Argon !Short name 7440-37-1 !CAS number Argon !Full name Ar !Chemical formula {Ar} R-740 !Synonym 39.948 !Molar mass [g/mol] 83.8058 !Triple point temperature [K] 87.302 !Normal boiling point [K] 150.687 !Critical temperature [K] 4863.0 !Critical pressure [kPa] 13.4074 !Critical density [mol/L] -0.00219 !Acentric factor 0.0 !Dipole moment [Debye]; (exactly zero for monatomic molecules) OT0 !Default reference state 298.15 101.325 6197.0 154.737 !Tref, Pref, Href, Sref 10.0 !Version number 1951 !UN Number :UN: cryogen !Family :Family: 0.0 !Heating value (upper) [kJ/mol] :Heat: A1 !Safety Group (ASHRAE Standard 34, 2010) :Safety: 1S/Ar !Standard InChI String :InChi: XKRFYHLGVUSROY-UHFFFAOYSA-N !Standard InChI Key :InChiKey: edbdc8e0 (nitrogen) !Alternative fluid for mixing rules :AltID: ed016370 !Hash number from InChI Key :Hash: !The fluid files contain general information about the fluid in the first 15 to 20 lines, followed by sections for the ! equations of state, transport equations, and auxiliary equations. Equations of state are listed first. The NIST recommended ! equations begin with a hash mark (#). The secondary equations begin with the @ symbol. These symbols can be swapped to ! select a secondary equation as primary and the primary as secondary. The equation of state section also contains auxiliary ! equations for the ideal gas heat capacity or ideal gas Helmholtz energy. Below the equations of state (both primary and ! secondary) are the transport equations, first viscosity and then thermal conductivity. These are then followed by the ! secondary equations if available. The transport section also contains auxiliary equations required to calculate either the ! dilute gas state or the critical enhancement. At the end of the file are additional but not necessary auxiliary equations, ! including simple equations for the vapor pressure, saturated liquid and vapor densities, melting line (for some fluids), and ! sublimation line (for even fewer fluids). This section also contains the equations for dielectric constant and surface ! tension if available. The sections are divided by different symbols (these being _-+=^*~) to aid the eye in locating a ! particular section. Secondary equations are indented 10 spaces to avoid confusion with the NIST recommended equations. The ! end of the fluid file is marked with @END. Anything below that is ignored. ! compiled by E.W. Lemmon, NIST Physical and Chemical Properties Division, Boulder, Colorado ! 12-03-97 EWL, Original version. ! 06-23-98 EWL, Add Tegeler equation of state as default equation. ! 06-24-98 EWL, Add Younglove BWR equation. ! 06-26-98 EWL, Add Younglove transport equations. ! 01-07-99 EWL, Change ECS reference fluid to nitrogen. ! 10-27-99 EWL, Add Span 12 term equation. ! 11-15-99 EWL, Change default reference state. ! 03-20-00 EWL, Change max density to the density at p=2*pmax along melting line. ! 05-20-01 EWL, Add sublimation line. ! 11-26-02 EWL, Change reference state to OT0 with values from CODATA. ! 06-10-03 EWL, Finalize transport equations. ! 08-05-04 EWL, Add Harvey and Lemmon dielectric correlation. ! 11-18-04 MLH, Add tPR. ! 09-14-06 EWL, Change upper T limit from 700 to 2000 K. ! 12-02-06 MLH, Update LJ for ECS. ! 06-10-10 CKL, Add ancillary equations. ! 12-06-12 EWL, Add surface tension coefficients of Mulero et al. (2012). ________________________________________________________________________________ #EOS !---Equation of state--- FEQ !Helmholtz equation of state for argon of Tegeler et al. (1999). :TRUECRITICALPOINT: 150.687 13.40742965 !True EOS critical point [K, mol/L] (where dP/dD=0 and d^2P/dD^2=0 at constant T) :DOI: 10.1063/1.556037 ? ?``````````````````````````````````````````````````````````````````````````````` ?Tegeler, Ch., Span, R., and Wagner, W., ? "A New Equation of State for Argon Covering the Fluid Region for ? Temperatures from the Melting Line to 700 K at Pressures up to 1000 MPa," ? J. Phys. Chem. Ref. Data, 28(3):779-850, 1999. ? ?The estimated uncertainty in density is less than 0.02% for pressures up ? to 12 MPa and temperatures up to 340 K with the exception of the ? critical region and less than 0.03% for pressures up to 30 MPa and ? temperatures between 235 and 520 K. Elsewhere, the uncertainty in ? density is generally within 0.2%. In the region with densities up to ? half the critical density and for temperatures between 90 and 450 K, the ? estimated uncertainty of calculated speeds of sound is in general less ? than 0.02%. In the liquid and supercritical regions, the uncertainty is ? less than 1%. The uncertainty in heat capacities is within 0.3% for the ? vapor and 2% for the liquid. The formulation gives reasonable ? extrapolation behavior up to very high pressures (50 GPa) and ? temperatures (17000 K). ? !``````````````````````````````````````````````````````````````````````````````` 83.8058 !Lower temperature limit [K] 2000.0 !Upper temperature limit [K] 1000000.0 !Upper pressure limit [kPa] 50.65 !Maximum density [mol/L] CPP !Pointer to Cp0 model 39.948 !Molar mass [g/mol] 83.8058 !Triple point temperature [K] 68.891 !Pressure at triple point [kPa] 35.465 !Density at triple point [mol/L] 87.302 !Normal boiling point temperature [K] -0.00219 !Acentric factor 150.687 4863.0 13.40742965 !Tc [K], pc [kPa], rhoc [mol/L] 150.687 13.40742965 !Reducing parameters [K, mol/L] 8.31451 !Gas constant [J/mol-K] 37 4 4 12 0 0 0 0 0 0 0 0 !# terms and # coefs/term for normal terms, Gaussian terms, and Gao terms 0.08872230499 0.0 1. 0. !a(i),t(i),d(i),l(i) 0.705148051673 0.25 1. 0. -1.68201156541 1.0 1. 0. -0.149090144315 2.75 1. 0. -0.120248046009 4.0 1. 0. -0.121649787986 0.0 2. 0. 0.400359336268 0.25 2. 0. -0.271360626991 0.75 2. 0. 0.242119245796 2.75 2. 0. 0.00578895831856 0.0 3. 0. -0.0410973356153 2.0 3. 0. 0.0247107615416 0.75 4. 0. -0.321813917507 3.0 1. 1. 0.332300176958 3.5 1. 1. 0.0310199862873 1.0 3. 1. -0.0307770860024 2.0 4. 1. 0.0938911374196 4.0 4. 1. -0.090643210682 3.0 5. 1. -0.000457783492767 0.0 7. 1. -0.826597290252e-4 0.5 10. 1. 0.000130134156031 1.0 10. 1. -0.011397840002 1.0 2. 2. -0.0244551699605 7.0 2. 2. -0.064324067176 5.0 4. 2. 0.0588894710937 6.0 4. 2. -0.00064933552113 6.0 8. 2. -0.0138898621584 10.0 3. 3. 0.404898392969 13.0 5. 3. -0.386125195947 14.0 5. 3. -0.188171423322 11.0 6. 3. 0.159776475965 14.0 6. 3. 0.0539855185139 8.0 7. 3. -0.028953417958 14.0 7. 3. -0.0130254133814 6.0 8. 3. 0.00289486967758 7.0 9. 3. -0.00226471343048 24.0 5. 4. 0.00176164561964 22.0 6. 4. 0.00585524544828 3.0 2. 2. 2. -20.0 -250.0 1.11 1.0 0. 0. 0. -0.6925190827 1.0 1. 2. 2. -20.0 -375.0 1.14 1.0 0. 0. 0. 1.53154900305 0.0 2. 2. 2. -20.0 -300.0 1.17 1.0 0. 0. 0. -0.00273804474498 0.0 3. 2. 2. -20.0 -225.0 1.11 1.0 0. 0. 0. eta beta gamma epsilon EXP[eta*(delta-epsilon)^2+beta*(tau-gamma)^2] #AUX !---Auxiliary function for Cp0 CPP !Ideal gas heat capacity function for argon of Tegeler et al. (1999). ? ?``````````````````````````````````````````````````````````````````````````````` ?Tegeler, Ch., Span, R., and Wagner, W., ? "A New Equation of State for Argon Covering the Fluid Region for ? Temperatures from the Melting Line to 700 K at Pressures up to 1000 MPa," ? J. Phys. Chem. Ref. Data, 28(3):779-850, 1999. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 1.0 8.31451 !Reducing parameters for T, Cp0 1 0 0 0 0 0 0 !Nterms: polynomial, exponential, cosh, sinh 2.5 0.0 #AUX !---Auxiliary function for PX0 PX0 !Helmholtz energy ideal-gas function for argon of Tegeler et al. (1999). ? ?``````````````````````````````````````````````````````````````````````````````` ?Tegeler, Ch., Span, R., and Wagner, W., ? "A New Equation of State for Argon Covering the Fluid Region for ? Temperatures from the Melting Line to 700 K at Pressures up to 1000 MPa," ? J. Phys. Chem. Ref. Data, 28(3):779-850, 1999. ? !``````````````````````````````````````````````````````````````````````````````` 1 2 0 0 0 0 0 0 !Nterms: ai*log(tau**ti); ai*tau**ti; ai*log(1-exp(bi*tau)) 1.5 1.0 !ai, ti for [ai*log(tau**ti)] terms -10.2938148004759711 0.0 !aj, ti for [ai*tau**ti] terms -0.0003415237881503 1.0 !aj, ti for [ai*tau**ti] terms #AUX !---Auxiliary function for PH0 PH0 !Ideal gas Helmholtz form for argon. ? ?``````````````````````````````````````````````````````````````````````````````` ?Tegeler, Ch., Span, R., and Wagner, W., ? "A New Equation of State for Argon Covering the Fluid Region for ? Temperatures from the Melting Line to 700 K at Pressures up to 1000 MPa," ? J. Phys. Chem. Ref. Data, 28(3):779-850, 1999. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 1 2 0 0 0 0 0 0 !Nterms: ai*log(tau**ti); ai*tau**ti; ai*log(1-exp(bi*tau)); cosh; sinh 1.5 1.0 !ai, ti for [ai*log(tau**ti)] terms -10.2938148005 0.0 !aj, ti for [ai*tau**ti] terms -0.0003415238 1.0 -------------------------------------------------------------------------------- @EOS !---Equation of state--- FEK !Helmholtz equation of state for argon of Kunz and Wagner (2004). ? ?``````````````````````````````````````````````````````````````````````````````` ?Kunz, O., Klimeck, R., Wagner, W., Jaeschke, M. ? "The GERG-2004 Wide-Range Equation of State for Natural Gases ? and Other Mixtures," GERG Technical Monograph 15, ? Fortschritt-Berichte VDI, VDI-Verlag, Düsseldorf, 2007. ? !``````````````````````````````````````````````````````````````````````````````` 83.8058 !Lower temperature limit [K] 700.0 !Upper temperature limit [K] 1000000.0 !Upper pressure limit [kPa] 50.65 !Maximum density [mol/L] PHK !Pointer to Cp0 model 39.948 !Molar mass [g/mol] 83.8058 !Triple point temperature [K] 69.03 !Pressure at triple point [kPa] 35.5 !Density at triple point [mol/L] 87.29 !Normal boiling point temperature [K] -0.0006 !Acentric factor 150.687 4879.8 13.407429659 !Tc [K], pc [kPa], rhoc [mol/L] 150.687 13.407429659 !Reducing parameters [K, mol/L] 8.314472 !Gas constant [J/mol-K] 12 4 0 0 0 0 0 0 0 0 0 0 !# terms and # coefs/term for normal terms, Gaussian terms, and Gao terms 0.85095714803969 0.250 1. 0. -2.4003222943480 1.125 1. 0. 0.54127841476466 1.5 1. 0. 0.016919770692538 1.375 2. 0. 0.068825965019035 0.25 3. 0. 0.00021428032815338 0.875 7. 0. 0.17429895321992 0.625 2. 1. -0.033654495604194 1.75 5. 1. -0.13526799857691 3.625 1. 2. -0.016387350791552 3.625 4. 2. -0.024987666851475 14.5 3. 3. 0.0088769204815709 12.0 4. 3. @AUX !---Auxiliary function for PH0 PHK !Ideal gas Helmholtz form for argon of Kunz and Wagner (2004). ? ?``````````````````````````````````````````````````````````````````````````````` ?Kunz, O., Klimeck, R., Wagner, W., Jaeschke, M. ? "The GERG-2004 Wide-Range Equation of State for Natural Gases ? and Other Mixtures," GERG Technical Monograph 15, ? Fortschritt-Berichte VDI, VDI-Verlag, Düsseldorf, 2007. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 1 2 0 0 0 0 0 0 !Nterms: ai*log(tau**ti); ai*tau**ti; ai*log(1-exp(bi*tau)); cosh; sinh 1.5 1.0 !ai, ti for [ai*log(tau**ti)] terms 8.3166315 0.0 !aj, ti for [ai*tau**ti] terms -4.9465026 1.0 @EOS !---Equation of state--- FE1 !Helmholtz equation of state for argon of Stewart and Jacobsen (1989). ? ?``````````````````````````````````````````````````````````````````````````````` ?Stewart, R.B. and Jacobsen, R.T, ? "Thermodynamic Properties of Argon from the Triple Point to 1200 K at ? Pressures to 1000 MPa," ? J. Phys. Chem. Ref. Data, 18(2):639-798, 1989. ? !``````````````````````````````````````````````````````````````````````````````` 83.804 !Lower temperature limit [K] 1200.0 !Upper temperature limit [K] 1000000.0 !Upper pressure limit [kPa] 45.814 !Maximum density [mol/L] CP1 !Pointer to Cp0 model 39.948 !Molar mass [g/mol] 83.804 !Triple point temperature [K] 68.961 !Pressure at triple point [kPa] 35.475 !Density at triple point [mol/L] 87.293 !Normal boiling point temperature [K] -0.004 !Acentric factor 150.6633 4860.0 13.29 !Tc [K], pc [kPa], rhoc [mol/L] 150.6633 13.29 !Reducing parameters [K, mol/L] 8.31434 !Gas constant [J/mol-K] 28 4 0 0 0 0 0 0 0 0 0 0 !# terms and # coefs/term for normal terms, Gaussian terms, and Gao terms 0.7918675715 0.25 1. 0. !a(i),t(i),d(i),l(i) -1.633346151 1.0 1. 0. -0.439530293 3.0 1. 0. 0.1033899999 4.0 1. 0. 0.2061801664 0.25 2. 0. -0.2888681776 1.0 2. 0. 0.439801055 2.5 2. 0. -0.08429550391 3.5 2. 0. -0.2155658654 0.75 3. 0. 0.4786509099 1.0 3. 0. -0.3525884593 1.5 3. 0. 0.03015073692 2.5 3. 0. 0.02987679059 1.0 4. 0. -0.01522568583 2.0 4. 0. 0.0007435785786 2.0 6. 0. 0.07099541624 5.0 1. 3. -0.02904237185 7.0 1. 3. -0.06223078525 5.0 2. 2. 0.0001410895187 22.0 2. 4. -0.001481241783 16.0 2. 6. 0.03023342784 10.0 3. 3. -0.06126784685 14.0 3. 3. 0.0270996709 16.0 3. 3. 0.09411034405 4.0 4. 2. -0.007291645114 8.0 4. 2. -0.001586314976 10.0 4. 4. 0.0009510948813 5.0 8. 2. 0.0007786181844 6.0 8. 2. @AUX !---Auxiliary function for Cp0 CP1 !Ideal gas heat capacity function for argon. ? ?``````````````````````````````````````````````````````````````````````````````` ?Stewart, R.B. and Jacobsen, R.T, ? "Thermodynamic Properties of Argon from the Triple Point to 1200 K at ? Pressures to 1000 MPa," ? J. Phys. Chem. Ref. Data, 18(2):639-798, 1989. doi: 10.1063/1.555829 ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 1.0 8.31434 !Reducing parameters for T, Cp0 1 0 0 0 0 0 0 !Nterms: polynomial, exponential, cosh, sinh 2.5 0.0 @EOS !---Equation of state--- FES !Helmholtz equation of state for argon of Span and Wagner (2003). ? ?``````````````````````````````````````````````````````````````````````````````` ?Span, R. and Wagner, W. ? "Equations of State for Technical Applications. II. Results for Nonpolar Fluids," ? Int. J. Thermophys., 24(1):41-109, 2003. doi: 10.1023/A:1022310214958 ? ?The uncertainties of the equation of state are approximately 0.2% (to ? 0.5% at high pressures) in density, 1% (in the vapor phase) to 2% in ? heat capacity, 1% (in the vapor phase) to 2% in the speed of sound, and ? 0.2% in vapor pressure, except in the critical region. ? !``````````````````````````````````````````````````````````````````````````````` 83.8058 !Lower temperature limit [K] 600.0 !Upper temperature limit [K] 100000.0 !Upper pressure limit [kPa] 50.65 !Maximum density [mol/L] CPP !Pointer to Cp0 model 39.948 !Molar mass [g/mol] 83.8058 !Triple point temperature [K] 69.026 !Pressure at triple point [kPa] 35.498 !Density at triple point [mol/L] 87.289 !Normal boiling point temperature [K] -0.002 !Acentric factor 150.687 4863.0 13.40743 !Tc [K], pc [kPa], rhoc [mol/L] 150.687 13.40743 !Reducing parameters [K, mol/L] 8.31451 !Gas constant [J/mol-K] 12 4 0 0 0 0 0 0 0 0 0 0 !# terms and # coefs/term for normal terms, Gaussian terms, and Gao terms 0.85095715 0.25 1. 0. !a(i),t(i),d(i),l(i) -2.4003223 1.125 1. 0. 0.54127841 1.5 1. 0. 0.016919771 1.375 2. 0. 0.068825965 0.25 3. 0. 0.00021428033 0.875 7. 0. 0.17429895 0.625 2. 1. -0.033654496 1.75 5. 1. -0.135268 3.625 1. 2. -0.016387351 3.625 4. 2. -0.024987667 14.5 3. 3. 0.0088769205 12.0 4. 3. @EOS !---Equation of state--- BWR !MBWR equation of state for argon of Younglove (1982). ? ?``````````````````````````````````````````````````````````````````````````````` ?Younglove, B.A., ? "Thermophysical Properties of Fluids. I. Argon, Ethylene, ? Parahydrogen, Nitrogen, Nitrogen Trifluoride, and Oxygen," ? J. Phys. Chem. Ref. Data, Vol. 11, Suppl. 1, pp. 1-11, 1982. ? !``````````````````````````````````````````````````````````````````````````````` 83.80 !Lower temperature limit [K] 400.0 !Upper temperature limit [K] 101000.0 !Upper pressure limit [kPa] 50.65 !Maximum density [mol/L] CP2 !Pointer to Cp0 model 39.948 !Molar mass [g/mol] 83.80 !Triple point temperature [K] 68.906 !Pressure at triple point [kPa] 35.4 !Density at triple point [mol/L] 87.302 !Normal boiling point temperature [K] -0.002 !Acentric factor 150.86 4905.8 13.41 !Tc [K], pc [kPa], rhoc [mol/L] 150.86 13.41 !Reducing parameters [K, mol/L] 13.418 !gamma 0.0831434 !Gas constant [L-bar/mol-K] 32 1 !Nterm, Ncoeff per term -0.0006569731294 0.1822957801 -3.649470141 123.2012107 -8613.578274 0.7978579691e-4 -0.0291148911 7.581821758 8780.488169 0.1423145989e-6 0.001674146131 -0.3200447909 0.2561766372e-4 -0.0005475934941 -0.4505032058 0.2013254653e-4 -0.1678941273e-6 0.0004207329271 -0.5444212996e-5 -8004.855011 -131930.4201 -49.5492393 80921.32177 -0.09870104061 2.020441562 -0.0001637417205 -0.7038944136 -0.1154324539e-6 0.1555990117e-4 -0.1492178536e-9 -0.1001356071e-7 0.2933963216e-6 @AUX !---Auxiliary function for Cp0 CP2 !Ideal gas heat capacity function for argon of Younglove. ? ?``````````````````````````````````````````````````````````````````````````````` ?Younglove, B.A., ? "Thermophysical Properties of Fluids. I. Argon, Ethylene, ? Parahydrogen, Nitrogen, Nitrogen Trifluoride, and Oxygen," ? J. Phys. Chem. Ref. Data, Vol. 11, Suppl. 1, pp. 1-11, 1982. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 1.0 8.31434 !Reducing parameters for T, Cp0 1 0 0 0 0 0 0 !Nterms: polynomial, exponential, cosh, sinh 2.5 0.0 @EOS !---Cubic equation of state--- PRT !Translated Peng-Robinson equation for argon. ? ?``````````````````````````````````````````````````````````````````````````````` ?Volume translation of Peng Robinson EOS. ? Translation computed so that sat. liquid density at Tr=0.7 matches FEQ Helmholtz equation ? of state for Ar of Tegeler et al. (1999). ? !``````````````````````````````````````````````````````````````````````````````` 83.8058 !Lower temperature limit [K] 2000.0 !Upper temperature limit [K] 1000000.0 !Upper pressure limit [kPa] 50.65 !Maximum density [mol/L] CPP !Pointer to Cp0 model 39.948 !Molar mass [g/mol] -0.00219 !Acentric factor 150.687 !Critical temperature [K] 4863.0 !Critical pressure [kPa] 13.4074 !Critical density [mol/L] 8.314472 !Gas constant [J/mol-K] 1 !Number of parameters -0.0034 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ #ETA !---Viscosity--- VS1 !Pure fluid viscosity model for argon of Lemmon and Jacobsen (2004). :DOI: 10.1023/B:IJOT.0000022327.04529.f3 ? ?``````````````````````````````````````````````````````````````````````````````` ?Lemmon, E.W. and Jacobsen, R.T, ? "Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air," ? Int. J. Thermophys., 25:21-69, 2004. ? ?The uncertainty is 0.5% in the dilute gas. Away from the dilute gas ? (pressures greater than 1 MPa and in the liquid), the uncertainties are ? as low as 1% between 270 and 300 K at pressures less than 100 MPa, and ? increase outside that range. The uncertainties are around 2% at ? temperatures of 180 K and higher. Below this and away from the critical ? region, the uncertainties steadily increase to around 5% at the triple ? points of the fluids. The uncertainties in the critical region are ? higher. ? !``````````````````````````````````````````````````````````````````````````````` 83.8058 !Lower temperature limit [K] 2000.0 !Upper temperature limit [K] 1000000.0 !Upper pressure limit [kPa] 50.65 !Maximum density [mol/L] 1 !Number of terms associated with dilute-gas function CI1 !Pointer to reduced effective collision cross-section model 0.335 !Lennard-Jones coefficient sigma [nm] 143.2 !Lennard-Jones coefficient epsilon/kappa [K] 1.0 1.0 !Reducing parameters for T, eta 0.168729283 0.5 !Chapman-Enskog term 0 !Number of terms for initial density dependence 0 6 0 0 0 0 !# resid terms: close-packed density; simple poly; numerator of rational poly; denominator of rat. poly; numerator of exponential; denominator of exponential 150.687 13.40742965 1.0 !Reducing parameters for T, rho, eta 12.19 -0.42 1. 0. 0 !Simple polynomial terms 13.99 0.0 2. 0. 0 0.005027 -0.95 10. 0. 0 -18.93 -0.5 5. 0. 2 -6.698 -0.9 1. 0. 4 -3.827 -0.8 2. 0. 4 NUL !Pointer to the viscosity critical enhancement auxiliary function (none used) #AUX !---Auxiliary function for the collision integral CI1 !Collision integral model for argon of Lemmon and Jacobsen (2004). ? ?``````````````````````````````````````````````````````````````````````````````` ?Lemmon, E.W. and Jacobsen, R.T, 2004. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 5 !Number of terms 0.431 0 !Coefficient, power of Tstar -0.4623 1 0.08406 2 0.005341 3 -0.00331 4 ================================================================================ #TCX !---Thermal conductivity--- TC1 !Pure fluid thermal conductivity model for argon of Lemmon and Jacobsen (2004). :DOI: 10.1023/B:IJOT.0000022327.04529.f3 ? ?``````````````````````````````````````````````````````````````````````````````` ?Lemmon, E.W. and Jacobsen, R.T, ? "Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air," ? Int. J. Thermophys., 25:21-69, 2004. doi: 10.1023/B:IJOT.0000022327.04529.f3 ? ?The uncertainty for the dilute gas is 2% with increasing uncertainties ? near the triple point. For the non-dilute gas, the uncertainty is 2% ? for temperatures greater than 170 K. The uncertainty is 3% at ? temperatures less than the critical point and 5% in the critical region, ? except for states very near the critical point. ? !``````````````````````````````````````````````````````````````````````````````` 83.8058 !Lower temperature limit [K] 2000.0 !Upper temperature limit [K] 1000000.0 !Upper pressure limit [kPa] 50.65 !Maximum density [mol/L] 2 0 !# terms for dilute gas function: numerator, denominator 150.687 0.001 !Reducing parameters for T, tcx 0.8158 -97.0 !Coefficient, power in T -0.4320 0.77 7 0 !# terms for background gas function: numerator, denominator 150.687 13.40742965 0.001 !Reducing parameters for T, rho, tcx 13.73 0. 1. 0. !Coefficient, powers of T, rho, exp(rho) 10.07 0. 2. 0. 0.7375 0. 4. 0. -33.96 -0.8 5. 2. 20.47 -1.2 6. 2. -2.274 -0.8 9. 2. -3.973 -0.5 1. 4. TK3 !Pointer to critical enhancement auxiliary function #AUX !---Auxiliary function for the thermal conductivity critical enhancement TK3 !Simplified thermal conductivity critical enhancement for argon of Lemmon and Jacobsen (2004). ? ?``````````````````````````````````````````````````````````````````````````````` ?Lemmon, E.W. and Jacobsen, R.T, 2004. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 9 0 0 0 !# terms: terms, spare, spare, spare 1.0 1.0 1.0 !Reducing parameters for T, rho, tcx [mW/(m-K)] 0.63 !Nu (universal exponent) 1.2415 !Gamma (universal exponent) 1.01 !R0 (universal amplitude) 0.065 !Z (universal exponent--not used for t.c., only viscosity) 1.0 !C (constant in viscosity eqn = 1/[2 - (alpha + gamma)/(2*nu)], but often set to 1) 0.13e-9 !Xi0 (amplitude) [m] 0.055 !Gam0 (amplitude) [-] 0.32e-9 !Qd_inverse (modified effective cutoff parameter) [m] 301.374 !Tref (reference temperature) [K] ******************************************************************************** @TCX !---Thermal conductivity--- TC3 !Pure fluid thermal conductivity model for argon of Younglove (1982). ? ?``````````````````````````````````````````````````````````````````````````````` ?Younglove, B.A., ? "Thermophysical Properties of Fluids. I. Argon, Ethylene, ? Parahydrogen, Nitrogen, Nitrogen Trifluoride, and Oxygen," ? J. Phys. Chem. Ref. Data, Vol. 11, Suppl. 1, pp. 1-11, 1982. ? !``````````````````````````````````````````````````````````````````````````````` 83.8058 !Lower temperature limit [K] 600.0 !Upper temperature limit [K] 100000.0 !Upper pressure limit [kPa] 50.65 !Maximum density [mol/L] 0.3297 !Lennard-Jones coefficient sigma [nm] 152.8 !Lennard-Jones coefficient epsilon/kappa [K] 0.16871158559818 !Const in Eq 20 = 5/16*(k*MW/1000/pi/Na)**0.5*1.0d12 0. !Exponent in Eq 20 for T 0.0264712871543 !Eta0 (eq 20): coeffs of {(e/kT)**((4-n)/3)} -0.216629583011974 0.709700888884514 -1.21908891344223 1.20168985706305 -0.700084760049098 0.24816605762696 -0.0479479287295 0.00393679190444 9.64428741429e-4 !Coefficient for initial density dependence of viscosity (eq 21); Fv(1) 3.02391316601e-4 !Fv(2) 1. !Fv(3) 152.8 !Fv(4) -33.327027332 !Coefficients for residual viscosity, eqs (22 - 25) -355.59415848 !Ev(2) 22.2441164817987 !Ev(3) 1663.62775376509 !Ev(4) 0. !Ev(5) 0. !Ev(6) 0. !Ev(7) 25.0325423049965 !Ev(8) 1.7124 !F 0.00000003669 !Rm TK3 !Pointer to the critical enhancement auxiliary function @ETA !---Viscosity--- VS2 !Pure fluid viscosity model for argon of Younglove (1982). ? ?``````````````````````````````````````````````````````````````````````````````` ?Younglove, B.A., ? "Thermophysical Properties of Fluids. I. Argon, Ethylene, ? Parahydrogen, Nitrogen, Nitrogen Trifluoride, and Oxygen," ? J. Phys. Chem. Ref. Data, Vol. 11, Suppl. 1, pp. 1-11, 1982. ? !``````````````````````````````````````````````````````````````````````````````` 83.8058 !Lower temperature limit [K] 600.0 !Upper temperature limit [K] 100000.0 !Upper pressure limit [kPa] 50.65 !Maximum density [mol/L] CI2 !Pointer to collision integral model 0.3297 !Lennard-Jones coefficient sigma [nm] 152.8 !Lennard-Jones coefficient epsilon/kappa [K] 0.16871158559818 !Const in Eq 19 = 5/16*(k*MW/1000/pi/Na)**0.5*1.0d12 0.0 !Exponent in Eq 20 for T 0.00585384107393 !Coefficient for initial density dependence of viscosity (eq 21); Fv(1) -0.0030954676525 !Fv(2) 1.4 !Fv(3) 152.8 !Fv(4) -12.313579086 !Coefficients for residual viscosity, eqs (22 - 25) 40.136071933 !Ev(2) 11.6160872385243 !Ev(3) -413.04094973717 !Ev(4) 0.0413624595833 !Ev(5) 7.96883967907912 !Ev(6) 234.196850483958 !Ev(7) 13.4424752177831 !Ev(8) NUL !Pointer to the viscosity critical enhancement auxiliary function (none used) @AUX !---Auxiliary function for the collision integral CI2 !Collision integral model for argon of Younglove (1982). ? ?``````````````````````````````````````````````````````````````````````````````` ?Younglove, B.A. (1982). ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 9 !Number of terms 25.7830291943396 0 !eta0 (eq 20): coeffs of {(e/kT)**((4-n)/3)} -234.320222858983 0 814.636688705024 0 -1452.04353466585 0 1467.17535558104 0 -870.164951237067 0 313.024934147423 0 -61.2072628957372 0 5.07700488990665 0 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ @TRN !---ECS Transport--- ECS !Extended Corresponding States model (Nitrogen reference); predictive mode for argon. ? ?``````````````````````````````````````````````````````````````````````````````` ?Klein, S.A., McLinden, M.O., and Laesecke, A., "An Improved Extended Corresponding States Method for Estimation of Viscosity of Pure Refrigerants and Mixtures," Int. J. Refrigeration, 20(3):208-217, 1997. doi: 10.1016/S0140-7007(96)00073-4. ?McLinden, M.O., Klein, S.A., and Perkins, R.A., "An Extended Corresponding States Model for the Thermal Conductivity of Refrigerants and Refrigerant Mixtures," Int. J. Refrigeration, 23(1):43-63, 2000. doi: 10.1016/S0140-7007(99)00024-9 ? ?The Lennard-Jones parameters were taken from Reid, R.C., Prausnitz, J.M., and Poling, B.E., "The Properties of Gases and Liquids," 4th edition, New York, McGraw-Hill Book Company, 1987. ? !``````````````````````````````````````````````````````````````````````````````` 83.8058 !Lower temperature limit [K] 700.0 !Upper temperature limit [K] 1000000.0 !Upper pressure limit [kPa] 50.65 !Maximum density [mol/L] FEQ NITROGEN.FLD VS1 !Model for reference fluid viscosity TC1 !Model for reference fluid thermal conductivity NUL !Large molecule identifier 1 !Lennard-Jones flag (0 or 1) (0 => use estimates) 0.335 !Lennard-Jones coefficient sigma [nm] 143.2 !Lennard-Jones coefficient epsilon/kappa [K] 1 0 0 !Number of terms in f_int term in Eucken correlation, spare1, spare2 0.00132 0. 0. 0. !Coefficient, power of T, spare1, spare2 1 0 0 !Number of terms in psi (visc shape factor): poly,spare1,spare2 1.0 0. 0. 0. !Coefficient, power of Tr, power of Dr, spare 1 0 0 !Number of terms in chi (t.c. shape factor): poly,spare1,spare2 1.0 0. 0. 0. !Coefficient, power of Tr, power of Dr, spare TK3 !Pointer to critical enhancement auxiliary function ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #STN !---Surface tension--- ST1 !Surface tension model for argon of Mulero et al. (2012). :DOI: 10.1063/1.4768782 ? ?``````````````````````````````````````````````````````````````````````````````` ?Mulero, A., Cachadiña, I., and Parra, M.I., ? "Recommended Correlations for the Surface Tension of Common Fluids," ? J. Phys. Chem. Ref. Data, 41(4), 043105, 2012. doi: 10.1063/1.4768782 ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 1 !Number of terms in surface tension model 150.687 !Critical temperature used in fit (dummy) 0.037 1.25 !Sigma0 and n #DE !---Dielectric constant--- DE3 !Dielectric constant model for argon of Harvey and Lemmon (2005). :DOI: 10.1007/s10765-005-2351-5 ? ?``````````````````````````````````````````````````````````````````````````````` ?Harvey, A.H. and Lemmon, E.W., ? "Method for Estimating the Dielectric Constant of Natural Gas Mixtures," ? Int. J. Thermophys., 26(1):31-46, 2005. doi: 10.1007/s10765-005-2351-5 doi: 10.1007/s10765-005-2351-5 ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 273.16 1000.0 1.0 !Reducing parameters for T and D 0 1 3 0 0 0 !Number of terms in dielectric constant model 4.1414 0. 1. 0. !Coefficient, T exp, D exp 1.597 0. 2. 0. 0.262 1. 2. 0. -117.9 0. 3.1 0. #MLT !---Melting line--- ML1 !Melting line model for argon of Tegeler et al. (1999). :DOI: 10.1063/1.556037 ? ?``````````````````````````````````````````````````````````````````````````````` ?Tegeler, Ch., Span, R., and Wagner, W., ? "A New Equation of State for Argon Covering the Fluid Region for ? Temperatures from the Melting Line to 700 K at Pressures up to 1000 MPa," ? J. Phys. Chem. Ref. Data, 28(3):779-850, 1999. doi: 10.1063/1.556037 ? !``````````````````````````````````````````````````````````````````````````````` 83.8058 !Lower temperature limit [K] 700.0 !Upper temperature limit [K] 0. ! 0. ! 83.8058 68.891 !Reducing temperature and pressure 5 0 0 0 0 0 !Number of terms in melting line equation 1.0 0.0 !Coefficients and exponents -7476.26651 1.05 9959.06125 1.275 7476.26651 0.0 -9959.06125 0.0 #SBL !---Sublimation line--- SB3 !Sublimation line model for argon of Lemmon (2002). :DOI: ? ?``````````````````````````````````````````````````````````````````````````````` ?Lemmon, E.W., 2002. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 83.8058 !Upper temperature limit [K] 0. ! 0. ! 83.8058 68.891 !Reducing temperature and pressure 0 1 0 0 0 0 !Number of terms in sublimation line equation -11.1307 1. !Coefficients and exponents #PS !---Vapor pressure--- PS5 !Vapor pressure equation for argon of Tegeler et al. (1999). ? ?``````````````````````````````````````````````````````````````````````````````` ?Functional Form: P=Pc*EXP[SUM(Ni*Theta^ti)*Tc/T] where Theta=1-T/Tc, Tc and Pc ? are the reducing parameters below, which are followed by rows containing Ni and ti. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 150.687 4863.0 !Reducing parameters 4 0 0 0 0 0 !Number of terms in equation -5.9409785 1.0 1.3553888 1.5 -0.4649761 2.0 -1.5399043 4.5 #DL !---Saturated liquid density--- DL4 !Saturated liquid density equation for argon of Tegeler et al. (1999). ? ?``````````````````````````````````````````````````````````````````````````````` ?Functional Form: D=Dc*EXP[SUM(Ni*Theta^(ti/3))] where Theta=1-T/Tc, Tc and Dc are ? the reducing parameters below, which are followed by rows containing Ni and ti. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 150.687 13.40742965 !Reducing parameters 4 0 0 0 0 0 !Number of terms in equation 1.5004264 1.002 -0.3138129 2.0 0.086461622 7.0 -0.041477525 12.0 #DV !---Saturated vapor density--- DV6 !Saturated vapor density equation for argon of Lemmon (2010). ? ?``````````````````````````````````````````````````````````````````````````````` ?Equation of Tegeler appears to be wrong, and new equation was fitted here. ? ?Functional Form: D=Dc*EXP[SUM(Ni*Theta^(ti/3))*Tc/T] where Theta=1-T/Tc, Tc and Dc are ? the reducing parameters below, which are followed by rows containing Ni and ti. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 150.687 13.40742965 !Reducing parameters 4 0 0 0 0 0 !Number of terms in equation -1.3721 0.96 -2.9182 2.16 0.097930 3.75 -2.2898 13.02 @END c 1 2 3 4 5 6 7 8 c2345678901234567890123456789012345678901234567890123456789012345678901234567890 @TCX !Thermal conductivity model specification TC1 pure fluid thermal conductivity model of Younglove and Hanley (1986). ? ?``````````````````````````````````````````````````````````````````````````````` ?Younglove, B.A. and Hanley, H.J.M., ? "The Viscosity and Thermal Conductivity Coefficients of Gaseous and ? Liquid Argon," ? J. Phys. Chem. Ref. Data, 15(4):1323-1337, 1986. ? !``````````````````````````````````````````````````````````````````````````````` 83.8058 !Lower temperature limit [K] 700.0 !Upper temperature limit [K] 1000000.0 !Upper pressure limit [kPa] 50.65 !Maximum density [mol/L] 9 0 !# terms for dilute gas function: numerator, denominator 1.0 0.001 !Reducing parameters for T, tcx -67009.76192 -1. !Coefficient, power in T 61522.55283 -0.666666666667 -20492.18286 -0.333333333333 2216.966254 0. 357.9189325 0.333333333333 -136.4658914 0.666666666667 17.18671649 1. -1.018933154 1.333333333333 0.02397996932 1.666666666667 11 3 !# terms for background gas function: numerator, denominator 1.0 1.0 0.001 !Reducing parameters for T, rho (rho_c), tcx 1.536300190 0. 1. 0. !Coefficient, powers of T, rho, spare for future use -233.2533199 -1. 1. 0. -0.03027085824 0. 2. 0. 18.96279196 -1. 2. 0. 10.54230664 -2. 2. 0. 0.2588139028e-4 0. 3. 0. -0.4546798772 -1. 3. 0. 4.320206998 -2. 3. 0. 0.1593643304e-4 0. 4. 0. 0.0001262253904 -1. 4. 0. -0.002937213042 -2. 4. 0. 1.0 0. 0. 0. -0.02262773007 0. 1. 0. -0.1445619495 -1. 1. 0. TK4 !Pointer to critical enhancement auxiliary function @AUX !---Thermal conductivity critical enhancement model TK4 thermal conductivity critical enhancement ? ?``````````````````````````````````````````````````````````````````````````````` ?Younglove, B.A. and Hanley, H.J.M., 1986. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 6 0 0 0 !# terms 150.86 4905.8 13.41 0.001 !Reducing parameters for T, rho, tcx [mW/(m-K)] 1.02 1.380658e-23 0.46807 39.8 5.45 0.60795 @TCX !Thermal conductivity model specification TC1 pure fluid thermal conductivity model of Perkins et al. (1991). ? ?``````````````````````````````````````````````````````````````````````````````` ?Perkins, R.A., Friend, D.G., Roder, H.M., and Nieto de Castro, C.A., ? "Thermal Conductivity Surface of Argon: A Fresh Analysis," ? Int. J. Thermophys., 12(6):965-984, 1991. doi: 10.1007/BF00503513 ? ?The uncertainty in thermal conductivity is 2.2%. ? !``````````````````````````````````````````````````````````````````````````````` 55.0 !Lower temperature limit [K] 2500.0 !Upper temperature limit [K] 1000000.0 !Upper pressure limit [kPa] 50.65 !Maximum density [mol/L] 9 0 !# terms for dilute gas function: numerator, denominator 1.0 0.001 !Reducing parameters for T, tcx 12250.67272 -1. !Coefficient, power in T -9096.222831 -0.66666666666666 2744.958263 -0.33333333333333 -417.0419051 0. 25.27591169 0.33333333333333 1.604421067 0.66666666666666 -0.2618841031 1. 0.01381696924 1.33333333333333 -0.0002463115922 1.66666666666666 4 0 !# terms for background gas function: numerator, denominator 1.0 1. 1. !Reducing parameters for T, rho (rho_c), tcx 0.000757894 0. 1. 0. !Coefficient, powers of T, rho, spare for future use 0.612624e-4 0. 2. 0. -0.205353e-5 0. 3. 0. 0.745621e-7 0. 4. 0. TK4 !Pointer to critical enhancement auxiliary function !The following model was moved here on 2/24/2016 because the VS3 model was changed ! and this one will no longer work with version 9.2 and higher. @ETA !Viscosity model specification VS3 pure fluid viscosity model of Younglove and Hanley (1986). ? ?``````````````````````````````````````````````````````````````````````````````` ?Younglove, B.A. and Hanley, H.J.M., ? "The Viscosity and Thermal Conductivity Coefficients of Gaseous and Liquid Argon," ? J. Phys. Chem. Ref. Data, 15(4):1323-1337, 1986. doi: 10.1063/1.555765 ? ?The uncertainty in viscosity is 2% below 100 MPa and 3% for higher pressures. ? !``````````````````````````````````````````````````````````````````````````````` 55.0 !Lower temperature limit [K] 2500.0 !Upper temperature limit [K] 1000000.0 !Upper pressure limit [kPa] 50.65 !Maximum density [mol/L] 9 0 !# terms for dilute gas function: numerator, denominator 1.0 1.0 !Reducing parameters for T, eta -89731.88257 -1.0 !Coefficient, power in T 82591.13473 -0.666666666667 -27664.75915 -0.333333333333 3068.539784 0.0 455.3103615 0.333333333333 -179.3443839 0.666666666667 22.72225106 1.0 -1.350672796 1.333333333333 0.0318369323 1.666666666667 11 3 !# terms for background gas function: numerator, denominator 1.0 1.0 1.0 !Reducing parameters for T, rho (rho_c), eta 0.5927733783 0. 1. 0. 0 !Coefficient, powers of T, rho, spare for future use -42.51221169 -1. 1. 0. 0 -0.02698477165 0. 2. 0. 0 37.27762288 -1. 2. 0. 0 -3958.508720 -2. 2. 0. 0 0.003636730841 0. 3. 0. 0 -2.633471347 -1. 3. 0. 0 293.6563322 -2. 3. 0. 0 -0.3811869019e-4 0. 4. 0. 0 0.04451947464 -1. 4. 0. 0 -5.385874487 -2. 4. 0. 0 1.0 0. 0. 0. 0 -0.01115054926 0. 1. 0. 0 -1.328893444 -1. 1. 0. 0 TK3 !Pointer to critical enhancement auxiliary function