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Reference Correlations for Thermophysical Properties of Liquid Water at 0.1 Mpa

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Reference Correlations for Thermophysical Properties of Liquid Water at 0.1 Mpa Reference Correlations for Thermophysical Properties of Liquid Water at 0.1 MPa Jaroslav Pátek, Jan Hrubý,a… Jaroslav Klomfar, and Monika Součková Institute of Thermomechanics AS CR, v.v.i., Dolejškova 5, Prague 8 CZ-182 00, Czech Republic Allan H. Harveyb… Thermophysical Properties Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA ͑Received 7 November 2008; accepted 18 November 2008; published online 15 January 2009͒ Simple but highly accurate correlations have been developed for the thermodynamic properties ͑including density, heat capacity, and speed of sound͒, viscosity, thermal con- ductivity, and static dielectric constant of liquid water as a function of temperature at a pressure of 0.1 MPa. The calculations may be simply extended to a pressure range from the saturation pressure to 0.3 MPa. The temperature range covered in most cases is from 253.15 to 383.15 K; this includes some temperatures where liquid water is metastable. These correlations are designed to reproduce the best available data, which in most cases are described by formulations issued by the International Association for the Properties of Water and Steam ͑IAPWS͒. The equations presented here are simple enough to be used in applications such as spreadsheets. They provide a convenient alternative to the more complicated IAPWS formulations in cases where only liquid properties at near- atmospheric pressure are of interest without increasing the uncertainty beyond that of the more complex formulations. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3043575͔ Key words: calibration; density; dielectric constant; heat capacity; speed of sound; thermal conductivity; ther- modynamic properties; viscosity; water. CONTENTS 5.3. Range of Validity and Uncertainty........ 28 6. Calculations at Other Pressures.............. 28 7. Discussion............................... 28 1. Introduction.............................. 22 8. Acknowledgments......................... 29 2. Thermodynamic Properties.................. 23 2.1. Input Data........................... 23 2.2. Correlation Results.................... 23 List of Tables 2.3. Range of Validity and Uncertainty........ 24 2.4. Application at Standard Atmospheric 1. Coefficients and exponents of Eqs. ͑2͒–͑4͒..... 23 Pressure............................. 25 2. Thermodynamic properties of liquid water at 2.5. Application in a Limited Pressure Range. 25 0.1 MPa obtained by differentiating Eqs. 3. Viscosity................................ 26 ͑2͒–͑4͒.................................. 23 3.1. Input Data........................... 26 3. Thermodynamic properties of liquid water at 3.2. Correlation Results.................... 26 0.1 MPa given by algebraic combinations of 3.3. Range of Validity and Uncertainty........ 26 Eqs. ͑2͒–͑4͒ and their derivatives............. 24 4. Thermal Conductivity...................... 26 4. Relations for thermodynamic properties of 4.1. Input Data........................... 26 liquid water at pressure p different from 4.2. Correlation Results.................... 26 0.1MPa................................. 25 4.3. Range of Validity and Uncertainty........ 27 5. Parameters for calculation of viscosity with ͑ ͒ 5. Static Dielectric Constant................... 27 Eq. 7 .................................. 26 5.1. Input Data........................... 27 6. Parameters for calculation of thermal ͑ ͒ 5.2. Correlation Results.................... 28 conductivity with Eq. 9 ................... 27 7. Parameters for calculation of static dielectric ͒ constant with Eq. ͑11͒...................... 28 a Electronic mail: [email protected] ͒ b Electronic mail: [email protected] 8. Sample points for computer-program © 2009 American Institute of Physics. verification of calculated properties at 0.1 MPa.. 29 0047-2689/2009/38„1…/21/9/$45.0021 J. Phys. Chem. Ref. Data, Vol. 38, No. 1, 2009 22 PÁTEK ET AL. List of Figures pressure requires first solving the IAPWS-95 thermodynamic formulation to obtain the density to be input to the formula- 1. Relative deviation of the specific volume at tion for the property of interest. 0.1 MPa given by the present formulation For many purposes, a simpler option would be desirable. from the IAPWS-95 formulation.1,2........... 24 For example, water is widely used as a calibration fluid, and 2. Relative deviation of the specific isobaric heat many of these calibrations use liquid water at atmospheric capacity at 0.1 MPa given by the present pressure. A one-dimensional correlation of the relevant prop- formulation from the IAPWS-95 erty as a function of temperature would be suitable for these formulation.1,2............................ 24 purposes. The desire for simplicity has led people to use 3. Relative deviation of the speed of sound at tabulated numbers from handbooks ͑which may not represent 0.1 MPa given by the present formulation the best current knowledge͒ or obsolete and less accurate from the IAPWS-95 formulation.1,2........... 25 equations such as the density correlation of Kell,9 in prefer- 4. Relative deviation of the density at ence to the official IAPWS formulations. 0.101 325 MPa given by the present In this work, we provide simple formulas as a function of ͓ ␯ ͑ ͔͒ formulation reciprocal of atm from Eq. 6 temperature for properties of liquid water at 0.1 MPa pres- 1,2 and by the IAPWS-95 formulation from the sure. They are designed to reproduce the more comprehen- CIPM recommended values for the density of sive IAPWS standards to a precision at least a factor of 10 15 water between 0 and 40 °C. ............... 25 smaller than the uncertainty of the original IAPWS formula- 5. Relative deviation of correlations for viscosity tion, so that the correlations developed here contribute neg- ͓Eq. ͑7͔͒ and thermal conductivity ͓Eq. ͑9͔͒ ligibly to the overall uncertainty of the property calculation. from the corresponding IAPWS standards.. 26 The formulas can be programmed easily in common appli- 6. Deviation from the correlation of Hamelin et cations such as spreadsheets, allowing users to obtain prop- 18 al. of dielectric-constant data from studies erties of the best accuracy with relatively little effort. that measured data for supercooled water....... 27 The temperature range covered by these correlations is 7. Deviation of accepted dielectric-constant data ͑with exceptions to be noted below͒ 253.15–383.15 K. This from Eq. ͑11͒............................. 28 exceeds the range in which liquid water is the thermody- namically stable phase at 0.1 MPa by approximately 20 K at the low-temperature end and 10 K at the high-temperature end. Properties in this extended range are useful for the study 1. Introduction of metastable water and for the study of aqueous solutions that are stable over a wider temperature range than the pure Water is probably the most important chemical substance solvent. in science and industry. International efforts to produce stan- The formulas presented here were adopted as a Supple- dardized, high-accuracy values of water’s thermophysical mentary Release by IAPWS at its meeting in Berlin, Ger- properties began in the 1920s; these efforts are now orga- many, in September 2008.10 nized by the International Association for the Properties of In this paper, we begin by discussing thermodynamic Water and Steam ͑IAPWS͒. properties in Sec. 2. Sections 3 and 4 present the viscosity IAPWS has produced comprehensive formulations for and thermal conductivity, respectively. Section 5 describes general and scientific uses for a variety of properties, includ- the static dielectric constant, for which the publication of ing the thermodynamic properties,1,2 the viscosity,3,4 the ther- more accurate data subsequent to the IAPWS release re- mal conductivity,5,6 and the static dielectric constant.7,8 quired a different approach. Application at different pres- These formulations are designed to describe ͑within the un- sures ͑particularly the commonly used standard atmospheric certainty of available experimental data͒ the behavior of va- pressure of 0.101 325 MPa͒ is discussed in Sec. 6. por, liquid, and supercritical water over wide ranges of tem- Before we present our correlations, we mention three de- perature and pressure. tails. First, we use “water” to refer to what is often called However, the comprehensive IAPWS formulations are not “ordinary water substance” in IAPWS formulations. This ͑ simple to use unless one obtains software where someone means chemically pure H2O with the standard isotopic com- else has done the work of implementation͒. For example, the position for hydrogen and oxygen given by Vienna Standard formulation for thermodynamic properties,1,2 commonly Mean Ocean Water ͑VSMOW͒.11 Most water in nature or in known as IAPWS-95, is a fundamental equation for the the laboratory will have isotopic composition differing Helmholtz energy as a function of temperature and density, slightly from that of VSMOW, but the difference is negli- containing eight terms in the ideal-gas part and 56 terms, gible for all properties considered here, with the exception of some rather complicated, in the residual part. Differentiation the density, where isotopic composition could affect the most and iterative solution are required to obtain common proper- precise measurements. Second, these formulations are for ties such as density and heat capacity as a function of tem- pure, air-free water. In some applications, the interest may be perature and pressure. For other properties such as the vis- in water in contact
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