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An Equation of State for Fluid Ethylene

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An Equation of State for Fluid Ethylene ! Publi- cations NATL INST. OF STAND & JECH AlllDb aMOETb NBS TECHNICAL NOTE 1 045 "ffAU Of U.S. DEPARTMENT OF COMMERCE / Notional Dureou of Stondords An Equation of State for Fluid Ethylene IOC .U5753 NO.10A5 1981 NATIONAL BUREAU OF STANDARDS The National Bureau of Standards' was established by an act ot Congress on March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is per- formed by the National Measurement Laboratory, the National Engineering Laboratory, and the Institute for Computer Sciences and Technology. THE NATIONAL MEASUREMENT LABORATORY provides the national system of physical and chemical and materials measurement; coordinates the system with measurement systems of other nations and furnishes essential services leading to accurate and uniform physical and chemical measurement throughout the Nation's scientific community, industry, and commerce: conducts materials research leading to improved methods of measurement, standards, and data on the properties of materials needed by industry, commerce, educational institutions, and Government: provides advisory and research services to other Government agencies; develops, produces, and distributes Standard Reference Materials; and provides calibration services. The Laboratory consists of the following centers: Absolute Physical Quantities' — Radiation Research — Thermodynamics and Molecular Science — Analytical Chemistry — Materials Science. THE NATIONAL ENGINEERING LABORATORY provides technology and technical ser- vices to the public and private sectors to address national needs and to solve national problems: conducts research in engineering and applied science in support of these efforts: builds and maintains competence in the necessary disciplines required to carry out this research and technical service: develops engineering data and measurement capabilities; provides engineering measurement traceability services; develops test methods and proposes engineering standards and code changes; develops and proposes new engineering practices; and develops and improves mechanisms to transfer results of its research to the ultimate user. The Laboratory consists of the following centers: Applied Mathematics — Electronics and Electrical Engineering- — Mechanical Engineering and Process Technology- — Building Technology — Fire Research — Consumer Product Technology — Field Methods. THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and economy in Government operations in accordance with Public Law 89-306 {40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing the Federal Information Processing Standards Program, developing Federal ADP standards guidelines, and managing Federal participation in ADP voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and provides the technical foundation for computer-related policies of the Federal Government. The Institute consists of the following centers: Programming Science and Technology ^ Computer Systems Engineering. 'Headquarters and Laboratories at Gailhersburg, MD. unless otherwise noted; mailing address Washington, DC 20234. ^Some divisions within the center are located at Boulder, CO 80303. NATIONAL BUBEAU OF 8TAKOASa)8 UBBART An Equation of State SEP 2 3 1981 not O-U - i^UA. for Fluid Ethylene ClUOo , u 5 71? /ot/C I ^11 R. D. McCarty R. T. Jacobsen Thermophysical Properties Division National Engineering Laboratory National Bureau of Standards Boulder, Colorado 80303 /*.t"^ <^o^ \ ^''ftAU O* \- U.S. DEPARTMENT OF COMMERCE, Malcolm Doldrige, Secrerory NATIONAL BUREAU OF STANDARDS, Ernesr Ambler, Direcror Issued July 1981 ) NATIONAL BUREAU OF STANDARDS TECHNIOXL NOTE 1 045 Nor. Dur Srond. (U S), Tech. Nore 1 045, 1 64 pages (July 1 981 CODEN: NDTNAE US. GOVERNMENT PRINTING OFFICE WASHINGTON: 1981 For sole by rhe Superinrendenr of Documenrs. US Governmenr Pnnring Office. Woshlngron, D C 20402 Price S5 50 (Add 25 percenr for orher rhon U.S. moiling) Contents Page 1. Introduction 1 2. Experimental Measurements of the Thermodynamic Properties of Ethylene 4 2.1 Pressure-Density-Temperature Data 4 2.2 Coexistence Properties 4 2.3 Calorimetric Data 4 2.4 Velocity of Sound Measurements 8 2.5 Second Virial Coefficients 8 3. Weighting of the Data 11 4. The Determination of the Equation of State 11 4.1 Analysis of the Functional Form of the Equation of State . 11 4.2 The Selection of Data for Multiproperty Fitting 12 5. Liquid-Vapor and Liquid-Solid Coexistence 14 5.1 Liquid-Vapor Coexistence 14 5.2 Liquid-Solid Coexistence 21 6. The Ideal Gas Heat Capacity Equation 21 7. Derived Thermodynamic Properties 23 8. Comparisons of the Equation of State to P-p-T Data 26 9. Comparisons of the Equation of State With Related Thermodynamic Data 26 10. Estimated Accuracy of the Equation of State 41 11. Conclusion 43 12. References 45 Nomenclature 49 APPENDIX A. Comparisons to Available Data Sets Including Those Used in the Determination of the Coefficients of the Equation of State (1) 51 APPENDIX B. Thermodynamic Properties of Fluid Ethylene 73 APPENDIX C. Guide for Use of Computer Programs for the Calculation of Thermodynamic Properties of Ethylene 129 111 List of Figures Page Figure 1. Ethylene PVT Data 6 Figure 2. Ethylene Heat Capacity Data 7 Figure 3. Ethylene Velocity of Sound Data 9 Figure 4. Ethylene PVT Data Used in the Determination of the Equation of State 13 Figure 5. Ethylene Velocity of ^Sound Data Used in the Determination of the Equation of State 15 Figure 6. Comparisons of PVT Values of Saturation 18 Figure 7. Comparisons of Ideal Gas Heat Capacity Values 24 Figure 8. Deviations of Calculated Values of Density from Selected PVT Data 27 Figure 9. Deviations of Calculated Values of Heat Capacity From Data 33 Figure 10. Deviations of Calculated Values of Velocity of Sound From Selected Data 34 Figure 11. Deviation of Calculated Values of Velocity of Sound From Selected Data for the Saturated Liquid of Gammon [9] . 36 Figure 12. Comparisons of Calculated Values of Cp with Data .... 38 Figure 13. Accuracy of the Equation of State for Assumed Errors in Temperature and Pressure 42 Figure A-1. Comparisons to PVT Data 52 Figure A-2. Comparisons to Velocity of Sound Data 68 List of Tables Table 1. Summary of P-p-T Data for Ethylene 5 Table 2. Recent Velocity of Sound Measurements for Ethylene ... 8 Table 3. The Second Virial Coefficient 3(T) for Ethylene in the Infinite Series PV/RT = 1 + B(T)/V + 10 Table 4. Coefficients for the Equation of State (1) for Ethylene . 16 Table 5. Summary of Vapor Pressure Data for Ethylene 17 Table 6. Coefficients for the Vapor Pressure Equation for Ethylene 19 Table 7. Summary of Saturation Density Data Used in This Work . 19 1 v List of Tables (Continued) Page Table 8. Coefficients for Approximating Functions for Saturation Densities for Ethylene 20 Table 9. Tabulated Differences Between Saturation Properties Calculated From Equation of State (1) Alone and the Intersection of the Vapor Pressure eq (2) With the Equation of State (1) 22 Table 10. Coefficients for the Ideal Gas Heat Capacity Equation for Ethylene 23 Table 11. Comparison of Calculated and Experimental Data for the Enthalpy of Vaporization 40 Table A-1. Data Points With Deviations Exceeding the Scale of Figure A- 1 64 Table A-2. Heat Capacity Data With Deviations Exceeding the Scales of Figures 9 and 12 66 Table A-3. Velocity of Sound Data With Deviations Exceeding the Scale of Figure A-2 71 Table B-1. Thermodynamic Properties of Saturated Ethylene 74 Table B-2. Thermodynamic Properties of Ethylene 83 Table C-1. SUBROUTINE PROPS and Its Entry Points 133 Table C-2. Iterative Solutions for Density 134 Table C-3. FUNCTION CPI and Its Entry Points 135 Table C-4. Functions for Thermodynamic Properties 136 Table C-5. Subprograms for Coexistence Properties 137 . AN EQUATION OF STATE FOR FLUID ETHYLENE^ R. D. McCarty and * 2 R. T. Jacobsen Thermophysical Properties Division National Engineering Laboratory National Bureau of Standards Boulder, Colorado 80303 A thermodynamic property formulation for ethyl ene^ developed as a part of a joint industry-government project, is presented. The formulation includes an equation of state, vapor pressure equation, and equation for the ideal gas heat capacity. The coefficients were determined by a least squares fit of selected experimental data. Comparisons of property values calculated using the equation of state with measured values are given. The equation of state is not valid in the critical region (p^ + 0.3 p^ for temperatures of T^ + 0.05 T^) Errors on the order of 20 percent for derived properties and 10 percent for density may be encountered near the critical point. Tables of the thermodynamic properties of ethylene for the liquid and vapor phases for temperatures from the freezing line to 450 K with pressures to 40 MPa are presented. The equation of state and its derivative and integral
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