A Reference Equation of State for the Thermodynamic Properties of Nitrogen for Temperatures from 63.151 to 1000 K and Pressures to 2200 MPa Roland Span, Eric W. Lemmon, Richard T Jacobsen, Wolfgang Wagner, and Akimichi Yokozeki Citation: Journal of Physical and Chemical Reference Data 29, 1361 (2000); doi: 10.1063/1.1349047 View online: http://dx.doi.org/10.1063/1.1349047 View Table of Contents: http://scitation.aip.org/content/aip/journal/jpcrd/29/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A Reference Equation of State for the Thermodynamic Properties of Ethane for Temperatures from the Melting Line to 675 K and Pressures up to 900 MPa J. Phys. Chem. Ref. Data 35, 205 (2006); 10.1063/1.1859286 A New Functional Form and New Fitting Techniques for Equations of State with Application to Pentafluoroethane (HFC-125) J. Phys. Chem. Ref. 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Downloaded to IP: 132.163.193.104 On: Fri, 23 Jan 2015 20:42:46 A Reference Equation of State for the Thermodynamic Properties of Nitrogen for Temperatures from 63.151 to 1000 K and Pressures to 2200 MPa Roland Spana…,d… Lehrstuhl fu¨r Thermodynamik, Ruhr-Universita¨t Bochum, D-44780 Bochum, Germany Eric W. Lemmonb… Physical and Chemical Properties Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305-3328 Richard T Jacobsenc… Center for Applied Thermodynamic Studies, College of Engineering, University of Idaho, Moscow, Idaho 83844-1011 Wolfgang Wagner Lehrstuhl fu¨r Thermodynamik, Ruhr-Universita¨t Bochum, D-44780 Bochum, Germany Akimichi Yokozeki DuPont FluoroProducts Laboratory, Chestnut Run Plaza 711, Wilmington, Delaware 19880 Received December 10, 1999; revised manuscript received November 20, 2000 A new formulation for the thermodynamic properties of nitrogen has been developed. Many new data sets have become available, including high accuracy data from single and dual-sinker apparatuses which improve the accuracy of the representation of the p␳T surface of gaseous, liquid, and supercritical nitrogen, including the saturation states. New measurements of the speed of sound from spherical resonators yield accurate information on caloric properties in gaseous and supercritical nitrogen. Isochoric heat capacity and enthalpy data have also been published. Sophisticated procedures for the optimization of the mathematical structure of equations of state and special functional forms for an improved representation of data in the critical region were used. Constraints regarding the structure of the equation ensure reasonable results up to extreme conditions of tempera- ture and pressure. For calibration applications, the new reference equation is supple- mented by a simple but also accurate formulation, valid only for supercritical nitrogen between 250 and 350 K at pressures up to 30 MPa. The uncertainty in density of the new reference equation of state ranges from 0.02% at pressures less than 30 MPa up to 0.6% at very high pressures, except in the range from 270 to 350 K at pressures less than 12 MPa where the uncertainty in density is 0.01%. The equation is valid from the triple point temperature to temperatures of 1000 K and up to pressures of 2200 MPa. From 1000 to 1800 K, the equation was validated with data of limited accuracy. The extrapolation behavior beyond 1800 K is reasonable up to the limits of chemical stability of nitrogen, as indicated by comparison to experimental shock tube data. © 2001 by the U.S. Sec- retary of Commerce on behalf of the United States. All rights reserved. Key words: caloric properties; density; equation of state; fundamental equation; nitrogen; thermodynamic properties. Contents a͒Electronic mail: [email protected] b͒Electronic mail: [email protected] c͒Current Address: Idaho National Engineering and Environmental Labora- 1. Introduction................................ 1365 tory, Idaho Falls, Idaho 83415-3790. 1.1. Prior Correlations of Nitrogen Properties.... 1365 ͒ d Current address: ALSTOM Power Technology Ltd., Segelhof 1, CH-5405 1.2. The Equation of State for Nitrogen. ....... 1365 Baden-Da¨ttwil, Switzerland. © 2001 by the U.S. Secretary of Commerce on behalf of the United States. 2. Vapor–Liquid and Solid–Liquid Coexistence All rights reserved. Properties................................. 1366 Õ Õ Õ Õ Õ 0047-2689 2000 29„6… 1361 73 $35.001361 J. Phys. Chem. Ref. Data, Vol. 29, No. 6, 2000 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 132.163.193.104 On: Fri, 23 Jan 2015 20:42:46 1362 SPAN ET AL. 2.1. Critical Point........................... 1366 13. Summary of enthalpy, heat of vaporization, and 2.2. Triple Point............................ 1367 Joule–Thomson coefficient data............... 1377 2.3. Vapor Pressure......................... 1367 14. Dissociation of nitrogen at high temperatures. 1380 2.4. Saturation Densities..................... 1367 15. Summary of comparisons of the selected data in 2.5. Melting Pressure........................ 1367 six different regions of the surface of state...... 1383 2.6. Ancillary Equations. .................... 1368 16. Data types used in linear and nonlinear 3. Experimental Data for the Single-Phase Region... 1370 optimization algorithms...................... 1384 3.1. p␳T Data and Virial Coefficients. ......... 1370 17. Parameters and coefficients of the equation of 3.2. Caloric Data. ......................... 1371 state...................................... 1385 4. The Equation of State for Nitrogen............. 1374 18. Parameters of the Gaussian bell shaped terms in 4.1. Properties of the Ideal Gas................ 1374 the equation of state......................... 1385 4.1.1. Ideal Gas Heat Capacity............ 1376 19. Parameters and coefficients of the calibration 4.1.2. Effects of Vibrational Relaxation equation of state............................ 1398 Time on the Speed of Sound......... 1381 4.1.3. Ideal Gas Helmholtz Energy......... 1382 4.2. Properties of the Real Fluid............... 1382 List of Figures 4.2.1. Selected Database.................. 1382 1. Comparisons of vapor pressures calculated with 4.2.2. Fitting Procedures. ................. 1382 the ancillary equations to experimental data...... 1368 4.2.3. Equation for the Residual Helmholtz 2. Comparisons of saturated liquid densities Energy........................... 1384 calculated with the ancillary equations to 4.3. Derived Thermodynamic Properties......... 1384 experimental data........................... 1369 5. Comparisons of the Equation of State to 3. Comparisons of saturated vapor densities Experimental Data.......................... 1387 calculated with the ancillary equations to 5.1. Comparisons with Vapor Pressures and experimental data........................... 1369 Saturation Densities..................... 1387 4. Comparisons of melting pressures calculated 5.2. Comparisons of the Equation of State for with the ancillary equation to experimental data.. 1369 Nitrogen with other Experimental Data...... 1388 5. p␳T data.................................. 1373 5.3. Representation of Properties in the Critical 6. p␳T data between 250 and 400 K. ͑Author Region................................ 1393 labels are given in Fig. 5.͒.................... 1373 5.4. Extrapolation Behavior................... 1395 7. Critical region p␳T data. ͑Author labels are 5.4.1. Ideal Curves of Nitrogen............ 1395 given in Fig. 5.͒............................ 1373 5.4.2. Hugoniot Curve................... 1395 8. Speed of sound data......................... 1376 5.4.3. Property Plots..................... 1396 9. Isobaric and isochoric heat capacity data. ...... 1377 6. Estimated Uncertainty of Calculated Properties... 1397 14 10. Low temperature ideal gas heat capacity of N2. 7. The Calibration Equation..................... 1398 14 The curves for normal N2 and naturally 8. Acknowledgments.......................... 1398 occurring nitrogen are nearly identical.......... 1379 9. References................................. 1399 15 11. Low temperature ideal gas heat capacity of N2 10. Appendix: Thermodynamic Properties of and 14N15N................................ 1379 Nitrogen.................................. 1401 12. Ideal gas heat capacity of naturally occurring nitrogen ͑solid line͒ and calculations from the List of Tables RRHO model without electronic states or 1 Summary of critical point measurements........ 1366 quantum mechanical corrections ͑dashed line͒. 1380 2. Summary of triple point measurements.......... 1367 13. Comparisons of ideal gas heat capacities 3. Summary of vapor pressure data. ............. 1367 calculated with the ancillary equation to 4. Summary of saturated liquid and vapor density experimental