO vi) vO vi) LP IP IP IP IP lp lp lp lp IP IP IP ip lp P

X

C\J CM CM CM t-4 t—4 t-4 t-4 t-4 ^-4 ^-4 H ^-4 t-4 t-4 t-4 t-4 t-4

LL ii p CM VU IP O CM CM CP d CO CM ,H ao CM ro CP CD ro CD IP ro LP d CM CM T-4 P* vi) ro Vi) ro CM ro d CD d lp tH lp CO CM CM au vi) d O P t-4 t-4 C-J CD t-4 CM d vu o d CD vi) ro o CP co CO CO CO O' CD IP ro ro tH CD O' CP O' ao P- IP CM CD ro CD CM vO O' CM O' vi) ro CM CM o CO CD CD CO CO ao ao CO O' CP CD CD rl (M CM ro d LP vO P- CD a t-4 CM d P- 00 CP O' CD tH CM IO d IP IP vO vO P- ao ao O' CD t-4 CM X vO vO vO vO Vp vO vD VD vO vP r^ rw r^ P- r^ K- p- K- r^ co CO CO CO ao CO CO CO O' CP CP O' O' O' O' O' O' O' CP O' O' O' O' CD CD CD V“5

t-4 t-4 t—4 > * ro CM kD p CP ro t-4 Vi) p p» IP CM CP ro lp ro r^ ro CM ro vC P- CD vD CM t-4 O' CD t-4 <D o IP ro CM CM ro ro ro CM t-4 O' ro d CD ro ro O V d ro CD p d CM CD 00 p p- CO o ro v0 4 vD CM CO LP CM CP vD d IP <P CM CO P- vO IP vO vO <D O' CD tH CM ro d d vO P- CO ao co o vU Vi) vi) ip ip IP IP d d d d LP lp LP VD v£> r- p. CO CP CP o ^4 CM ro vi) p- CD O' CD t-4 CM ro d IP CD O' CD t-4 CM d VU CO CD CM X

s

d d d d d d d d d d d d d d d d d d d d d IP IP IP IP LP lp IP LP IP vO vD vO vO vO s£> vO Vi) vi) K r^ P- r^ P- P CO CO

l/) dc IP if' d ip d d p IP d d o CM P- CP CM lp CO OJ tH CM N- CD 00 d T-4 d O' tH ro co CO CM o ro O' O' CM CD T-4 p- O' vU ro O' vO lp V ro «c p <p d CP CD ro CD v£> ro d CD ro lp 00 t-4 vO d vD tH CD LP d tH vO CD O' LP vD ro P- CD IP CO P- ro v0 IP O H O' vO t-4 d CO ro

_J CD CM p vi) t-4 t-4 (P ro IP d CM 00 ro vD CD <P CD CP CO vO d t-4 P- ro CP d CD d CP ro r- o ro vO CO CD CM ro d IP IP d ro T-4 p. CM p

X P t-4 p ro CP d CO ro p IP ao CM LP oo t-4 IP r^ CD ro vi) O' tH d vO CP CM d vO CP t-4 d vO ao CD ro LP r^ O' t-4 ro ip O' ro vO CD ro p P ao CD O' CP o o r4 (M CM CM ro ro ro d d d IP IP LP IP Vi) vi) vO vD r- co CO CD CP O' O' O' O' O o CD CD ^4 t—4 CM CM

*"* t-4 ri *-1 t-4 t-4 T-4 T-4 t-4 T-4 t-4 tH tH tH t-4 T-4 T-4 T-4 CM CM CM CM CM CM CM CM X _J P CM O ip CM CO CP d O IP CP CP lp d ro o t-4 CD tH r^ 00 P- o CP LP (X) ro CM CO ro ro ro vO IP CO CD t-4 p*» O ao CD O' CM t-4 tH O' X d t-4 CM CM ro d p ro CM d d d *-4 Vi) CD ro Vi) CP CM vD t-4 P- vU CP ro CD vO T-4 LP CD d p- CD CM d CD CD IP CM d LP tH t-4 P t-4 V CO CM CD ao vD d CM t-4 o CP CP CP CD CM d CO CM P- ro T-4 <P CP CP t-4 d o CO vD vO vO OO o ro P- CM ao d t-4 CO IP ro t-4 CD P P (O (M ~) O' ro CD vO ro CD P- d t-4 p- d CP vD ro CD co IP ro tH co vi) d no t-4 CD ao vO IP d d ro CM CM T-4 t-4 T-4 CD CD CD CD CP O' CP O' CD w p aj CO O' CD CD T-4 Pi CM ro -T d LO vLl p- ac on CD CD t-4 CM ro d IP LP vi) P- CD O' CD T-4 CM ro d LP Vi) r^ <JD O' CD t-4 ro IP p- CD

t-4 t-4 t-4 t-4 H •H •H vH ^4 w-4 •H •H ^4 CM CM CM CVJ CM CM CM CM CM CM CM CM ro ro ro ro ro ro IO ro ro IO d d d d d LP

LU m ro LP CP CP th CD d CO CD CP CD ro ro P- t-4 CP IP CP d CD CD ro t-4 IP IP CO t-4 CP CM O' d d d ao CM ro CD O' d lp CM lp d t-4 X CO ro CO vD ro CP vO d d CO d vD OJ d CM CO CD t-4 CP vD CD ro PD CM d t-4 CD CP vi) P- IP LP ro CM lp CD ao p- CD lp d vD d t-4 O' V CM IP t-4 vD ro p ro O' ip •-4 CO IP ro •4 CD CP CD ^4 CM IP CP ro to d t4 CD CD »4 ro IP to •4 IP O' d CP d CD IP •4 OO d <D ro CD O' O'

-> d P d CD P ro CD VO ro CD vO ro CD P- d CD au U^ CM O' VJJ d T-4 CP IP ro T-4 o r- LP d CM o O' vi) U' ro CM CD O' vi) d CM O' p

in ip vO p P CO CP CP CD *-4 *—

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CM ro ro J LP LP vD r- P- ao (P o CD t-4 CM ro d d LP vi) r^ CD O' O' CD t-4 CM ro d IP lp P- O' t-4 CM d

t-4 ^-4 *4 t-4 T-4 t-4 t-4 t-4 t4 t-4 CM CM CM CM CM CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro ro d d d o vO P p LP o CM IP p ro CM CP P- vD d CM CP d t-4 CM vi) O' P- vO IP d CP CP t-4 CM O' p- t-4 O' vO O' CO CM vD p- CD p- P- lp vD P CD o o CP O' CO U) u

\

CO d O CM co 4 CD CM CM lp CP d IP vU d aj O' CP CD IP CO CM CM CM d CM t-4 d IO d CP ro CD ro ao CD LP O' CO vi> lp ro \ X IT* CO ro vD CP p d LP vO LP p- CP CP d CM CM t-4 <o CM tH LP ro IP CO ro CD r^ d CD IP CO CO ip ao vO CD co O' ro t-4 CD d d CO d t-4 o _J CD vO CM p CO LP CD vD CO d d p- ro CM d 00 d CM t-4 ro vO CD VP ro r4 t-4 CM io vD CD d O' LP CM CP P- vD d ro ro ro IO ro d IP P CP

1 CM p O' t-4 d CO CM p CM au d o P- d 00 vD d CD CO P- lp d ro CM t4 CD CP O' CO r^ N- P- vO vi) vi) vi) v£ vi* vO vi> vi) vi) vD vU vU

CL O CP CO CO P vC vD ip IP d d d ro ro ro CM CM CM CM CM t-4 t-4 t-4 t-4 t-4 t-4 t-4 t-4

CL

<X

CD

CL b- * ro lp t-4 LP (P CP t-4 tH d vL) ip p- vO co vjQ d vD vO CM <P d CD CM ao vU CD CM d ro t-4 d vi) CM P- CO O' CP ro t-4 T-4 d O' ro d IP O' IP

(_) P CP CD vi) ro lp P LI

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p ro O CD co ro LP P- CM d CP ro t-4 CM CM CO co t-4 LP P- vi) t-4 CD T-4 ro IP d CD t-4 vi) d ro CM o vi) t-4 CP VU CD IO

CD \ CL vu ro d CM ip vD CD CM CD ro d LP ro CO CD p> CP r^ CP LP LP CO IP vO CP LP d vi) CD vO d d Vi) CD IP t-4 CP CO CD O' o vi) ro ro d P

• CL d ro vD LP CP vd vU O' ro O' VO d ro ro d u^ CO CD ro p- T-4 VU tH VD CM CD d tH co IP ro CD CD VIJ d ro t-4 CD CD r- vi) IP lp ro CM t-4 CD O' o O CD d ro ( GO IP ro t-4 CP ao vD IP d ro CM ^-4 o CP CP CO p- r- vO vf IP IP d d d ro ro ro ro CM CM (M CM CM CM t-4 t-4 t-4 t-4 T—4 t-4 t-4 t-4 t-4 CD

ro ro ro CM CM CM CM *"* r4 -4 H H

a. _J _J 00 CM CM d CP vD vO CP LP IP ao vO CP v£) CP CO CM ro CM <D ro Pt o d CP ip d LP O' IP d d vD O' t-4 CD N- CP IP IP vD CM P CO ro t-4 o O p tH ao LP CM CP p IP ro CM ^-4 o o CD r-4 CM d P- o d CO d CD CO vi) lp vi) co tH LP T-4 ao vi) IP IP O' t-4 d ao CM VU IP ro t-4 O' vO

b- X LP vD vD p CO aO CP CD v-4 CM ro d LP v£> CO (P CD CM ro d vO CO CP t-4 ro LP r- CD CM LP r- CD ro vi) O' CM vO O' CM vi) O' vi) ro CD vi) ro d p d d d d d d d LP LP IP LP lp IP IP lp LP lp vO vi) vi) vO vi) vD vi) P- r- P- p- CO <XD CD CO O' CP CP CP CD CD CD t-4 t-4 t-4 CM ro d d lp

CLd

CD

o o o CD CD CD CD CD O CD o CD CD CD o CD CD CD CD CD CD CD CD CD CD CD CD o CD CD CD o CD CD CD CD *“• t-4 tH t-4 T—4 t-4 t—4 T-4 t-4 t-4

CD CD o CD CD CD CD CD o CD o o o CD o CD O O CD CD O CD O CD CD o CD CD CD CD CD o CD CD CD CD CD CD CD O CD CD CD CD CD CD CD O

LC z -J IP d ro d CO CM v£> CP CD CP JD o •H CP d IP d CP CD CO CM ro tH vO <o CP r- P- CP d IP CM CO ro CP a) O' ro t-4 CM P- d ao ro v£> O

H UJ P d CD vO d CM t-4 (P P v£> ro yb CP v£) CM CP IP t-4 vO CM vO LP CP CM IP ao tH d P- CD d co ro ao LP CM t-4 t-4 ro vO a IP o O' ro O t-4 o -J CO vD ro CD P d O p d H CO d CO d t-4 CO d t-4 P- d CD vD ro CP LP CM CO d t-4 p- ro o vO ro o P- d t-4 CO vO ro O' d t-4 CO IP u o z X -4 tH t-4 t4 CD CD CD CP CP CP CO CO CO r^ P- vD vD vO LP ip IP d d ro ro ro CM CM CM t-4 t-4 t-4 CD CD CD O' O' CP ao co <D r^ P P vi) vi) d

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CM CM CM CM CM CM CM yb ^4 h ^4 •H tH ^4 t-4 tH tH *4 t-4 tH 4 tH t-4 t4 «H t-4 4 t-4 t-4

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b- * CM CD o CD CD o o CD O CD CD O O CD CD CD o CD o CD o O CD CD O CD CD CD CD CD O CD CD O CD O o CD CD CD o CD CD o O o O

vi) o CD CD CD CD CD CD CD CD CD o CD CD CD CD o CD CD CD o CD CD CD CD CD CD O O CD CD CD CD CD CD CD CD CD CD CD CD CD CD o CD CD o

o CD CD CD CD CD CD o CD O CD CD CD O CD O CD o CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD o U

»

o CD CD O CD CD CD CD CD CD CD o CD CD CD CD CD O CD CD CD CD CD CD O CD CD CD CD CD CD CD CD CD CD CD CD CD CD O CD CD CD CD CD CD

O' CD PJ ro d LO M) P- ro CP CD v-4 CM ro d LP Vi) r^ ao CP CD t-4 CM ro d LP vO r^ ao CP CD T-4 (M ro d IP Vi) P- co CP CD CM d vO CD CD

t—4 r4 t-4 H H t—4 tH y-i CM PO CM CM CM CM CM CM CM CM ro ro ro ro ro ro ro ro IO ro d d d d d d d d d d IP LP lp IP IP v£)

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NBS-1 14A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 74-398

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

PROVISIONAL VALUES FOR THE THERMODYNAMIC

FUNCTIONS OF ETHANE

5. Publication Date June 1, 1974

6. Performing Organization Code

7. author(S) Robert D. Goodwin 8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project /Task Work Unit No. 2750364

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

American Gas Association

1515 Wilson Boulevard

Arlington, VA 22209

13. Type of Report & Period Covered

Technical 6-73/6-74

14. Sponsoring Agency C ode AGA

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less (actual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) Thermophysical properties are tabulated at uniform temperatures over the entire

range of fluid states from 90 to 600 K along isobars to 700 bar. A new, rational

equation of state is employed for the first time. Thermodynamic functions in the

compressed liquid at T < T are obtained by use of specific heats C (T) along a high

pressure isobar. P

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Densities; enthalpies, entropies; equation of state; internal

energies; isobars; isochores; isotherms; Joule -Thomson inversion; latent heats of

vaporization; melting line; orthobaric densities; specific heats; speeds of sound;

vapor pressures.

18. AVAILABILITY fx Unlimited

[ For Official Distribution. Do Not Release to NT1S

|

I Order From Sup. of Doc., U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. Cl

3

! Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF P \GES

22. Price

USCOMM-DC 29042-P74

USCOMM • fcRL
765

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MOL/L

L/MOL

RAR/K

BAR-L/MOL

J/MOL

J/FCL

4/MCL/K

J/MOL/K

J/MOL/K

M/SEC

6.828

21.975

0.04551

32.5332

1072.177

5532.1

0262.4

78.774

47.79

67.99

2252
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l I£C

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Table

27.

Thermophysical

properties

along

isobars

(Continued)

ETHANE

ISOBAR

ATP

=

550.0

BAR
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