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An Equation of State for the Thermodynamic Properties of Dimethyl Ether

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An Equation of State for the Thermodynamic Properties of Dimethyl Ether An Equation of State for the Thermodynamic Properties of Dimethyl Ether ͒ Jiangtao Wu (吴江涛͒a and Yong Zhou (周永͒ State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an Shaanxi 710049, People’s Republic of China Eric W. Lemmon Thermophysical Properties Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA ͑Received 11 January 2011; accepted 31 March 2011; published online 8 June 2011͒ A thermodynamic property formulation for dimethyl ether has been developed based on a selection of experimental thermodynamic property data. The formulation includes a fundamental equation, a vapor-pressure equation, and saturated-density equations for liquid and vapor states. In determining the coefficients of the equation of state, multi- property fitting methods were used that included single-phase pressure-density- temperature ͑p␳T͒, heat capacity, vapor pressure, and saturated density data. Deviations between experimental and calculated data are generally within the experimental accuracy. The equation of state has been developed to conform to the Maxwell criterion for two- phase liquid-vapor equilibrium states, and is valid for temperatures from the triple-point temperature to 550 K, with pressures up to 50 MPa and densities up to 19 mol dm−3. The uncertainties of the equation of state in density are 0.1% for the liquid phase and 0.3% for the vapor phase. In the extended critical region, the uncertainties in density are 0.5%, except for very near the critical point. The uncertainties in vapor pressure are 0.2% above 230 K, and increase as temperature decreases. The uncertainties in saturated liquid den- sity are 0.05%, except for near the critical point. The uncertainties in heat capacity are 2.0%. Detailed comparisons between the experimental data and calculated values are given. © 2011 American Institute of Physics. ͓doi:10.1063/1.3582533͔ Key words: correlation; dimethyl ether; equation of state; thermodynamic properties. CONTENTS 5. Conclusions.............................. 15 6. Acknowledgments......................... 15 List of Symbols................................ 2 7. References............................... 15 1. Introduction.............................. 2 2. Critical and Triple Parameters of Dimethyl List of Tables Ether................................... 3 3. Auxiliary Equations....................... 3 1. Physical constants and characteristic properties 3.1. The vapor-pressure equation. ............ 3 of dimethyl ether.......................... 3 3.2. The saturated-liquid density equation. 4 2. Published critical parameters of dimethyl ether.. 4 3.3. The saturated-vapor density equation. .... 6 3. Summary of vapor-pressure data for dimethyl 4. The Equation of State...................... 6 ether.................................... 5 4. Summary of saturated-liquid density data for 4.1. Ideal-gas Helmholtz energy............. 6 dimethyl ether. .......................... 6 4.2. Residual Helmholtz energy.............. 7 5. Summary of saturated-vapor density data for 4.3. Comparisons with experimental data. ..... 9 dimethyl ether. .......................... 6 4.3.1. Comparisons with saturation 6. Summary of p␳T and virial-coefficient data for thermal data.................... 9 dimethyl ether. .......................... 8 4.3.2. Comparisons with p␳T data and 7. Summary of caloric data for dimethyl ether. 8 virial coefficients................ 11 8. The coefficients and exponents of the equation 4.3.3. Comparisons with caloric data. ..... 11 of state.................................. 9 4.4. The extrapolation behavior of the equation of state. ..................... 13 List of Figures ͒ a Author to whom correspondence should be addressed. Electronic mail: [email protected]; Fax: 86-29-82668789. 1. Reported critical temperatures Tc of dimethyl © 2011 American Institute of Physics. ether as a function of the year published....... 4 0047-2689/2011/40„2…/023104/16/$47.00023104-1 J. Phys. Chem. Ref. Data, Vol. 40, No. 2, 2011 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: 129.6.105.191 On: Tue, 30 Dec 2014 17:29:03 023104-2 WU, ZHOU, AND LEMMON ␳ 2. Reported critical densities c of dimethyl ether pressure. ............................... 15 as a function of the year published............ 4 24. Characteristic ͑ideal͒ curves of the equation of 3. Reported critical pressures pc of dimethyl state as a function of reduced temperature / / ether as a function of the year published....... 5 T Tc and reduced pressure p pc.............. 15 0 4. Comparisons of ideal gas heat capacities cp calculated with Eq. ͑7͒ to experimental and List of Symbols theoretical data as a function of temperature.. 7 ϭ ai, ni, vi Coefficients 5. Comparisons of vapor pressures p␴ calculated B ϭ Second virial coefficient with the equation of state to experimental data ϭ ͑ C Third virial coefficient as a function of temperature the range of the ϭ Ϯ ͒ cp Isobaric heat capacity y-axis is 0.5% .......................... 9 ϭ cv Isochoric heat capacity 6. Comparisons of vapor pressures p␴ calculated c␴ ϭ Saturation heat capacity with the equation of state to experimental data d, l, t, u, ␤, as a function of temperature ͑the range of the ␥, ␧, ␩ ϭ Exponents y-axis is Ϯ5.0%͒.......................... 10 f ϭ Helmholtz energy 7. Comparisons of saturated liquid densities ␳Ј h ϭ Enthalpy calculated with the equation of state to i, k ϭ Serial numbers experimental data as a function of temperature.. 10 M ϭ Molar mass 8. Comparisons of saturated vapor densities ␳Љ p ϭ Pressure calculated with the equation of state to R ϭ Molar gas constant experimental data as a function of temperature.. 10 S ϭ Sum of squares 9. Experimetal p␳T data as a function of s ϭ Entropy temperature and pressure.. .................. 11 T ϭ Absolute temperature 10. Comparisons of densities ␳ calculated with the v ϭ Molar volume equation of state to experimental data as a W ϭ Statistical weight function of pressure....................... 11 w ϭ Sound speed 11. Comparison of second virial coefficients B Z ϭ Compressibility factor calculated with the equation of state to experimental data as a function of temperature.. 12 Greek Letters 12. Comparison of third virial coefficients C ⌬ϭDeviation calculated with the equation of state to ␦ ϭ Reduced density experimental data as a function of temperature.. 12 ␸ ϭ Dimensionless Helmholtz energy ͑ ͒/␳ 13. Calculations of Z−1 along isotherms ␪ ϭ Functions ␳ versus density in the vapor-phase region and ␳ ϭ Molar density two-phase region. ....................... 12 ␶ ϭ Inverse reduced temperature 14. Experimental caloric data as a function of ␻ ϭ Acentric factor temperature and pressure.. .................. 12 15. Comparisons of saturation heat capacities c␴ Superscripts calculated with the equation of state to o ϭ Ideal gas experimental data as a function of temperature.. 13 r ϭ Residual 16. Comparisons of two-phase isochoric heat Ј ϭ Saturated-liquid state capacities c calculated with the equation of ϭ v2 Љ Saturated-vapor state state to experimental data as a function of temperature.............................. 13 Subscripts ϭ 17. Comparisons of isobaric heat capacities cp 0 Reference-state property calculated with the equation of state to c ϭ Critical experimental data as a function of temperature... 13 calc ϭ Calculated ϭ 18. Comparisons of isochoric heat capacities cv expt Experimental calculated with the equation of state to l ϭ Liquid property experimental data as a function of temperature... 13 nbp ϭ Normal-boiling-point property ϭ 19. Isochoric heat capacity cv versus temperature... 14 tp Triple-point property ϭ 20. Isobaric heat capacity cp versus temperature.... 14 v Vapor property 21. Sound speed w versus temperature. ...... 14 ␴ ϭ Saturation property 22. Isobaric behavior of the equation of state for dimethyl ether. .......................... 14 1. Introduction 23. Isothermal behavior of the equation of state at ͑͑ ͒ ͒ Dimethyl ether CH3 2O, RE-170 is the simplest ether extreme conditions of temperature and and is a colorless gas at atmospheric conditions. The physical J. Phys. Chem. Ref. Data, Vol. 40, No. 2, 2011 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: 129.6.105.191 On: Tue, 30 Dec 2014 17:29:03 EQUATION OF STATE FOR DIMETHYL ETHER 023104-3 TABLE 1. Physical constants and characteristic properties of dimethyl ether tions and the equation of state for dimethyl ether on the basis of an extensive collection of experimental data. Symbol Quantity Value R Molar gas constant 8.314 472 J mol−1 K−1 2. Critical and Triple Parameters of M Molar mass 46.068 44 g mol−1 Dimethyl Ether Tc Critical temperature 400.378 K pc Critical pressure 5336.8 kPa The critical parameters are important fundamental proper- ␳ −3 c Critical density 5.940 mol dm ties for the fluid and are a prerequisite for the development of Ttp Triple-point temperature 131.66 K the auxiliary equations and equation of state. The authors ptp Triple-point pressure 2.2 Pa launched a search on the existing critical parameters of dim- ␳ ϫ −6 −3 tpv Vapor density at the triple point 2.020 10 mol dm ethyl ether and found that the differences between these data ␳ −3 tpl Liquid density at the triple point 19.150 mol dm are significant. Detailed information can be found in Table 2 Tnbp Normal-boiling-point
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