NBSIR 74-357

A MODIFIED BENEDICT WEB6-RUBIN EQUATION OF STATE

FOR PARAHYDROGEN

R.D. McCarty

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Final Report

February 1974

Prepared for:

NASA-Lewis F^esearch Center

Cleveland, Ohio

NBSIR 74-357

A MODIFIED BENEDICT WEBB-RUBIN EQUATION OF STATE

FOR PARAHYDROGEN

R.D. McCarty

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Final Report

February 1974

Prepared for:

NASA-Lewis Research Center

Cleveland, Ohio

u s. DEPARTMENT OF COMMERCE. Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS. Richard W Roberts, Director

CONTENTS

1. Introduction 1

2. Summary of Data Used 1

3. Saturated Liquid and Vapor PVT 2

4. The Equation of State for Hydrogen 9

5. References 13

Figure 1. The Lorentz- Lorenz Function for Hydrogen 2

Figure 2. Rectlinear Diameters for Parahydrogen 6

Table 1. Lease Squares Estimates of the Coefficients

for Equation (1) 3

Table 2. Comparison of Densities Near the Critical Point ... 4

Table 3. Coefficients for Equation (5) 7

Table 4. Coefficients for Equation (6) 7

Table 5. Saturation Densities and Deviations from

Equation (6) 8

Table 6. Coefficients for Equation (7) 9

Table 7. Vapor Pressures and Deviations 10

Table 8. Coefficients for Equation (8) 11

Appendix A. Computer Listings 14

Appendix B. Table of Symbols 71

iii

A MODIFIED BENEDICT- WEBB-RUBIN EQUATION OF

STATE FOR PARAHYDROGEN

Robert D. McCarty

A 32 term modified Benedict- Webb-Rubin equation of state has been

applied to data for parahydr ogen. The adjustable parameters in the equation

of state were determined using data from the triple point to 2500 K, with

pressures to 680 atmospheres. Extensive modifications have been made to the previously accepted PVT surface for the saturated liquid and vapor

phases in the near critical region. These modifications have been made on

the basis of subsequent refractive index data and the application of scaling

law equations. Comparisons between experimental and calculated data are

given.

Key words: Critical point; equation of state; hydrogen; index of refraction

PVT; saturation properties; scaling laws

1. Introduction

For some applications of the equation of state for cryogenic fluids, it is advantageous to use a modified Benedict- Webb-Rubin equation of state (hereafter

referred to as MBWR). One part of the work performed under NASA-LeRC Purchase

Request C-32369-C was to provide a MBWR equation of state for hydrogen. Another

part of the work to be performed here for NASA is an experimental program to supplement the existing data for parahydrogen (Roder, et al. , 1965) with PVT data to higher pressures and temperatures. The equation of state work was to include these new

experimental data in the estimation of the coefficients to a MBWR type of an equation of

state. At the time of this writing, the experimental part of the total program is in progress and the funds for the continuation of the equation of state work do not seem to be

available, at least in the near future. The purpose of this report is to collect and document the equation of state work performed to date. There are two reasons for reporting

the equation of state work at this time. First, the work already accomplished is of

sufficient importance that it should be made available to prospective users; and second,

should the funds become available in the future to allow the continuation of the study, the

earlier work will be preserved here.

2. Summary of Data Used

The PVT data of Goodwin, et al. (1963) and the specific heat capacity data of Younglove and Diller (1962) were used as the primary set of experimental data in the

estimation of the coefficients to the equation of state. These data cover the pressure

range of 0 to 340 atmospheres with temperatures from the triple point to 100 K. The

NBS 1955 temperature scale was used to determine the temperatures of these data;
therefore, a conversion of the experimental temperatures to the International Practical

Temperatures Scale of 1968 was made. In addition to the data set just mentioned, 173

PVT points from McCarty and Weber (1972) were used. These points were generated

from equations which were used to extrapolate the PVT surface to higher pressures and

higher temperatures. The equations used by McCarty and Weber are based on thermodynamic data selected from the literature and rely heavily on the data by Michels et al,

(1963). Appendix A contains complete tables of deviations between the data used in the fit and the values predicted by the equation of state.

3. Saturated Liquid and Vapor PVT

Equations for the density of the saturated liquid and vapor were published by

Roder, et al. (1963). These equations were based on the single phase experimental PVT

data by Goodwin, et al. (1963) and the vapor pressure by Weber, et al. (1962). Since the

data of Goodwin, et al. (1963) were converted to the 1968 International Practical

Temperature Scale, these older equations for the saturation densities were no longer

consistent with the experimental data, and it was decided to derive new equations for the

saturation densities as well as the vapor pressures. After the saturation densities were

published by Roder, et al. (1963), an index of refraction experiment by Diller (1968)

indicated that the saturation densities in the very near critical region were in error by as much as 6%. This conclusion is based on the behavior of the saturation boundary shown

on Diller' s plot which is given here as fig. 1.

DENSITY, g/cm'

Figure 1. The Lorentz- Lorenz Function for Hydrogen
The Lorentz-Lorenz function of the saturation bovmdary, shown in fig. 1, should

have the same general shape as do the isotherms.

The experiment involved measuring the index of refraction, the temperature and

the pressure. The densities were then obtained from the data of Goodwin, et al. (1963).

The reason for the two legs of the saturation curve not meeting in a smooth manner at the

critical point is ascribed to incorrect densities in the critical region. To adjust the

saturation densities in the critical region the function

N

p =S A n^^ (1)

K = l

was fit to the 35 K isotherm, where p is density in g/cm^ and n is the index of refraction.

Equation (1) was fit to 24 points ranging in density from 0. 003969 to . 078833 g/cm^ .

Statistical significance of the coefficients to eq (1) was lost when more than 4 terms were

used and the 4 term equation was chosen, the coefficients to eq (1) are given in table 1.

Table 1. Lease Squares Estimates of the Coefficients

for Equation (1

)

= -1.0880215243 ± 0,214

Ag = 1.8280271481 ± 0.604

A3 = -1.0378774469 ± 0.567

A4 = 0.29788205862 ± 0.177

The measured index of refraction along the saturation liquid and vapor lines were

then used to calculate the corresponding densities according to eq (1). A comparison of

densities reported by Roder, et al. (1963) and those calculated by eq (1) is given in

table 2.

3
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4
To estimate the critical density and critical temperature, the equation

(2)

was fit to the corrected densities above 28 K. The liquid and vapor densities were fit separately, where AT = (T^ - T)/T and p and T are the density and temperature

respectively. The parameters Gj , (Gj corresponds to the critical density) Gg , T and fl were estimated from the least squares fit of the data. Equation (2) is the first two terms

of eq (6) and is only valid for densities very near the critical point. The truncation of

eq (6) was used with the densities near the critical point to prevent any influence on the

estinnation of p and T by densities too far removed from the critical region. A critical

c c density of 0.03254 g/cm^ and a critical temperature of 32.433 K resulted from this fit. The p and T from the fit seemed reasonable, but the estimate of 0 was 0.407 which is c c higher than the 0.35 predicted by theory. The higher value of 3 suggests that some of the

input densities may not be within the range of validity of eq (2). The method of rectilinear diameters was tried next. A plot of (p + p )/2 against

temperature, fig. 2, quickly shows that under the rectilinear diameter assumption, the

critical density cannot possibly be much greater than 0.314 g / cm^ and the 0. 325 g /cm^

estimated by eq (2) is not possible.

Forming an equation for the rectilinear diameter from eq (2) results in

(p^ + pW2 = Gi +^(G2^ + G2g)|AT|^ (3)

however, G_ » is usually assumed to be equal to -G and the second term of eq (3) 2* 2g

vanishes. There is some doubt about the validity of this assumption, but in this particular case at least, the assumption cannot be disproved on the basis of the available data, and

the problem of estimating 3 is eliminated. Taking the next two terms from eq (6) gives

Pg + Px = ^Pc+ (^3g + ^3£^l^^l^"°'+ ^% + ^4^^l^^l

assuming a = 0. 1 and T = 32. 933 K, a least squares fit of the eight pairs of liquid-vapor

c data in table 2 resulted in a critical density of 0.03136 g/cm^. The fit was repeated

several times with values of of and T ranging from or = 0. 1 to cr = 0. 25 and T = 32.938 to c c T = 32.95. The resulting estimates of p did not vary significantly (i.e., maximum

c c variation was less than ±.00001 g/cm^).

A refit of eq (2) fixing the critical density to the value found by the rectilinear

diameter analysis gave results essentially the same as the first fit, i.e. , a B of about

0.4 and T of 32. 933 K. To achieve an interpolation formula for temperatures between

c 32.0 and 32. 9 K, the function

5
6
n = + ri (AT)^ , (5)

where n is the index of refraction and AT = (T - T)/T , was fit to the index of refraction

c c data of the saturation boundary between 28 and 32. 9 K. Table 3 gives the coefficients to eq (5). Combining eq (5) with eq (1) densities were calculated every 0. 1 K between 31.9

ajid 32.8 K. These interpolated data were then used in a refit of eq (2) which resulted in T = 32.938, 8 = 0. 3483 , and 9 . = 0.3478. Using these values for 8 and T the

c gas jCq c equation

8

1=1

was fit to the saturated liquid and vapor data of Roder, et al. (1963). The coefficients for

eq (6) are given in table 4. Table 5 gives the deviations between calculated and input

dens ities.

Table 3. Coefficients for Equation (5)

r = 1.0509586594

c T = 32.93313976

c

r^ = 0.091463402563

a' = 0.41043983745

Table 4. Coefficients for Equation (6)

Vapor L iqu id

Pc 0. 03136 g/cm^ 0. 03136 g/cm^

8 0. 3483 0. 3479

Gi -0. 047501571529 0. 048645813003

G, 3. 4871213005x10"^ -3.4779278186x10"^

Ga -4. 1221290925x10"^ 4. 0776538192x10"^

G4 1. 5666598550 -1. 1719787304

Ge -2. 8061427339 1.62139244

Ge 2. 7105455626 - 1 . 1531096683

G7 - 1

.

3074773595 0. 33825492039

Ge 0. 22921285922 0.0

7
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8
The vapor pressure data of Weber, et al. (1962) was converted to the 1968

International Practical Tennperature Scale and fit to the vapor pressure equation of Goodwin (1969). That equation is

In (P/P^) = BiX + BgX^ + BgX^ + B^X (1-X)^^ , (7)

where X = (1- T^/T) / (1 - T^/T^) , T is in kelvins. The coefficients to eq (7) are given in table 6. The two data points given by Weber, et al. (1962) for T = 22 and 23 K were left

out of the fit because their inclusion degraded the representation of the rest of the data.

The IPTS-68 triple point temperature of hydrogen of 13.81 K was not used because it also

degraded the fit. Table 7 gives the vapor pressures from Weber, et al. (1962) and the

deviations between the experimental and calculated data points.

Table 6. Coefficients for Equation (7)

^t

13. 8K

T

c 32. 938 K

^t

= 0. 0695 atm

Bi 3.05300134164

Bs 2.80810925813

Ba = -0.655461216567

B4 1.59514439374

Bb 1.5814454428

4. The Equation of State for Hydrogen

Since the first major modification of the Benedict- Webb-Rubin equation of state by

Strobridge (1962), there have been many more. Each author claims his particular

modification to be the best of several he has tried for the particular fluid being correlated.

In some cases the particular form was chosen because it worked well for a number of

fluids.

Two of these MBWR's have been used with good success for several different

fluids. The first is a 19 term version by Bender (1970) and the other is a 32 term version

by Jacobsen (1972). The data set mentioned in section 2 was fit to both of these equations

and not too surprisingly the 32 term equation worked the best, and consequently is used

here. In addition to the data summarized in section 2, PVT values for the saturated

liquid and vapor phases were generated from the equations in section 3 and included in the

fit. The equation of state is

9
Table 7. Vapor Pressures and Deviations

Pressure, atm

Experimental Temp.K

Pressure, atm

Eq (7) PercentDiff.

1. 6124 22. 0088 1.6143 -0. 12*

2.0688 23.0086 2. 0712 -0.11*

1.0000 20.2770 1 . 0000 -0. 00

3.2462 25. 0078 3.2469 -0. 02

3. 9826 26. 0073 3. 9822 0. 01

4. 8285 27. 0071 4. 8275 0. 02

5.7920 28. 0071 5. 7918 0. 00

6.8863 29. 0073 6. 8847 0. 02

8. 1162 30. 0076 8. 1169 -0. 01

8.1169 30. 0076 8. 1169 -0. 00

8.1171 30. 0076 8. 1169 0. 00

8.7873 30.5078 8. 7891 -0.02

8.7885 30. 5078 8. 7891 -0.01

8. 7886 30. 5078 8.7891 -0. 01

9. 5029 31 . 0080 9.5010 0. 02

9. 5023 31 . 0080 9. 5010 0.01

9. 5005 31 . 0080 9.5010 -0.01

9. 5003 31 . 0080 9. 5010 -0.01

10. 2525 31 . 5082 10. 2546 -0. 02

10. 2535 31. 5082 10.2546 -0.01

10. 2539 31 . 5082 10. 2546 -0.01

1 1 . 0502 32. 0084 1 1 . 0528 -0.02

11.0516 32. 0084 11.0528 -0.01

1 1 . 0522 32. 0084 11. 0528 -0.01

11. 8988 32.5087 11. 8992 -0. 00

11. 8976 32. 5087 1 1 . 8992 -0.01

1 1 . 8989 32.5087 1 1 . 8992 -0. 00

12. 0749 32. 6087 12. 0748 0. 00

12. 0742 32.6087 12.0748 - 0. 00

12. 0751 32. 6087 12. 0748 0. 00

12. 2526 32. 7088 12.2527 -0.00

12. 2520 32. 7088 12. 2527 -0.01

12.2536 32.7088 12. 2527 0.01

12. 4326 32. 8089 12. 4330 -0. 00

12.4330 32.8089 12. 4330 0. 00

12.4352 32. 8089 12. 4330 0. 02

12. 6168 32. 9089 12.6160 0.01

12. 6187 32. 9089 12. 6160 0. 02

12. 6183 32. 9089 12. 6160 0. 02

0. 0778 13. 9977 0. 0778 -0. 03

0. 1327 15.0020 0. 1327 0.01

0.2129 16. 0051 0.2129 0.01

0. 3250 17. 0071 0. 3250 0.01

0.4759 18.0084 0. 4759 -0.00

0.6726 19.0088 0. 6727 -0. 00

0. 9228 20.0090 0. 9229 -0. 02

0. 0695 13.8000 0. 0695 -0. 00

32. 9380 12.6698**

* Points not included in the least squares fit. ** Critical pressure resulting from least squares fit, critical pressure and

temperature given by Roder, et al. (1965) is 12. 759 atm at 32.476 K.

10
P = pRT + (Ni T + Na T^^^ + N3 + N4 /T + Ng /T^) + (Ne T + N7 + Ne /T + Ng/T^

)

+ p'^ (NioT + Nil + Nia/T) + Pb (N13) + p^ (Ni^/T + Nig/T^) + p'' (Nie/T)

+ p^ (N17/T + Nie/T^) + P^ (Nig/T^)

+ P^ (Nao/T^ +Nai/T^) exp (-yp^ ) (8) + (Naa/T^ + Ngg/T*) exp (-yP^) + P"' (Ng^/T^ + Nas /T^) exp (-yp^ ) + p^ (Nge it" + N37 /T*) exp (-yp^ ) + p'^ (Ngg/T^ + Ngg /T^) exp (-yp^) + p^^ (N^°/T^ + N31 /T^ + Nga /T*) exp (-yp^)

where p is in moles per liter, P is in atmospheres, T is in kelvins, and R is 0.08205616 i. atm/mol.K. The critical point was constrained to the value P = 12.670 atm,

p = 15. 556 moles per liter, T = 32. 938 K and SP/^p = a'P/Sp^ = 0. The thermodynamic

conditions for phase equilibrium for the coexisting liquid and vapor phases have been

included as data in the least squares estimating procedure. The least squares estimates

of the parameters (N^) are given in table 8.

Table 8. Coefficients for Equation (8)

Ni = 9. 7724756841x10"* Nl7 6. 1714686495x10"^

Na : 2. 7152251047x10"^ Nie 5. 0101024725x10"®

N3 == -4. 0181051493x10"^ Nl9 = -5. 5717474190x10"^

N4 = 1. 6841979481 Nao = -1. 8913610938x10+^

N5 =: -2. 1489533487x10-^^ Nai = -3. 7831399504x10"^^

Ne == -1. 6675599518x10"® Naa = -8. 4616109347x10"^

N7 = 8. 4131860302x10"^ Na3 1. 3760409852x10*^

Ne := -5. 7557476830x10"^ Na4 = -1. 1323039340x10"^

Ng = 2. 1149417739x10*^ Nas 1. 3554583722x10"^

Nio = 1. 2387354960x10"® Nae = -1. 8443884951x10"®

Nil == -3. 1280580947x10"* Na7 = -5. 1666928590x10"®

N12 = 2. 5945419913x10"^ Nae = -2. 9044621463x10"^°

Ni3 = 5. 2494587855x10"® Nao 5. 0870054382x10"^

Ni4 == -9. 5113449800x10"'' N30 = -1. 0229323667x10"^^

Ni5 == -7. 2316698085x10"^ N31 = -2. 0248578837x10"^^

N16 == -3. 8383727284x10"'' Nas 1. 1900504363x10"^^

R = 0.8205616 X.atm/mol.K

11
A complete listing of the computer program which was used to estimate the

coefficients in table 8 is given in Appendix A. The listing includes a point by point

comparison of the input experimental data with the corresponding values calculated using

eq (8).

€

Conclusion

The equation of state, eq (8), is the best MBWR representation of the PVT surface

of hydrogen which could be formulated at this time, as is always the case with the MBWR,

the behavior at the critical point is analytic and, therefore, does not qualitatively or

quantitatively represent the specific heat capacity at constant volume. When new

experimental data for the high pressure region become available, the parameters for eq (8) should be re- estimated using the new data. The saturation boundary (liquid- vapor ) as defined by eqs (6) and (7) need no further numerical treatment until new experimental data

become available or the international practical temperature scale is re-defined. One of

the objectives of this task was to develop an equation of state explicit in density. The

curtailment of funding did not allow the pursuit of this objective to a degree of completion

which could be reported here.

12
5. References

Bender, E. , Equations of State Exactly Representing the Phase Behavior of Pure

Substances, (Proc. 5th Symp. of Ther mophy s ical Properties) 227-35, ASME,

N. Y. (1970).

Diller, D. E. , Refractive Index of Gaseous and Liquid Hydrogen, J. Chem. Phys. 49 , No. 7, 3096-3105 (Oct 1968).

Goodwin, R. D. , Diller, D. E. , Roder, H. M. , and Weber, L. A., Pressure-DensityTemperature Relations of Fluid Para- hydrogen from 15 to ICQ K at Pressures to 350 Atmospheres, J. Res. Nat. Bur. Stand. (U.S.) 67A (Phys. and Chem.), No. 2,

173-192 (Mar-Apr 1963).

Goodwin, R. D. , J. Res. Nat. Bur. Stand. (U. S. ) 73A (Phys. and Chem. ), 487 (1969).

Jacobsen, R. T. , The Thermodynamic Properties of Nitrogen from 65 K to 2000 K with

Pressures to 10, 000 atm, Ph.D. Thesis, Washington State University (Jun 1972).

McCarty, R. D. , and Weber, L. A., Thermophysical Properties of Parahydrogen from

the Freezing Liquid Line to 5000 R for Pressures to 10,000 psia, Nat, Bur. Stand.

(U.S.), Tech. Note 617 (Apr (1972).

Michels, A., de Graaff, W. , Wassenaar, T., Levelt, J. M. H. , andLouwerse, P.,

Compressibility Isotherms of Hydrogen and Deuterium at Temperatures between

-175°C and +150° C (at densities up to 960 Amagat), Physica 25_, 25-42 (1959).

Roder, H. M. , Diller, D. E. , Weber, L. A., and Goodwin, R. D. , The Orthobaric

Densities of Parahydrogen, Derived Heats of Vaporization, and Critical Constants,

Cryogenics 2, No. 1, 16-22 (Mar 1963).

Roder, H. M. , Weber, L. A., and Goodwin, R. D. , Thermodynamic and Related

Properties of Parahydrogen from the Triple Point to 100 K at Pressures to 340

Atmospheres, Nat. Bur. Stand. (U.S.), Monogr. 94, 112 pages (Aug 1965).

Strobridge, T. R. , The Thermodynamic Properties of Nitrogen from 64 to 300 K between

0.1 and 200 Atmospheres, Nat. Bur. Stand. (U.S.), Tech. Note 129 (Jan 1962).

Weber, L. A., Diller, D. E. , Roder, H. M. , and Goodwin, R. D. , The Vapour Pres sure

of 20 K Equilibrium Hydrogen, Cryogenics 2_, No. 4, 236-238 (Jun 1962).

Younglove, B. A. , and Diller, D. E. , The Specific Heat of Saturated Liquid Parahydrogen from 15 to 32 K, Cryogenics Z, No. 5, 283-287 (Sep 1962).

13
Appendix A. Computer Listings

1) /lit/73

PROGRAM H2 FIT 1 DIMENSION P(20C0),O(2000),T(2000),PCV{300),TCV(300),DCV(303),

lC\/( 3 00 ) ,A (33 ) , G (32) ,P (i^O ) ,Q (32)

COMMON FjYjNFUN

COMMON/DATA/A, G ,PP, ID ,TT ,GAMMA ,ID

COM:iON/GIBS/RHOV,RHOL

TYPE DOUBLE A , G

, PP , 0 J , T T , GA MMA , F , Y ,

Q

DATA (SIGP = .01) , (3IGD = .0 0 1), (GAMMA = .0 01) , (SIGT = .0 2)

- DATA (SI GCV = . Ct) , (RE = 3. 31 !»3'*) , (R=. 03205616)

DO 10 1=1,2000

READ 100,P (I) , D (I) , T ( I)

IF (P (I ) .LE. 0 . 0 ) GO TO 11

IC D(I)=D(I)»i01J0.

100 FORMAT (i+FlS. 1)

11 NP\/T=I-1

DO 15 1=1,300

READ 100,PC\/ (I ) ,TC\/ ( I ) ,DCV( I) ,C\/ (I)

IF(OC\/(I) .LE.O. 0)GO TO 16

15 OCV ( I) =OCV (I) 1030.

16 NCV=I-1

NPV T=NIPVT + 1 DO 800 I = NP\/T, 20 00

REAO 801,P (I) , D (I) , T (I)

IF(P(I) .LT..001)GO TO 802

800 CONTINUE

801 FORMAT (3F10. 1) 602 NP\/T=I-1

606 FORMAT (11X,D30. 20)

GAMMA = -. 00^+1

NFUN=32

NP=MFUN

CALL CPCON

DO 20 I = 1,NP\/T

DO=D (I

)

TT = T (I

)

PP=P(I)

W = l . /(PP*1G0G. ) IF(DD.LT.20. )W=W»3.

IO=0

CALL PRESS

DO 17 J=1,NP

17 F(J)=A(J)»W

Y=A ( NP+1) *W

CALL FIT

20 CONTINUE

IF{ IC3N.EQ. 1) GO TO I4 1 00 3 0 I=1,NC\/

W=7./10aQ.

DO=DC\/(I)

TT=TCV(I)

ID=3

CALL TOSOT

DO 21 J=l,NO

21 Q(J)=A(J)

1 4
H2FIT1 1) /ltt/73

00=0

CALL TOSDT

DO 22 J=1,NP

22 F(J) =(A(J)-Q(J) )*W

Y=(CV(I)-CPO(TT, l)f RE) W/10 1.325

CALL FIT

30 CONTINUE

IF(IC0N.E(J.2)G0 TO t*i DO '0 I = li+,32

TT=I

IF(ICON.EQ.£»)GO TO 33

Y=-DPDTVP{TT)»(1./0SAT7(TT) -l./DSATL (TT) )»W

OOsOSATV(TT)

ID=0

CALL OSON

00 31 J=1,NP

31 G(J)=A{J)

DD=OSATL(TT)

ID=0

CALL DSON

00 32 J=1,NP

32 F(J)=(A{J)-G(J) )»W

CALL FIT

33 M=1./1Q000.

PP=\/PN(TT)

DO=OSATL{TT)

NP»/T=NP\/T4-1

P(NPVT)=PP

T{NPVT)=TT

0(NP\/T)=DD

IO=0

CALL PRESS

DO 3k J=1,NP

3k F(J)=A(J)»W

Y = A (NP*-1) W

CALL FIT

CALL OUDN

DO 36 J=1,NP

36 Q(J)=A{J)

DO=OSATV(TT)

NPVT=NPVT+1

P(NPVT) =PP

T(NPVT) =TT

O(NPVT) =00

W=l, /(PP»1000.

)

W=W*3,

IF(TT.GT.25. )W=W*5.

10= J CALL PRESS

DO 35 J=1,NP

35 F{J)=A(J)»W

Y=A (NP+1) W

CALL FIT

CALL OUDN

15
H2FIT1 l)/l«»/73

DO 37 J=1,NP

37 F(J)=(A(J)-(l(J))»M

Y=P(NPVT) • (l./D (NPVT-l) -l./D(NPVT) ) +R»TT»( L OGF ( 0 (NP VT- 1) R»TT)

1-L0GF(D(NP\/T)»R»TT) ) Y = Y»W

CALL FIT

kO CONTINUE

t»l CONTINUE

CALL COEFF

00 1*3 1=1, NP

805 FORMAT(* G

( * , I 2

, ) * ,03 0 . 2 0

)

Q(I)=G(I)

^3 G(I)=F(I)

105 FORMAT(F10.it,3F10.3,2F10.2)

DO ^i* 1=1, NP

''+ PUNCH 805,I,G(I)

CALL STAT

DO 50 I=1,NPVT

IFdNDEXd ,50) .GT.O) GO TO kZ

PRINT 101

PRINT 102

t»2 DO=0(I)

TT=T(I)

10=1

CALL PRESS

PCAL=PP

DQ=0(I)

PQ=P<I)

TQ=T(I)

DCAL=FIND D(PQ,DQ,T3)

ODIF = (0(I) -OCAL) lOO . /D( I)

POIF = (P<I)-PCAL)»10 0. /P(I)

50 PRINT 103, P(I) ,D(I) , T (I) ,PCAL,DCAL, PDIF, ODIF

IF{ ICON.EQ. 1) GO TO 99

10 3 FORMAT (2F 10. 3, 2(F10.i+,F10,3),2F10.2)

101 FORfiATClHl)

102 FORrlATC* PIN 0 IN T IN P CAL D CAL P DIF

1 0 DIF*)

lOV FORMAT(» D IN T IN CV IN CV CAL CV GIF*)

DO 60 1=1, NCV

IFdNDEXd, 50) .GT.O) GO TO 51

PRINT 101

PRINT 10'+ 51 OD=OCV(I)

TT=TCVd)

10= 1 CALL TDSDT

P1 = PP

00= 0 CALL TOSDT

P2 = PP

C\/CAL=CP0(TT,1) -RE-(P1-P3)*101.325

UIF = (Cy/(I)-CVCAL)»10 3./CV(I)

OCAL=FIND 0{PC\/ (I) ,DCV{I) ,TC\/d) ) DOIF = (DC\/ d) -OCAL) *10 O./OCy/ (I)

16
H2FIT1 1) /lt»/73

60 PRINT 105,D3\/(I) ,TC\/{I) ,CV(I) ,CVCAL,OIF,DDIF

00 70 I=l*t,32

TT=I

TG=TT

VP=VPN(TG)

OL = OSATL(TG)

OV=DSATV(TG)

DD=DL

PP=VP

10 = 1 CALL GIBBS

PlsPP

0O=DV

CALL GIBBS

P2=PP

P12=P1-P2

PRINT 185,TT,P1,P2,P12,07,0L

185 FORMAT (6E15. if) 70 CONTINUE

80 CONTINUE

99 CONTINUE

END

SUBROUTINE GPSON

DIMENSION G(32) , A(33) ,F(<»0)

COM HON/ DAT A/ A, G,PP, 00, TT, GAMMA, ID

COMHON F,Y,NFUN

TYPE DOUBLE A, G , PP , 00 , TT , GAMMA ,F ,

Y

TC=TT=32. 938

DC=0D=15, 556

PC = PP=12.67

PRINT 100,PP,DD,TT

100 FORMAT (3F20. 3) NP=32

IO=0

CALL PRESS

00 1 1=1, NP

1 F(I)=A(I)

Y=A (NP+1)

CALL CONSTR

PP=0

CALL OPOO

DO 2 1=1, NP

2 F(I)=A(I)

Y=A (NP+1)

CALL CONSTR

CALL DP202

00 3 1=1, NP

3 F(I)=A(I)

Y = 0 CALL CONSTR

RETURN

END

17
SUBROUTINE FITTER

DIMENSION F(t»0) ,A(«*0 , ,B( '+0,'«1)

COMMON F,Y,NFUN

TYPE DOUBLE SY , SYY , RES , A ,B

TYPE DOUBLE F,Y

COMMON /7777777/ A,SY,SYY,RES

DATA (NDIM = ifO)

DATA (NTR=-1)

EaUIVALENCE ( A , 8) , ( CCC, RES) ,(DOD,SYY)

EGIUIVALENCE(NC,FNC)

ENTRY FIT

IF(NTR) 1,3,3 ' 1 NP=0

NF=NFUN

IFCNF.GT.NOIM) GO TO

NC=0

SY=0.

SYY = 0. NY=NF+1

00 2 1=1, NY

DO 2 J=1,NF

2 A(J,I)=0.

IF(NTR.EQ.O) GO TO 11

NTR=0

3 SY=Y+SY

SYY=SYY+Y*Y

00 if J = 1,NF

A{J,NY) =A( J,NY) +Y»F ( J)

DO k 1=1, NF

k A(I,J)=A(I,J)4-F(I)»F{J)

NP=NP-H

RETURN

ENTRY GONSTR

IFCNTR) 10,11,11

10 NTR=0

GO TO 1 11 N=NY-1

IF(NY.GT.NOIM) GO TO

00 12 1=1,

N

A{I,NY + 1)=A(I,NY)

12 A(I ,NY) =A (NY,I) =F(I)

NC=NC*1

DO 13 I=NF,N

13 A(I+i,NY)=A(NY,I + l)=a.

NY=NY+1

a(NY-l,NY)=Y

RETURN

ENTRY COEFF

N=NY-1

00 20 1=1, NF

20 F(I)=A(I,NY)

DO 22 1=2,

N

00 21 J=I,NY

21 A(I-l,J)=A(I-l,J)/A(I-l,r-l)

DO 22 J=I,N

18
FITTER 1) /l*»/73

00 22 K=I,Nr

22 A{J,K) =A(J,<)-fl (J,I-1)*A (I-1,K)

A(N,NY) =A (N,Nr) /A(N|,N)

DO 21* 1=2,

N

L=N-I^2

DO 2'* J=L,N

Zk A(L-1,NY) =A(L-1,NY) -A (L-1,J) »A (J,NY)

NTR=-1

RES=SYY

DO 25 1=1, NF

RES=RES-A(I,NY)»F(I)

25 F(I)=A(I,NY)

NFUN=NP

NDF=NP-NF+NC

DF=,MOF

Y=FNC

NTR=-1

RETURN

ENTRY STAT

TOT=SYY-SY»SY/NP

REG=TOT-CCC

SYY=RES/NOF

ST=1.96+2.72/0F+8. 0U/DF**3

DET = 1. DO 30 1=1, NF

OET=DET*B (1,1)

IF( A (1,1) .LE.O. 0)GO TO 30

A(I,I)=1./A(I,I)

30 CONTINUE

DO 32 1=2, NF

DO 32 J=2,I

SY = 0.

DO 31 K=J,I

31 SY=SY-A (I, K-1) *A(K-1, J-1)

32 A(I , J-l)=SY»a(I,I)

PRINT 37

DO 36 1=1, NF

L=NF-I

DO 33 J=1,L

K=NF-J

00 33 M=1,J

N=NF-M+1

33 A(K,I)=A(K,I)-A (K,N)*A(N,I)

00 3V J=2,I

3f* A(J-1,I) = A (I, J-1)*SYY

00 35 J=1,I

35 A(I,J)=A(I,J)*SYY

BB=B (1,1)

IF(3B.LT.0.0)BB=-33

FF=ST*SQRT (B8)

833=e( I ,NY)

36 PRINT 371,BB3,FF

37 F0RMAT(*1THE COEFFICIENTS AND THEIR ESTIMATED ERRORS AREO*//)

371 FORMAT(E19.10,» 0R-*E9.2)

IF ( DOD.LT. 0. 0) ODD=-ODD

19
FITTER l)/lk/73

OODsSaRTCOOD)

CORR=REG/TOT

PRINT 38,CCC,^EG,T0T,000,DET,C0RR,NP

38 FORMAT(*0»/»0»/»0E3TIMftTED RESIDUAL SUM OF SQUARES =*E17.g/

1 ESTIMATED REGRESSION SUM OF SQUARES =»E17.9/

2 * ESTIMATED TOTAL SUM OF SQUARES =*E17. 9/

1* VARIANCE OF FIT =»E17.9/» DETERMINANT OF THE MATRIX =»E17.9/

I** CORRELATION COEFFICIENT =»E17.9/» NUMBER OF POINTS =»I5)

Y=SQRT (CCC/OF)

NFUN=NDF

RETURN

tti* PRINT

it5 F0RMAT(»1THE ARRAYS IN THE FITTING PROGRAM ARE TOO SMALL TO HOLD T IHE NUMBER OF CONSTRAINTS AND FUNCTIONS ASKED FOR IN THE CALLING PR

20GRAM*)

STOP

END

FUNCTION FIND D(P,D,T)

DIMENSION A(33) ,G(32)

COMMON/DATA/A, G,PP,Da,TT,GAMMA,ID

TYPE DOUBLE A, G , PP , DD , TT , GA MMA

PP=P

TT=T

DO=D

00 10 1=1,50

10=1

CALL PRESS

P2 = PP

IF(ABSF(P-P2)-1.L-7»P)2 0,20 ,1

1 CALL OPDD

OP=PP

C0RR=(P2-P) /O^

IFCABSF (C0RR)-1.E-7*1) 20 ,20 ,10

10 DO=DD-CORR

FIND 0=0

RETURN

20 FINO D = DO

RcTURN

END

FUNCTION INDEX{I,J)

IF(I-l) 13, 13,2

2 IFF=I/J

IFF=IFF*J

IF(I.EQ.IFF) GO TO 13

INDEX=1

RETURN

13 INO£X=0 : RETURN

END

20
1) /I'+ZTS

SUBROUTINE PROPS S DIMENSION X{33)

DIMENSION 3(33) ,G(32)

COMHON/DATA/8, G,PP, 00, TT, GAMMA, ID

TYPE DOUBLE B, G ,PP , 00 , TT ,D, T , P ,D2 ,D3 ,0'» ,05 , D6 , 07 ,D8 , 09 , DIO , Dll , 0 12

1,013,TS,T2,T3,TU,T5,F ,F1,F21,F22, F 23, F 2 £ , F2 5, F26 , G AMMA

TYPE DOUBLE F2 1 2, F22 2 , F2 32, F2'+2 , F252 ,F262

1 ,F2 ,F3,Fit,F3 3,F35,F3 7,F3 9,F311,F313,F<t3,F4»5,F<»7,F<t9,Fi»ll ,Fif 13

TYPE DOUBLE Gl , G2,G3 , Gi*, G5, G6, X EQUIVALENCE (B,X)

PROPS FOR H2 USING THE S TEH ART- J ACQ BSEN EQUATION

1 CONTINUE

R=8. 205616D-2

0=00

P=PP

T=TT

GM=GAMMA

D2=D*D

03=D2»D

D4=03»0

DSsDW'O

D6=D5»0

D7=D6*D

08=07*0

09=08»D

D10=O9»D

Dll=O10»D

012=011*0

013=D12»D

TS=SQRTF(T)

T2=T*T

T3=T2»T

Tt» = T3*T

T5=T'«*T

F=EXPF (GM»02)

GO TO ( 100 , 200 , 300, '00, 500, 600 , 700, 800, 900 ) ,K

ENTRY PRESS

K = l GO TO 1 100 CONTINUE

B( 1) = D2*T

8( 2) =02*TS

3( 3) = 02

B( k) = 02/

T

a( 5) =02/T2

B( 6) = D3*T

9( 7) = 03

B( d) = 03/T

6( 3) =33/T2

B(10 ) = Oi»»T

8(11) = 0'+ 6(12) = Ok/l

B(13) = 05

B(li») = D6/T

8(15) =D6/T2

21
PROPSS 1) /lf»/73

B(16)=07/T

8(17) = D8/T

B(18)=08/T2

B(19)sD9/T2

B(20)=O3»F/T2

B(21)=03»F/T3

B{22}=05*F/T2

B(23) = D5»F/Tif

B(2i») = D7»F/T2

B(25)=D7*F/T3

B(26)=09*F/T2

B(27) = 09»F/Tt»

B(28)=011»F/T2

B{29)=011»F/T3

B(30)=013»F/T2

fl(31)=013»F/T3

B(32) = D13»F/Ti»

IF(I0.GT.0)GO TO 102

B(33)=P-R»0»T

RETURN

102 P=0

M=32

00 101 1=1,

M

101 P=P+e(I)»G(I)

P=P+R»0*T

PP=P

RETURN

ENTRY DPOD

K=2

GO TO 1 200 CONTINUE

F1=2.00*F»GM*0

F21=3. 000»F»D2 +F1»D3

F22 = 5. 000»F»Oit +F1»Q5

F23=7.000»F»D6 +Fl»07

F2't = 9. 000»F»D8 +F1»09

F25=ll. 0 0»F»D10+F1*D11

F26=13. 00»F»D12+Fl*O13

8( l)=2.00*O»T

9( 2)=2.00*D»TS

B( 3)=2.00»0

fl( ') = 2.C0»O/T

B( 5)=2.00»D/T2

B( 6>=3.C0*D2»T

9( 7)=3.00»D2

a( 8)=3.00»02/T

8( 9)=3.00»D2/T2

3(10) = i».00*D3»T

8(ll) = «t. 00*03

8(12)=<t.00*Q3/T

8(13) = 5.00»Oi»

B(l't) = 6.00*D5/T

8(15)=6.00»D5/T2

B{l&)=7.00»06/T

B(17)=8.00»D7/T

22
PROPSS 1) /l«»/73

B(18)=8.00*D7/T2

a{19)=9.00»D8/T2

8(20 ) = F21/T2

8(21)=F21/T3

B(22)=F22/T2

8(23)=F22/Tif

B(2tf ) = F23/T2

B(25)=F23/T3

e{26)=F2'+/T2

8(27) = F2i+/Tif

B(28)=F25/T2

B(29)=F25/T3

B(30)=F26/T2

8(31)=F26/T3

B(32)=F26/T'*

M=32

IF(ID.GT.0)GO TO 202

B(33)=P-R»T

RETURN

202 P=0

DO 201 1=1,

M

201 P=P*B(I)*G(I)

P=P+R»T

PP=P

RETURM

ENTRY OPDT K = 3 GO TO 1 30 0 C0NTI«4UE

X( 1)=02

X( 2)=02/ (2. 00»TS)

X( 3)=0

X( ')=-D2/T2

X( 5)=-2. 00»D2/T3

X{ 6)=03

X( 7)=0

X( 8)=-03/T2

X( 9)=-2. 00»O3/T3

X(10) = 0i* X(11)=0

X(12)=-D4/T2

X(13)=0 X (li*) = -D6/T2

X(15)=-2. 00*O6/'T3

X(16)=-07/T2

X(17)=-D8/T2

X(ld)=-2.00»08/T3

X{19)=-2. 00»O9/T3

X(20 )=-2. 00*O3»F/T3

X(21) = -3. 00*O3»F/T!»

X(22)=-2. 00»05»F/T3

X(23)=-'+. 00*O5»F/T5

X(2'+) = -2. 00»07*F/T3 X (25 ) = -3. 00»O7»F/T£»

X(26)=-2,00*O9»F/T3

23
PROPSS l)/l<»/73

X(27)=-<».00»O9»F/T5

X(28)=-2.00*Oll»F/T3

X(29) = -3. 00*011»F/Ttt

X{30)=-2,00»O13»F/T3

X(31)=-3. OO'DIS^F/T**

X(32) = -'», 00»O13»F/T5

IF(ID.GT.0)GO TO 302

X (33)=PP-R*0

RETURN

302 P=0

00 301 1=1,32

301 P=P-»-G{I)*X (I)

PP=P+R»D

RETURN

ENTRY DSDN

GO TO 1 '00 CONTINUE

S=S0-R*LOGF(D»R*T/P0)+(DSDN(D)-DSDN(0))*101.325 +CPOS(T)

Gl = F/( 2.00»GM)

G2= (F»02-2.00»Gl)/{2. 00»GM)

G3= {F»Oi»~i».00»G2)/(2. 00*GM)

Git= {F*D6-6.0 0»G3)/{2. 0 0*GM)

G5={F»O8-8.0 0*G'»)/(2. 0 0»GM)

G6= (F»0 10 -10,0 0 G?) / { 2. 0 0*GM)

X{ 1)=-D

X( 2)=-D/ (2. 00»TS)

X( 3)=0.D0

X( i») = + D/T2

X( 5)=2.00»D/T3

X( 6)=-D2/2.00

X( 7)=0.D0

X( d)=D2/ (2. 00»T2)

X( 9)=02/T3

X(10 )=-03/3. 00

X(ll)=0.O0

X(12) = O3/(3.00»T2)

X(13)=0.O0

X(li») = O5/(5.00»T2)

X(15)= 2.00»O5/ (5.00»T3)

X(16)=D6/(6.QD*T2)

X{17)=07/(7. 00»T2)

X(ld) = 2.00*D7*' (7.00*T3)

X(19)=08/ (i*. 00»T3)

X(20)=2.00*G1/T3

X(21) = 3.00»G1/T't

X(22)=2.00»G2/T3

X(23)=^.00»G2/T5

X(2'+) = 2.00*G3/T3

X{25) = 3.00*G3/T'»

X(26) = 2.00»G'+/T3

X(27) = '».00*S'*/T5

X(28)=2.00*G5/T3

X (29) = 3.00»G5/Ttf

X(30 )=2.00*G6/T3

24
PROPSS l)/lU/73

X(31)=3.00»G6/T4

X(32) = i+.C0*G6/T5

IF( ID.GT, 0)GO TO ^02

RETURN

kQ2 p=0

DO '01 1 = 1,32

'01 P=P + G(I)»X (I)

PP=P

RETURN

ENTRY OUDN

K=5

GO TO 1 500 CONTINUE

C H=Ha + (T*DSDvJ (0) -OSOS (0) ) lO 1. 325+ (OUDN ( D-D UDN (0 ) ) !0 1 . 32 5+CPOH (T)

C (P/0-R*T) 101. 325

G1=F/(2.00*GM)

G2= (F»D2-2.0 0»G1) /(2, 0 0* GM)

G3= (F* '-'. 0 0* G 2) / (2. 0 0*GM)

Gi+=(F*D6-6.0C*G3)/(2. 0 0 GM)

G5= (F»08-8. 0 0*Gi+)/(2. 0 0* GM)

G6= (F*D10-10. D0*G5) / (2. Oa*GM)

X( 1)=0*T

X( 2)=D*TS

X( 3)=0

X{ k)=0/l

X( 5)=0/T2

X( 6)=O2*T/2.00

X( 7)=O2/2.00

X( 8)=D2/(2. 00*T)

X( 9)=D2/(2.00*T2)

X(10)=O3*T/3.00

X(ll)=O3/3.00

X(12) = D3/(3. 00*T)

X(13)=O'+/i*.0 0 X(l(+) = 05/(5. 00*T)

X{15)=05/(5.0G*T2)

X(16)=O6/(6.00*T)

X(17)=D7/ (7.00*T)

X(18 ) = 07/ ( 7. 00*T2)

X(19)=D8/(8. 00*T2)

X(2 3 ) = G1/T2

X(21)=G1/T3

X (22)=G2/T2

X(23)=G2/T'+

X{2'4) = G3/T2

X(25)=G3/T3

X(26) = G'+/T2

X (27)=6'4/Ti^

X{28)=G5/T2

X (29)=G5/T3

X(30 )=G6/T2

X (3i)=G6/T3

X{32) = G6/T'+

IF( ID.GT. 0 ) GO TO 5Q2

RETURN

25
PROPSS

502 P=0

DO 501 1=1,32

501 P=P*G(I)*X(I)

PP=P

RETURN

ENTRY TDSDT

K=6

GO TO 1 600 CONTINUE

CV=CyO+(TDSDN(/)-TOSON(D) )»101.325

G1=F/(2.00»GM)

G2= {F»02-2.0D»Gl)/(2. 0 3»GH)

G3= (F*Di+-'».00»G2)/(2. 0 0* GM)

G'»=(F»O6-6.0 0*G3)/(2. 00»GM)

G5= (F»O8-8.Q0»5'+)/(2. 0 0»GM)

G6= (F»D10- 10.0 0*G5) / (2.0 0»GM)

X( 1)=0.D0

X( 2)=-D/('». CO»TS)

X{ 3)=0.DO

X( ^)=2.00*D/T2

X( 5)=6.00»D/T3

X( 6)=0.D0

X( 7)=0.O0

X( 3)=D2/T2

X{ 9)=3.G0»D2/T3

X(10)=0.OO

X{11)=0.D0

X(12)=(2. 00»D3) /(3. 03*T2)

X(13)=0.D0

X(lit)=(2.00»D5)/(5.00*T2)

X(15)= (6,0 0»D5) / (5. 0 0*T3)

X(i6)=06/ (3. 00»T2)

X(17)=(2,00»O7)/{7.00*T2)

X(ld)={6.0 0»O7) /(7,Q0*T3)

X(19)=(3.00*D8)/('t.00»T3)

X(20)=6.C00*G1/T3

X (21) = 12. 00»G1/TU

X(22)=6.000»&2/T3

X(23)=20. 00»G2/T5

X(2'») = 6.000»G3/T3

X (25) = 12. 00»G3/'Ti»

X(26) = 6. 000»G't/T3

X(27 ) = 20. 00»G'»/T5

X(28)=6.000»G5/'T3

X (29) = 12. 00»G5/Tit

X(33 ) = 6.0C0»G6/T3

X (31 ) = 12. OO^GS/Tit

X(32)=20.00*G6/T5

IF(ID.GT.0)SO TO 632

RETURN

602 P=0

DO 601 1=1,32

601 P=P+G(I)*X(I)

PP=P

RETURN

26
PROPSS 1) /ik/73

700

702

701

8Q0

ENTITY DP2D2

K=7

GO TO 1 CONTINUE

F1=2.*F»GM*0

F12=2.*F1»GM*D*2.»F»GM

F212=3.*Fl»0 2f3.»2. *a*F+Fl2*03+Fl*3.»02

F22 2 = 5.*F1*0'» +5.»'*. D3*F+5 .*D<*»F1 + F12*D5

F23 2=7,*Fl»06f 7.»6.*0 5»F+7. •06*F1+F12*D7

F2i«2=9.»Fl»08+9.»8.*3 7»F + 9. 08»F1+ F 12*09

F25 2=11.»F1»D10+10. 'll, *D9*F+ll,*D10*Fl+F12*Oll

F26 2=13.*F1*012+13,»12.*011»F+13.»D12*F1+F12*D13

B(1)=2.*T I9(2)=2.*TS t B(3)=2.

B('+)=2./T S 0(5)=2./T2 f B{6)=6.*0*T

B(7)=6.»D t 8(8)=6.»D/T « 3(9)=6.*D/T2

B (10 )=12. *02*T J B(11)=12.*D2 $ B (12 )= 12 . D2/T

3(13) = 20.»D3 $ B{l'+)=30.*Di+/T J 9 ( 1 5 ) = 30 . 0'+/T2

$ B ( 17) =56.*D6/T $ 6 ( 18 ) = 56. * D6/T2

t 3 (20)=F212/T2 "i B ( 21 ) =F212/T3

3(25)=F232/T3

B(28)=F252/T2

8(31)=F262/T3

8(16) = '+2. D5/r

P (19)=72.»D7/T2

B(22)=F222/T2

a(23)=F222/Ttt J 3 ( 2 =F23 2/T2 $

e(26)=F2<t2/T2 J 3 ( 2 7 ) =F2't 2/T U J 3(29)=F252/T3 $ 3 ( 3 0 ) =F26 2 / T 2 $

B(32)=F262/T'+

M=32

IF( ID. GT. 0 ) GO TO 702

B(33)=PP

RETURN

p=a

DO 701 1=1,

M

P=P+8(I)*G(I)

pp = p RETURN

ENT^Y DP3D3

K = 8 GO TO 1 CONTINUE

F1=2,*F*GM*D

F2 = 2.*F»GMt-GM»2. 'O^Fl

F3='+,*F1*GM4-&>1»2.*D*F2

F33 = 6.*F+18, 0»Fl+9. D2*F2+D3»F3

F35 = 60 .*D2»F + 6C.*O3*Pl*lS.»Di+*F2 + D5*F3

F37 = 22 0.*D'+»F+126.»0'3*F1+21 . *D6*F2 + 07*F3

F39 = 50 i».*06»F*- 2 16. *D7»F1 4-27. 08* F2 + 09»F3

F311=99 0. O8*F«-330 .*39*F l + 33.*D10*F2fDll*F3

F313 = 1716. O10*F4-'»6 8.*Oll»Fl + 39.*D12*F2 + ni 3»F3

a(l)=0.0 J B(2)=J.J S B(3)=C.O i B('+) = Q.O $

a(6)=6.»T t B(7)=6. a B(3)=6./T f 3(9)=6./T2

B (5) =0.

0

8(10 ) = 2i+. *0»T I '3(13) = 60.»02 ? B(16) = 210.*0it/'T

8 (19) = 5Qtt. 06/T2

B(20)=F33/T2 f B(23) = F35/Ttt $

G(26)=F39/T2 $

3(il)=2i*.*D S B ( 12) = 2'».*0/T

BClit) =120. *D3/T t B( 15) =120. *D3/T2

t 3 (17)=336.*05/T S B ( 1 8 ) = 33 * 05/ T2

B(21)=F33/T3 J 3(2:+)=F37/T2 S B(27)=F39/Tit t

8 (22) =F35/T2

3( 25) =F37/T3

9(28) =F311/T2

27
Pf?OPSS l)/li»/73

B(29)=F311/T3 $ 3 ( 3 0) =F31 3/T2

B{31)=F313/T3 S B ( 32) =F31 3/Tif

M = 32

IF(ID.GT.O) GO TO 832

8(33)=PP

RETURN

802 P=0

00 801 1=1,

M

801 P=P+B(I)»G(I)

PP=P

RETURN

ENTRY OPi*Ok

K=9

GO TO 1 900 CONTINUE

F1=2.»F»GM»D

F2=2.»F*GM+GM*2.»0»F1

F3=it.»Fl»6Mf GM»2.*D»F2

F«»=6.*F2»GM*GH*2.»0»F3

Fit3 = 2't.»Fl + 36. »0*F24-12.»02»F3 + D3»Fit

F'*5 = 12 0.»O*F + 2't0.*a2*Fl + 120 .O3F2+ 2 0.D^»F3+D5F^

Fi»7 = 88 0.*D3»F«-8 50.»D<t*Fl«-25 2.*O5*F2«-28.*O6»F3 + D7*F«f

F't9 = 30 2'+,»D5»F + 2016. * 06*Fl+ 32 . 07*F2 + 36 . D8»F3 + D9* Fi» Fi+11 = 7920.»D7*F + 3960.*D8»F1 +660 . D9»F2 + 01 0 * F3* 0 1 1 »F U F'tl3=17l60.»O9*F+65 7 8.*Di0»Fl*93 6.»Dll*F2*-52. *D12*F3*D13»F«»

B(1)=0.0 S 3(2) = 3.a $ 3(3)=0.0 "5 9(t»)=0.0 $ 8{5)=0.0

e(6)=0.0 t B(7)=0.0 S B(8)=0.0 « 9(9)=0,0

B(10) = 2'f.*T $ 8(ll)=2i+, $ B{12)=2W./T

B(13) = 120.*D t Bdt) =360. 02/T J B ( 1 5) =3 60 . *D2/T2

B{16) = 8'fC.»D3/T S 3 ( 1 7 ) =1 680 . Qtt/ T $ B ( 1 8 ) = 1 68 0 . 0'f/T2

8(19) = 302'+.»D5/T2

8(20 )=Fit3/T2 8 8 ( 2 1 ) =F 143/ T 3 J B ( 22 ) =Fit 5/T2

B(23) = F/»5/Tit $ B(2i»)=Fi47/T2 $ B ( 25) =Fi»7/T3

B(2&) = F't9/T2 $ B(27) =Fi»9/T'* % 3 ( 28) =Ff» 1 1/T2

B(29)=F'tll/T3 $ 3{30)=Fi+13/T2 $ 3(31) = F«»13 /T3

B(32) = Fi+13/T'+

M=32

IF(IO.GT.0)GO TO 902

9(33)=PP

RETURN

902 P=0

DO 901 1=1,

M

901 P=P+B(I)*G(I)

PP = P. RETURN

END

28
l)/lU/73

SUBROUTINE GIB8S

DIMENSION A(33) ,G(32

)

COMMON/DAT A/A, G,PP, 00, TT, GAMMA, ID

TYPE DOUBLE A, G , PP , 00 , TT , GA MM

A

R=. 08205616

DQ=OD

PQ=PP

10=1

CALL DUON

U1=PP

DO=0

CALL OUDN

UO=PF

PP=Ul-UC+PQ/Oa

PP=PP*-R»TT*LOGF (OQ*R*TT)

DO=OQ

RETURN

END

FUNCTION WEIGHT (DO)

DIMENSION G(32) ,A{33) jFCftO)

COMMON/ DAT A/ A, G , PP , DD , T T , GA MMA , I

D

TYPE DOUBLE A , G , PP , 00 , TT , GA MMA , F , Y COMMON F,Y,MFUM

SIGO=. 001*DD

SIGP=.01

ID=1

pa=pp

TQ=TT

DQ=OD

dcal=find o(Pa,Dq,Ta)

CALL PRESS

PCAL=PP

CALL OPDO

DP=PP

PP=PQ

W£IGHT = SQRTF ( ( ( ( PC AL - PQ ) *10 0 . /PQ ) * 2* ( (OCAL-OO) lO 0 . /DQ) •»2 ) / ( ( S IG

10»0P)**2 + SIGP»»24-Pa **2))

RETURN

END

FUNCTION VPN(T)

DIMENSION G(5)

DATA (G = 3. 05 3 00 1 3(tl6't, 2. 6 081 0925813, -0.655'+61 216567, 1, 595 li+i»393 7«» , 11. 5dl'ti+5'+£»28) , (TC = 3 2. 938) , (PR=0. 0 695 ) , ( TR= 1 3 . 8

)

A=(1,-TR/T)/(1.-TR/TC)

X = A»G(l)+A*»2»G(2)+A»»3*G(3)+A*((l.-A)»*G(5))»G(it>

VPN=PR*EXPF(X)

RETURN

END

29
FUNCTION DSftTV(T)

DIMENSION GV (8 ) ,GL{7)

DATA {GL = 0. Ot»86t»5813 0 OSt-l.it/Zea/eiaeE-Zttt, 0 7 7653 819 2E-1,

1-1. 171 9787 30«t, 1. 621 3 a 2if <,-!. 15 31096683, 0.3 3 825tf9?0 3 9)

DATA (RHOC=0. 03136) , ( JETAL = . 3'f7 860 27 325) , (TC=32.938)

DATA (Gi/=- 0.0 '7 5 0157 15 29, 3. i+ 8 71 21 30 0 5E-2 , . 1221 290 925E-1 , 11.56665985 5,-2,8 061i»2 73 3 9,2.7105'*55626,-l. 3 0 7«t77359,

2 0. 2 2 92128 5 922) , (BETA 7 =. 3 '83 123 7625) , (FACT='»96. 0'»651

)

A=( TC-T)/TC

0»/=RHOC-»-G\/ (1) 'A^^BETA V DO 1 1=1,7

1 DV=DV+GV(I+1)»A**(1. + {I-l)/3.)

DV=3V»FACT

DSATV=OV

RETURN

ENTRY OSATL

A=(TC-T)/TC

DV=RHOC+GL (1)»A»»3ETAL

DO 2 1=1,6

2 D\/=D\/+GL(I+1)»A»*(1. + (I-l)/3. ) DV=DV»FACT

OSATV=D\/

RETURN

END

FUNCTION DPDT\/F(T)

DIMENSION G(5)

DATA (G=3. 053 0013'+16'+, 2. 8 0810 92 5813,-0.65 5<t61216567, 1.5 951i»'t393 7't , 11.5dlki*5ht*26) 1 (TC=32. 938) , ( PR=0. 0 695) , (TR=13.8)

A={1.-TR/T)/(1.-TR/T0)

0A0T=(TR/T»»2) / (l.-T ^/TO

DP0T=G(1) DADTf 2.*3(2)»A»0ADT + G(3)*3.»A»»2»0A0T*G{'»)*( (l.-A) GC 5)

l)»OADT+G(i»)*A»{ (l.-A) ** {G(5)-l.) )»G(5)* (-OAOT)

DPDT=DPDT»\/PN(T)

DPDTVP = OPDT

RETURN

END

30
1) /l«»/73

FUNCTION ATKINT ( X , Y -i 41 , X 1AT , NELM TS, NMAX , N^ SSY , ACRC Y ) C THIS PROGRA^I HAS BEEM CH4NGED SO THAT THE OSCILLATING NATURE OF

C THE MATRIX TO BE I ^^T ERPOL AT EO EXISTS ONLY AT THE UPPER END OF THE

C TABLE

C THIS ROUTINE HILL TAKE INPUT MATRICES OF UP TO 999 ELEMENTS EACH,

C ARRANGED SO THAT THE X MATRIX(XMAT) IS IN EITHER ASCENDING OR

C DESCENDING ORDER, SELECT NMAX OF THESE POIN TS , CHOSEN SO THAT

C SUCESSIVE X VALUES 03CILATE ABOUT TH£ VALUE OF THE ARGUMENT X C UNLESS THE ENDS OF HE XMATRIX INTERFERE (IN THIS CASE THE

C OSCILATORY NATURE IS LOST BUT THE PROGRAM WILL STILL PERFORM AN

C INTERPOLATION), INTERPOLATE ON THESE NMAX PAIRS OF DATA PY

C AN OSCILATI^^G VARIABLE POINT AITKEN INTERPOLATION ALGORITHM

C EITHER UNTIL THE PERCENTAGE CHANGE IN THE INTERPOLANT IS LESS

C THAN THE ACRCY ARGUMENT(THE ARGUMENT NESSY INDICATES THE

C NUMBER OF THE POINT JUST BEFORE THE LAST ONE CHECKED) OR UNTIL

C THE NMAX POINTS ARE ALL USED. IT IS SUGGESTED THAT NMAX

C BE LESS THAN 10, ASO OF COURSE LESS THAN NELMTS. NELMTS

C INDICATES THE NUMBER OF ELEMENTS IN XMAT DP YMAT.

C IF NESSY IS ZERO IT INDICATES THAT THE INTERPOLATION REQUIREMENT

C HAS NOT BEEN SATISFIED. IF NESSY IS 1 IT MEANS THAT THE VALUE OF

C X LIES OUT SIDE THE ^ANGE OF XMAT.

DIMENSION YMAT(999), X M A F (9 99 ) , A ( 21 , 20

)

100 F0R1AT ( 1+2HINTERP0LATI0N REQUIREMENT NOT SA T ISFI E D ( X = , E 16 . 8 , 1 H> / 3 3H

ILAST 2 APPROXIMATIONS OF Y ARE ( Y = , E 1 6. 6 , IH , , E 16 . 8 , 1 H )

)

200 FORMAT (55HTHIS REPRESENTS AN EXTRAPOLATION OF THF XMAT MATRIX(X=,

1E16. 8, IH) /33HN0 CAL^JLATION HAS PEEN PERFORMED)

300 FORMAT ( 2'tHNELMTS IS LESS THAN NMAX)

UOO FORMAT ( 22HNMAX IS LARGER THAN 20)

IF(NMAX-20)71,71,69

69 WRITE OUTPUT TAPE 6,^00

ATKINT=0.

0

RETURN

71 IF ( NMAX-NELMTS) 75, 75 , 73

73 WRITE OUTPUT TAPE 6,?00

AT<INT = 0. 0 RETURN

75 CONTINUE

C FIRST TWO SUC:ESSI7E values OF THE XMATRIX THAT STRADDLE THE

C VALUE X WILw Bfc SOUGHT

JJ1=NELMTS-1

00 20 1=1, JJl

0IF1=X-XMAT( I)

0IF2=XMAT (I<-1) -X

IF (D IF 1)1 6, 15, 16

15 AT<INT=YMAT(I)

NESSY =NMAX

RETURN

16 IF ( •:IF2) 18 , 1 7, 18

17 AT<INT = YMAT(H-1)

NESSY =NMAX

RETURN

18 RATI0=DIF1/ 0IF2

IF ( -?ATI0) 20 , 20 , 19

19 HIO=I

G"; TO 5?

31
ATKINT

20 CONTINUE

C AT THIS POINT ONE COULD PRINT THE FOLLOWING STATEMENT

G WRITE OUTPUT TAPE 6,200,X

NESSY=1

ATKINT=0.0

RETURN

32 CONTINUE

C NOTE THAT RATIO IS POSITIVE IF THE TWO POINTS STRADDLE X C REGARDLESS WHICH 13 LARGER

JJJ=IMID

JUP=IMID

JON=IMIO

IF( JJJ+NMAX-NELMTS+1) 93, 38, 102

98 00 201 J=1,NMAX

JJJ=IMID+J-1

A(l , J) =XMAT( JJJ)

201 A(2, J)=YMAT(JJJ)

GO TO 203

102 00 i*l J=l,NiAX

JJ= J/2

J0E=J-2*JJ

C JOE IS 0 IF J IS ErfE^^ ANT 1 IF J IS ODD

IF(J-l) 33,'fO ,33

33 IF( JON-1) 3tf,36,3't

Zk IF(JUP-NELMTS) 35,37, 35

35 IF( JOE) 37,36,37

36 JUP=JUP+1

JJJ= JUP

GO TO t^O 37 J0N=J0N-1

JJJ= JON

GO TO '0

kO A(l , J) =XMAT( JJJ)

A (2 , J) =YMAT ( JJJ)

f+l CONTINUE

203 NNN=NMAX4-1

DO 6 J=3,NNN

L = J-1

CO 5 K = L,N'iAX

C J IS THE COlUIN NU'iR-IR

C K IS THE ROW NUMHE?

0A(J,K)=(A(J-l,K)-A(J-l,J-2))*(X-A(l,J-2))/(A(l,K)-A(l,J-2))

1 +A(J-1,J-?)

IF(<-L) 3,2,3

2 IF(AeSF((A(J,L)-A(J-l,L-l)) / A ( J , L )

) - ACRC Y/ 1 0 0 . 0 ) 7,7,3

3 CONTINUE

5 CONTINUE

6 CONTINUE

NcSSY=0

C AT THIS POI^^T ONE CO JLO ^RI N f OUT THE FOLLOWING STATEMENT,

C WRITE OUTPUT TAPE 5 , I 0 J , X , A ( NN N , NM AX ) , A ( NN N- 1 , NM AX - 1

)

aTKINT=A( NNN ,NMAX)

R1TURN

7 N£SSY=J-1

ATKINT=A{ J,.

)

RETURN

END

32
1) /l«t/73

FUNCTION CP3(ri,N)

DIMENSION T(58) ,CPP(58) ,CPN ( 56 ) , CP 0 ( 58 ) , CP E ( 58

)

COM HON/ PAR ft/, PERC EN

C CALCULATES lOESL GAS SPECIFIC HEAT FOR H2 BY INTERPOLATING

C DATA TAKEN FROM RP 1132, UNITS OF THE TABLES ARE CAL/MOL DEG 5.

C UNITS OF OUTPUT AR£ JOULES/MOL DEG K. THE INDEX N DETERMINES THE

C SPECIES, FOR N=i,PARaHY0RaGEN,N=2 NORMAL, N=3 OPTHO, U=h EQUILIB

C N = 5,S0M£ ORTHO-PARA "FIXTURE SPECIFIED BY COMMON /PARA/ , PERCENT

C RANGE OF TEMP IS FR3^ IQ TO 5000K.

DAT A (T =

1 10.0, 12.0, lk,0, 16 . 0 , 18 . 0 , 20, 0 , 25, 0, 3 0, 0 , 35 . 0 , i+O.O, 'S.O,

2 50 . 0, 55. 0 , SCO, 65, 0 , 70 . 0 , 75. 0 , 80. 0, 85. 0 , 90 . 0 , 95. 0 , 10 0. 0,

3105, 0, 110, 0,115, 0,120, 3, 125, 0,13C.0, 135. 0,ltf0,C,li»5, 0, 15 0,0, 16 0, 0,

'170.0,180.0,l9 0.0,203.0,210 .0, 22C.O, 23 0.0j2i+0.0, 25 0.0, 26 0.0, 27 0,0,

5 280 . 0, 290. 0, 30 0.0, 350. 0,i*00. 0,500. 0, 60 0., 700. ,1000., 1500. ,20 00 ., 6300 0 . ,i+00 0 . , 50 0 0 . ) DATA ((CPE (I) ,I = l,5d)='*.9 68 ,'+.9 68 8'+,'t. 9 76't7,5.01153,5.C7«t51,5.208

11, 5. 83 508, 6. 81 282, 7. 3 79 8 9, 8. 60613, 9. 00231, 9. 0800 5, 8. 93 273, 3. 65 89i«,

28, 33 60 3 , 8. 0 120 7 , 7. 710 0 9, 7. i+i+16 , 7. 21109, 7.0 1858 , 6. 85857, 6. 72 5 57, 6. 6

32 0 5 5 ,6 , 535 55 , 6 . '69 J , 6 , ^4 2 P 0 3 , 6 , 3 e i+0 3 , 6 , 3 61 5 1 , 6 , 3 0 2 , 6 , 3 375 3 ,6 , 3 i*

0

'01, 6. 3i+ 57 7, 5. 37276, 6. i+13, 6, '5925, 6. 50975, 6, 5605, 6, 6095 , 6, 65 7 2<t, 7 6. 692, 6. 73^,6.771, 6.804,6.832,

56. 356, 6. 877, 6. 6 95, 5. 950 , 5. 97'+, 6. 993 , 7. 0 0 9, 7 , 0 36 , 7. 2 1 9 , 7. 720 , 8. 19 5,

6b.d59,9.3i^2,9.7'^d)

DATA (CPO = m.9 6 8, 4,96 3, i+, 96 8,<t, 16 8, '4,9 6 8, 96 8,'+. 96 8, 96 8,'^.96e,'^. 968, 96 6,

2'+.96a,'+.96 8,'+, 9 68,4, 3 6 9 , 4 , 9 7 2 , , 975 , 4 , 9 8 1, 4 , 99 D , 5, 0 0 2 , 5 , 0 18 , 5. 0 3 9 , 35. 06'+, 5. 09'+, 5. 129, 5. 159, 3. 213, 5. 261, 5. 31 3, 5. 36 9, 5. '27, 5. 'S?, 5. 61 2,

45. 7'+l, 5. 66 8, 5. 9 92, 6. 109, 6. 219, 6. 320 , 6. '11, 6. '93, 6, 5 66, 6, 629, 6. 68 !,

56. 732, 6. 773, 6. 805, 6. 917, 5. 962, 6. 993 , 7. 0 0 9, 7. 0 36 , 7. 2 1 9 , 7. 720 , 8. 1 9 5 , 6{).859,9,3'+2,9, 7'+8)

DAT A {CPP=

It^. 968, '.963, 4. 968,4. 9 63 , 4. 9 6 8 , '+. 968 , '. 96 8, '+ . 96 8 , *. 969 , « . 972 , 98 3

,

25. 00 6, 5. 048, 5. 114, 5. 207, 5, 328, 5. 475, 5. 646, 5. 835, 6, 036, 6. 2 45 , 6, 454,

36. 559, 6, 854, 7, G37, 7. 203, 7. 351, 7, 48 0 ,7. 590, 7, 681 , 7, 753, 7, 607, 7, 870,

47. 63 3, 7. 853, 7, 603, 7. 7 42, 7. 667, 7. '=;91 , 7. 51 6, 7. 445 , 7. 3 8 0 , 7 , 322 , 7, 27 0 , 57. 225, 7. 185, 7. 1 52 , 7. 0 50, 7. 010, 6. 998 ,7.010,7.037, 7. 219, 7. 7 20 , 8. 159,

68,359,9.342,9. 748)

DATA (CPN=

14.966,4.968,4, 963,4, 963, 4.968,4. 968,4.968, 4, 968,4,968,4,969,4, 972,

24. 977, 4. 98 3, 5. C05, 5. 029, 5. 061, 5, 100, 5, 147, 5, 201, 5, 261, 5, 325, 5, 39 3,

35. 46 3, 5. 534, 5. t06, 5. 677, 5. 743, 5. ei6, 5. 632, 5. 947, 6. 008, 6. 0 67, 6. 177,

46. 276, 5. 366, 6. 445, 5. 517, 6. 581, 6. 638, 6. 687, 6. 731, 6. 769, 6, 602, 6, 831,

56. 855, 6. 876, 6. 8 94, 5. 950, 5. 974, 6. 993, 7. 00 9, 7. 0 36, 7. 219, 7. 720, 8. 195,

68,6 59,9,342,9, 743)

GO TC(1,2, 3,'+, 5) ,N

1 CP0 = AT<INT(TI,CPP,T,58, 5 , N ES , . 0 1

) * 4 , 1 84

RETURN

2 C?0=AT<INT(TI,CPN,T,56, 6 , N ES , . 0 1

) 4 . 1 8

4

RETURN

3 CPO = AT<INT(TI,CPO,T,56, 6 , N E S , . C 1) * 4 . 1 84

RETURN

4 C^OsATKINT (TI, :pE,T, 58, 5 , N E S , . 0 1

) * 4 . 1 8

4

RETURN

5 TUP=TI*.5

T0N=TI-.5

HUP=CP0H(TUP,5)

HIDN = CP0H(TDN,5)

CO0= (HUP-HO^)

RETURN

END

33
1) /l**/73

FUNCTION CPOH{TI,N)

DIMENSION T(58) ,HP(59) ,HN(58) ,H0(58) ,HE(58)

COM HON /PARA/, PERCEM

CALCULATES THE ENTHALPY OF THE IDEAL GAS FOR H2 BY INTERPOLATION

DATA TAKEN FROM RP 1932, UNITS OF TABLES ARE CAL/MOL

UNITS OF OUTPJT ARE JOULE/MOL. THE INDEX N DETERMINES THE SPECIES

SPECIES, FOR N=l ,PARAHY0R3GEN,N=2 NORMAL, N = 3 ORTHO, N = t» EQUILI8

N=5,S0ME ORTHO-PARA ilXTURE SPECIFIED BY COMMON /PARA/ , PERCENT

RANGE OF TEMP IS FROM 10 TO 5C00K,

DATA (T =

1 10.0, 12.0, Ik.Qj 16.0 , 18. 0 , 20. 0 , 25. 0, 30. 0 , 35.0 , (»0.0, itS.O,

2 50.0, 55.0, 60.0, 65.0, 70.0, 75.0, 60.0, 85.0, 90.0, 95.0,100.0,

3105. 0, 1 10, 0, 115. 0, 123. 0, 125. 0,130.0, 135. 0,li*0.0,lt»5. 0, 15 0.0, 16 0. 0,

'170.0,180 .0, 19 0.0,233.0,210.0, 22 0.0, 23 0.0,2'+0.0, 25 0.0, 26 0.0, 27 0.0,

5280 . 0, 290. 0, 30 0.0, 353. Ot^fO 0.0, 50 0.0, 60 0. ,700. ,1000. ,1500. ,20 00 ., 6300 0 .,it000 . , 50 0 0.)

OAT A (HN =

1 30 3.67

1 '27.86

3 623.02

51107.22

61626.93

72733 .9'+ 823230. 9 DATA (HP

1 i+9.6d

173.83

378.22

628. li+ 969. OU

61586.36

72729.17

823230. 9 DATA (HO

1 383.33

2 512.53

3 711.29

k 912. '9

51153.27

61&'»0 .'6

72731.52

82323 3.9

DATA (HE

1 it 9 . 6 3

2 195.77

3 538.05

k 315. 5(+ 51102.11

61626.75

72730.9'+

823230. 9 GO T0(1

313.60, 323, 5kt 333. '8, 3'»3.'+l, 353.35, 378.19, itOS.OS,

^52. 71, ^77. 56, 50 2. '3, 527. 3*+, 552.32, 577. kOi 602.62,

653. 6't, 679. 51, 705.66, 732.13, 758.92, 786.06, 813.55,

869.61, 898. 17, 927. 08, 956. 33, 9 85 . 9 1 , 10 1 5 . 6 0 , 1 0'* 5 .99 , 1169.1+9,1232. 71, 1296. 78,1361.60 ,l'+27. 10 ,1««93. 20 ,1559. 8<+,

1 69<+. 1+ It, 1 762. 30 , 183 0. '+8, 1898. 91, 19 67. 57, 20 36. '3,2 38 2. 7«+,

3'+29.'+6,'+129. 51, '831. 66,6966,23 , 10 697 . 2 , l't6 79 . 2

,

3234+5. ,i+1895. )

59.61, 69, 55, 79, ^+9, 89, '+2 , 99,36, 121+. 20, 11+9. 0*+,

198.73, 223. 61, 2^+8, 58, 273.71, 299. 11, 32*+. 90, 351.22,

'+0&.01, 1+3I+.71, '6'+. 38, 4+95.09, 526. 8^+, 559.62, 593. «+l,

663.75 , 730 . 11+, 737,23, 77i+, 92, 813, 10 , 851,69, 890.60 , 101+7. 81+, 11 26, 58, 1201+. 93, 1282. 69, 13 59. 74+, 11+3 6. 03, 151 1.56,

1660.1+9,173 3, 99, 180 6.95, 187 9.1+2,19 51.1+7, 20 2 3. 15,237 7.83,

3 1+2 9. 2 '+,1+129. 1+3,1+831.6 5,6966.23,10 697.2,11+6 79.2,

3231+5, , 1+1895, )

398. 27 , 1+0 6. 20 , 1+1 8. 1'+, £+28. 07, 1+38. 01 , 1+62. 85, 1+87.69,

537.37, 562. 21, 587.05, 611.89, 636,73, 661,57, 686.1+2,

735.18 , 761. 11, 786.09, 811. l'*, 836.28, 861.51+, 836.93,

938.23 , 961+. 18, 99 0 . 3 7 , 1 0 1 6 . 8 0 , 10 '3 . 51 , 10 7 0 . 5 0 , 1 097 .78 , 12 13. 01+, 1268, 09, 132 7, 39, 138 7, 91 , 11+1+9, 56, 151 2. 2 6, 1575.93,

1705. 76, 1771, 71+, 183 8, 32, 1905, 1+1 , 19 72, 91+, 20 1+0. 86, 238 1+. 38,

31+29.53,1+129.52,1+8 31. 6 6 , 696 6 . 2 3 , 10 69 7. 2, 11+679. 2,

3231+5. ,1+1895 . ) 59.62, 69.57, 79.56, 89.66, 99.96, 127.50, 159.12,

236.90 , 280 . 97, 326. 2i+, 371, 33, 1+15, 35, 1+57, 86, 1+98,71+,

575,93 , 612, 56, 61+8, 13, 682,82, 716,78 , 750, lU, 783.03,

81+7.76 , 379. 77 , 911.63, 9i+3.'+0 , 9 75 . 11 ,10 06. 80 , 1038.52,

,1166.0 3,123 0 , 33, 129 5. 2 3,13 60,58,11+26,43,11+9 2, 76,1559,55,

.16 91+. 32, 1762. 23, 183 0.1+3, 189 8, 88, 19 67, 55 , 20 36. 1+2, 238 2. 71+,

, 31+ 29. i+b ,1+12 9. 51,^+631.6 6, 6966 . 2 3 , 10 697 . 2 , li+6 79. 2

,

,3231+5. ,1+1395. ) ,2, 3, '+,5) ,N

1 CP0H=ATKINT(TI,HP,T,58, 6 , N ES , , 0 1 ) * i+ , 1 8 1+ RETURN

34
CPOH 1) /14/73

2 CP0H=ATKINT(TI,HN,T,58, 6 , N ES , . 0 1 ) * 'i. 18 4 RETURN

3 CP0H=ATKINT(TI,H0,T,58, 6,NES , . 0 1) i*. le^t RETURN

1+ CP0H=ATKINT(TI,HE,T,58,6 , N ES , . 0 1 ) * 18

RETURN

5 PERCENT=PERCEN /lOO.

CPOH=( ATKINT (TI ,HO,T , 58 , 6 , N ES ,. 0 1 )( 1

. -PERCENT )

+

lATKINT (TI,HP,T,5d,6,NES, .01 )*PERCENT)*«t.l8it

RETURN

END

FUNCTION CPOS(TI,N)

DIMENSION T(60) ,SP(6]) ,SN(60) ,SO(60) ,SE(60>

COMMON/PARA/, PERCEN

C CALCULATES THE ENTROPY OF THE IDEAL GAS FOR H2 BY INTERPOLATING

C DAKEN FROM RP 1932, JNIT3 OF THE TABLES ARE CAL/MOL DEG K, 1 C UNITS OF OUTPUT ARI JOULES/MOL DEG K. THE INDEX N DETERMINES THE

C SPECIES, FOR N=l ,PARAHY0R0GEN,N=2 NORMAL, N=3 ORTHO, H=k EGUILI9

C N=5,S0ME ORTHD-PAR<\ ilXTURE SPECIFIED BY COMMON /PARA/ , PERCENT

C RANGE OF TEMP IS FRO'^ 10 TO 500CK.

DATA (T =

1 10.0, 12.0, 11^. 0 , 16. 0 , 18. 0 , 20 . 0 , 25. 0, 30. 0 , 35. 0 , i*O.G, <*5.0,

2 50.0, 55.0, 50. 0, 65.0, 70.0, 75.0, 80.0, 85.0, 90.0, 95.0,100.0,

3105.0,llC.O,115.0,120.0,125 .0,130.0,135.0,l'tO,0,l'+5.0, 15 0.0, 16 0.0,

'fl70. 0, 180 . 0, 19 0.0,203. 0, 210. 0, 22 0.0, 230.0, 2^*0. 0, 25 0.0, 26 0.0, 27 0. 0,

5 280. 0, 290. 0, 30 0.0,35J.0,;+0 0.0,'45 0.0, 500. 0,550.0, 60 0.0, 70 0. ,100 0.,

61500. ,2000. , 30 00., to 3 0. , 50 00.)

OAT A (SP = U11.21'», 12. 120, 12.83b, 13. 5't9 , lit . 1 35 , 1 tf , 65 8, 1 5 . 766 , 16 . 6 7 2 , 17, i+ 38 , 113. 1 02 , 18. 688, 1 9. 21'*, 19. 693 , 20 . 135, 20 . 5 if8, 20. 938, 21. 310, 21. 6 69,

022. Q 17, 22. 356, 22. 633, 23. 0 lit, 23. 3 3i+, 23. 6 (+8, 23. 95 7, 2it. 260, 2'*. 5 57,

'2U. 3 i«8, 25. 13 2, 2 5. t^lO , 25. 681 , 25. 9U5, 26. tt51, 26. 929,27.3 79,27.8 02 , 528. 201, 28. 577, 28. 932, 29. 268 , 29. 586, 29. 889, 30. 177, 30. '5 2, 30. 7 16,

63G.9 69, 31,212,32.305,33.2t*'+,3i+.C69,3'+.80 6, 35.'+73,36.C62,37.165,

7 39. 7 01 , i+2. 72 0, 5. 0 0 7, 51. 221 ,53. 8 39, 5 5.96 9)

DATA (S0 = 11 5. 5 81, 16. '36, 17. 252, 17, 316, 18. 501, 19. 024+, 20. 133, 21. 038, 21.8 0'+, 2 22. 63, 23. 053, 23. 576 , 2'+. 050 , 2if. '82,2'+, 880, 25. 2'+ 8, 25. 591, 25. 9 12,

326. 2 15, 26. 500, 26. 771 , 27. 029 , 27. 2 75, 27. 512, 27. 739, 27. 95 8, 28. 170 , '23. 3 75, 28.5 7 5, 2 8. 769 , 2 3. 958 , 29. 1^4 3, 2 9. 5 0 2, 29. e^+e, 30. 177,30.'+ 93,

530. 3 08 , 31. 10 9, 31. '01, 31. 68'+, 31. 956, 32. 22 5, 32. '8'+, 32. 735, 32. 9 79 , 6 33. 216, 33. ''6, 3 '.50 5 , 35. '32 , 36.2 53, 36. 939, 37.656,38.265, 39. 3'+8 , 7'+l. 3 8'+,'+'+. 90 3, '+7. 190 , 51. 221 ,53. 839,55. 969)

DATA (SN = 115. 6 07 , 16. 512, 17. 273, 17. 9'+l, 18. 527, 19. 050, 20. 159, 21. 06'+, 21. 8 30 , 2 22. '9'+, 23. 079, 23. 60 3 , 2'+. 0 78 , 2'+. 513, 2'+. 91'+, 25. 28 8, 2 5. 638, 25. 969,

3 26. 2 83, 26. 53 2, 26. 863 , 27. l'+3, 27. '07, 27. 663, 27. 911, 28. 151, 28. 3 8'+, '28. 6 11, 28. 832, 29. 0'+7, 29. 256 , 29. '61, 29. 8 56, 30. 23i+, 30. 59 5, 30, 9'*2,

531. 2 7'+, 31. 59'+, 31. 90 1,32. 197 , 32. '83, 32. 75 8, 33. 025, 33. 282, 3 3. 5 31 , 733. 7 72 , 3'+. 005, 35. C73 , 36. DC3 , 36. 8 25, 37. 561, 38. 228, 3d. 836, 39. 920 , 7'»2. '55, '5. 1+75, '7. 762, 51. 221 , 53. 8 39, 55. 969)

35
DATA (Se = 111. 215, 12. 12 0, 12.83 7,13. S?**,!**. 1^49, 692, 15.918,17.0 69,18. 196

219. 29'*, 20. 331, 21.28 5, 22. l'«5 ,22.911,2 3.592, Z'*. 19 8, 2t».7itO, 25. 229

325. 6 7it,26. 0 80, 26.'»55,26. SOit ,27.129,27.ti35, 2 7 . 72 ,27 , 999, 2 8. 260

^28. 5 10, 28. 750, 28. 98 0,29. 20 3, 29. 'IS, 29. 8 28, 3 0.216, 3 0. SS**, 30. gS** 5 31. 2 69,31. 591,31.899, 32.196 ,32. t» 8 2, 32.758, 3 3.0 2it, 33. 282, 33. 5 31

6 33. 772, 3«t. 00 5, 35.073 , 36. 003 , 36. 825, 37.561, 38. 22 8,38. 836,39. 920

7 '2. i» 55, '5. i»75,tt 7.762 , 51. 221 ,53.8 39,55.969)

GO T0< 1,2, S,!*, 5) ,N

1 CPOS=ATKINT(TI ,SP,T,60, 6 ,N ES , . 0 1 ) * . 18'+ RETURN

2 CPOS=ATKINT(TI,SN,T,60, 6 , N ES , . 0 1 ) < . 18

RETURN

3 CP03=ATKINT(TI,S0,T, SO, 6 ,NES, . 0 1) 18<t RETURN

k CPOS=ATKINT(TI ,SE,T,50, 5 ,N ES , . 0 1 ) * 18 U RETURN

5 PERCENT=PER3£H /lOO.

CP0S = {ATKINT (TI ,SO,T ,60 ,6,NES,.01)* (1 .- PERCE NT ) 1ATKINT(TI,SP,T,60,6,'>IES, .Cl)*PERCENT)»U.18't

RETURN

END

12. 670 15. 556 32.938

36
THE COEFFICIENTS AND THEIR ESTIMATED ERRORS AREO

9. 772k75b6ki- •OR- 1.33- QQk

2.71522510't7- 002 + 0R- 3.28- 003

-if. 0181051i*93- 001 + 0R- 2.87- 002

1.68'*1979«»QH-0 0 0 + 0R- 7.68- 001

-2. I'i89533'*87> 001 OR- 1.10* 001

-1.6675599518- 006 + 0R- 9.90- 006

8. '131860302- 003 + 0R- 2.61- 003

-5.7557t»76830- 001 + 0R- 1.95- 001

2. ll'*9'tl7739 + 0 02 + 0R- 1.05+002

1. 238735i»960- 006 OR- 3.t»3- 007

-3.12805809'»7- OQi* OR- l.'*'*- 00^4 2.59'*5m9913- 002 OR- 1.29- 002

5.2'»9'*5878 55- 0 06 + 0R- 1.85- 006

-9.5113'*it98G0- 007 +-0R- 1.89- 005

-7.23166980 85- 003 + 0R- 3.56- 003

-3. 83837272 8't- 007 OR- 5.81- 007

6.17lit6 86'»95- 0 09 + 0R- 5.W5- 009

5. 010102'+725- 006 + 0R- 2.i»5- 006

-5.5717't7i»190- 006 + 0R- 2.70- 008

-1. 8913610938* 002 OR- 1.0i» + 002

-3.7d3139950'« + 002 + 0R- 6.92+001

-8.'*6161093it7- 001 + 0R- tf.lS- 001

1.3760i»098 52 + 0 01 + 0R- 3.11+000

-1. 13230 393i»0- 003 OR- 5.69- OOit 1. 355'»583722- 003 + 0R- 5.10- QQk

-1. 8«»i»38 8it9 51- 006 + 0R- 8.89- 007

-5. 1666928690- 005 + 0R- 1.30- 005

010 + 0R- 1.77- 013

5. 087005it382- 0 39 + 0R- 2.t»0- 009

-1. 0229323667- 012 + 0R- 5,05- 013

-2.02it8578837- 012 + 0R- l,i*7- 012

1.190050'»363- Oil + 0R- '.60- 012

ESTIMATED RESIDUAL SUM OF SQUARES = ^ 3 91 5 0 81 5- 0 0 7 ESTIMATED REGRESSION SUM OF SQUAR-IS = 9 . 2 2 21 96^+ 6 0- 0 0 2 ESTIMATED TOTAL SUM OF S3UAR:ES = 9. 2 222 0 851- 0 0 2 VARIANCE OF FIT = 1 . 6 75 1 23 0 3i*- 0 0 5 DETERMINANT OF THE MATRIX = i*. 0 8 268 1 36 + 0 6tt CORRELATION COEFFICIENT = 9.99 99 51865-0 01

NUMBER OF POINTS = 1611

37
PIN D IN T IN p CAL 0 CAL P D IF

1.783 1. 0 85 23.00 86 1. 798 1. 0816 — D • ?5fi u . o u l.d78 1. 0 85 2km 00 8 3 1. 833 1,0815 -0.261 0 , 30

1.972 1. 085 25. 00 78 1. 977 1. C815 -0.255 0 , 29

2*066 1. 085 26. 0073 2. 0 72 1. 081'+ -0 . 256 0, 29

2.160 1. Q6k 27, 0071 2, 165 1. 0815 -0 ,235 0. 26

2.251* 1. a8<t 28.0071 2.259 1. 0815 -0 . 228 0. 25

2.31*7 1. 08<f 29. 0073 2.352 1, 0815 -0 .219 0. 2<+ 2,kkO 1. 0 8'» 30.00 76 2. ''5 1.0816 -0.201+ 0.22

2.533 1. 0 8(» 31.0080 2. 538 1.0816 -0.197 0.21

2.626 1. 08<» 32.008t+ 2.631 1. 0817 -0.180 0. 20

2.719 1. 0 8't 33,0090 2. 723 1.0818 -0.163 0.18

2.812 1. 08't 3^+. 0099 2. 816 1. C819 -0.11+1+ 0 . 15

2.90W 1. 0 83 35.0110 2. 908 1.0819 -0 . 136 0. 15

2.997 1. 083 36. 0122 3.0 00 1. 0820 -0 . 120 0 . 13

3.089 1. 0 83 37.0133 3, 092 1.082 0 -0.108 0 . 12

3.181 1. 083 38.01'+2 3. 18U 1. 0820 -0.098 0. 10

3.273 1. 083 39. 01tf9 3. 276 1. 0819 -0.090 0,10

3.366 1. 0 83 t+0 . 01 5*+ 3 • 3 o 8 1. 0820 -0.0 75 0.06

3.550 1.0 83 t*2. 0158 3. 552 1.0819 -0 . 0 59 0.06

3.733 1. 0 82 ''+.0155 3. 735 1. 0817 -0.053 0.06

3.916 1. 0 82 '6, Ol'+d 3.918 1. 0816 -0.01+3 0,05

.099 1. 0 82 '+8. Ql'*2 '.101 1. 081'+ -0 . 0 39 0 , 0(+ t*»2b2 1. 0 82 50. 0131 '.2 3'+ 1.0812 -0.0 30 0.03

**»7ZQ 1. 0 81 55.00 71 (», 7 39 1. 0807 -0.018 0.02

5.193 1. 0 80 59, 9992 5.19*+ 1. 0802 -0.010 0.01

5.6(f8 1. Q 80 6'+. 9999 5.61+8 1. 0796 -0.0 03 0.00

6.101 1. 0 79 70.00 0 3 6. 132 1. 0789 -0.006 0. 01

6.553 1. 078 7'+. 9^'^ 6.55'+ 1. 0782 -0. 011+ 0.01

7.005 1. 078 79. 9910 7.005 1. 0777 -0.003 0. 00

7.^57 1. 077 8'+. 9971 7. '+57 1. 0770 -0.001+ 0. OC

7.907 1. 0 76 90.0096 7.909 1. 0762 -0 . 016 0. 02

8.356 1. 0 76 95.0121 8. 359 1. 075*+ -0.027 0.03

8. 805 1. 0 75 10 0.0099 8. 807 1. 07'+8 -0 . 029 0. 03

2.'»59 1. '97 2'+. 00 83 2. '+6'* 1. '936 -0 . 191+ 0.21+

2.592 1. '97 25. 00 78 2.598 1. '931 -0.216 0. 26

2.726 1. ^^97 26.00 73 2. 711 l.'+930 -0.211+ 0,26

2 • 858 1. '97 2 7. 00 71 2. 86*+ 1 . 1+927 -0 .225 0.27

2.990 1. '+97 28.00 71 2. 996 1. '929 -0,209 C. 21+ 3.121 1. '96 29. 00 73 3. 127 1. '927 -0 . 211+ 0. 25

3.251 1. '+96 30.0076 3, 258 1.1+923 -0 . 226 0. 26

3.382 1 . ^+96 31,0080 1 3. 339 1. 1+926 -0 . 20't 0.23

3.513 1. '+96 32. CO 8 U 3.519 1. 1+929 -0.178 0.20

3 .6<f 3 1. '96 33. 0090 3.61+9 1. 1+927 -0.176 0.20

s/ • f f tJ w " • \J \J ^ J 3. 779 1. 1+929 -0.157 0.17

3.903 1. '+95 35,0110 3.938 1.1+929 -0 ,11+8 0. 16

<t.a32 1. '95 36. 0122 <+. 038 1. 1+930 -0 .131+ 0.15

'.162 1. '95 37.0133 '.167 1. 1+932 -0.113 0.12

h.291 1. ^95 38. 01'+2 t*. 296 1. 1+931 -0 . 105 0.11

t*,t*2i 1. '95 39. ai'+9 1**1*25 1. 1+932 -0.092 0. IC

38
PIN

D INT IN => CAL

D CAL P DIF 0 DIF

U.550 1. '95 '0. 015'+ '. 553 1. '+932 -0 . 079 0.09

t».807 1. '9'+ '2.0158 '. 8 10 1. '931 -0 .066 0. 07

5,Qbk 1. '9'+ ''. 0155 5.057 l.'+931 -0 . 0'+6 0. 05

5.320 1. '93 '6. Ol'^e 5. 323 l.t+927 -0.01+3 0. 05

5.576 1. '93 '3. 01'+2 5. 578 1. 4+925 -0 . 036 C. 01+ 5.832 1. 493 50. 0131 1. '+92'+ -0. 022 0.02

6,i*71 1. '92 55. 00 71 6, '+70 1. 1+919 0.003 -0.00

7.106 1. '91 59.9992 7. 106 i.i+gii 0.010 -C. 01

7.7<+l 1. ^+90 6'+. 9999 7.7kO 1. 1+901 0.003 -0.00 6 .375 1. '89 7 0.0003 8. 37k 1. '893 0.007 -0,01

9.005 1. '88 7k, 33kk 9. 0 36 1. '882 -0 . C 01+ 0.00

9.635 1. '87 79.991C 9.636 1. 1+872 -0.010 G. 01

IC .265 1. '86 8'+.9971 10. 267 1. '862 -0 .016 0,02

10.89'* 1. '86 90.0096 10.917 1. 1+851 -0 , 028 0.03

11.521 1. '85 95. 0121 11.525 1. '8'+l -0.037 0. 01+ 12.1«»6 1. '8'+ 100. 0099 12. 151 1. '+830 -0 . 0'+6 0.05

2. 161 26. 0073 3. 6'+8 2. 1581 -0,0 88 0. 12

2. 160 27. 0071 3.8'+7 2. 1570 -0 .119 0. 16

h.QkO 2. 160 28. 00 71 '. 0'+5 2. 1565 -0 . 13t+ C. 17

'.235 2. 160 29. 0073 k, Zk2 2.1557 -0 . 155 0. 19

'.'30 2. 160 30.0076 k,k37 2. 1555 -0.159 0. 20

'.62'^ 2. 159 31. 0080 '.631 2. 1553 -0 . 159 0. 19

'.817 2. 159 32. 008'^ '.825 2. 1550 -0 . 161 0. 19

5.010 2. 159 33.0090 5.018 2.1551 -0 .152 0. 18

5.203 2. 159 3'+. 0099 5.210 2. 1551 -0. l'+2 0. 17

5.395 2. 158 35.0110 5. '02 2. 1553 -0 .127 0. 15

5.587 2. 158 36. 0122 5.59'+ 2.155'+ -0.111+ 0.13

5.779 2. 158 37. 0133 5. 735 2. 155'+ -0 . 105 0. 12

5.970 2. 158 38. 01'+2 5.975 2. 1556 -0.083 0 . 09

6.161 2. 157 39. 01%9 6. 166 2. 1557 -0 .069 0.06

6.352 2. 157 kO, QiSk 6,356 2. 1556 -0 .065 0.07

6.732 2. 157 '2. 0156 6. 735 2. 1556 -0.01+2 0,05

7.111 2. 156 ''. 0155 7, 113 2. 1553 -0 . 032 0. 0<+ 7.'^89 2. 156 '6. 01'+8 7.k91 2. 1551 -0.022 0. 02

7.867 2. 155 '8, 01'+2 7. 858 2. 15'+8 -0.010 0.01

8.2i+'^ 2. 1 55 50.0131 8. 2'+'+ 2. 15'+5 -0.0 02 0 . OG

9.18'* 2. 153 55. 00 71 9. 182 2. 1537 0.022 -0.02

10.119 2. 152 59. 9992 10. 117 2. 152'+ 0 . 019 -0,02

11. 05'^ 2. 151 &'. 9999 11.0 51 2. 1511 0.022 -0.0?

11.98'+ 2. l'^9 70. 00 0 3 11.95'+ 2. l'+9'+ 0.006 -0. 01

12.912 2. I'^e 7k, '^3ki* 12.913 2. l'+80 -0 . 003 0.00

13.839 2. l'+7 79. 9910 13. Si+O 2. l'+65 -0.008 0.01

1'^.763 2. l'+5 8'+. 9971 1'+. 767 2. Ikk3 -0.02'+ C. 02

15.667 2. 1'^'+ 90.0096 15.693 2. 11+33 -0.036 0. 01+ 16.608 2. t'+3 95. 0121 16.616 2.11+17 -0.01+6 0.05

17.526 2. !'! 100.0099 17. 535 2. IkQZ -0 .056 0. 06

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40
PIN 0 IN T IN = CAL D C&L P DIF D DIF

3.3 07 9 0. G 0 96 2 1+. 1 ^5 3.306 0 -0.0 36 0.01+

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6.509 3, 962 2 9. G 0 7 3 6.502 3. 9901+ 0.115 -0.20

6.901 3. 982 3 3 . 00 7 6 6,8 97 3. 9858 0.056 -0.09

7 .267 3. 981 31. CO 8 u 7.2 36 3.9812 -0.005 0.01

7.673 3. 981 3 2. 00 81+ 7, 575 3 . 9797 -0.0 22 0.03

e,056 3. 980 33.00 90 8. 059 3.9785 -0.031+ 0 , 05

8. 1+36 3. 980 3 1+ . G 0 9 9 8, 1+1+0 3. 9771+ -0.01+6 0.06

8,816 3. 9 79 35.0110 8.3 20 3.9772 -0 . Qi+2 0. 06

9.193 3, 9 79 3 6.3122 9. 197 3. 9766 -0 . Oi+5 0.06

9.570 3. 978 37. 3133 9.57k 3. 9755 -0.0 38 0 . 05

9.91+5 3, 978 33.011+2 9.91+8 3. 9751+ -0.0 29 0 . Ok

10.319 3. 9 77 39.011+9 10. 322 3, 9762 -0.0 25 0. 03

10 .692 3. 9 77 1+0.0151+ 1 0 . 591+ 3. 9761 -0.0 16 0. 02

11. '36 3. 975 1+2. 0153 11.1+36 3.9756 -0,0 01 C . OC 12.177 3.975 1+1+. C155 12.175 3. 9751+ 0.010 -0.01

12. 911+ 3. 971+ 1+6. oii+e 12.912 3. 971+8 0 . 0 19 -0. 02

13.650 3. 973 i+S. Gli+2 1 3. 6-t7 3. 971+0 0.025 -0 . 03

l'+.385 3. 9 72 50.0131 1 U , 3 3 0 3. 9731+ 3.0 31+ 'C.Qk

16.213 3.969 55 . 3 0 71 16.205 3.9711+ 0.01+8 -0.05

18.0 31 3. 967 59. 9992 18.0 22 3.968 8 0.01+7 -0.05

IS' iko 3. 961+ 61+. 99 9 9 19.837 3.9651 0.01+0 -0.01+

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2 3 .

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25. 21+5 3.957 79. 991

0

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26.821 3.952 9 0. G 0 96 2 8.332 3, 9501+ -0 . Oif 0 0.01+

30.600 3. 9i+9 95.0121 3 0.616 3.91+73 -0.053 0.05

32.369 3, 91+7 103.0Q99 32.391+ 3. 91+39 -0.0 76 0.06

7,803 k, 956 3 0. 00 7 6 7.796 i+. 9753 0.091 -0.18

6.309 i+. 9 65 3 1, 00 3 C 8.335 k, 9692 0.01+0 -0.07

6.306 k, 9 65 32. 0 0 3 1+ 8,336 i+. 961+2 -0.006 C . 0 1 9. 3 C 3 1+ . 9 61+ 3 3. G 0 9 0 9.336 k. 9612 -0 . 0 37 C . 0 6 9.79'+ •+. 9 51+ 31+. GO 99 9.3 30 k, 9590 -0.0 58 C . 09

IC .263 i+. 963 3 5, 0110 10.291 1+ . 9576 -0.071 0.11

10.771 1*, 962 35.0122 1 0 . 7 76 i+. 9571 -0.0 71 C . 10

11.256 k. 9 62 37. C133 11. 253 i+. 9558 -3 . C 69 C . IC 11.738 i+. 961 33, Gli+2 1 1. 7i+6 i+. 9553 -0 . 069 0 . 09

12.220 '.960 39. 011+9 12.227 i+. 9562 -0.061 C . 08

12.700 £.950 1+0. G151+ 12.736 i+. 9561+ -0.01+9 0.07

13.656 i+. 958 1+2. 3153 13. 550 i+. 9561 -0 . 035 0 . 05

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1 5 . 5 5 H 4. 956 1+6.011+8 15.556 i+. 951+9 -0.013 C . 02

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PIN 0 IN T IN P CAL D CAL P OIF 0 OIF

29.062 «. 937 7'^.99«*'t 29.060 '.9376 0 . 006 -0. 01

31.360 '.93'* 79. 9910 31. 361 -0 .OOi^ 0. 00

33.653 £.931 8'+.9971 33,659 '+.9302 -0. 017 0. 02

35,9ki '.928 90. 0096 35.953 '.9262 -0.033 0.03

38.217 '.925 95.0121 38. 235 '.922i^ -0 . 0'^6 C. 05

'C.'»83 '.921 100. 0099 (0.5 38 '.918'^ -0 . 062 0. 06

10.266 6. 785 32. OOtt'^ 10, 266 6. 78'^6 0.000 -0. 00

10.989 6, 78'^ 33. 0090 10. 992 6. 7796 -0.026 0. 06

11.702 6. 783 3'^. 0099 11.710 6. 77'^0 -0.063 0.13

12.i*ll 6, 782 35. 0110 12,'+21 6, 7710 -0 . 085 0.16

13.11«t 6. 781 36. 0122 13. 128 6. 7686 -0.102 0.18

13. SI** 6. 780 37.0133 13.829 6. 7676 -0 .108 0.18

l^t.Sll 6. 779 38. 01'^2 !'. 527 6, 7672 -0. 109 C,17

15.206 6. 7 78 39. 01'*9 15. 221 6. 7680 -0 .096 0.15

15.896 6. 777 '0.015'+ 15.912 6.7667 -O.lOi^ 0.15

17.271 6. 775 kZ. 0158 17. 287 6. 7663 -0 .09'^ 0. 13

18.6tfO 6. 773 ''. 0155 18.65'+ 6. 7662 -0 .079 0.10

20.003 6. 771 (6. oii^e 20. 015 6. 7662 -0. 060 0. 08

21.360 6. 770 '8. 01'*2 21.371 6. 7bi*9 -0.055 0. 07

22.71t» 6. 768 50.0131 22.723 b.7bk5 -0 .039 0.05

26.087 6. 763 55. 0071 26. 097 6.7630 -0.002 COO

29. '35 6. 759 59.9992 29. '3'+ 6. 7590 0. 005 -0.01

32.775 6. 75'^ 6'^.9999 32.772 6.75'^8 0 . 009 -0.01

36.097 6. 750 70. 00 G3 36. 098 6.71*96 -0.002 0.00

39.398 6.7'^5 7k, SBkk 39. '06 6.7'^39 -0.020 0.02

1*2. 69'* 6. 7<^1 79. 9910 '2. 70'^ 6. 7393 -0, 022 0. 02

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52.518 6. 727 95. 0121 52. 5t*7 6. 7238 -0 .05'* 0. 05

55.759 6. 723 100. 0099 55. 800 6. 7183 -0.073 0.07

lC.9'+6 8. 310 32. 00 8'^ 10.951 8. 29'^6 -0. 0'^5 0. 19

11.878 8. 309 33.0090 11.330 8. 30'^5 -0 . 016 0, 05

12.79tt 8. 308 3'^. 0099 12, 798 8. 2999 -0.035 0,09

13.699 8. 306 35. 0110 13. 708 8. 29'^1 -0 .06'^ C. 15

11*. 597 8. 305 36. C122 !'. 611 8. 2891 -0 . 09'^ 0 ,19

15.t»89 8. 3 0'^ 37. 0133 15. 537 8.2857 -0.115 C, 22

16.378 8. 303 38. 01'^2 16. 3 38 8, 28'^6 -0.123 0,22

17.261 8. 302 39. 01'^9 17.235 8.2830 -0 . 13'^ 0. 22

18.1U2 8.300 '0. 015'^ 18. 167 8.2822 -0 .138 0.22

19.89'* 3. 298 '2. 0158 19. 923 8. 2806 -0. l'^2 0.21

21.639 8. 2 96 ''. 0155 21.668 8. 280'* -0.133 0, 18

23,377 5. 293 kb. Ol'^S 23. '05 8. 2802 -0.120 0. 16

25.110 8. 291 '8.01'*2 25, 136 8. 2801 -0 . lOi^ 0, 13

26.839 8. 289 50.0131 26, 362 8. 2799 -0 . 087 0,11

31.138 8. 283 55, 0071 31, 155 8. 2776 -0 . 056 0, 06

35.'tltf 3. 277 59.9992 3 5. '26 8. 27'^1 -0.035 O.Qi*

39.673 a, 2 72 bk, 9999 ^9. 635 8. 2690 -0.030 0,03

'3.911 3. 2 66 70, 00 C3 (3,926 8. 2630 -0 . 035 0, OU

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42
PIN D IN T IN P CAL D CAL P OIF 0 DIF

Sb.51k 8. 21+9 8'^.9971 56. 5'+l 8. 2'+5'+ -0 . 0'+8 0. 05

60.691 8, 2'+'+ 90. 0096 60. 72'+ 8. 2392 -0 .055 0. 05

6(f.8<46 8. 238 95.0121 6'^.d32 8. 2336 -0 .056 0.05

66.980 8. 232 100.0099 69. 019 8. 2278 -0.057 0. 05

12. 1*73 10. 1*^5 33.0090 12. '66 10. 181'+ 0.059 -0. 36

13.6U<t 10. I'+i^ 3'+. 0099 13.633 10. 1777 0 . 085 -0. 3*+ 1'».797 10. l'^2 35. QUO !<. 790 10. 157'+ 0 . 0'+9 -0. 15

15.9'»2 10. li^l 36. 0122 15.9'+0 10. l'+3'+ 0.011 -0.03

17.078 1 G . 1 39 37. 0133 17. 033 10. 1322 -0.031 0.07

18.209 10. 138 38. 01 '2 18. 220 10. 1256 -0 . 059 0. 12

19.337 10. 136 39, 01I+9 19. 352 10. 1212 -0 .079 0. 15

20. '65 10, 135 '0. 015'^ ?0.'^80 10. 1218 -0.072 0.13

22.699 10. 132 '2.0158 22. 725 10. 1136 -0.11'+ 0. 18

2*».929 10, 129 ''. 0155 2'+. 959 10. 1109 -0 .122 C, 17

27.151 10, 126 '6. omb 27.185 10. 1090 -0.122 0, 16

29.369 10, 123 '8.01<+2 29. '03 10. 1075 -0.117 0. 15

31.581 10. 120 50,0131 3 1.616 10.1061 -0.110 0,13

37.090 10. 112 55, 0071 57. 121 10. 1028 -0 .08'+ 0, 09

'2.570 10. 105 59,9992 (2. 598 10. 0980 -0 . 065 0,07

'8.02d 10. 0 98 6'^.9999 '8. 059 10. 0912 -0 . 065 0.07

53. ^58 10. 091 70.0003 53. '95 10. 0839 -0 .069 0,07

58.856 10. 08'+ 7k, 931*1* 58. 899 10. 0766 -0.073 0,07

6'^.238 10. 077 79,9910 &'. 282 10. 0700 -0, 069 0. 07

69.609 10. 070 8'+. 9971 69. 650 10. 06'+0 -0 .059 0. 06

7'^.951 10, 3 63 90. 0096 75. 001 10. 0563 -0.067 o.oe

80.263 10, 055 95. 0121 30. 318 10. 0<+92 -0 . 068 0, 06

85.5'^7 10. 0'+8 100,0099 35. 606 10. 0'»21 -0 .069 0. 06

12.709 11. 318 33.0090 12. 695 12. 0093 Q.li'* -1. 62

I'+.ll'^ 11. 816 3'+, 0099 l'+.0 37 11. 9'+ '2 0.192 -1, 09

15. '97 11, 81'+ 35, 0110 15. £^73 11. 8816 0,153 -0,57

16.870 11. 812 36. 0122 16.853 11.8'+6'+ 0.100 -0.29

18.239 11. 810 37. 0133 18. 229 11. 8258 0.051+ -0. 13

19.603 11. 808 38. LlkZ 19.630 11.812'+ 0.016 -0,03

20.963 11. 807 39. oit^g 20.967 11. 8025 -0.018 0,03

22.322 11. 805 '0. 015'+ 22. 331 11. 7962 -0, Oi+O 0.07

25.035 11.801 '2. 0158 25, 052 11. 788'+ -0 . 068 0.11

27.737 11. 797 ''. 0155 ^7. 763 11. 7818 -0 .093 0.13

30. '36 11. 79'+ '6. Gl'^8 30. '+67 11. 7779 -0.102 0,13

33,129 11, 790 '8. 01'+2 33, 165 11.77'+2 -0 . 109 0. 1*+ 35.820 11. 787 50. 0131 35,858 11.7718 -0 . 106 0.13

'2.520 11. 7 78 55. 0071 (2. 563 11. 7650 -0.100 0.11

'9.190 11. 7 69 59.9992 '9. 2 3'+ 11. 758'+ -0 .089 0.09

55.8'+l 11. 761 bh. 9999 35. 886 11. 7512 -0.080 0. 08

62.1+57 11. 7 52 70.0003 62.535 11. 7'+33 -0 . 0 77 0. 07

69.030 11. 7'+3 7'+.99'^'^ 69. 033 11. 7350 -0 . 077 0.07

75.580 11. 735 79. 9910 75.632 11.7277 -0 .068 0.06

82.108 11. 726 8'+.9971 32. 159 11. 7199 -0. 062 0. 06

88.610 11. 718 90.0096 38.663 11.7118 -0 .060 0.05

95.070 11. 710 95. 0121 95. 123 11. 7039 -0 .056 0,05

101. '91 11. 701 100.0099 101.5'+5 11.6956 -0 . 05'+ 0.05

43
PIN 0 IN T IN ° CAL D CAL P DIF D DIF

118.392 ik* 99'+ 90. 0096 118. '30 1<+. 990<+ -0.0 32 0.03

127.<»05 Ik, 983 95. 0121 127. '22 ik, 981'+ -0 • 01'+ 0.01

136.361 li*. 972 100. 0099 136. 356 1'+, 972'+ 0. 00<+ -0.00

12,601* 15. 52«» 33. 0090 12. 803 15. 5786 0 .00<+ -0. 35

l<f .663 15. 521 3<t. 00 99 l'+.693 15. '578 -0 . 0 65 0 . ^1

16.563 15. 519 35. 0110 16. 596 15, '7'+2 -0,060 0. 29

18.<»96 15. 516 36. 0122 18.510 15, '90 3 -0,063 0. 17

20.'f22 15. SI** 37. 0133 20. '32 15. '969 -0 . 050 0. 11

22.353 15. 511 38. 01'»2 22. 362 15. '995 -0,0 39 0. 07

2<».289 15. 508 39. 01 '9 2'*,2^7 15. '998 -0,033 0. 06

26.228 15. 5 06 '0. 015't 26. 2 36 15, '98 3 -0.032 0.05

12.607 16. 398 33. 00 90 12.813 15. 8799 -0 . Ot+5 3. 16

1U.799 16. 395 3'f . 00 99 1 '• 8 ?8 16, 212 7 -0.196 1,11

16.632 16. 392 35.0110 X16.6 U « Www63 16. 2925 -0W .187 • X w • 16.886 16. 389 36.0122 18.915 16. 3278 -0.156 0 . 38

20.955 16. 387 37. 0133 20. 980 16. 3'+76 -0.120 0 , 2<+ 23.0 35 16. 36<» 38, 01 (f 2 2 3.0 56 16. 3583 -0 . 090 0 . 16

25.123 16. 361 39. 01 '9 25, mo 16. 3637 -0.068 0,11

27.216 16. 378 <i0. 015<« 27. 2 31 16. 365'+ -0.055 0.08

l't.798 16. 395 3't. 00 99 !'. 328 16. 2093 -0.20 0 1. 13

16.633 16. 392 35. 0110 16, 863 16. 2963 -0 . 180 0.59

18.891 16. 390 36. 0122 18. 915 16. 3383 -0.130 0. 31

20.962 16. 387 37. 0133 20.980 16. 3587 -0. 087 0.17

23.0'*3 16. ZQk 38. Gl'»2 23. a 56 16. 3679 -0 . 057 0.10

25.132 15. 381 39. 01U9 25. It+C 16. 3737 -0 . 030 0.05

27.227 16. 378 i*Z, 015if 27, 231 16. 37'+6 -0 . 016 0. 0?

31. '+30 16. 373 '2. 0158 31. '29 16. 373'+ 0.003 -0. 00

35.61+8 16. 367 ''.0155 35.6'+l 16.3710 0. 020 -0.02

39.835 16. 362 '6. 01(+8 39. 862 16. 3501 -0.067 0. 07

1*1*, QSk 16. 356 f+d. 01'+2 ''. 036 16,3i+'+'+ -0. 072 0.07

^8.269 16. 351 50.0131 (8. 310 16. 3375 -0 . 08<+ 0,08

58.797 16. 337 55. 00 71 58. 8'+7 16. 32'+7 -0.085 0.08

69.27'+ 16. 32't 59. 9992 69. 339 16. 3107 -0 , 09<+ 0.08

79.725 16. 311 6'+. 9999 79, 79'» 16. 2991 -0 , 086 0. 07

90 .ll^* 16. 298 70. 00 C 3 9 0. ll** 16. 2876 -0 . 078 0.06

100. '33 16. 285 7'+. 99'+ ' 1 3 0 , '95 16. 2769 -0 , 062 0.05

110.701 16. 272 79, 99 1

0

110, 7'+5 16. 2672 -0 , Ot+O 0.03

120.913 16. 260 8'+. 9971 120.9'«8 16. 2561 -0 . 029 0.02

131.078 16. 90.00 96 131.098 16. ?'+53 -0.016 0.01

l'*l .166 16. 2 35 95.0121 1 < 1 • 1 66 16.2352 0,002 -0.00

151 .191 16 • 2 23 100.0099 151.161 16. 2251 0,020 -0.02

12.8'fl 18 . 1 16 33. 009 Q 12.855 1 7, 7i+86 -0.113 2.03

15. 098 13. 113 Si^. GO 99 1 5. 1 '7 17.8821 -0.329 1 . 27

17.'»32 18.110 35. 0110 1 7, '72 18,0088 -0,232 0. 56

19.792 13. 107 36. 0122 19, 82'» 18, 0523 -0 , 162 0. 30

22.175 18. 103 37. 0133 22.197 18. 0753 -0.100 0. 16

2'+.583 18. 100 36.01'+2 18. 09'+3 -0.02U 0.03

26.990 13. 397 39. Jl'+9 ?6,99'+ 18. 0936 -0,015 0.02

29. '13 18. 09'» i+O. 015'+ 29, i+ll 18, 0952 0,007 -0.01

3<+.280 13. 087 '2. 0158 3'+. 270 18. 0928 0. 0 28 -0.03

44
PIN D IN T IN o CAL D CAL P DIF D DIF

12. /g^ i.k* 099 33. 0090 12.737 1'+. 6'+0'+ 0. 058 -3.8'+

1'+. 396 3'+. 0099 1'+. '32 lk. 19k2 0.101 -0. 69

16.19'* l'^. 09'+ 35,0110 16. 182 lk, 1367 0 , 076 -0. 3C

17,392 Ik, 092 36. 0122 17. 33'+ 1'+. 1111 0 . 0'+7 -0 , lk

19.593 i.k. 089 37. 0133 19.5 38 l**. 0983 0 . 026 -0. 06

21. 29'* l'*. 0 87 38. 01'*2 21.29'+ 1'+. 0876 0.0 02 -0,00

22.997 Ik, 085 39. 01k9 23.0 31 1'+. 080 3 -0.017 0 ,03

2U.699 1'+. 0 83 kO, Q15k 2*+. 738 1'+. 07'+l -0 , 036 0. 06

1'».502 ik, 131 3'+. 0099 l'+.'+88 1'+. 22'+8 0.0 96 -0.66

16.202 129 35.0110 16. 192 1'+. 1655 0 .065 -0,26

17.908 Ik, 126 36. 0122 17. 839 li». l'+68 Q,0k9 -0, 1<+ 19. 61'* Ik, 12k 37. 0133 19. 608 1'+. 1338 0, 029 -0,07

21.321 Lk.LZZ 38. 01'+2 21. 319 11+. 1239 0.007 -0.01

23.029 li^. 120 39. oi'^g ?3. 0 32 lk, 1171 -0,010 0.02

Zk»7k0 1'+. 117 '0. 015'+ 2k, 7k5 1'+. 1128 -0.019 0. 03

26.158 Lk, 113 kZ, 0158 28. 173 lk, 1023 -0,051 0.07

31.578 Ik. 108 ''. 0155 31. 631 1'*. 09'+7 -0 . 073 0. IG

35.000 ik, iOk '6. oi'+e 35. 028 1'+. 0900 -0.080 0. 10

38. '21 l^*. 099 k6. Qlk2 38. '5it lk. 0851 -0. 087 0. 10

'1.837 l'^. 095 50.0131 '1.876 1'+. 080 3 -0.093 0. 10

50.362 ik, 0 8'^ 55. 0071 50. t+07 1'*. 0706 -0 .091 0, 09

58.850 l^*. 073 59.9992 58.901 1'+. 0608 -0 . 088 0.08

67.315 lk. 062 bk. 9999 67. 369 1'+. 0516 -0.080 0.07

75.730 li*. 051 70. 00 0 3 75. 791 1'*. Ctll -0 ,081 0.07

6'4.096 I'*. Qkl 7k,3<ikk 3'+. 155 1'+. 0320 -0 ,070 0. 06

92. '23 lk, 0 30 79.9910 12. '76 1'+. 0232 -0 .057 0.05

100.71'* 1'+. 0 20 8'+. 9971 13 0. 7 66 lk. 0135 -0 .052 0. 0*+ 108.972 l'^. 0 09 90. CO 96 139. 019 1'*. OC+l -0 . 0'+'+ C. 01+ 117.166 13. 999 95. 0121 117. 210 13. 99'+5 -0 . 037 0. 03

125.316 13. ^88 100.0099 1 25. 3i*6 13,9856 -0 . 025 0.02

12.801 15. 1 30 33. 00 90 12.830 15. 283'+ 0.012 -1.01

l'^,630 15. 1 27 3'+. 00 99 1'+. 6 35 15.0987 -0 . 029 0 , 19

16. '77 15. 125 35. 0110 16. t+SO 15. llf+S -0 . 019 0,07

18 .332 15, 1 22 36. 0122 18.3 3'+ 15. 1181 -0.011 0.03

20.192 15. 120 37,0133 20.19'+ 15. 1158 -0.012 0,03

22.061 15. 117 36. 31 '2 22. 0 51 15. 1183 0.003 -0,01

23.930 15. 115 39. 01'*9 23.931 15. ll'+3 -0 . 002 0. 00

25.800 15. 1 12 '0.015'+ 25.805 15. 1076 -0.020 0.03

29.51+9 15.107 kZ, 0158 29. 560 15. IGO 1 -0 . 036 0. 05

33.305 15. 102 ''. 0155 33. 321 15. 0933 -0 . 0'+9 0.06

37.060 15. 098 kb, Olkii 37. 035 15. 0856 -0.068 0.06

'0.816 15. 093 k6. QlkZ kO. 351 1 5. 0785 -0.086 0. 09

''.576 15. 3 88 50.0131 ''+.61'+ 15. C7'+6 -0,08'+ 0. 09

53.9'*5 15. 076 55. 00 71 53. 998 15. 0612 -0, 099 0.10

63.286 1 5 . 0 &' 59. 9992 63. 3'+3 15, 0511 -0 . 091 0. OP

72.593 15. 052 bk. 9999 72.658 15. C+OO -0 . 089 0 .06

81.85i^ 15, OkQ 70.0003 31. 919 15. 0299 -0,080 0. C7

91.053 15. 029 7'+. 99'»'+ 91.115 15. 0201 -0 .067 0.06

100.208 15. 017 79.9910 130.259 15.0107 -0 .052 Q,Qk

109.316 15. 006 8'+. 9971 139.366 15,0001 -0 , 0'»5 0. 0(+

45
PIN 0 IN T IN P CAL D CAL P DIF D DIF

39.153 16. 061 kk,Ql55 39.153 18. 0812 0.001 -0.00

kk.Q33 18.075 '6. oii^e ''.o'+g 18. 0708 -0.023 0. 02

'6.928 18. 068 t»8. 01«+2 '8. 953 18. 0600 -0 .052 0. 05

53.820 18. 062 50. 0131 53.857 18. 0513 -0. 066 0. 06

66.031 18. 0'i& 55. 0071 66. 0 89 18. 0335 -0 .068 0.07

78.193 18. 031 59.9992 78.263 18. 0186 -0 .089 0.07

90. sot* 18. 016 6'».9999 ^0.3d'+ 18. OO'+l -0 .088 0. 07

102.3'»5 18. 001 70. 0003 102. '20 17.9915 -0.07'* 0. 06

114.296 17. 987 7tf.99't'+ lli^. 355 17. 9799 -0. 052 0.0(+

126.175 17. 9 72 79.9910 126.211 17.9687 -0.029 0. 02

137.978 17.958 6(*.9971 13 8. 0 05 17.9558 -0.020 0. 01

lit9.739 17. 90. 0096 l'*9.731 17. 9'+ '9 0.005 -0.00

161.397 17. 930 95. 0121 161.356 17. 9337 0 . 026 -0.02

172.960 17. 917 100.0099 172.891 17.9217 0. O'+O -0. 03

12.999 19. SO'* 33.0090 13. 015 19. 7000 -0 .126 0.52

15.605 19.300 Zk, 0099 15.635 19.7192 -0.193 0.<+l

16. 28'* 19. 796 35. 0110 18. 297 19. 7731+ -0 .075 0.12

21.002 19. 793 36. 0122 20.995 19. 8015 0 .035 -0.0'+

23.7i*9 19. 789 37. 0133 23.721 19. 8160 0 .119 -0.1'+

26. SI** 19. 785 38. 01'»2 26. '69 19. 8199 0.166 -0. 17

29.283 19.782 39.01«»9 29.2 36 19.8130 0 .162 -0. 16

32.0&<» 19. 778 ifO. 015't 32. 017 19. 8050 Q*lk7 -0.11+

37.661 19.771 kZ, 0158 37. 611 19. 7931 0.132 -0. 11

*f3.268 19. 763 ''.Ot55 (3. 233 19.7765 0.081 -0. 07

«f8.887 19. 756 '*6.01if6 '8.870 ig.761'+ 0 .035 -0.03

5it.512 19. 7't9 ifd. 011*2 5'+. 51'+ 19. 7'+82 -0 .003 0. 00

60.131 19. 7^2 50.0131 60. 156 19. 735'+ -0.0'+2 0.03

7t». 156 19. 72i» 55.0071 ?!. 221 19. 7117 -0 . 087 0. 06

66.106 19. 707 59.9992 56.230 19. 6923 -0.10'+ 0.07

101.998 19. 690 6'*. 9999 132. 1Q2 19. 6758 -0.102 0.07

115.808 19. 673 70. 000 3 115.8 35 19.6632 -0.075 0.05

129.t»95 19. 657 71*. 129. 559 19. 6503 -0 .Oi+g 0.03

l'»3.069 19. oki 79. 9910 l!+3. 120 19. 6360 -0.036 0. 02

156.597 19. 625 8'*.9971 156.631 19.62'+'+ -0.003 0.00

170. 02'* 19.6 09 90.0096 169.999 19.6111 0.01'+ -0.01

163. 348 19. 53k 95. 0121 133.27«+ 19.5993 0 . O'+O -0. 03

196.571 19. 578 100.0099 136. '36 19.587'* 0 .069 -0. 05

13.216 20. 705 33. 0090 13. 217 20. 7013 -0.008 0.02

le.Qkl 20. 701 3'+. 0099 16. O'+l 20. 7012 0.001 -0. 00

16.932 20.697 35. 0110 18.911 20. 72'+8 0 . 113 -0. 13

21.862 20. 693 36. 0122 21. 819 20. 735'+ 0.197 -0.20

2tf .820 20. 689 37. 0133 20. 7393 0 . 256 -0. 2«+ 27.79't 20. 685 38. 01U2 27.719 20. 73'+9 0 .271 -0. 2'+ 30.782 20. 681 39. 01'*9 30.730 20. 7277 0 .266 -0.22

33.781 20. 677 33.697 20. 719'+ 0.250 -0. 20

39.802 20. 670 hZ, 0158 39. 723 20. 7012 0 .199 -0. 15

^5.837 20. 662 '+'.0155 1+5. 776 20. 6822 0.135 -0. 10

51.876 20. 65'* '6. 01'+8 51. 8 '3 20.6633 0 .063 -0. 0'+ 57.920 2 0 . 6 i»6 t+S. 01'+2 57.915 20. 6'*7'+ 0.008 -0.01

63.961 20. 639 50. 0131 63,932 20.6338 -0.033 0.02

46
PIN 0 IN TIN P CAL D CAL P DIF D DIF

79. 026 20. 620 55.00 71 79, 0 96 20,6073 -0 . 089 0. 06

9k,Q15 20 . 601 59. 9992 9'+. 1 36 20. 5880 -0 . 097 0. 06

108.922 20 . 583 6'+. 9999 1 09, 0 23 20. 5708 -0 .093 0. 06

123.721 20. 566 7 0, 00 0 3 123. 812 20. 5558 -0.07*+ 0. 05

138.375 20. 5'+8 7k, 93kk 138. '57 20. 5'+05 -0 .059 0. 01+ 152.9'+0 20. 531 79. 9910 152. 93'+ 20. 5275 -0 . 029 0.02

167. '19 20 . 515 8'+, 9971 167, kZl 20. 51'+3 -0.002 0.00

181.791 20, i+98 90. 0096 131, 762 20. 5000 0 . 016 -0.01

196.038 20 . '82 95.0121 195.965 20. '+865 0 . 037 -0.02

21C.l'+9 20 . '65 10 0.0099 210.051 20. '715 0 . 0'+6 -0.03

13 .595 21. 6 22 3 3. 00 9 0 13,570 21. 6722 0.183 -0 . 23

16.665 21.618 6kt 00 99 16,62'+ 21. 6720 0 . 2 '+7 -0.25

19.79'* 21. Sl'+ 3 5*0110 19.7 27 21. 6792 0 • 3'+l -0. 30

22.961 21. 610 36. 0122 22.869 21. 6808 0,kOZ -0 . 33

26.153 21. 605 3 7.0133 26. O'+l 21. 6766 0 . '27 -0. 33

29.359 21.6 01 38. 01<+2 29. 2 38 21. 6668 0 . '11 -0. 30

32.582 21. 597 39. 01'^9 32. '55 21. 6572 0 . 389 -0.26

35.810 21 . 593 '0. 015'+ 3 5.636 21. 6'+'+9 0 . 3'+6 -0.2'+

'2.2 90 21. 5 6k '2.0158 ^2.181 21.6219 0.256 -0.17

^8 .779 21. 5 76 ''. 0155 '8,730 21, 5986 0.160 -0.11

55.273 21.568 '6. 01'+8 55. 2 31 21, 5782 0 . 076 -0.05

61.770 21. 559 kQ, Oik? 51.762 21. 5610 0.013 -0.01

68.258 21.551 5 0.0131 68.236 21. 5'+57 -0 . O'+O 0.03

8'^.'^39 21. 5 31 55, 00 71 3'+, 520 21. 518 0 -0 . 095 0. 06

10 0.505 21. 5 11 59, 9992 10 0, 627 21. '9'+9 -0 . 122 0.08

116. '9'+ 21. ^+92 6'+. 9999 116.622 21. '+776 -0.110 0. 07

132.353 70. 00 0 3 1 12, '69 21. '618 -0.088 0.05

l't8.062 21. ^+55 7k, 3^kk l'+8, 152 21. ''71 -0.061 0 . 0*+ 163.658 21, '37 79. 991

0

16 3, 7 06 21. '+33'+ -0 . 029 0.02

179.153 21. ^+20 Si^. 9971 1 79. 157 21. '+19'+ -0.0 02 0 . OC

19'+.5'^0 21. ^+02 90.00 96 19'+. '97 21. '051 0 . 022 -0 , 01

209.772 21. 385 95. 0121 2 0 9,690 21. 390 3 0 . 0 39 -0,02

21, 368 100.0099 22'+, 752 21. 37'+6 0 • 0'+9 -0.03

l'+.3'*6 22. 722 3 3. 0 0 9 0 1 2 37 22. 791

5

0.4+12 -0 . 31

1 7 . 7'+l 22, 717 3'+. 00 99 1 7, 6'+9 22. 7973 0,516 -0 . 35

21.185 22. 713 3 5.0110 21, 0 59 22 , 7996 0,593 - 0 . 36

2'+.663 22. 7 08 36. 0122 2'+. 5 38 22 . 797 0 0.628 -0 . 39

22. 7 03 3 7.0133 2 7.937 22. 7857 0.59*+ -0.36

31.658 22. 699 38. Jl'+2 Jl, '90 22. 7712 0,531 -0.32

35 . 1 75 22 . 69^ 3 9. 011+9 3 5.010 22. 7573 0 , '+68 -0.28

38.701 22. 690 '0. 015'+ 3 8 . 5 ' 5 22. 74+37 0 . '+0'+ -0.2'+

'5.770 22 . 660 '2.0158 k5,bkl 22.7179 0.283 -0.17

52.837 22. 6 71 ''+. 0155 52. 756 22. 6916 0.153 -0.09

59.911 22. 662 '6. 01'*8 59,8 75 22. 670'+ 0,061 -0. 0*+ 66.981 kd.QlkZ 66. 939 22. 6519 -0.012 0.01

7'*, 039 22. 6'+5 50.0131 71+, 0 39 22.6359 -0,0 67 0 . O** 91.632 22. 623 55,0071 91, 7 38 22, 6079 -0,115 0 . 07

109.07'+ 22. 602 59, 9992 109, 226 22. 5836 -0 .139 0. 08

126.'+09 22. 582 6'+. 9999 126. 57'+ 22. 56'+'+ -0.130 0.06

l'+3.603 22. 562 7 0, 00 0 3 1^+3. 7<+9 22.5'+33 -0.102 0.06

47
PIN 0 IN T IN P CAL D CAL P DIF D DIF

227.963 24. 641 84.9971 228. 069 24. 6350 -0 . 046 0.02

Zk7»Zi>Z 24. 620 90.0096 247, 311 24. 6177 -0,020 0. 01

266.278 24. 600 95, 0121 266. 359 24.5964 -0.030 0. 02

285.168 24. 580 100.0099 2*15. 218 24.5778 -0 . 017 0.01

10.210 25. 552 31.0080 10. 185 25.5663 0 .243 -0. 06

It*. '76 25. 546 32, 0084 14. 373 25, 5955 0.712 -C. 19

18.783 25, 540 33.0090 18.622 25. 6058 0.860 -0. 26

23.122 25. 534 34. 0099 22.919 25.6060 0 .877 -0. 28

27.483 25, 528 35,0110 27. 254 25. 600 5 0.836 -0. 28

31.848 25, 523 36. G122 31,617 25, 5879 0 .725 -0. 26

36.221 25, 5 17 37,0133 36. 0 30 25, 5737 0.609 -0. 22

40.599 25. 5 11 38. 0142 40. 397 25. 5590 0 . 497 -0 . 19

44.974 25. 506 39.0149 44, 834 25. 5430 0.380 -0. 15

49.356 25. 500 40. 0154 49, 215 25. 5288 0 .286 -0. 11

58.116 25, 489 42, 0158 5 8. 0 40 25.5027 0 , 131 -0. 05

66.648 25. 478 44. 0155 66. 854 25. 4771 -0.009 0. 00

75.566 25. 467 46. 0148 75,645 25. 4556 -0.104 0.05

84.267 25. 456 48. 0142 34,405 25. 4379 -0 .164 0. 07

92.929 25, 446 50,0131 93. 128 25.4212 -0.214 0. 10

114.456 25. 420 55. 00 71 114. 746 25. 3900 -0 . 254 0. 12

135.767 25. 395 59.9992 136.091 25, 3662 -0 .239 0.12

156.903 25. 372 64.9999 157. 218 25. 3467 -0.201 0. 10

177.808 25. 348 70. 00 0 3 178.091 25. 3282 -0.159 0.08

196.459 25. 326 74. 9944 198.707 25.3097 -0.125 0.06

218.934 25. 304 79. 9910 219. 115 25. 2927 -0.083 0. 04

239.206 25. 282 84,9971 239, 372 25, 2732 -0 ,070 0. 04

259.343 25. 261 90. 0096 259. 450 25.2551 -0 . 045 0.02

279.231 25,240 95. 0121 279.335 25. 2353 -0.037 0. 02

298.903 25. 220 100.0099 299, 321 25. 2143 -0 . 039 0.02

11.524 26. 225 31. 0080 11,465 26. 2430 0 .336 -0. 07

16.044 26, 219 32. 0084 15. 935 26. 2610 0 . 679 -0. 16

20.594 26. 213 33.0090 2 0. 4 40 26. 2643 0 . 747 -0. 19

25.170 26, 207 34,0099 24, 939 26. 2607 0 .723 -0. 20

29.765 26, 201 35.0110 29,570 26. 2529 0.656 -0.20

34.370 26. 195 36. 0122 34. 175 26. 2421 0 . 566 -0.18

38.981 26, 189 37.013 3 38.797 26. 2299 0 .471 -0. 16

43.589 26. 183 38, 0142 ^3, 429 26. 2159 0 . 366 -0.13

46.197 26. 177 39. 0149 '8, 068 26.2021 0 .268 -0.10

52.805 26. 1 71 40. 0154 52. 7 36 26. 1889 3.184 -0.07

62.000 26. 160 42,0158 61.981 26. 1627 0.031 -0.01

71.169 26. 1 48 44, 015 5 71,2 36 26, 1386 -0 . 094 0 , 04

80.330 26, 1 37 46.0148 i 0. 457 26.1201 -0 . 158 0. 06

89.445 26. 126 48.0142 39.642 26,1018 -0.219 0. 09

98.529 26. 1 15 50.0131 98. 732 26, C862 -0.257 0. 11

121.075 26. Q 88 55. 00 71 121.417 26, 0553 -0 .282 0.13

143.396 26. 063 59. 9992 1^3.751 26.0327 -0.248 0.11

165.485 26. 0 38 64.9999 165, d'*! 26, C112 -0 . 215 C. IC

187.342 25. 014 70.0003 13 7. 654 25, 9922 -0 ,172 0, 08

208.921 25. 990 74, 9944 209.237 25. 9729 -0 ,137 0,07

230.298 25. 968 79,9910 230, 533 25. 9543 -0 .102 0. 05

48
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git. 290 32. 032 38. 01'*2 9'+. 630 32.0075 -0.360 0. 08

101.083 32. 02<+ 39. Ql'*9 131. 4+72 31. 9966 -0 , 385 0,09

107.858 32. 016 ttO. 015'* 138.2 96 31. 9866 -0 .399 0. 09

121.32t» 32. 001 '2. 0158 121. 8'40 31. 9669 -0 . '+25 0.11

13'*. 70'* 31. 985 ''. 0155 135.276 31. 9'+95 -0 .'25 0.11

li»8.006 31. 970 '+6. 01'*8 l'+8. 61'+ 31. 931+1 -0 .1+10 0.11

161.2«+0 31. 956 '3. 01'f2 161. 851 31.9209 -0 .379 0.11

17'+.38*» Zl,<)kl 50. 0131 171+. 989 -0. 3'+7 0.10

206.870 31.907 55. 0071 2 37. '18 31. 8797 -0 ,265 0.09

238.882 31. 87'+ 59. 9992 239. 321 31. 85'+0 -0 .18'+ 0.06

270 .«*7<t 31. 8'43 6'+. 9999 270.830 31. 8275 -0. 131 0.05

301.616 31. 813 70. 00 0 3 33 1.9'+'+ 31. 7998 -0 .109 0.0'+

332.300 31. 78'* 7<+, 99'*'* 332.673 31. 7707 -0. 112 0,01+

7.<t6t» 3 3. 2 3'* 2'*. 0083 7. '+20 33.2385 0 .582 -0.01

1U.929 33. 22'* 25.0078 1'+. 7'*6 33. 2'+09 1.226 -0. 05

22.366 33. 21'* 26. 0073 22.120 33. 2358 1 .100 -0.07

29.775 33. 205 27. 0071 29. 5 31 33. 2252 0 . 818 -0.06

37.161 33. 195 28.0071 36.961 33.2113 0 .539 -C.05

''+,525 33. 186 29. 0073 '+'. '+3'+ 33. 1951 0 .271 -0.03

51.889 33. 176 30.0076 51,8k6 33. 1796 0 . 079 -0.01

59.230 33. 167 31. 0080 59. 236 33. 1633 -0.09'+ 0.01

66.583 33. 158 32. 00 8'* o6. 73'+ 33. l'+92 -0 . 183 0.03

73.901 33. l'»9 33. 0090 7h, 139 33. 13'+3 -0 .281 0. 01+ 81.220 33. IkQ 3'*. 00 99 33. 1212 -0 . 337 0.06

88.528 33. 131 35. 0110 ^8. 860 33. 1090 -0 .375 0. 07

95.813 33. 122 36. 0122 96. 231+ 33. C973 -0 . '+C8 0.08

103.070 33. 37. 0133 103.518 33. 0858 -0.'+35 0. 09

110.316 33. 105 38. 01'*2 110.796 33. 0756 -0.1+35 0. 09

117.533 33. 0 96 39.01'»9 1 18, Oi+l 3 3. C 65

7

-0.'+33 0. 09

121+.716 33. 0 88 '0.015'+ 12 5, 2 69 33, C558 -0 . ''+'+ 0.10
PIN D IN T IN P CAL D CAL P OIF D OIF

139.026 33. 0 73 £2. 0158 139. 635 33. 0383 -0 . '38 0 . IC 153.257 33. 0 57 ''.0155 153. 87'^ 3 3. 023'^ -0 . '0 3 u . X u 167,36't 33, Qtil '6. 01<^8 16 8,0 01 33,0082 -0 , 381 0. 10

181. 'OS 33. 025 '8, 01'+2 182,010 32, 9951 -0 ,335 0, 09

195.37't 33. 0 11 50.0131 195. 938 32. 98'+0 -0 . 269 0,06

229. 8'* « 32. 976 55. 0071 230. 317 32. 9552 -0.206 0,06

263.606 32. 9'+2 59. 9992 26'^. 179 32. 928'+ -0 . 126 0 . OU

297,292 32. 910 6'^.9999 . 2 9 7. 576 32. 6993 -0.096 0,03

33C.271 32. 680 70. CO C 3 3 3 0 . 63'+ 32. 8677 -0.10 7 0 , 0(+ 6.803 33. 8 71 23. 00 86 6. 6 16 33. 8697 -0 . 188 0,00

l'».'»95 33, 860 Zf*, 0083 It^. '01 33. 8681 0 . 6'+8 -0.02

22.179 33, 850 25, CO 78 22.0 35 33. 8615 0 . 6'+9 -0.03

29.860 33 . 8'+0 26, 0073 29.706 33. 8518 0.516 -0. 0<^ 37.532 33. 6 30 27, 00 71 3 7. 01 33,8398 0,350 -0,03

t»5, 199 33. 820 28. 00 71 '5. 139 3 3. 8267 0.200 -0,02

52.8<(9 33. 811 29.00 73 52. 8 21 33. 8126 0,052 -0.01

6 0 .<f 8<* 33. 8 01 3 0. 00 76 60. 528 33. 7982 -0.072 0.01

66.103 33. 792 31. 00 8 0 66,2 22 33.7838 -0 • 175 0,02

75.710 33. 782 3 2. Ofl 8 U 75. 897 33. 770 3 -0 • 2'+7 0 . 0^

6 7-71 1 33. 773 3 3. Q Q q n 77. 757q -n .266 w U •t 7 u . o o o u • n 0 Q Q ^ 1 . 1 a5 7 7. 7U5U -0 . 33n 0.05

96 •''8 33. 755 75.011

D

\J ^ % VJ X X u '9 a. 7 Ql* 3 3. 73'* 1 -0,352 0,06

10 5 . 99'* 33. 7'^6 36. G122 13 6.330 33. 7235 -0 , 3 6*+ 0.07

113.505 3 3. 7 37 37. 0133 113,95/4 33. 7129 -0.378 0.07

121.011 33. 728 38. 01'^2 121. 'SO 33.70 39 -0.363 0.07

128 •'67 33, 7 20 39, 01 i+g 1 2 6. 9'^1 33, 69*+ 0 -0.370 0.06

135.927 33. 712 '0. 015'^ 1 3 6. ' ]* 33, 6862 -0.351 0.06

15C .730 3 3. 696 '2. 0156 15 1. 2 33 33, 6696 -0.333 0.08

165. '60 33. 679 ''. 0155 165.9 31 33. f 557 -0.285 0. 07

180.076 33. 66'^ '6, 01 'e ISO. 523 33. £'22 -0 . 2'+8 0.06

l9'+.608 33. 6'48 ^8, 01'^2 19 5.006 33. 6299 -0.206 0 . 05

209. 055 33. 633 50.0131 209. 338 33. 6186 -0.159 0 . 0<« 2'^'t.736 33. 597 55. 0071 2!+'^. 639 33, 590 8 -0,062 0,02

279.679 33. 563 59. 9992 279.963 33. 5635 0.006 -0.00

31'+.532 33. 5 30 6'^. 9999 3 1 '. ^32 33. 5338 0 . 0 32 -0, 01

3<^8 .&'' 33 . '98 70. 00 0 3 3 !^8. 562 33. 500 7 0 . 02<+ -0, 01

5.565 Zk* k 13 22. 0066 5,572 3'+. '129 -0,138 0,00

3^ . h-QZ 2 3. 00 8 6 13. 352 3 1*. UO 89 0.609 -0,02

21 .Si^S Zk* 392 2'+. CO 8 3 21. 20'4 3*+. '+022 0.653 -0,03

29.236 3^+. 3 82 25.00 76 29. 0 85 Zk, 3922 0.515 -0.03

37.123 Zk,Z71 26. 00 7 3 3 6. 9 96 3'+, 380 1 0 , 3'+3 -0,03

u 5 . n n 5 7u . 7 fil 3 i* . 366 7 0,178 -0.02

52.873 3'^. 351 26. 0071 52. 660 Zi^, 3522 0.025 -0. 00

60. 7'^7 Zk, Zi*Z 29. 00 73 60. 795 3'^. 3386 -0 . 079 0.01

66,592 Zk. 332 30, 0076 68.719 Zk, Z2k2 -0 .185 0.02

76.1^32 3'+. 322 3 1, 00 60 76.627 3'+. 3107 -0 .255 0.03

6'+. 238 3'+. 313 32. ODSt^ 5'^. 513 Zt*, 2967 -0 .326 0. 05

92.055 3'+. 303 33. 0090 92. 37'^ 3'^. 28'+9 -0 . 3'^7 0. 05

99,8'+i^ 3'^, 29'^ 3'^, 0099 1 DO. aii^ 3i+, 2732 -0.371 0. 06

107.628 3'+. 285 35. olio 1 36. 025 ZU. 2629 -0 .369 0. 06

54
PIN D IN T IN P CAL D CAL P DIF D DIF

115.389 3^. 276 36.0122 115.309 3k, 2531 -0,365 C. 07

123.110 3t^. 267 37. 0133 123. 556 3k, 2k2<) -0 .371 0.07

130.820 3'^. 258 38. 01*^2 131.283 3k, Z3kQ -0

.

35k 0. 07

138.<»96 3'+. 250 39. OlkS 138. 976 3k. 2252 -0 . 3'^6 0. 07

li^e.iso 31+. 2'»1 kO, :}i5k l'^6.63'4 3'^.2170 -0.331 0.07

161.389 3'+. 22'+ '2.0158 161.852 3'^. 2021 -0 .287 0. 07

176.510 3k,2Q& ''. 0155 176.950 31^. 1877 -0 ,2'49 0, 06

191. 5U0 31*. 192 '6. Olt^d 191. 926 3'^. 17'^7 -0 . 202 0. 05

206.<»86 3'^. 1 77 '8, Ql't2 216. 81C 3k, 1628 -0 . 157 0. Ot* 221.330 3'^. 161 50. 0131 221. 575 3'^. 1512 -0.111 0.03

258.022 3'+. 125 55, 00 71 258.062 3'+. 123'^ -0 , 016 0 .00

29U.102 3i+. 090 59. 9992 2 9'+. 0 17 3'^. 0935 0 ,029 -0.01

329.732 3k, 058 6'^. 9999 329. 577 3'+. 0629 0 . 0'+7 -0. 02

36'*.785 3i+. 026 7 0. 00 0 3 3bk, 710 3k, 0280 0.015 -0,01

5.063 3k, 983 21.0099 5.107 3'^.g799 -0,861 0.01

13.171 3^+. 972 22. 00 68 13.133 3'^.9766 0 . 51'^ -0.01

21.288 3'+. 961 23. 00 66 21. 155 3k, 9699 0 .62'+ -0. 03

29. '16 3k, 950 2'4. 00 83 29.253 3*+. 9609 0.555 -0.03

37. S**** 3k, 9kQ 25. 00 78 J7. 3 83 3'^, 950 0 0 . '31 -0. 03

'5.662 3k, 929 26. 0073 k5,5^k 3'^.9373 0.279 -0.02

53.768 3k, 919 27. 00 71 53. 730 3'^. 923'^ 0 .126 -0.01

61.862 3k. 909 28. 0071 61. 86'4 3k, 9091 -0.003 0.00

69.939 3^. 899 29, 00 73 70. 023 3'^. 89'^5 -0 .120 0.01

77. 99'^ 3k, 890 30.0076 78.170 3k, 8797 -0.225 0.03

66.033 3'+. 880 31. 00 8 0 36. 295 3k, 8653 -0 . 305 0,0k

9't.065 3k,d7Q 32. OOBii 3k, 313 3'4. 8522 -0,355 0.05

102.087 3k. 861 33. 0090 132. '73 3'^. 6'^01 -0 . 378 0.06

lie. 085 3h. 351 3'+. QC99 110.523 3k. ezdk -0 .397 0.07

lie .068 3k, 8 k2 35. 0110 118. 5'48 3k, 8175 -0 . '06 0.07

126. 0'+'^ 3k, 8 33 36, 0122 1?6, 5'*3 3'+. 8079 -0 . 396 0.07

133.981 3k. d2k 37. 0133 1 J'+. 5 35 3'^. 7981 -0 .391 0. 07

li+l .906 3k, 815 38. ijl'+2 l'+2. * 35 3k, 7895 -0.373 0.07

l'^9.803 3^^. 806 39. 01'49 15 0. 3 3'* 3'^. 7812 -0 . 35'^ 0. 07

157, 68'^ 3'+. 798 '+0, IJ15'^ 15 8. 199 3'+, 773 8 -0,327 0.07

173.3^3 3'^. 7 81 '2.0158 1 73. 8 31 3k, 7589 -0.282 0 . 06

188 .912 3k, 7bk ''. 0155 1 39. S'^l 3*^. 7'^57 -0.227 0.05

2014. 36U 3k, 7kd '6. 01 '8 2 0'+. 738 3k, 733k -0.173 0,0k

219.720 3k, 733 '8. 01 '2 2 2 0.033 3k. 720

1

-0 . l'+2 0 . 0<4 235.012 3'+.718 50. 0131 235.218 3k, 7095 -0.087 0. 02

272.753 3^+. 681 55. C071 2 72. 75'+ 3k, 6809 -0.000 0.00

309.912 3i+. 6i+6 59. 9992 3 39. 7k7 3*^. 6515 0.053 -0.02

3'»6,529 3'+. 613 6*4.9999 3kb. 357 3'^. 6181 0.050 -0.02

5.797 35. 587 20, 0090 5. 718 35. 592*^ 1 .358 -0.01

1'*.033 35. 576 21.0069 13. 92'^ 35. 5826 0 .77'^ -0. 02

22.336 35. 565 22. Q0a8 22. m 35. 5737 0 .6'+9 -0.02

30.629 35.55k 23. 00 66 30.537 35. 5612 0 . 399 -0.02

38.933 35. 5'43 2*^. 00 83 38.851 35. 5'+73 0 .186 -0. CI 35. 533 25. 00 78 k7, 2ki 35. 5330 0.015 -0.00

55.598 35. 522 26. 0073 55.638 35. 5200 -0.071 0.01

63.936 35. 512 27. 00 71 bk. Ok3 35. 5062 -0 .167 0.02
PIN 0 IN T IN P CAL D CAL P OIF 0 DIF

72.275 35. 502 28. 0071 72. k'-tQ 35. '929 -0 . 229 0,02

80.590 35. 1*32 29. 0073 30. 331 35. '792 -0 . 298 0. 0*+ 88.918 35.it82 30.0076 89. 233 35. '672 -0.321 0. 0<+ 97.211 35. ^72 31. 0080 97.557 35.'+5'+7 -0 . 356 0.05

105.«f70 35. 'f63 32. QQbt* 135. 338 35. ''+20 -0 . 396 0.06

113.758 35. ^53 33.0090 1 lU. 1 78 35. it3ZZ -0 . 369 0.06

122.001 35. it '2 Zi*, 0099 12 2. '38 35. '217 -0.358 0.06

130.226 35. '33 35.0110 13 0.636 35. '119 -0 . 35*+ 0 . 06

138.'f«*l 35. kZ^* 36.0122 138. 902 35. '•031 -0.333 0.06

35. WIS 37. 0133 1^7. 031 35. 39'+8 -0.306 0.06

15<+.790 35. 'OS 38. OlkZ 155.236 35. 3866 -0 . 288 0. 06

162.91** 35. 397 39. Qii*9 153. 3'+'i 35. 3785 -0 •26U 0. 05

171.038 35. 389 '0.015i+ 171. '33 35.3719 -0. 231 0.05

187.185 35. 372 kZ. 0156 137. 516 35. 3585 -0 .177 0.0<>

203.196 35. 356 kt*, 0155 203. '62 35. 3't'+8 -0. 131 0.03

219.173 35, 339 kS. 01U8 219. 232 35. 33'+5 -0, 050 0. 01

23't.980 35. 322 k&. Qii*Z 23it.993 35. 3217 -0 .005 0.00

250.7t*3 35. 306 50.0131 250.610 35. 3113 0.053 -0.01

289.612 35. 270 55. 0071 239. 232 35. 2815 0.11t» -0.03

327.89tf 35. 235 59. 9992 327. t+ll 35. 2507 0 . Ik7 -0. Ot+ 7.950 36. 2t»3 19.0068 7.9'+5 36. 2'+30 0 .057 -0.00

16.«*29 36. 231 20.0090 16.369 36. 23'+ * 0 . 36(» -0.01

2tt.9«»3 36. 220 21. 0069 2'+.8'»8 36. 22'+9 0.379 -0.01

33.i»8't 36. 209 22.0088 33.333 36. 21'+0 0.301 -0. 02

tf2.0<48 36. 198 23. 0066 '1.966 36.2021 0.196 -0.01

50.613 36. 187 Zk. 0083 50.581 36. 1885 0. 062 -0.00

59.189 36. 176 25. 0078 59.218 36.17'+7 -0 . 050 0. oc 67.760 3 6. 166 26. 0073 57. 866 36. 1605 -0 ,158 0.01

76.335 36. 155 27. 0071 76. 518 36.1'+65 -0.2'+0 0.02

8'*. 911 36. IkS 28.00 71 35. 161 3 6. 1332 -0 .294 0.03

93. '71 36. 1 35 29. 0073 93. 793 36. 1198 -0 . 3'+5 0. 0<+ 102.019 36. 125 30. 0076 i3Z* k^t* 36. 1071 -0 . 378 0.05

110.561 36. 115 3 1. 00 a 0 110.990 36, 095'+ -0 . 389 0. 05

119.081 36. 105 32. 008'+ 119. 551 36. 06'+l -0.395 0. 06

127,601 36. 095 33. 0090 I H 8. 0 79 36. C7kl -0 . 375 0.06

136. lOU 36. 086 3t+. 0099 136. 585» 36. 06'+7 -0 .35'+ 0. 06

lkk,53Q 36. 076 35. 0110 l'+5. 059 36. 0550 -0 .325 0. 06

153.059 36. Q67 36.0122 153.511 36. 0't79 -0 . 295 0. 05

161.'+9'f 36. 358 37. 0133 161.927 36. G399 -0 .268 0. 05

169. 92<* 36, G'^9 38. QlkZ 170. 303 36. 0330 -0. 223

178.31'f 36. Qi^O 39. 01'+9 178. 657 36. 0260 -0 . 192 0. Otf 186.682 36. 0 31 '0. 015«+ 1 i6. 977 36. C193 -0.158 0.03

203.326 36. 0 !* ^2, 0158 233.512 36. 006'+ -0 . 091 0.02

219.858 35, 397 <', 0155 219.9'+2 35. 9938 -0 . 036 0.01

236.29't 35. 981 *+&. Olt+8 236. 261 35. 9820 Q.Qlk -0. 00

252.629 35.965 '8. Ql'+2 252. '79 35.9703 0 .059 -0.01

268.867 35.9'«9 50. 0131 266. 592 35. 9589 0.102 -0.03

308.982 35. 912 55. 0071 308. '76 35. 9286 0.16'+ -0. 05

35. 876 59. 9992 3^+7. 8 36 35. 8952 0 . 177 -0.05

11.609 36. J23 18. 008'* 11. 637 36.9191 -0.670 0.01

56
PIN

D IN

T IN ° CAL

D CAL P OIFD DIF

20.292 36.911 19. 0088 30.312 36.9103 -0 .101 COO

26.960 36.900 20. 0090 28.990 36. 699tf -0.032 0. 00

37.715 36. 889 21.0089 37.729 36.8879 -0 . 037 0.00

36. 3 78 22. 0088 ^+6. 527 36. 8758 -0.082 0.00

55.308 36. 866 23. 0086 35. 362 36. 8638 -0 . 098 0.01

36. 355 2k» 0083 f}k,233 36. 851t» -0 .136 0.01

72.982 36. 8'*5 25. 0078 73. 119 36. 838'* -0 .188 0.0?

61.818 36. 33^ 26. 0073 3?. 0 15 36.6253 -0.2'»0 0.02

90.655 36. iZk 27. 0071 90.912 36. 812't -0 .28t* 0.03

99.tf92 36. 813 28. 00 71 39. 79t» 36.8001 -0 . 30«* 0,0k

106.318 36. 803 29. 0073 ia8.669 36. 7881 -0.323 0. Ot« 117.132 36. 793 30.0076 117.5?0 36. 7767 -0 . 331 0.0<*

125.9't7 36. 763 31. 0080 126. 3 39 36. 7665 -0.311 0,0k

13'*.739 36. 773 32. 008'* 135. 139 36. 7566 -0.297 0. 0<t 36. 763 33, 0090 l'+3. 900 36. 7k7Q -0 . 273 0. O^f 152.2«»tf 36. 753 Zk, 0099 152.6'«3 36. 7372 -0 .262 0.0k

161. 01'* 36. 7kk 35. 0110 161.360 36. 7301 -0.215 0,Qk

169.727 36. 73U 36. 0122 170. 0!47 36. 7219 -0.189 0. 03

176. if 'O 36. 725 37. 0133 1 76. 698 36. 7151 -0 . l**** 0.03

187.119 36. 716 38. 01'*2 137. 317 36. 7082 -0 .105 0.02

195.753 36. 707 39. (jlk3 195.911 36. 7009 -0. 081 0.02

20'*.388 36. 698 'O. G15i* 2Q'+.i»69 36. 69i*8 -0 .OtfO 0.01

221.55't 36. 681 k2. 0158 221. Slk 36. 6623 0 .023 -0.00

236.585 36. 66'* kk, 0155 238. k25 36. 6693 0 . 067 -0. 02

255.583 36. 6'+7 '6. 01it8 2 3 5. 2 39 36. 6589 0»13k -0.03

272.i»ll 36. 632 US. 01^+2 271.97? 36. 6^+62 0. 161 -0.0*t

269.171 36. 617 50.0131 238.612 36.63it6 0.193 -0. 05

330.613 36. 578 55.00 71 339. 753 36. 60'+l 0.260 -0.07

5.158 37. 912 15. 0020 5. 040 37. 9169 2.285 -0.01

13.920 37. 899 16.0051 l**. 116 37. 8908 -1. ^07 C. 02

22.776 37. 888 17.0071 23.0 01 37. P780 -0 .979 0.03

31.706 37. 876 18. CO a't 31. 856 37. 8689 -0.507 0.0?

^0.695 19.0086 '0.737 37.6600 -0 . 227 0.01

'9.723 37. 853 20. 0090 k<). 717 37. Ck^S -0 . li*8 0.01

58.821 37. 3U1 21. C069 58. 8 30 37. 6388 -0.100 P. 01

67.9'»0 37. 830 22. 0088 68. 027 37. 8267 -0. 129 0.01

77.0 82 37. 819 23. 0086 77. 209 37. 8139 -0 . 165 0. 01

86.2tt8 37. 808 2k» 0083 36. '+30 37.6011 -0.211

C . 02

37. 798 25.0078 95.661 37. 7885 -0 . 2'*8 0.0?

10k. biZ 37. 787 26. 0073 lOit.335 37. 7763 -0.261 0.03

113.801 37. 776 27. 0071 Hi*. 110 37. 76'f5 -0 . 272 0.03

122.995 37. 766 28. 00 71 123, 326 37. 7535 -0 .270 0.03

132.172 37. 756 29. 0073 1 32. 535 37. 71+25 -0 .275 0. Ok

l'4l.3U9 37. 7kb 30.0076 li*l. 733 37. 7325 -0.250 0.03

150.it9fl 37. 736 3 1 . 0 0 8 G 150. 855 37. 7225 -0.236 0.03

159.653 37. 725 32. 00 8'* 159. 977 37. 7137 -0.203 0. G3

168.785 37. 716 33.0090 169. 0 75 37. 7052 -0 .172 0.03

177.928 37. 706 3t». 0099 178. 152 37.6981 -0.125 0.0?

187. Q50 3 7. 6 96 35. QUO 137. 136 37.6911 -0.073 0.01

196.1<»8 37. 686 36. ul22 1 96.233 37. 68i+5 -0.026 0.00
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68
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69
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2.7000+001 5.1967+000 5. 1983+000 -1.6302- 003 2.9718+000

2.8000+0 01 5.750'» + 00C 5. 7519+000 -l.'t717- 003 3.61<^7+000

2.9000+0 01 6.305'4 + OCO 6. 3 366 +000 -1.2209- 003 <. '00 7 + 00 0 3.0000+001 6.8618 + 0 C 0 6. 9527+000 -9.'*7'+3- 00<* 5.3898+000

3.1000+0 01 7.itl9't + 0Q0 7.it201 + 000 -7. 1197- 00<( 6. 7027+000

3.2000+0 01 7,978'* + 0G0 7.9789+000 7823- 00<4 8.6699+000

70
Appendix B. Table of Symbols

A = parameters for equation 1 B = parameters for vapor pressure equation

G = parameters for equation for saturation densities

N = parameters for equation of state n = index of refraction

P = pressure

R = gas constant

r = parameters for index of refraction equation

T = temperature

X = reduced temperature

3 = scaling law parameter

p = density

Subscr ipts:

c = critical point

g = gaseous phase

i = liquid phase

t = triple point

71
FORM NBS-114A (1-71) U.S. DEPT. OF COMM. 1 . PUBLICATION OR REPORT NO. 2. Gov't Accession

BIBLIOGRAPHIC DATA NBSIR 74-357

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

j\ ivioaiiica xjcneaiCL— w cod— xviiuin iiiqua tion oi ot3.tc lor

Parahydr og en

5. Publication Date February 1974

6. Perfotmiog Organization Code

7. AUTHORCS)

R. D. McCarty

8. Performing Organizatioa

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS, Boulde r Labs.

DEPARTMENT OF COMMERCE

Boulder, Colorado 80302

10. Project/Task/Work Unit No. 2750429

11. Contract/Grant No.

12. Sponsoring Organization Name and Address NASA-Lewis Research Center

Cleveland, Ohio

li, 1 ype or Keport & Period Covered Final

14. %>on soring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most si^ificant information. If document includes a significant

bibliography or literature survey, mention it here.) A 32 term modified Benedict- Webb-Rubin equation of state has been applied to data

for parahydrogen. The adjustable parameters in the equation of state were

determined using data from the triple point to 2500 K, with pressures to 680

atmospheres. Extensive modifications have been made to the previously accepted

PVT surface for the saturated liquid and vapor phases in the near critical region.

These modifications have been made on the basis of subsequent refractive index

data and the application of scaling law equations. Comparisons between experimental and calculated data are given.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Critical point; equation of state; hydrogen; index of refraction; PVT; saturation

properties; scaling laws.

18. AVAILABILITY STATEMENT 19. SECURITY CLASS

(THIS REPORT)

21. NO. OF PAGES

[3 UNLIMITED. UNCLASSIFIED

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TO NTIS.

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22. Price

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