STAND 4 TECH R.I.C NAT L INST. OF N!ST PUBLICATIONS A111D5 5b3HH3 United States Department of Commerce Technology Administration Nisr National Institute of Standards and Technology MST Technical Note 1334 (revised) Thermophysical Properties of Helium-4 from 0.8 to 1500 K with Pressures to 2000 MPa Vincent D. Arp Robert D. McCarty Daniel G. Friend QC 100 U5753 NO. 1334 1998 A/AS 7" Technical Note 1334 (revised) Thermophysical Properties of Helium-4 from 0.8 to 1500 K with Pressures to 2000 MPa Vincent D. Arp Robert D. McCarty Daniel G. Friend Physical and Chemical Properties Division Chemical Science and Technology Laboratory National Institute of Standards and Technology 325 Broadway Boulder, Colorado 80303-3328 September 1998 r*TES O* U.S. DEPARTMENT OF COMMERCE, William M. Daley, Secretary TECHNOLOGY ADMINISTRATION, Gary R. Bachula, Acting Under Secretary for Technology NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Director National Institute of Standards and Technology Technical Note Natl. Inst. Stand. Technol., Tech. Note 1334 (revised), 152 pages (September 1998) CODEN:NTNOEF U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 1998 For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325 CONTENTS REVISION NOTES iv 1. INTRODUCTION 1 2. TEMPERATURE SCALE, FIXED POINTS, AND UNITS 1 2.1 Conversion from the T58 to the EPT-76 Temperature Scale 2 3. STATE PROPERTIES 2 3.1 The Overlap Region for the Hel and Hell Equations 2 3.2 Density 3 3.3 Derived Properties 3 4. Transport Properties 4 4.1 Thermal Conductivity 4 4.2 Viscosity 4 4.2.1 Viscosity Between 100 K and 3.5 K 4 4.2.2 Viscosity Between 100 and 300 K 5 4.2.3 Viscosity Above 300 K 5 4.3 Thermal Diffusivity 5 4.4 Prandtl Number 6 5. SUPERFLUID PROPERTIES 6 5.1 Superfluid Density Fraction 6 5.2 Second and Fourth Sound 6 5.3 Mutual Friction, Conductivity, and Viscosity in Superfluid 6 6. DIELECTRIC AND OPTICAL PROPERTIES 7 6.1 Dielectric Constant 7 6.2 Index of Refraction 8 7. SURFACE TENSION 8 8. SOLID-FLUID BOUNDARY 9 9. CONCLUSIONS 9 10. BIBLIOGRAPHY 9 APPENDIX A. Properties of Coexisting Liquid and Vapor Along the Saturation Line 13 APPENDIX B. Properties of Fluid Helium 23 B.l Table Format 23 in REVISION NOTES This publication is a second printing of Technical Note 1334, 1989. There have been several minor revisions in this document. An error in the computer code for the viscosity led to some erroneous values in the tables at temperatures above 300 K especially at high pressures; these have been corrected. In addition, we present revised correlations for the dielectric constant, which slightly changes some tabulated values, and for the surface tension. Finally, we have included additional short discussions of correlations for the index of refraction, superfluid properties, and the solid-fluid transition. V.D. Arp and R.D. McCarty have retired from NIST and are currently affiliated with Cryodata, Inc. of Boulder, Colorado. IV Thermophysical Properties of Helium-4 from 0.8 to 1500 K with Pressures to 2000 MPa Vincent D. Arp, Robert D. McCarty, and Daniel G. Friend Physical and Chemical Properties Division Chemical Science and Technology Laboratory National Institute of Standards and Technology Boulder, Colorado 80303 Tabular summary data of the thermophysical properties of fluid helium are given for temperatures from 0.8 to 1500 K, with pressures to 2000 MPa between 75 and 300 K, or to 100 MPa outside of this temperature band. Properties include density, specific heats, enthalpy, entropy, internal energy, sound velocity, expansivity, compressibility, thermal conductivity, and viscosity. The data are calculated from a computer program which is available from the National Institute of Standards and Technology. The computer program is based on carefully fitted state equations for both normal and superfluid helium. Key words: conductivity; density; helium; sound velocity; specific heat; state equation; superfluid; thermodynamic properties; viscosity 1. INTRODUCTION The thermophysical properties of helium-4 have previously been tabulated in NBS Technical Note 63 1 [McCarty, 1972], and, for Hell (the superfluid phase), in NBS Technical Note 1029 for temperatures from to (almost) the lambda line [McCarty, 1980]. These two publications were based on two different computer codes, neither of which was valid within about ±0. 1 K of the lambda line which separates Hel (the normal fluid phase) from Hell. The Hel computer code has been revised [McCarty and Arp, 1989] to remove some thermodynamic inconsistencies, particularly for the dense liquid. It is valid from about 2.5 to 1500 K with pressures to 100 MPa; between 75 and 300 K it is valid to 2000 MPa, but at reduced accuracy. A new code [Arp, 1989] includes Hell, the lambda line, and compressed liquid Hel from 0.8 to 2.5 K. These two codes have been joined smoothly to produce a single code valid from 0.8 to 1500 K, from which the data of this publication have been calculated. 2. TEMPERATURE SCALE, FIXED POINTS, AND UNITS The data tabulated in this publication are consistent with the ITS-90 temperature scale [Preston-Thomas, 1990] to within appropriate uncertainties. In the liquid helium range, primary data were adjusted to the EPT-76 provisional temperature scale [Durieux and Rusby, 1983]. Differences between the ITS-90 and EPT-76 temperature scales are negligible in this range. Fixed point pressures and temperatures on the EPT-76 scale are included in table 1. The molar mass of helium-4, M, was approximated as 4.0026 g/mol. Table 1. Fixed points on the EPT-76 temperature scale. Critical point Normal boiling point Lower lambda point = = = 5041.8 Pa P c 227 460 Pa P 101 325 Pa ~YX = = 4.2221 = 2.1768 T c 5.1953K T K T x K = 69.64 3 = 146.15 kg/m 5 p c kg/m p xiiquid 2.1 Conversion from the T58 to the EPT-76 Temperature Scale Much of the available literature on liquid helium properties is based on the older T58 temperature scale, whereas this document and its related computer program are based on the newer EPT-76 temperature scale in the liquid range. We have developed a computer subroutine to convert from the T58 to the EPT-76 temperature scale. The FORTRAN code for the subroutine is: DOUBLE PRECISION FUNCTION T7658 (T58) * T76 as a function of T58; valid from 0.8 to Tc * RMS fitting error = 66 microdegrees * constrained for error at T58 = 2. 172 and 5. 190 DIMENSION A(4), B(3), C(3) DATA A /- 0. 1 89 1 260993E-02, 0. 8508937840E-02, 0.4836428596E-02, 0. 1 0760754 1 9E-02/ DATA B / 0.7530201452E-02, - 0.268 1259464E-02, 0.9784628670E-03/ DATA C/ 0.61 1560275 1E-02, 0.1146742367E-02, -0.2767840460E-03/ IF (T58.LE. 2.1720) THEN T7658 = T58 + A(l) + T58*(A(2) + T58*(A(3) + T58*A(4))) ELSE IF (T58 .LE. 4.082) THEN X=1./(T58-1.70) T7658 = T58 + B(l) + X*X*(B(2) + X*B(3)) ELSE IF (T58 .LE. 4.619) THEN T7658 = T58 + 0.00713 ELSE IF (T58 .LE. 5.190) THEN X = 17(5.4 -T5 8) T7658 = T58 + C(l) + X*(C(2) + X*C(3)) ELSE T7658 = -l. ENDIF END 3. STATE PROPERTIES 3.1 The Overlap Region for the Hel and Hell Equations The equations used to generate the state properties are detailed in other publications [Arp, 1990; McCarty and Arp, 1990] and will not be repeated here. It is important to note, however, that the tabulated values, being derived from a state equation, are thermodynamically consistent at a given state point, with a mild exception in the overlap region, where weighted averages between the two state equations are used. The boundaries of the overlap region are defined by two lines in the density-temperature plane of the compressed liquid. When the 3 density, p, is < 140 or > 190 kg/m , the Hel equation is always used. Between these densities, the Hell equation is used for temperatures less than - - - TA - 2.53 0.0056 (p 140)- 0.035 Max (0,p 180) and the Hel equation is used for temperatures greater than TM = 2.98 - 0.0056(p - 140)-0.035 Max (0,p - 180). In these expressions, the temperature is expressed in Kelvins and the density is expressed in kilograms per cubic and the calculated state property is a linearly meter. For temperatures between TA TM , temperature-dependent weighted average of the state properties calculated from the Hel and Hell equations. Thus, in the overlap region, the various calculated thermodynamic properties are not exactly consistent with one another; e.g. the Maxwell relations are only approximate, the numerical integral of CP along an isobar is not exactly the tabulated enthalpy difference, etc. In practice, the errors are on the order of 3 percent or less in the compressed liquid for pressures up to about 0.2 MPa, but rise to 20 percent or more as the melting line is approached. The problem of obtaining thermodynamic consistency in this overlap region is compounded by the general lack of experimental data in this region, especially at higher pressures. 3.2 Density Estimated uncertainties in the tabulated densities are given in table 2. Table 2. Uncertainties in the PVT data. Temperature range Pressure range Uncertainty in density (K) (MPa) Average Maximum (%) (%) 0.8-20 0-0.2 0.1 0.5* 0.8-20 0.2-100 0.15 1.5* Critical Region Tc ±5%, p c ±20% 3.0 8.0 20-70 0-2 0.25 0.75 20-70 2-100 0.1 1.0 70-50 0-10 0.1 0.5 70-150 10-100 0.5 2.0** 75-300 100-2000 1.0 5.0 150-400 0-10 0.1 0.25 150-400 10-100 0.1 0.5 400-1500 0-10 0.1 0.5 400- 1500 10-100 0.2 2.0 * Except in critical region ** No reliable data 3.3 Derived Properties Derived properties are those which can be obtained by differentiation and/or integration of the PVT surface.