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AlllUnited States Department ofCommerceTechnology AdministrationNational Institute of Standardsand TechnologyNISTIR 5078ThermodynamicProperties of Water:Tabulation from the lAPWS Formulationfor the Thermodynamic Properties ofOrdinary Water Substance for GeneralandScientificAllan H. HarveyQC100.056NO. 5078198Use1995

NISTIR 5078ThermodynamicProperties of Water:Tabulation from the lAPWS Formulation 1995for the Thermodynamic Properties of OrdinaryWater Substance for General and Scientific UseAllan H. HarveyPhysical and Chemical Properties DivisionChemical Science and Technology LaboratoryNational Institute of Standards and TechnologyBoulder, Colorado 80303-3328OctoberU.S.1998DEPARTMENT OF COMMERCE,William M. Daley, SecretaryTECHNOLOGY ADMINISTRATION, Gary R. Bachula, Acting Under Secretary for TechnologyNATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Director

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CONTENTSIntroduction12.Generation of the Tables23.Notes on the Tables24.References31.4Table1.Saturation (Temperature)Table2.Saturation (Pressure)11Table3.Compressed Water and Superheated Steam16Appendix A.on the lAPWS Formulation 1995 forThermodynamic Properties of Ordinary Water SubstanceGeneral and Scientific UseReleaseiiithefor76

List ofSymbolshenthalpy, kJ/kgppressure,5entropy, kJ/(kg-K)ttemperature, degrees CelsiusVvolume, cm /gMPaSubscriptsLliquid at saturationVvaporssaturationat saturationGreek LettersAproperty change on vaporizationPdensity,kg/m

Thermodynamic Properties of Water:lAPWSTabulation from theFormulation 1995 for theThermodynamic Properties of Ordinary Water SubstanceGeneral and Scientific UseforAllan H. HarveyPhysical and Chemical Properties DivisionChemical Science and Technology LaboratoryNational Institute of Standards and Technology325 BroadwayBoulder,CO80303Tables are provided for the density, enthalpy, entropy, and volume of water andsteam calculated from theProperties of Ordinaryformulationproperties,lAPWSFormulation 1995 for the ThermodynamicWater Substancefor Generalandisimplementedinand Scientific Use.Thisstandard for water’s thermodynamicthe current internationalisNIST Standard Reference Database10.Theproperties are tabulated along the vapor-liquid saturation curve as a function ofboth temperature and pressure. They are also tabulated for single-phase states ona grid of temperatures and pressures extending toKey words:density;enthalpy;2000 C and 1 000 MPa.entropy; steam;steamtables;thermodynamicproperties; volume; water1.IntroductionThethelAPWSfor Generalcurrent international standard for theandScientificUse[1,2].isWe will refer to this formulation as IAPWS-95.Unfortunately, the paper describingis tothermodynamic properties of ordinary waterFormulation 1995 for the Thermodynamic Properties of Ordinary Water SubstanceIAPWS-95[2]has not yet been published, and thereour knowledge no source of tabulated property values other than the small number of valuesgiven in theLAPWSReleaseanticipate that the r thepurpose of checking computer codes.While weof most users will be met by the software implementation ofThe purpose ofstill some demand for printed “Steam Tables.”demand, thoughthis reportmay besupersededata later time by athisthismorethorough Steam Tables book such as the one that was produced for the previous standard by Haaret al. [4].1

2.Generation of the TablesThe numbersIAPWS-95were generated from the Fortran codein these tablesformulation inNISTthatimplements theThey wereword processing program. Most computed values wereThe number of digits printed for any value should not be takenStandard Reference Database 10, Version 2.1[3].then copied directly into tables in aroundedto five significant digits.of the accuracy of the formulation at that point; theAppendix A) should be consulted for that information.as an indicationlAPWSRelease (reprinted asThese tables largely follow the example of Haar et al. [4]. However, in the 14 years sincebook was published, the purpose of printed Steam Tables has changed. Users who need highaccuracy for scientific research or industrial design will use software, not printed tables. Theprinted tables are now mainly useful for quick estimates and therefore need not be as finelyspaced in their coverage of pressures and temperatures. For this reason, the largest table in thisreport (the single-phase table. Table 3) is somewhat less than half the size of the correspondingtable in the book of Haar et al. The tables for saturation properties are also somewhat shorter.that3.Notes on the Tablesbe self-explanatory. Standard notation (documented in thebeen used, and traditional formatting has been followed. Here, a fewspecifics which may not be obvious are described.In general, these tables should“List of Symbols”) hasIntwoTable3,Thethe subcritical isobars cross the vapor-liquid saturation boundary.lines printed forfirsteach isobar give the values of properties for the saturated liquid andsaturated vapor, respectively.Asiscustomary, a horizontal lineisdrawn betweenthe pointsimmediately above and below the phase boundary.The IAPWS-95 formulation is recommended for fluid states at temperatures up to1 000 C and 1 000 MPa, and tests have shovm it to extrapolate reasonably to higher temperaturesand pressures and also to metastable liquid conditionsmoreatsubfreezing temperaturesatambienton the range of validity and on extrapolation capabilities, consult theRelease reprinted as Appendix A.) All points in Table 3 above 1000“C should be consideredextrapolations. Some of the low-temperature points in Table 3 correspond to conditions wherethe equilibrium phase would be a solid. For those points at low pressures, this is indicated byitalicizing the values. At high pressures, these points are not printed at all since there is no waypressures. (Fordetailsto verify the formulation’saccuracyatthose conditions.were determined from the formulas given by WagnerThesolid-fluid equilibrium boundarieset al. [5].The author thanks the ASME Research and Technology Committee on Water and Steamin Thermal Power Systems, Subcommittee on Properties of Water and Steam, for advice andencouragement on this project.2

4.[1]ReferenceslAPWSRelease on theWater SubstanceisResearchInstitute,A. PruB and[3]AofLAPWSthis report; copiesof this and otherLAPWSreleasesmayExecutive Secretary: Dr. R.B. Dooley, Electric Power3412 Hillview Avenue, Palo Alto, CA, 94304, USA.W. Wagner, “The LAPWS Formulation 1995Properties of OrdinaryJ.and Scientific Use, Fredericia, Denmark, 1996. This releasefor Generalreproduced as Appendixbe obtained from the[2]Formulation 1995 for the Thermodynamic Properties of OrdinaryWater Substancefor Generalfor theand Scientific Use,”Thermodynamictobe submittedtoPhys. Chem. Ref. Data.A.LI. LLarvey, A.P. Peskin,and S.A. Klein,NIST/ASME SteamProperties, Natl. Inst.Stand. Technol. Standard Reference Database 10, Version 2.1 (1997).[4]L. Haar, J.S. Gallagher,and G.S. Kell,NBS/NRC SteamTables, Hemisphere,NewYork(1984).[5]W. Wagner, A.Saul, and A. PruB, “International Equations for the Pressure along theMelting and along the Sublimation Curve of Ordinary Water Substance,”Ref Data23, 515-527 (1994).3J.Phys. Chem.

11Table1.Saturation (Temperature)Density, kg/m’t, cp,MPaPiPvhvVolume, cm’/gEntropy, kJ/(kg K)Enthalpy, kj/kgAlAhjlAsVvVl0.000 611 7999.790.004 8550.002500.92500.90.000 009.15559.15551.000 21205 991.10.000 657999.850.005 1964.182502.72498.60.015 269.12919.11381.000 15192 439.20.000 706 0999.890.005 5638.392504.62496.20.030 619.10279.0720130.000 758999.920.005 95212.602506.42493.80.045 899.07659.03061.000 08168 008.40.000 813 5999.930.006 36516.812508.22491.40.061 109.05058.98941.000 07157 116.50.000 872 6999.920.006 80221.022510.12489.00.076 259.02488.94861.000 08147 011.60.000 935 4999.8925.222511.92486.70.091 348.99938.90801.000137 633.70.001 002999.860.007 2660.007 75729.432513.72484.30.106 378.97418.86771.000 14128 923.80.001 073 0999.800.008 27633.632515.62481.90.121 338.94918.82781.000 20120 829.90.001 148 3999.740.008 82637.822517.42479.60.136 248.92438.78811.000 26113 304.100.001 228 2999.650.009 40742.022519.22477.20.151 098.89988.74871.000 35106 303.110.001 313 0999.560.010 02146.222521.02474.80.165 878.87548.70961.000 44120.001 402 8999.450.010 67050.412522.92472.50.180 618.85138.67071.000 5599 787.93 719.130.001 498999.330.011 35554.602524.72470.10.195 288.82748.63211.000 67140.001 599 0999.200.012 07858.792526.52467.70.209 908.80378.59381.000 800.011111.00011179 758.88 064.82 793.150.001 705 8999.060.012 84162.982528.32465.40.224 468.78038.55581.000 94160.001 818 8998.900.013 64567.172530.22463.00.238 978.75708.51801.001 10170.001 938 4998.730.014 49371.362532.02460.60.253 431.001 270.002 064 7998.550.015 38575.542533.82458.30.267 838.73398.71118.4805188.44331.001 4577736964190.002 198 3998.360.016 32579.732535.62455.90.282 188.68848.40631.001 6461 256.0.296480.310738.36951.001848.33301.002 0557 757.54 483.875.286.001.998.200.002 339 383.912537.42453.50.002 488 2998.16997.950.017 314210.018 35488.102539.32451.222230.002 645 3997.730.019 44892.282541.12448.80.324 938.66608.64378.62178.29671.002 2851 418.0.002 811997.500.020 59896.462542.92446.40.339 088.59988.26071.002 5148 548.45 858.1240.002 985 8997.250.021 806100.652544.72444.00.353 188.57818.22501.002 75250.003 169 9997.000.023 075104.832546.52441.70.367 228.55668.18941.003 0126270.003 363 90.024 406109.012548.32439.30.381 238.53538.15411.003 270.003 5681996.74996.470.025 804113.192550.12436.90.395 188.51428.1191128290.003 7831996.190.027 269117.372551.92434.60.409 088.49338.08421.003 820.004 009 2995.900.028 805121.552553.72432.20.422 948.47258.04961300.004 247 0995.610.030 415125.732555.52429.80.436 758.45208.01521.004 41310.004 496 9995.300.032 102129.912557.32427.40.450 527.98101.004 7231 151.3233340.004 759 60.033 868134.092559.22425.10.464 247.94711.005 040.005 035 4994.99994.668.43168.41130.035 717138.272561.02422.70.477 928.39137.91341.005 370.005 325994.330.037 651142.452562.82420.30.491 558.37147.87991.005 7029 526.27 998.26 560.3536370.005 629 0993.99993.640.039 674146.632564.52417.90.505 138.35177.84661.006 0525 205.0.041 790150.812566.32415.50.518 678.33217.81351.006 4023 929.0.044 001154.992568.12413.10.532 178.31277.78061.006 7622 727.38390.006 632 80.007 000 2993.29992.920.046 311159.172569.92410.80.545 628.29357.74791.007 1321 593.992.550.048 723163.352571.72408.40.559 038.27457.71541.007 5020 524.400.007 384 9992.180.051 242167.532573.52406.00.572 408.25557.68311.007 8919515.410.007 787 80.053 871171.712575.32403.60.585 738.23687.65111.008 2818 563.4243440.008 209 6991.79991.400.056 614175.892577.12401.20.599 018.21827.61921.008 6817 664.0.008 650 8991.000.059 474180.072578.92398.80.612 258.19987.58751.009 090.009 112 4990.590.062 457184.252580.62396.40.625 458.18157.55601.009 5016814.16011.45464748490.009 595 00.010 099990.170.065 565188.432582.42394.00.638 618.16337.52471.009 9215 252.989.750.068 803192.622584.22391.60.651 738.14537.49361.010 3614 534.0.010 627989.320.072 176196.802586.02389.20.664 818.12757.46271.010 7913 855.0.011 177988.890.075 688200.982587.82386.80.677 858.10987.43201.011 2413 212.0.011 752988.440.079 343205.162589.52384.40.690 858.09227.40141.011 6912 603.500.012 352988.000.083 147209.342591.32381.90.703 818.07487.37101.012 1512 027.510.012 9780.087 103213.522593.12379.50.716 731.012 6211 481.0.013 6310.091 217217.712594.82377.10.729 618.05768.04047.340852987.54987.087.31081.013 0910 963.53540.014 312986.610.095 494221.892596.62374.70.742 457.28101.013 5710 472.0.015 022986.140.099 938226.072598.32372.30.755 268.02348.00667.25131.014 0610 006.10.005 947 90.006 282 34.003 54.00414340383634337.973.754.672.716.32 878.