Revised Formulation for the Refractive Index of Water and Steam as a Function of Wavelength, Temperature and Density

Journal of Physical and Chemical Reference Data 27, 761 (1998); https://doi.org/10.1063/1.556029 27, 761

Revised Formulation for the Refractive

Index of Water and Steam as a Function of

Wavelength, Temperature and Density

Cite as: Journal of Physical and Chemical Reference Data 27, 761 (1998); https://doi.org/10.1063/1.556029

Submitted: 23 February 1998 . Published Online: 15 October 2009

Allan H. Harvey, J. S. Gallagher, and J. M. H. Levelt Sengers

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Revised Formulation for the Refractive Index of Water and Steam

as a Function of Wavelength, Temperature and Density

Allan H. Harvey

a…

Physical and Chemical Properties Division, National Institute of Standards and Technology, Boulder, Colorado 80303

John S. Gallagher and J. M. H. Levelt Sengers

Physical and Chemical Properties Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899

Received February 23, 1998; revised manuscript received March 31, 1998

Schiebener et al. published a formulation for the refractive index of water and steam in

1990 @J. Phys. Chem. Ref. Data 19, 677 ~1990!#. It covered the ranges 0.2 to 2.5

min

wavelength, 212 to 500 °C in temperature, and 0 to 1045 kg m

in density. The for-

mulation was adopted by the International Association for the Properties of Water and

Steam ~IAPWS! in 1991. In the present article, the data, after conversion to ITS-90, have

been reﬁtted to the same functional form, but based on an improved equation of state for

water adopted by IAPWS in 1995. The revised coefﬁcients are reported, and some tabular

material is provided. The revised refractive-index formulation was adopted by IAPWS in

1997 and is available as part of a National Institute of Standards and Technology Stan-

dard Reference Database. For most conditions, the revised formulation does not differ

signiﬁcantly from the previous one. A substantial improvement has been obtained in

supercooled water at ambient pressure, where the previous formulation was defective.

Special attention has been paid to the behavior of the refractive index in the near infrared,

where strongly oscillating data were reported after the correlation of Schiebener et al. had

appeared, leading to subsequent curtailing of the range of validity of the formulation.

Newer results do not show these oscillations. They are compared with the revised for-

@S0047-2689~98!00204-9#

Key words: formulation; infrared; ITS-90; molar refraction; refractive index; steam; supercooled water;

supercritical steam; ultraviolet; visible; water

Contents

1. Introduction................................ 761

2. Data and Method........................... 762

3. Revised Formulation........................ 762

3.1. Description and Tabulation................ 762

3.2. Comparison with Data................... 763

4. Refractive Index and Density of Supercooled

Water..................................... 764

5. Refractive Index in the Near Infrared........... 765

5.1. Previous Concerns....................... 765

5.2. Obtaining Refractive Indices from

Absorption............................. 765

5.3. Critique of Data in the Near Infrared....... 765

5.4. Temperature Dependence in the Near

Infrared............................... 766

5.5. Recommendations....................... 766

6. Summary.................................. 766

7. Acknowledgments.......................... 767

8. References................................. 767

9. Appendix 1. Text of IAPWS Release........... 767

10. Appendix 2. Tables of Refractive Index Values... 770

List of Tables

1. Coefﬁcients of the formulation................ 768

2. Estimated uncertainty of the refractive-index

formulation................................ 769

3. Refractive index values from the formulation.... 769

4. Refractive index for water for wavelength

0.488

m................................. 770

5. Refractive index for water for wavelength

0.5145

m................................ 771

6. Refractive index for water for wavelength

0.589 26

m............................... 772

7. Refractive index for water for wavelength

0.6328

m................................ 773

8. Refractive index for water and steam at

vapor-liquid saturation....................... 774

1. Introduction

Schiebener et al.,

in 1990, published a formulation for the

refractive index of water and steam. It extended over the

ranges of 0.2 to 2.5

m in wavelength, 212 to 500 °C in

Electronic mail: [email protected]

Physics and the American Chemical Society.

Reprints available from ACS; see Reprints List at back of issue.

0047-2689/98/27„4…/761/14/$26.00 J. Phys. Chem. Ref. Data, Vol. 27, No. 4, 1998

761

temperature, and 0 to 1045 kg m

in density. It made use of

a comprehensive data collection by Thorma

hlen et al.,

com-

pleted in 1985, from which the most reliable sources were

selected. Some additional vapor-phase data

3,4

were also used.

The formulation was based on the assumption that the

Lorentz–Lorenz function

LL5

, ~1!

where n is the refractive index, is a smooth, slowly varying

function of molar density

and temperature. This assump-

tion was validated on the basis of the existing data. In par-

ticular, for ﬁxed wavelength, LL does not vary more than 1%

between the liquid at ambient temperatures and the vapor

above the normal boiling point. The wavelength dependence

of LL is pronounced. Strong variations occur near the ﬁrst

major infrared resonance, at around 2.9

m in wavelength,

and near the ultraviolet resonance at around 0.18

m. The

original correlation was limited to a region between these

two resonances.

Since most of the data were obtained as a function of

pressure and temperature, an equation of state was needed to

convert measured pressures to densities. For this purpose, the

NBS/NRC Steam Tables

were used; these had been adopted

by the International Association for the Properties of Steam

@now the International Association for the Properties of Wa-

ter and Steam ~IAPWS!# in 1984. The formulation of Schie-

bener et al.

represented most of the selected data to near

their experimental uncertainty, which, in some cases, was

within 10

2 6

in n. A notable exception was the substantial

departure from the precise data available in supercooled wa-

ter. This departure was due to extrapolation of the equation

of state and was therefore not curable within the chosen

framework.

Just after the publication of Ref. 1, the international prac-

tical temperature scale ~IPTS-68! was replaced by ITS-90.

The differences between the scales are signiﬁcant for the

refractive index formulation only in those regions where

highly accurate data are available, that is, for liquid water at

ambient pressure and temperatures between 212 and 60 °C.

Furthermore, in 1995, IAPWS adopted a new formulation

for the equation of state of water and steam, which was of

improved accuracy and had been ﬁtted to the available den-

sity data in supercooled water, representing them well.

7,8

Shortly after Ref. 1 appeared in print, some reported re-

fractive indices in the near infrared

were brought to the

authors’ attention; these data showed strong oscillations in n

as a function of wavelength at 1.2

m and up. Schiebener

et al. then published an Erratum,

recommending that the

correlation not be used beyond 1.1

m. Further investiga-

tion, however, strongly suggests that these oscillations are

not real; this will be discussed in Sec. 5.

The purpose of the present work is the following: ~1! to

base the refractive index formulation on the new temperature

scale, ITS-90; ~2! to base it on the newly adopted equation of

state, in the hope of obtaining better performance in super-

cooled water; and ~3! to clarify some issues related to the

behavior of the refractive index in the near infrared.

2. Data and Method

The selected database of Ref. 1, with temperatures trans-

formed to the ITS-90 temperature scale according to the

method given by Rusby,

was used for the revised correla-

tion. The data of highest accuracy and internal consistency,

thus anchoring the correlation, are those of Tilton and

Taylor

12,13

at ambient pressure and at temperatures up to

60 °C, and the data of Saubade

in low-temperature and

supercooled water down to 212 °C, both with claimed un-

certainty of 10

2 6

in n; the data for pressurized water from 2

to 54 °C by Waxler et al.,

15,16

with claimed uncertainty of

2 4

; and the data for pressurized steam from 100 to 225 °C

by Achtermann,

3,4

with claimed uncertainty of 23 10

2 7

The method of correlation was to write LL as a function of

density, temperature, and wavelength, with as few adjustable

parameters as possible, so as to control unwanted oscillations

in the large regions where no data are available ~liquid at

temperatures above the normal boiling point; vapor below

the boiling point; supercritical steam!. The functional depen-

dence on the wavelength was dominated by the customary

mathematical poles near the resonances. The correlating

equation, of the same form as that used in Ref. 1, is Eq. ~A1!

in Appendix 1. The densities of the experimental data were

calculated from the new IAPWS formulation of 1995.

8,17

The

wavelength range of the ﬁt was from 0.2 to 1.1

3. Revised Formulation

3.1. Description and Tabulation

The optimized coefﬁcients from the new ﬁt of the data to

Eq. ~A1! in Appendix 1 are listed in Appendix 1, Table 1.

Table 2, which gives the estimated uncertainty in various

ranges of temperature, pressure, and wavelength, remains

nearly unchanged from the previous formulation, except for

the supercooled liquid, where substantial improvement has

been obtained. In Table 3 of Appendix 1, values of the re-

fractive index are listed for three wavelengths, four tempera-

tures, and four pressures, with more digits than the uncer-

tainty of the formulation warrants, for the purpose of

checking computer codes.

In Appendix 2, the refractive index as calculated by the

formulation is tabulated as a function of temperature and

pressure for four widely used wavelengths in the visible

spectrum ~Tables 4–7!. The upper temperature and pressure

limits in these tables are 500 °C and 100 MPa; we must

emphasize that the data do not cover this entire region, so

portions of these tables are extrapolations ~Table 2 in Appen-

dix 1 gives the regions in which data do exist!. The wave-

lengths used are the argon-ion laser wavelengths of 0.488

and 0.5145

m, the sodium-D line wavelength ~intensity-

weighted mean of the doublet! of 0.589 26

m, and the

helium-neon laser wavelength of 0.6328

m. For these four

wavelengths, the refractive index is also tabulated for the

762762 HARVEY, GALLAGHER, AND LEVELT SENGERS

J. Phys. Chem. Ref. Data, Vol. 27, No. 4, 1998

saturated liquid and vapor ~Table 8!. In Tables 4–8, the num-

ber of digits given is sometimes more than that justiﬁed by

the uncertainty in the formulation; consult Table 2 to esti-

mate the uncertainty at any given state point.

3.2. Comparison with Data

For data of moderate accuracy, the revised formulation is

not signiﬁcantly different from the previous one. We there-

fore refrain from comparing it with the complete database.

We make exceptions for the highly accurate data of Tilton

and Taylor,

12,13

Achtermann,

3,4

and Saubade.

The devia-

tions of the data of Tilton and Taylor from the new ﬁt are

shown in Fig. 1 ~with temperature as the x axis! and Fig. 2

~with wavelength as the x axis!. The deviations are very

similar to those from the previous ﬁt ~within 10

2 5

!, except

that the present ﬁt shows substantial improvement at 0 and

5 °C for reasons to be discussed in Sec. 4. The ﬁt to the data

of Achtermann

3,4

is insigniﬁcantly, less than 10

2 6

, different

from that of the correlation by Schiebener et al. A marginal

change is observed at the highest temperature ~Fig. 3!.

FIG. 1. Deviations of Tilton and Taylor data ~Refs. 12 and 13! from the revised formulation vs temperature.

FIG. 2. Deviations of Tilton and Taylor data ~Refs. 12 and 13! from the revised formulation vs wavelength.

763763REVISED FORMULATION FOR THE REFRACTIVE INDEX OF WATER AND STEAM

J. Phys. Chem. Ref. Data, Vol. 27, No. 4, 1998

4. Refractive Index and Density of

Supercooled Water

Figure 11 of Ref. 1 showed that the high-quality Saubade

data

increasingly and systematically departed from the

original formulation as the temperature decreased below

5 °C. At 212 °C the departure had increased to 23 10

2 4

two orders of magnitude beyond the claimed uncertainty of

the data. At that time it was concluded that the departure was

due to the extrapolation of the NBS/NRC equation of state,

which had not been ﬁtted to any data in supercooled water.

The IAPWS-1995 equation of state

7,8

was ﬁtted to data in

supercooled water, and also beneﬁted from density data now

available

for liquid water from 0 to 85 °C with a relative

accuracy near 10

2 6

In Fig. 4, we show the departures of the Saubade data ~and

also the low-temperature data of Tilton and Taylor at the

same wavelength! from both the present formulation and the

previous one. The low-temperature systematic errors have

been reduced by a factor of 3. The remaining systematic

FIG. 3. Deviations of Achtermann data ~Refs. 3 and 4! at 225 °C from the revised and 1990 formulations.

FIG. 4. Deviations of low-temperature data ~Refs. 12–14! from the revised and 1990 formulations.

764764 HARVEY, GALLAGHER, AND LEVELT SENGERS

J. Phys. Chem. Ref. Data, Vol. 27, No. 4, 1998

errors are most likely still due to the equation of state, since

the experimental liquid density data below 0 °C are less ac-

curate than the data now available in the range 0 to 85 °C.

5. Refractive Index in the Near Infrared

5.1. Previous Concerns

The previous formulation

was ﬁtted to a few selected data

points for the refractive index of liquid water in the near

infrared at wavelengths up to 2.5

m. However, after that

work was completed, its authors were made aware of new

data by Ichikawa

which exhibited strong oscillations in the

refractive index associated with the known weak absorption

peaks at roughly 1.46 and 1.93

m. Since the refractive in-

dex from the formulation varied smoothly through this re-

gion, it could not represent these oscillations. Therefore, an

Erratum was issued

in which the upper wavelength limit of

the formulation was restricted to 1.1

m. The same upper

limit was used to restrict the data used in the reﬁt reported

here.

5.2. Obtaining Refractive Indices from Absorption

While water is essentially transparent at visible wave-

lengths, it contains strong absorption bands in the infrared.

The ﬁrst such peak is near 2.9

m, but there is signiﬁcant

absorption at all wavelengths beyond about 1

m. This can

introduce signiﬁcant errors if experiments are performed un-

der the assumption of complete transparency.

In absorbing ﬂuids, one must treat the refractive index as a

complex number, where the imaginary part describes the ab-

sorption. The real and imaginary parts, denoted n(l) and

k(l), are connected by the Kramers-Kronig relations, which

give the real part as an integral over the imaginary spectrum,

and vice versa. For determining the real part from the ab-

sorption, the Kramers-Kronig relation is

5 11

2 l

. ~2!

Two aspects of Eq. ~2! are worth noting. First, while absorp-

tion at all wavelengths contributes to n(l), that at wave-

lengths close to l is weighted more heavily. Therefore, if

one is concerned with n(l) in a speciﬁc wavelength range, it

is important to know k(l) accurately in that range, but the

absorption need only be known approximately at distant

wavelengths. Second, the integrand in Eq. ~2! is positive for

l.l

and negative for l,l

. Therefore, in the neighbor-

hood of a strong absorption, n(l) will decrease as the ab-

sorption is approached from a shorter wavelength, increase

sharply at the absorption, and then decline again as l in-

creases further.

If accurate absorption data are available, Kramers-Kronig

analysis provides a rigorous tool for obtaining accurately

changes of n with wavelength; it is particularly useful in

regions where absorption renders direct measurement un-

workable.

5.3. Critique of Data in the Near Infrared

Direct measurement of water’s refractive index in the near

infrared is impractical due to absorption. However, the ab-

sorption spectrum k(l) can be measured more easily; there

have been several such studies including the recent precise

work of Kou et al.

in liquid water from 0.65 to 2.5

The available absorption data were collected by Bertie and

Lan,

who performed a Kramers-Kronig analysis to obtain

n(l) for liquid water at 25 °C. For the region of interest

here ~near-infrared wavelengths shorter than that of the

strong resonance near 2.9

m!, their analysis is estimated to

be accurate within 0.001 in n(l).

Their refractive indices

in this region are in good agreement with the earlier analysis

of Hale and Querry,

who worked from a more limited set

of absorption data.

The important aspect for our purposes of the results from

Kramers-Kronig analysis is that they do not show the severe

oscillations exhibited by Ichikawa’s

data. The weak absorp-

tion peak at 1.46

m produces only a barely perceptible

change in the slope of n(l), while the slightly stronger peak

at 1.93

m produces a small shoulder in the spectrum. Fig-

ure 5 shows n(l) in the region of interest here, along with

the extrapolation of our formulation. The data of Ichikawa

are not shown, but their oscillations would be well off the

scale of Fig. 5.

We think that Ichikawa’s measurements in this region do

not give correct values for n(l). We come to this conclusion

not only because they disagree with rigorous Kramers-

FIG. 5. Refractive index in the near infrared at 25 °C.

765765REVISED FORMULATION FOR THE REFRACTIVE INDEX OF WATER AND STEAM

J. Phys. Chem. Ref. Data, Vol. 27, No. 4, 1998

Kronig analysis, but also because they show a steady in-

crease of n(l) as the strong absorption near 2.9

misap-

proached. As mentioned above, physics demands that n(l)

decrease prior to such a strong absorption. In addition, it has

been pointed out to us that Ichikawa’s experimental tech-

nique in this region, which involved counting interference

fringes generated by water in a small gap, is prone to errors

when there is absorption.

5.4. Temperature Dependence in the Near Infrared

When this formulation was developed, the only available

data covering a signiﬁcant range of temperatures were at

visible and ultraviolet wavelengths. These data therefore de-

termined the temperature dependence of the formulation at

infrared ~IR! wavelengths.

Recently, Richerzhagen

measured the refractive index of

liquid water at a wavelength of 1.064

m from 20 to 60 °C.

These data provide a test of our implicit assumption that the

temperature dependence of the refractive index can be ex-

trapolated from visible wavelengths into the near infrared.

Figure 6 compares these data to the new formulation. The

reported uncertainty in these data is approximately 2

3 10

2 4

. While the formulation is consistent with Rich-

erzhagen’s data in the middle of the temperature range, the

highest and lowest temperature points are clearly in disagree-

ment, suggesting that the temperature dependence of the for-

mulation in the IR in this region is not quantitatively correct.

5.5. Recommendations

The new formulation is ofﬁcially endorsed by IAPWS

only for the wavelength region in which data were ﬁtted,

which extends to 1.1

m. However, we can judge its perfor-

mance at longer wavelengths by comparing it to the results

of Bertie and Lan.

As shown in Fig. 5, the extrapolation is

accurate up to the shoulder associated with the absorption at

1.93

m. It is therefore our judgment that this formulation

can be extrapolated safely for liquid water at ambient tem-

perature up to a wavelength of 1.9

m. In addition, the com-

parison to the data of Richerzhagen

in Fig. 6 suggests that

the accuracy of the formulation is diminished at higher and

lower temperatures in the near infrared.

6. Summary

The formulation of the refractive index of water and steam

as a function of temperature, density, and wavelength by

Schiebener et al.

has been revised. The same database has

been used as in the previous work. The data were trans-

formed to the new ITS-90 temperature scale, and conver-

sions from experimental pressure to density were made with

the IAPWS-1995 formulation for water’s equation of state.

The data were ﬁtted in the wavelength range from 0.2 to 1.1

The ﬁt shows substantial improvement in the range from

2 12 to 5 °C, reﬂecting the improvement of the equation of

state for supercooled water. The remaining offset below 0 °C

likely arises because the equation of state is based on data of

limited accuracy in this region.

Strong oscillations in the refractive index had been re-

ported in one study in the near infrared; this report led to a

cutoff of the range of the formulation. Further examination,

particularly by Kramers-Kronig analysis, does not support

the existence of these oscillations. Extrapolation of the

present formulation beyond 1.1

m gives results that are

consistent with the best estimates from Kramers-Kronig

analysis up to 1.9

m at ambient temperature. The database

of Schiebener et al. contains very limited information on the

temperature dependence of the refractive index in the near

infrared. Recent data at 1.064

m from 20 to 60 °C suggest

that the formulation does not quite produce the correct tem-

perature dependence in the near infrared. The estimated un-

certainty in this range given in the IAPWS release ~Table 2,

Appendix 1! may therefore be overly optimistic. A change in

the form of the ﬁtting equation would probably be required

to accommodate these new data.

There are no data on the temperature dependence of the

refractive index above 225 °C in the vapor and above the

normal boiling point in the liquid. All results of this formu-

lation should be viewed with caution in regions where data

are not available.

This formulation is available in the form of computer code

as part of a NIST Standard Reference Database.

FIG. 6. Temperature dependence of refractive index at 1.064

766766 HARVEY, GALLAGHER, AND LEVELT SENGERS

J. Phys. Chem. Ref. Data, Vol. 27, No. 4, 1998

7. Acknowledgments

The Working Group for Thermophysical Properties of

Water and Steam of the International Association for the

Properties of Water and Steam provided a framework and

part of the information needed for this revision. The authors

are grateful to Professor J. Bertie for clarifying issues regard-

ing the refractive index in the near infrared and for providing

his results plotted in Fig. 5. They also acknowledge helpful

correspondence with Professor M. Querry and Professor M.

Ichikawa, and they thank Dr. B. Richerzhagen for providing

the coordinates of his data plotted in Fig. 6.

8. References

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, and J. S. Gallagher, J.

Phys. Chem. Ref. Data 19, 677 ~1990!.

I. Thorma

hlen, J. Straub, and U. Grigull, J. Phys. Chem. Ref. Data 14, 933

~1985!.

H.-J. Achtermann, Ph.D. thesis, University of Hannover, 1978.

H.-J. Achtermann and H. Ro

gener, in Proceedings of the 10th Interna-

tional Conference on the Properties of Steam, edited by V. V. Sytchev and

A. A. Aleksandrov ~Mir, Moscow, 1986!, Vol. 2, p. 29.

L. Haar, J. S. Gallagher, and G. S. Kell, NBS/NRC Steam Tables ~Hemi-

sphere, New York, 1984!.

H. Preston-Thomas, Metrologia 27,3~1990!.

A. Pruss and W. Wagner ~unpublished!.

Release on the IAPWS Formulation 1995 for the Thermodynamic Prop-

erties of Ordinary Water Substance for General and Scientiﬁc Use, Fre-

dericia, Denmark, 1996. Copies of IAPWS releases may be obtained from

the IAPWS Executive Secretary: Dr. R. B. Dooley, Electric Power Re-

search Institute, 3412 Hillview Avenue, Palo Alto, CA 94304.

M. Ichikawa, Proc. SPIE 1157, 318 ~1989!.

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, and J. S. Gallagher, J.

Phys. Chem. Ref. Data 19, 1617 ~1990!.

R. L. Rusby, J. Chem. Thermodyn. 23, 1153 ~1991!.

L. W. Tilton, J. Res. Natl. Bur. Stand. 17, 639 ~1936!.

L. W. Tilton and J. K. Taylor, J. Res. Natl. Bur. Stand. 20, 419 ~1938!.

Ch. Saubade, J. Phys. ~France! 42, 359 ~1981!.

R. M. Waxler and C. E. Weir, J. Res. Natl. Bur. Stand. 67A, 163 ~1963!.

R. M. Waxler, C. E. Weir, and H. R. Schamp, J. Res. Natl. Bur. Stand.

68A, 489 ~1964!.

A. H. Harvey, A. P. Peskin, and S. A. Klein, NIST/ASME Steam Proper-

ties, NIST Standard Reference Database 10, Version 2.1, Standard Refer-

ence Data Program, NIST, Gaithersburg, MD, 1997.

M. Takenaka and R. Masui, Metrologia 27, 165 ~1990!.

L. Kou, D. Labrie, and P. Chylek, Appl. Opt. 32, 3531 ~1993!.

J. E. Bertie and Z. Lan, Appl. Spectrosc. 50, 1047 ~1996!.

J. E. Bertie, Dept. of Chemistry, University of Alberta, personal commu-

nication, 1997.

G. M. Hale and M. R. Querry, Appl. Opt. 12, 555 ~1973!.

B. Richerzhagen, Appl. Opt. 35, 1650 ~1996!.

Release on the Refractive Index of Ordinary Water Substance as a Func-

tion of Wavelength, Temperature and Pressure, Erlangen, Germany, Sep-

tember 1997. Copies of IAPWS releases may be obtained from the

IAPWS Executive Secretary: Dr. R. B. Dooley, Electric Power Research

Institute, 3412 Hillview Avenue, Palo Alto, CA 94304.

9. Appendix A. Text of IAPWS Release

This Appendix contains the text of the release as accepted

by the International Association for the Properties of Water

and Steam.

Section 1 contains the nomenclature, Sec. 2 the

formulation and table of coefﬁcients. Section 3 gives the

information on the equation of state used. Section 4 deﬁnes

the range of the formulation. Section 5 gives the estimates of

uncertainty. For the purpose of checking computer code, Sec.

6 presents a short table of values, with more signiﬁcant digits

than the uncertainty of the formulation warrants. Section 7

gives the references associated with the release.

Minor formatting changes have been made in the original

IAPWS release for clarity within the context of this article.

767767REVISED FORMULATION FOR THE REFRACTIVE INDEX OF WATER AND STEAM

J. Phys. Chem. Ref. Data, Vol. 27, No. 4, 1998

The International Association for the

Properties of Water and Steam

Erlangen, Germany

September 1997

Release on the Refractive Index of

Ordinary Water Substance as a Function

of Wavelength, Temperature and

Pressure

of Water and Steam

Publication in whole or in part

is allowed in all countries provided that attribution

is given to the International Association for the Properties

of Water and Steam

President:

Dr. Roberto Ferna

ndez-Prini

CNEA

Av. Libertador 8250,

Buenos Aires-1429, Argentina

Executive Secretary:

Dr. R. B. Dooley

Electric Power Research Institute,

3412 Hillview Avenue,

Palo Alto, California 94304-1395

This release replaces the corresponding release of 1991.

This release has been authorized by the International As-

sociation for the Properties of Water and Steam ~IAPWS! at

its meeting in Erlangen, Germany, September 1997, for issue

by its Secretariat. The members of IAPWS are Argentina,

Canada, the Czech Republic, Denmark, Germany, France,

Italy, Japan, Russia, the United Kingdom, and the United

States of America.

Details about the original formulation, the data sources

and their evaluation are given in the paper ‘‘Refractive Index

of Water and Steam as Function of Wavelength, Tempera-

ture and Density,’’ by P. Schiebener, J. Straub, J. M. H.

Levelt Sengers and J. S. Gallagher @1#. In the present formu-

lation, the data have been converted to the ITS-90 Tempera-

ture Scale, and the equation of state in the previous release

has been replaced by the IAPWS Formulation 1995 for the

Thermodynamic Properties of Ordinary Water Substance for

General and Scientiﬁc Use @2#. The refractive index data

have been reﬁtted to the original functional form, but in a

reduced wavelength range, see @3#.

Further information about this release and other releases

issued by IAPWS can be obtained from the Executive Sec-

retary of IAPWS @4#.

Release on the Refractive Index

of Ordinary Water Substance as a

Function of Wavelength, Temperature

and Pressure

1. Nomenclature

n refractive index with respect to vacuum

sat

saturation pressure

T absolute temperature, ITS-90

t temperature in degrees Celsius

l wavelength of light

mass density

Reference constants

Reference temperature T

5 273.15 K

Reference density

5 1000 kg m

Reference wavelength l

5 0.589

Dimensionless variables

Temperature

5 T/T

Density

Wavelength

5 l/l

2. Formulation

The refractive index is represented by the following equa-

tion @1#:

2 1

1 2

5 a

1 a

2 l

1 a

. ~A1!

The coefﬁcients a

–a

, and the constants l

are

given in Table 1.

3. Equation of State of Water and Steam

In the conversion of the input independent variable pres-

sure to density, preceding the optimization of Eq. ~A1!, the

‘‘IAPWS Formulation 1995 for the Thermodynamic Proper-

ties of Ordinary Water Substance for General and Scientiﬁc

TABLE 1. Coefﬁcients of the formulation, Eq. ~A1!

5 0.244 257 733 a

5 1.589 205 703 10

2 3

5 9.746 344 763 10

2 3

5 2.459 342 593 10

2 3

523.732 349 963 10

2 3

5 0.900 704 920

5 2.686 784 723 10

2 4

521.666 262 193 10

2 2

5 0.229 202 0

5 5.432 937

768768 HARVEY, GALLAGHER, AND LEVELT SENGERS

J. Phys. Chem. Ref. Data, Vol. 27, No. 4, 1998

Use’’ @2# has been used. In employing Eq. ~A1!, with the

constants in Table 1, for calculating the refractive index as a

function of pressure, the IAPWS Formulation 1995 should

be used.

4. Range of the Formulation

IAPWS endorses the formulation of the refractive index in

the following range @1,3#:

Temperature 2 12 °C<t<500 °C

Density 0 kg m

<1060 kg m

Wavelength 0.2

m<l<1.1

Extrapolation of the formulation to longer wavelengths has

been tested. The formulation is in good agreement with re-

cent results @5# in liquid water at wavelengths up to 1.9

5. Estimates of Uncertainty

The estimated uncertainty of the representation of the re-

fractive index, in the absence of error in the independent

variables, is given in Table 2. In the range where data exist,

the estimate represents the largest departure of the most re-

liable, validated data from the formulation. Note that above

225 °C there are no data supporting the estimate. In the ab-

sence of data, the estimate is based on the assumption @1#

that the Lorentz-Lorenz function will vary smoothly and un-

eventfully with temperature and density throughout the range

represented in this release.

6. Values for Program Veriﬁcation

Table 3 contains refractive index values calculated from

the formulation, Eq. ~A1!. If the densities are calculated from

IAPWS Formulation 1995 @2# to one part in 10

, and the

coefﬁcients in Table 2 are carried to the number of signiﬁ-

cant digits stated, the formulation should produce the values

listed in Table 3 to within one unit in the least signiﬁcant

digit.

7. References

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, and J. S. Gallagher, J.

Phys. Chem. Ref. Data 19, 677 ~1990!.

Release on the IAPWS Formulation 1995 for the Thermodynamic Prop-

erties of Ordinary Water Substance for General and Scientiﬁc Use, Fre-

dericia, Denmark, September 1996.

P. Schiebener, J. Straub, J. M. H. Levelt Sengers, and J. S. Gallagher, J.

Phys. Chem. Ref. Data 19, 1617 ~1990!.

IAPWS releases prepared up to 1994 have been published in Proceedings

of the 12th ICPWS, Orlando, FL, 1994, H. J. White, Jr., J. V. Sengers, D.

B. Neumann, and J. C. Bellows ~Eds.!, Begell House, New York ~1995!.

Up-to-date versions can be obtained from the Executive Secretary of

IAPWS, Dr. R. B. Dooley, Electric Power Research Institute, 3412 Hill-

view Avenue, Palo Alto, CA 94304-1395.

J. E. Bertie and Z. Lan, Appl. Spectrosc. 50, 1047 ~1996!.

TABLE 2. Estimated uncertainty of the refractive-index formulation

Wavelength

Temperature

range

~°C!

Pressure range

~MPa! Phase

Absolute

uncertainty

of refractive

index

0.40 to 0.70 212 to 5 ambient liquid , 6310

2 5

0.40 to 0.70 5 to 60 ambient liquid 1.5310

2 5

0.40 to 0.60 60 to 100 ambient liquid , 3310

2 4

0.47 to 0.67 0 to 60 up to 150 liquid 2310

2 4

0.63 100 to 225 0 to 2 vapor 5310

2 6

0.70 to 1.1 ambient ambient liquid 1310

2 3

0.21 to 0.40 0 to 100 ambient liquid 5310

2 4

In the following ranges there are no supporting data

0.40 to 0.70 0 to 374 0 to 0.1 P

sat

vapor 5310

2 6

0.40 to 0.70 225 to 374 0.1 P

sat

to P

sat

vapor 1310

2 4

0.40 to 0.70 60 to 374 P

sat

to 200 liquid 1310

2 3

0.40 to 0.70 . 374 , P(

/3) low density 1310

2 5

0.40 to 0.70 . 374 . P(

) high density 2310

2 3

TABLE 3. Refractive index values from the formulation

Wavelength

Temperature

~°C!

Pressure/MPa

0.1 1 10 100

0.226 50 0 1.394 527 1.394 711 1.396 526 1.412 733

100 1.000 216 8 1.375 622 1.377 286 1.391 983

200 1.000 168 3 1.001 775 4 1.338 299 1.359 330

500 1.000 100 8 1.001 015 5 1.010 990 6 1.198 312

0.589 00 0 1.334 344 1.334 494 1.335 969 1.349 101

100 1.000 187 6 1.318 725 1.320 084 1.332 057

200 1.000 145 6 1.001 535 9 1.287 891 1.305 191

500 1.000 087 1 1.000 877 3 1.009 493 9 1.170 231

1.013 98 0 1.326 135 1.326 279 1.327 710 1.340 435

100 1.000 183 7 1.311 257 1.312 577 1.324 202

200 1.000 142 7 1.001 505 2 1.281 529 1.298 369

500 1.000 085 6 1.000 861 9 1.009 326 7 1.167 119

769769REVISED FORMULATION FOR THE REFRACTIVE INDEX OF WATER AND STEAM

J. Phys. Chem. Ref. Data, Vol. 27, No. 4, 1998

10. Appendix 2. Tables of Refractive Index Values

The following ﬁve tables ~Tables 4–8! contain values of the refractive index computed from the revised formulation given

in Appendix 1.

The number of digits printed in these tables should not be considered indicative of the formulation’s accuracy; estimates of

the uncertainty are given in Table 2 of Appendix 1. Table 2 also shows the regions in which no data are available ~and

therefore no uncertainty estimates are possible!; in these regions the numbers in Tables 4–8 are extrapolations. Finally, we

note that, in Tables 4–7, some of the low-temperature state points listed are for the metastable liquid; the thermodynamic

equilibrium state for these points would be a solid. These points are indicated by italicizing their refractive index values.

TABLE 4. Refractive index for water for wavelength 0.488

T/°C

p/MPa

0.1 0.2 0.5 1 2 5 10 20 50 100

2 10 1.338 06

1.338 08 1.338 14 1.338 23 1.338 41 1.338 96 1.339 87 1.341 64 1.346 68 1.354 20

0 1.338 40 1.338 42 1.338 47 1.338 55 1.338 72 1.339 22 1.340 05 1.341 68 1.346 33 1.353 38

10 1.338 12 1.338 14 1.338 18 1.338 26 1.338 42 1.338 89 1.339 67 1.341 20 1.345 59 1.352 31

20 1.337 39 1.337 41 1.337 45 1.337 53 1.337 68 1.338 13 1.338 88 1.340 35 1.344 56 1.351 04

30 1.336 32 1.336 33 1.336 37 1.336 45 1.336 59 1.337 03 1.337 76 1.339 19 1.343 29 1.349 61

40 1.334 95 1.334 96 1.335 01 1.335 08 1.335 22 1.335 66 1.336 37 1.337 78 1.341 81 1.348 03

50 1.333 34 1.333 35 1.333 39 1.333 47 1.333 61 1.334 04 1.334 75 1.336 14 1.340 15 1.346 31

60 1.331 51 1.331 52 1.331 56 1.331 64 1.331 78 1.332 21 1.332 92 1.334 32 1.338 33 1.344 48

70 1.329 48 1.329 50 1.329 54 1.329 61 1.329 76 1.330 19 1.330 91 1.332 32 1.336 35 1.342 53

80 1.327 28 1.327 29 1.327 34 1.327 41 1.327 56 1.328 00 1.328 73 1.330 16 1.334 24 1.340 47

90 1.324 91 1.324 92 1.324 97 1.325 05 1.325 20 1.325 65 1.326 39 1.327 85 1.332 00 1.338 31

100 1.000 190 1.322 40 1.322 44 1.322 52 1.322 68 1.323 14 1.323 90 1.325 39 1.329 63 1.336 05

120 1.000 179 1.316 89 1.316 94 1.317 02 1.317 19 1.317 68 1.318 49 1.320 08 1.324 55 1.331 26

140 1.000 170 1.000 343 1.310 85 1.310 94 1.311 12 1.311 66 1.312 53 1.314 24 1.319 03 1.326 12

160 1.000 161 1.000 326 1.000 835 1.304 27 1.304 47 1.305 06 1.306 02 1.307 89 1.313 08 1.320 65

180 1.000 154 1.000 310 1.000 791 1.001 647 1.297 20 1.297 86 1.298 94 1.301 01 1.306 70 1.314 86

200 1.000 147 1.000 296 1.000 752 1.001 552 1.289 24 1.290 00 1.291 23 1.293 57 1.299 89 1.308 77

220 1.000 141 1.000 283 1.000 717 1.001 472 1.003 127 1.281 37 1.282 80 1.285 49 1.292 62 1.302 36

240 1.000 135 1.000 271 1.000 686 1.001 402 1.002 941 1.271 81 1.273 51 1.276 68 1.284 84 1.295 63

260 1.000 130 1.000 261 1.000 658 1.001 339 1.002 786 1.261 04 1.263 15 1.266 99 1.276 51 1.288 57

280 1.000 125 1.000 251 1.000 632 1.001 283 1.002 651 1.007 541 1.251 32 1.256 17 1.267 54 1.281 17

300 1.000 120 1.000 241 1.000 608 1.001 232 1.002 533 1.007 020 1.237 30 1.243 83 1.257 82 1.273 41

320 1.000 116 1.000 233 1.000 586 1.001 185 1.002 427 1.006 605 1.016 546 1.229 19 1.247 22 1.265 26

340 1.000 112 1.000 225 1.000 565 1.001 142 1.002 331 1.006 259 1.014 813 1.210 47 1.235 50 1.256 70

360 1.000 108 1.000 217 1.000 546 1.001 102 1.002 244 1.005 961 1.013 625 1.180 22 1.222 37 1.247 70

380 1.000 105 1.000 210 1.000 528 1.001 065 1.002 163 1.005 700 1.012 718 1.038 70 1.207 35 1.238 23

400 1.000 102 1.000 204 1.000 512 1.001 030 1.002 089 1.005 468 1.011 986 1.032 03 1.189 74 1.228 28

420 1.000 099 1.000 198 1.000 496 1.000 998 1.002 020 1.005 258 1.011 371 1.028 39 1.168 57 1.217 83

440 1.000 096 1.000 192 1.000 481 1.000 967 1.001 956 1.005 067 1.010 842 1.025 91 1.143 70 1.206 90

460 1.000 093 1.000 186 1.000 467 1.000 939 1.001 896 1.004 892 1.010 377 1.024 05 1.117 94 1.195 54

480 1.000 090 1.000 181 1.000 454 1.000 912 1.001 840 1.004 731 1.009 963 1.022 57 1.097 06 1.183 85

500 1.000 088 1.000 176 1.000 441 1.000 886 1.001 787 1.004 581 1.009 591 1.021 35 1.082 45 1.172 04

Values in italics indicate points where the thermodynamic equilibrium state would be a solid; the computed values are for the metastable liquid.

770770 HARVEY, GALLAGHER, AND LEVELT SENGERS

J. Phys. Chem. Ref. Data, Vol. 27, No. 4, 1998

TABLE 5. Refractive index for water for wavelength 0.5145

T/°C

p/MPa

0.1 0.2 0.5 1 2 5 10 20 50 100

2 10 1.336 79

1.336 81 1.336 86 1.336 95 1.337 14 1.337 68 1.338 59 1.340 35 1.345 36 1.352 85

0 1.337 12 1.337 14 1.337 19 1.337 27 1.337 44 1.337 94 1.338 77 1.340 38 1.345 01 1.352 04

10 1.336 85 1.336 86 1.336 91 1.336 99 1.337 15 1.337 61 1.338 39 1.339 91 1.344 28 1.350 97

20 1.336 12 1.336 14 1.336 18 1.336 26 1.336 41 1.336 86 1.337 60 1.339 06 1.343 26 1.349 71

30 1.335 05 1.335 07 1.335 11 1.335 18 1.335 33 1.335 77 1.336 49 1.337 91 1.342 00 1.348 28

40 1.333 69 1.333 71 1.333 75 1.333 82 1.333 97 1.334 40 1.335 11 1.336 50 1.340 52 1.346 71

50 1.332 09 1.332 10 1.332 14 1.332 22 1.332 36 1.332 79 1.333 49 1.334 88 1.338 87 1.345 00

60 1.330 27 1.330 28 1.330 32 1.330 39 1.330 54 1.330 97 1.331 68 1.333 07 1.337 06 1.343 18

70 1.328 25 1.328 27 1.328 31 1.328 38 1.328 53 1.328 96 1.329 67 1.331 08 1.335 09 1.341 24

80 1.326 06 1.326 07 1.326 12 1.326 19 1.326 34 1.326 78 1.327 50 1.328 92 1.332 99 1.339 19

90 1.323 70 1.323 71 1.323 76 1.323 84 1.323 99 1.324 43 1.325 17 1.326 62 1.330 76 1.337 04

100 1.000 189 1.321 20 1.321 25 1.321 32 1.321 48 1.321 94 1.322 70 1.324 18 1.328 40 1.334 79

120 1.000 179 1.315 72 1.315 77 1.315 85 1.316 02 1.316 51 1.317 31 1.318 89 1.323 34 1.330 02

140 1.000 169 1.000 342 1.309 71 1.309 80 1.309 98 1.310 51 1.311 38 1.313 08 1.317 85 1.324 90

160 1.000 161 1.000 324 1.000 833 1.303 16 1.303 36 1.303 94 1.304 90 1.306 76 1.311 93 1.319 46

180 1.000 153 1.000 309 1.000 788 1.001 641 1.296 12 1.296 78 1.297 85 1.299 92 1.305 58 1.313 70

200 1.000 147 1.000 295 1.000 750 1.001 547 1.288 20 1.288 95 1.290 17 1.292 50 1.298 80 1.307 63

220 1.000 140 1.000 282 1.000 715 1.001 467 1.003 117 1.280 36 1.281 78 1.284 46 1.291 56 1.301 26

240 1.000 135 1.000 270 1.000 684 1.001 397 1.002 931 1.270 84 1.272 53 1.275 69 1.283 82 1.294 56

260 1.000 129 1.000 260 1.000 656 1.001 335 1.002 776 1.260 12 1.262 21 1.266 04 1.275 52 1.287 53

280 1.000 125 1.000 250 1.000 630 1.001 279 1.002 643 1.007 516 1.250 44 1.255 27 1.266 59 1.280 16

300 1.000 120 1.000 241 1.000 606 1.001 228 1.002 525 1.006 997 1.236 47 1.242 97 1.256 91 1.272 43

320 1.000 116 1.000 232 1.000 584 1.001 181 1.002 419 1.006 584 1.016 493 1.228 39 1.246 35 1.264 32

340 1.000 112 1.000 224 1.000 563 1.001 138 1.002 324 1.006 239 1.014 765 1.209 75 1.234 68 1.255 79

360 1.000 108 1.000 217 1.000 544 1.001 098 1.002 236 1.005 942 1.013 580 1.179 61 1.221 60 1.246 83

380 1.000 105 1.000 210 1.000 527 1.001 061 1.002 156 1.005 682 1.012 677 1.038 57 1.206 64 1.237 40

400 1.000 101 1.000 203 1.000 510 1.001 027 1.002 082 1.005 450 1.011 947 1.031 92 1.189 09 1.227 49

420 1.000 098 1.000 197 1.000 494 1.000 994 1.002 014 1.005 241 1.011 334 1.028 30 1.168 00 1.217 08

440 1.000 095 1.000 191 1.000 479 1.000 964 1.001 950 1.005 051 1.010 807 1.025 83 1.143 22 1.206 19

460 1.000 093 1.000 186 1.000 466 1.000 936 1.001 890 1.004 876 1.010 344 1.023 98 1.117 55 1.194 87

480 1.000 090 1.000 180 1.000 452 1.000 909 1.001 834 1.004 716 1.009 931 1.022 50 1.096 74 1.183 23

500 1.000 088 1.000 176 1.000 440 1.000 883 1.001 781 1.004 567 1.009 560 1.021 28 1.082 18 1.171 46

Values in italics indicate points where the thermodynamic equilibrium state would be a solid; the computed values are for the metastable liquid.

771771REVISED FORMULATION FOR THE REFRACTIVE INDEX OF WATER AND STEAM

J. Phys. Chem. Ref. Data, Vol. 27, No. 4, 1998

TABLE 6. Refractive index for water for wavelength 0.589 26

T/°C

p/MPa

0.1 0.2 0.5 1 2 5 10 20 50 100

2 10 1.334 00

1.334 02 1.334 07 1.334 17 1.334 35 1.334 89 1.335 78 1.337 53 1.342 48 1.349 90

0 1.334 34 1.334 35 1.334 40 1.334 49 1.334 65 1.335 15 1.335 96 1.337 56 1.342 14 1.349 09

10 1.334 06 1.334 08 1.334 13 1.334 20 1.334 36 1.334 82 1.335 59 1.337 10 1.341 42 1.348 04

20 1.333 35 1.333 37 1.333 41 1.333 48 1.333 63 1.334 08 1.334 81 1.336 26 1.340 41 1.346 79

30 1.332 29 1.332 31 1.332 35 1.332 42 1.332 57 1.333 00 1.333 71 1.335 12 1.339 16 1.345 38

40 1.330 95 1.330 96 1.331 00 1.331 08 1.331 22 1.331 64 1.332 35 1.333 73 1.337 71 1.343 83

50 1.329 36 1.329 37 1.329 42 1.329 49 1.329 63 1.330 05 1.330 75 1.332 13 1.336 08 1.342 15

60 1.327 56 1.327 57 1.327 62 1.327 69 1.327 83 1.328 26 1.328 96 1.330 33 1.334 28 1.340 34

70 1.325 57 1.325 58 1.325 63 1.325 70 1.325 84 1.326 27 1.326 98 1.328 37 1.332 34 1.338 42

80 1.323 40 1.323 42 1.323 46 1.323 53 1.323 68 1.324 11 1.324 83 1.326 24 1.330 26 1.336 40

90 1.321 07 1.321 08 1.321 13 1.321 20 1.321 35 1.321 80 1.322 53 1.323 96 1.328 05 1.334 27

100 1.000 188 1.318 59 1.318 64 1.318 72 1.318 87 1.319 33 1.320 08 1.321 55 1.325 72 1.332 05

120 1.000 177 1.313 17 1.313 22 1.313 30 1.313 47 1.313 95 1.314 75 1.316 31 1.320 72 1.327 33

140 1.000 168 1.000 339 1.307 22 1.307 31 1.307 49 1.308 02 1.308 88 1.310 57 1.315 28 1.322 27

160 1.000 160 1.000 322 1.000 827 1.300 74 1.300 94 1.301 52 1.302 47 1.304 31 1.309 42 1.316 89

180 1.000 152 1.000 307 1.000 783 1.001 629 1.293 77 1.294 42 1.295 49 1.297 53 1.303 14 1.311 19

200 1.000 146 1.000 293 1.000 744 1.001 536 1.285 93 1.286 68 1.287 88 1.290 20 1.296 43 1.305 18

220 1.000 139 1.000 280 1.000 710 1.001 457 1.003 095 1.278 17 1.279 57 1.282 23 1.289 26 1.298 87

240 1.000 134 1.000 268 1.000 679 1.001 387 1.002 911 1.268 74 1.270 42 1.273 55 1.281 60 1.292 24

260 1.000 128 1.000 258 1.000 651 1.001 325 1.002 757 1.258 12 1.260 19 1.263 99 1.273 38 1.285 28

280 1.000 124 1.000 248 1.000 625 1.001 270 1.002 624 1.007 463 1.248 53 1.253 31 1.264 53 1.277 99

300 1.000 119 1.000 239 1.000 602 1.001 219 1.002 507 1.006 948 1.234 68 1.241 13 1.254 95 1.270 33

320 1.000 115 1.000 230 1.000 580 1.001 173 1.002 402 1.006 537 1.016 376 1.226 68 1.244 48 1.262 29

340 1.000 111 1.000 222 1.000 559 1.001 130 1.002 307 1.006 195 1.014 661 1.208 19 1.232 91 1.253 84

360 1.000 107 1.000 215 1.000 541 1.001 090 1.002 221 1.005 900 1.013 485 1.178 30 1.219 95 1.244 96

380 1.000 104 1.000 208 1.000 523 1.001 054 1.002 141 1.005 642 1.012 588 1.038 30 1.205 11 1.235 62

400 1.000 101 1.000 202 1.000 506 1.001 019 1.002 068 1.005 412 1.011 863 1.031 70 1.187 71 1.225 79

420 1.000 098 1.000 196 1.000 491 1.000 987 1.002 000 1.005 204 1.011 255 1.028 10 1.166 78 1.215 48

440 1.000 095 1.000 190 1.000 476 1.000 957 1.001 936 1.005 016 1.010 731 1.025 65 1.142 19 1.204 68

460 1.000 092 1.000 184 1.000 462 1.000 929 1.001 877 1.004 843 1.010 272 1.023 81 1.116 72 1.193 45

480 1.000 090 1.000 179 1.000 449 1.000 902 1.001 821 1.004 683 1.009 862 1.022 34 1.096 06 1.181 90

500 1.000 087 1.000 174 1.000 437 1.000 877 1.001 769 1.004 535 1.009 494 1.021 13 1.081 60 1.170 23

Values in italics indicate points where the thermodynamic equilibrium state would be a solid; the computed values are for the metastable liquid.

772772 HARVEY, GALLAGHER, AND LEVELT SENGERS

J. Phys. Chem. Ref. Data, Vol. 27, No. 4, 1998

TABLE 7. Refractive index for water for wavelength 0.6328

T/°C

p/MPa

0.1 0.2 0.5 1 2 5 10 20 50 100

2 10 1.332 75

1.332 77 1.332 82 1.332 91 1.333 09 1.333 63 1.334 52 1.336 26 1.341 19 1.348 57

0 1.333 08 1.333 10 1.333 15 1.333 23 1.333 40 1.333 89 1.334 70 1.336 30 1.340 86 1.347 77

10 1.332 82 1.332 83 1.332 88 1.332 95 1.333 11 1.333 57 1.334 33 1.335 84 1.340 14 1.346 72

20 1.332 11 1.332 12 1.332 17 1.332 24 1.332 39 1.332 83 1.333 56 1.335 00 1.339 14 1.345 49

30 1.331 05 1.331 07 1.331 11 1.331 18 1.331 33 1.331 76 1.332 47 1.333 87 1.337 90 1.344 08

40 1.329 72 1.329 73 1.329 78 1.329 85 1.329 99 1.330 41 1.331 11 1.332 49 1.336 45 1.342 54

50 1.328 14 1.328 16 1.328 20 1.328 27 1.328 41 1.328 83 1.329 53 1.330 90 1.334 83 1.340 87

60 1.326 35 1.326 37 1.326 41 1.326 48 1.326 62 1.327 04 1.327 74 1.329 11 1.333 04 1.339 07

70 1.324 37 1.324 38 1.324 43 1.324 50 1.324 64 1.325 07 1.325 77 1.327 15 1.331 11 1.337 16

80 1.322 21 1.322 23 1.322 27 1.322 34 1.322 49 1.322 92 1.323 64 1.325 04 1.329 04 1.335 15

90 1.319 89 1.319 91 1.319 95 1.320 03 1.320 17 1.320 62 1.321 35 1.322 77 1.326 85 1.333 04

100 1.000 187 1.317 43 1.317 48 1.317 55 1.317 71 1.318 16 1.318 91 1.320 37 1.324 53 1.330 83

120 1.000 177 1.312 04 1.312 09 1.312 17 1.312 33 1.312 81 1.313 61 1.315 16 1.319 55 1.326 13

140 1.000 167 1.000 338 1.306 12 1.306 21 1.306 38 1.306 91 1.307 77 1.309 45 1.314 14 1.321 10

160 1.000 159 1.000 321 1.000 824 1.299 67 1.299 86 1.300 44 1.301 39 1.303 22 1.308 31 1.315 74

180 1.000 152 1.000 306 1.000 780 1.001 624 1.292 73 1.293 38 1.294 44 1.296 48 1.302 06 1.310 07

200 1.000 145 1.000 292 1.000 742 1.001 531 1.284 93 1.285 67 1.286 87 1.289 17 1.295 38 1.304 10

220 1.000 139 1.000 279 1.000 708 1.001 452 1.003 085 1.277 20 1.278 60 1.281 25 1.288 25 1.297 81

240 1.000 133 1.000 268 1.000 677 1.001 383 1.002 901 1.267 81 1.269 48 1.272 60 1.280 62 1.291 22

260 1.000 128 1.000 257 1.000 649 1.001 321 1.002 748 1.257 23 1.259 30 1.263 08 1.272 44 1.284 29

280 1.000 123 1.000 247 1.000 623 1.001 266 1.002 616 1.007 439 1.247 68 1.252 45 1.263 63 1.277 03

300 1.000 119 1.000 238 1.000 600 1.001 215 1.002 499 1.006 926 1.233 90 1.240 32 1.254 08 1.269 40

320 1.000 115 1.000 230 1.000 578 1.001 169 1.002 395 1.006 517 1.016 325 1.225 92 1.243 66 1.261 40

340 1.000 111 1.000 222 1.000 558 1.001 126 1.002 300 1.006 175 1.014 615 1.207 50 1.232 14 1.252 99

360 1.000 107 1.000 214 1.000 539 1.001 087 1.002 214 1.005 882 1.013 443 1.177 72 1.219 22 1.244 14

380 1.000 104 1.000 208 1.000 521 1.001 050 1.002 135 1.005 625 1.012 549 1.038 18 1.204 45 1.234 84

400 1.000 100 1.000 201 1.000 505 1.001 016 1.002 061 1.005 395 1.011 827 1.031 60 1.187 10 1.225 05

420 1.000 097 1.000 195 1.000 489 1.000 984 1.001 994 1.005 188 1.011 221 1.028 01 1.166 25 1.214 77

440 1.000 095 1.000 189 1.000 475 1.000 954 1.001 930 1.005 000 1.010 698 1.025 57 1.141 74 1.204 02

460 1.000 092 1.000 184 1.000 461 1.000 926 1.001 871 1.004 828 1.010 240 1.023 74 1.116 36 1.192 83

480 1.000 089 1.000 179 1.000 448 1.000 900 1.001 816 1.004 669 1.009 832 1.022 28 1.095 77 1.181 33

500 1.000 087 1.000 174 1.000 436 1.000 875 1.001 763 1.004 521 1.009 465 1.021 07 1.081 35 1.169 69

Values in italics indicate points where the thermodynamic equilibrium state would be a solid; the computed values are for the metastable liquid.

773773REVISED FORMULATION FOR THE REFRACTIVE INDEX OF WATER AND STEAM

J. Phys. Chem. Ref. Data, Vol. 27, No. 4, 1998

TABLE 8. Refractive index for water and steam at vapor-liquid saturation

~°C!

~MPa!

l5 0.488

m l5 0.5145

m l5 0.589 26

m l5 0.6328

liq

vap

liq

vap

liq

vap

liq

vap

0.01 0.0006 1.338 38 1.000 002 1.337 11 1.000 002 1.334 32 1.000 002 1.333 07 1.000 002

5 0.0009 1.338 31 1.000 002 1.337 03 1.000 002 1.334 25 1.000 002 1.333 00 1.000 002

10 0.0012 1.338 10 1.000 003 1.336 83 1.000 003 1.334 05 1.000 003 1.332 80 1.000 003

15 0.0017 1.337 79 1.000 004 1.336 52 1.000 004 1.333 74 1.000 004 1.332 49 1.000 004

20 0.0023 1.337 38 1.000 006 1.336 11 1.000 006 1.333 34 1.000 006 1.332 09 1.000 006

25 0.0032 1.336 88 1.000 007 1.335 61 1.000 007 1.332 85 1.000 007 1.331 60 1.000 007

30 0.0042 1.336 30 1.000 010 1.335 04 1.000 010 1.332 28 1.000 010 1.331 04 1.000 010

35 0.0056 1.335 65 1.000 013 1.334 39 1.000 013 1.331 64 1.000 013 1.330 41 1.000 013

40 0.0074 1.334 94 1.000 017 1.333 68 1.000 016 1.330 93 1.000 016 1.329 71 1.000 016

45 0.0096 1.334 16 1.000 021 1.332 90 1.000 021 1.330 17 1.000 021 1.328 95 1.000 021

50 0.0124 1.333 32 1.000 027 1.332 07 1.000 027 1.329 35 1.000 027 1.328 13 1.000 026

55 0.0158 1.332 43 1.000 034 1.331 19 1.000 034 1.328 47 1.000 033 1.327 26 1.000 033

60 0.0199 1.331 49 1.000 042 1.330 25 1.000 042 1.327 55 1.000 042 1.326 34 1.000 041

65 0.0250 1.330 51 1.000 052 1.329 27 1.000 052 1.326 58 1.000 051 1.325 37 1.000 051

70 0.0312 1.329 47 1.000 064 1.328 24 1.000 064 1.325 56 1.000 063 1.324 36 1.000 063

75 0.0386 1.328 39 1.000 078 1.327 17 1.000 078 1.324 50 1.000 077 1.323 30 1.000 077

80 0.0474 1.327 27 1.000 095 1.326 05 1.000 094 1.323 39 1.000 094 1.322 21 1.000 093

85 0.0579 1.326 11 1.000 114 1.324 89 1.000 114 1.322 25 1.000 113 1.321 07 1.000 112

90 0.0702 1.324 90 1.000 136 1.323 70 1.000 136 1.321 06 1.000 135 1.319 89 1.000 135

95 0.0846 1.323 66 1.000 162 1.322 46 1.000 162 1.319 84 1.000 161 1.318 67 1.000 160

100 0.1014 1.322 38 1.000 192 1.321 18 1.000 192 1.318 58 1.000 190 1.317 42 1.000 190

110 0.1434 1.319 71 1.000 266 1.318 52 1.000 265 1.315 95 1.000 263 1.314 80 1.000 262

120 0.1987 1.316 89 1.000 360 1.315 72 1.000 359 1.313 17 1.000 357 1.312 04 1.000 355

130 0.2703 1.313 93 1.000 481 1.312 77 1.000 479 1.310 26 1.000 476 1.309 14 1.000 474

140 0.3615 1.310 83 1.000 631 1.309 68 1.000 629 1.307 20 1.000 624 1.306 09 1.000 622

150 0.4762 1.307 58 1.000 817 1.306 45 1.000 814 1.304 00 1.000 809 1.302 91 1.000 806

160 0.6182 1.304 20 1.001 045 1.303 08 1.001 041 1.300 67 1.001 034 1.299 59 1.001 030

170 0.7922 1.300 66 1.001 320 1.299 56 1.001 316 1.297 18 1.001 307 1.296 13 1.001 302

180 1.0028 1.296 98 1.001 652 1.295 90 1.001 646 1.293 55 1.001 634 1.292 51 1.001 629

190 1.2552 1.293 14 1.002 046 1.292 07 1.002 040 1.289 77 1.002 025 1.288 75 1.002 019

200 1.5549 1.289 13 1.002 514 1.288 08 1.002 506 1.285 82 1.002 488 1.284 81 1.002 480

210 1.9077 1.284 95 1.003 065 1.283 92 1.003 055 1.281 70 1.003 034 1.280 71 1.003 024

220 2.3196 1.280 58 1.003 712 1.279 57 1.003 700 1.277 39 1.003 674 1.276 42 1.003 662

230 2.7971 1.276 02 1.004 468 1.275 03 1.004 453 1.272 89 1.004 421 1.271 94 1.004 407

240 3.3469 1.271 23 1.005 349 1.270 26 1.005 331 1.268 16 1.005 293 1.267 24 1.005 277

250 3.9762 1.266 20 1.006 374 1.265 25 1.006 354 1.263 21 1.006 308 1.262 30 1.006 289

260 4.6923 1.260 91 1.007 568 1.259 98 1.007 543 1.257 98 1.007 490 1.257 10 1.007 466

270 5.5030 1.255 31 1.008 958 1.254 41 1.008 929 1.252 46 1.008 866 1.251 60 1.008 838

280 6.4166 1.249 38 1.010 58 1.248 50 1.010 55 1.246 60 1.010 47 1.245 77 1.010 44

290 7.4418 1.243 04 1.012 49 1.242 19 1.012 44 1.240 35 1.012 36 1.239 54 1.012 32

300 8.5879 1.236 24 1.014 73 1.235 42 1.014 68 1.233 64 1.014 58 1.232 86 1.014 53

310 9.8651 1.228 87 1.017 41 1.228 08 1.017 35 1.226 36 1.017 23 1.225 61 1.017 17

320 11.2843 1.220 80 1.020 63 1.220 03 1.020 57 1.218 38 1.020 42 1.217 66 1.020 36

330 12.8581 1.211 80 1.024 61 1.211 07 1.024 53 1.209 50 1.024 36 1.208 81 1.024 28

340 14.6007 1.201 54 1.029 65 1.200 85 1.029 55 1.199 36 1.029 35 1.198 71 1.029 25

350 16.5294 1.189 32 1.036 36 1.188 67 1.036 24 1.187 28 1.035 98 1.186 67 1.035 87

360 18.6660 1.173 36 1.046 15 1.172 78 1.045 99 1.171 52 1.045 67 1.170 97 1.045 53

370 21.0436 1.147 72 1.064 99 1.147 23 1.064 78 1.146 16 1.064 32 1.145 70 1.064 12

774774 HARVEY, GALLAGHER, AND LEVELT SENGERS

J. Phys. Chem. Ref. Data, Vol. 27, No. 4, 1998