Thermodynamic Properties of Helium 4 from 8 2 to 1500 K at Pressures to 10 Pa Cite as: Journal of Physical and Chemical Reference Data 2, 923 (1973); https://doi.org/10.1063/1.3253133 Published Online: 29 October 2009 Robert D. Mc Carty ARTICLES YOU MAY BE INTERESTED IN The Observed Properties of Liquid Helium at the Saturated Vapor Pressure Journal of Physical and Chemical Reference Data 27, 1217 (1998); https:// doi.org/10.1063/1.556028 The calculated thermodynamic properties of superfluid helium-4 Journal of Physical and Chemical Reference Data 6, 51 (1977); https://doi.org/10.1063/1.555549 Thermodynamic Properties of Nitrogen Including Liquid and Vapor Phases from 63K to 2000K with Pressures to 10,000 Bar Journal of Physical and Chemical Reference Data 2, 757 (1973); https:// doi.org/10.1063/1.3253132 Journal of Physical and Chemical Reference Data 2, 923 (1973); https://doi.org/10.1063/1.3253133 2, 923 © 1973 The U. S. Secretary of Commerce on behalf of the United States. Thermodynamic Properties of Helium 4 from 2 to 1 500 K at Pressures to 1 0 8 Pa Robert D. McCarty Cryogenics Division, Institute for Basic Standards, National Bureau of Standards, Boulder, Colorado 80302 Tabular values of density, internal energy, enthalpy, entropy, heat capacity, and speed of sound for liquid and gaseous helium are presented for temperatures from 2 to 1500 kelvin at pressures from 1.0 X 10 4 to 1.0 X 1O1! pascals. Diagrams of temperature vs entropy are also given. The properties pre­ sented are calculated from an equation of state which was fitted to experimental P-V-T and other thermodynamic data from the world's literature. The equation of state was fitted to these data in three separate regions of pressure and temperature. The regional equations are forced to join smoothly at the preconceived boundaries. Extensive comparisons between the equation of state and experimental data have been made, and deviation plots are presented. A particularly careful determination of the second virial coefficient over the full temperature range 2-1500 kelvin is presented. The louIe-Thomson inversion curve has been calculated and comparisons made with other sources. Equations for the den­ sity of the saturated liquid and vapor are included as well as an equation which represents the 1958 helium vapor pressure temperature scale. Key words: Critical point; critically evaluated data; enthalpy; entropy; equation of state; helium; internal energy; Joule-Thomson coefficient; lambda line; melting line; P-V-T; specific heat; vapor pressure; speed of sound; viral coefficient. Contents Page Page 1. Intl·oductiull.... ...... .................. ......... ...... 924 9_2_ Specific Heat in the f:ritir.al Regions... 948 2. Survey of the Literature........................... 925 9.3. Speed of Sound in the Critical 3. Vapor Pressure....................................... 925 Region ............ ; . .. .. .. 950 4. Density of the Saturated Liquid and Gaseous 10. Thermodynamic Properties Near the Lambda Phases................................................... 927 Line ..................................................... 950 5. The Second Virial Coefficient.................... 928 II. The Melting Curve .................................. 951 6. The Equation of State.............................. 933 12 . .Toule-Thomson Inversion Curve ................. 952 6.1. Estimation of the Coefficients for the 13. References ..... -....................................... 953 Equation of State........................... 934 Appendix A. Temperature-Entropy Diagrams... 955 6.2. Estimation of the Coefficients for Appendix B. Symbols ............................... _.. 958 Region I of the Multi-Function Appendix C. Conversion Factors and Fixed Equation of State........................... 935 Points..................................... 958 6.3. Estimation of the Coefficients for Appendix D. Thermodynamic Properties of Co­ Region II of the Multi-Function Equa- existing Liquid and Gaseous tion of State... ... ... ......................... 935 Phases of Helium-4................... 959 6.4. Estimation of the Coefficients for Appendix E. Isobaric Tables of the Thermody­ Region III of the Multi-Function namic Properties of Helium-4...... 963 Equation of State........................ ... 935 List of Figures 7. Derived Thermodynamic Properties Rela- F"i!(ure Page 1. Deviations Between the 1958 Helium tionships ... ... ............................. ............ 936 Temperature Scale and Equations (1) 8. Evaluation of the Equation of State and and (2) .........•..•..••••••.•.....••.••.•..•.••...•.. 926 Tables...... ............................................ 936 2. Differences Between Experimental Meas­ 8~. Comparison of Experimental and Cal- urements of Temperature and the 1958 culatedP-V-TData........................ 936 Helium Scale ..................................... 927 8.2. Comparisons of Experimental and 3. Deviations Between Equations (4), (5) and Calculated Cv Data......... ................ 941 (17) and the Experimental Data by el Hadi 8.3. Comparison of Experimental and [22,23]. ............................................. 928 Calculated Speed of Sound............... 942 4. The Second Virial Coefficient frol)1 2 to 10 8.4. Comparison with Other Correlations... 943 K. The Solid Line is from Equation (8) ..... 929 8.5. Discussion of Errors........................ 943 5. The Second Virial Coefficient from 10 to 9. Thermodynamic Properties in the Critical 48 K. The Solid Line is from Equation (8) ... 929 Region.................................................. 945 6. The Second Virial Coefficient from 48 to 9.1. P-V-Tin the Critical Region...... ...... 946 200 K. The Solid Line is from Equation (8) ... 930 7. The Second Virial Coefficient from 200 to Cupyri!(ht © 1973 by the 1I.S. Secretary nf Commerce on behalf nf Ihe linited Slates. This copyright will be assi!(ned tn the American Institute nf Physics and the American Chemical 1500 K. The Solid Line is from Equation Suciety. to whom all requests rel!ardin~ reprndurtion should be addressed. (8) ................................................... 930 923 J. Phys. Chem. Ref. Data, Vol. 2, No.4, 1973 924 ROBERT D. M~CARTY figure Page Figure Page 8. Second Virial Coefficient from 2 to 1500 K... 932 3S. Joule-Thomson Inversion Curve Calculated 9. Schematic p-T Diagram for Helium Show­ from Equation of State.......................... 953 ing Regions Represented by Different 36. Temperature-Entropy Diagram for Helium Equations ..................... " . .. .. 933 for Temperatures from 2 to 12 K............. 955 10. Comparison of Densities from Wiebe, et a1. 37. Temperature-Entropy Diagram for Helium [77] with Equation of State..................... 936 Between 10 and no K.......................... 956 11. Comparison of Densities from Canfield, et 38. Temperature-Entropy Diagram for Helium a1. [9] with Equation of State.................. 937 Between 100 and 1500 K....................... 957" 12. Comparison of Compressibility Factors from Briggs, et al. [8] with Equation of Table List of Tables State ................................................. 937 1. Constraints on Equation (1).................... 926 13. Comparison of Densities from White, et a!. 2. Constraints on Equation (2).................... 926 [76] with Equation of State..................... 937 3. Coefficients for Equation (1)................... 926 14. Comparison of Densities from Sullivan [71] 4. Coefficients for Equation (2)................... 926 . with Equation of State... ....................... 938 5. Coefficients for Equations (4) and (S) ......... 928 15. COIVparison of Densities from Hall and 6. Coefficients for Equation (8)................... 932 Canfield [30] with Equation of State......... 939 7. Second Virial Coefficients for Helium-4..... 933 16. Comparison of Densities from Lounasmaa 8. Coefficients for Equation (17) (Region I).... 934 [50] with.tht! El{uatiull uf SlaLt!...... ......... 939 9. Coefficients for Equation (17) (Region II)... 934 17. Comparison of Densities from Edeskuty 10. Coefficients for Equation (17) (Region III)... 934 and Sherman [17] with the Equation of 11. Coefficients for-Equations (31) and (32)..... 948 State ... .............................................. 940 12. Cocfficients for Equation (33).................. 948 18. Comparison of Densities from Glassford 13. C for Helium·4 Along the A Curve... ....... 949 and Smith [2S] with the Equation of State... 94() v 14. Coefficients of Equations for P>. and p"..... 950 19. Comparison of Densities from Crilly and IS. P-p-T of the Lambda Line.................... 950 Mill::; [28] with the Equation of State........ 941 16. Parameters for Equation (38).................. 952 20. Comparison of Densities from Kierstead 17. Melting Line for Helium-4...... ............... 952 [47] with the Equation of State ............... 941 18. louIe-Thomson Inversion Curve... ..... ...... 952 21. Comparison of Pressures from Keller [41] 19. Compiiril!SOIl uf Joule-Thom:son Coefficients with the Equation of State..................... 941 at 1 Atmosphere... ............................... 952 22. Comparison of C v's from Lounasmaa [50] with Values Calculated using Equation (17) ...... ............................................. 942 23. Comparison of C v's from Dugdale and 1. Introduction Frank [16] with Those Calculated from the The investigation of the properties of helium has been Equation of State................................. 942 one of the more popular endeavors in science since it 24. Comparison of Speed