Krypton !Short name 7439-90-9 !CAS number Krypton !Full name Kr !Chemical formula {Kr} R-784 !Synonym 83.798 !Molar mass [g/mol] 115.775 !Triple point temperature [K] 119.73 !Normal boiling point [K] 209.48 !Critical temperature [K] 5525.0 !Critical pressure [kPa] 10.85 !Critical density [mol/L] -0.000894 !Acentric factor 0.0 !Dipole moment [Debye]; (exactly zero for monatomic molecules) NBP !Default reference state 10.0 !Version number 1056, 1970 !UN Number :UN: cryogen !Family :Family: 0.0 !Heating value (upper) [kJ/mol] :Heat: 1S/Kr !Standard InChI String :InChi: DNNSSWSSYDEUBZ-UHFFFAOYSA-N !Standard InChI Key :InChiKey: 434e2a40 (ethane) !Alternative fluid for mixing rules :AltID: d7c8c510 !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 ! 04-06-98 EWL, Original version. ! 11-18-98 EWL, Add equation of state of Polt et al. (1992). ! 07-11-00 EWL, Remove Juza equation and replace with Lemmon and Span equation. ! 04-12-00 EWL, Update Lemmon and Span short EOS. ! 05-20-01 EWL, Add sublimation line. ! 03-29-04 EWL, Update Lemmon and Span short EOS. ! 07-07-04 EWL, Update Tmax for transport equations. ! 08-05-04 EWL, Add Harvey and Lemmon dielectric correlation. ! 08-08-05 EWL, Change first coef. in melting line equation slightly to match EOS at Ttrp. ! 01-30-07 EWL, Change triple point from 115.77 to 115.775 in accordance with Bedford et al., Metrologia, 33:133, 1996. ! 07-01-10 CKL, Add ancillary equations. ! 12-06-12 EWL, Add surface tension coefficients of Mulero et al. (2012). ! 04-03-17 MLH, Revise thermal conductivity, viscosity. ! 08-06-17 EWL, Change melting point at Ttrp to match triple point pressure of Lemmon and Span. ! 12-11-17 MLH, Adjust dilute gas viscosity to match ref. value at 25 C from Berg and Moldover, JPCRD 41(4) 043104 (2012). ! 02-15-18 MLH, Revise thermal conductivity to account for changes in viscosity made 12.11.17 ! 03-01-18 MLH, Revise cutoff in critical enhancement. ! 04-02-18 MLH, Revise k to reflect bug fix due to different R values for internal contribution of thermal conductivity. ________________________________________________________________________________ #EOS !---Equation of state--- FEQ !Helmholtz equation of state for krypton of Lemmon and Span (2006). :TRUECRITICALPOINT: 209.48 10.85 !True EOS critical point [K, mol/L] (where dP/dD=0 and d^2P/dD^2=0 at constant T) :DOI: 10.1021/je050186n ? ?``````````````````````````````````````````````````````````````````````````````` ?Lemmon, E.W. and Span, R., ? "Short Fundamental Equations of State for 20 Industrial Fluids," ? J. Chem. Eng. Data, 51(3):785-850, 2006. doi: 10.1021/je050186n ? ?The equation of state is valid from the triple point to 750 K with ? pressures to 200 MPa, although the uncertainties increase substantially ? above 100 MPa. The uncertainties in density are typically 0.2% below 100 ? MPa, increasing to 1% at pressures up to 200 MPa. The uncertainty in vapor ? pressure is 0.2% and the uncertainties in speed of sound are 0.01% in the ? vapor phase (including supercritical conditions) at low pressures, 1% below ? 20 MPa in the liquid phase, and 3% below 100 MPa at other state points. ? The limited amount of heat capacity data show that the uncertainty is 1% ? near the triple point, and uncertainties in heat capacities at other states ? are probably within 2%, at least at pressures up to 20 MPa. ? !``````````````````````````````````````````````````````````````````````````````` 115.775 !Lower temperature limit [K] 750.0 !Upper temperature limit [K] 200000.0 !Upper pressure limit [kPa] 33.42 !Maximum density [mol/L] CPP !Pointer to Cp0 model 83.798 !Molar mass [g/mol] 115.775 !Triple point temperature [K] 73.53 !Pressure at triple point [kPa] 29.2 !Density at triple point [mol/L] 119.73 !Normal boiling point temperature [K] -0.000894 !Acentric factor 209.48 5525.0 10.85 !Tc [K], pc [kPa], rhoc [mol/L] 209.48 10.85 !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 0.83561 0.25 1. 0. !a(i),t(i),d(i),l(i) -2.3725 1.125 1. 0. 0.54567 1.5 1. 0. 0.014361 1.375 2. 0. 0.066502 0.25 3. 0. 0.0001931 0.875 7. 0. 0.16818 0.625 2. 1. -0.033133 1.75 5. 1. -0.15008 3.625 1. 2. -0.022897 3.625 4. 2. -0.021454 14.5 3. 3. 0.0069397 12.0 4. 3. #AUX !---Auxiliary function for Cp0 CPP !Ideal gas heat capacity function for krypton of Lemmon and Span (2006). ? ?``````````````````````````````````````````````````````````````````````````````` ?Lemmon, E.W. and Span, R., 2006. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 1.0 8.314472 !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 krypton of Lemmon and Span (2006). ? ?``````````````````````````````````````````````````````````````````````````````` ?Lemmon, E.W. and Span, R., 2006. ? !``````````````````````````````````````````````````````````````````````````````` 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 -3.7506404605274408 0.0 !aj, ti for [ai*tau**ti] terms 3.7798013718120207 1.0 !aj, ti for [ai*tau**ti] terms #AUX !---Auxiliary function for PH0 PH0 !Ideal gas Helmholtz form for krypton. ? ?``````````````````````````````````````````````````````````````````````````````` ?Lemmon, E.W. and Span, R., 2006. ? !``````````````````````````````````````````````````````````````````````````````` 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 -3.7506412806 0.0 !aj, ti for [ai*tau**ti] terms 3.7798018435 1.0 -------------------------------------------------------------------------------- @EOS !---Equation of state--- FE1 !Helmholtz equation of state for krypton of Polt et al. (1992). ? ?``````````````````````````````````````````````````````````````````````````````` ?Polt, A., Platzer, B., and Maurer, G., ? "Parameter der thermischen Zustandsgleichung von Bender fuer 14 ? mehratomige reine Stoffe," ? Chem. Tech. (Leipzig), 44(6):216-224, 1992. ? !``````````````````````````````````````````````````````````````````````````````` 115.775 !Lower temperature limit [K] 780.0 !Upper temperature limit [K] 375000.0 !Upper pressure limit [kPa] 33.55 !Maximum density [mol/L] CP1 !Pointer to Cp0 model 83.7 !Molar mass [g/mol] 115.775 !Triple point temperature [K] 73.476 !Pressure at triple point [kPa] 29.249 !Density at triple point [mol/L] 119.73 !Normal boiling point temperature [K] -0.0015 !Acentric factor 209.4 5502.2 10.860215 !Tc [K], pc [kPa], rhoc [mol/L] 209.4 10.860215 !Reducing parameters [K, mol/L] 8.3143 !Gas constant [J/mol-K] 22 4 0 0 0 0 0 0 0 0 0 0 !# terms and # coefs/term for normal terms, Gaussian terms, and Gao terms -0.402218741560 3.0 0. 0. !a(i),t(i),d(i),l(i) 0.679250544381 4.0 0. 0. -0.187886980286 5.0 0. 0. 0.603399982935 0.0 1. 0. -1.77297564389 1.0 1. 0. 0.581208430222 2.0 1. 0. -0.733585469788 3.0 1. 0. 0.164651929067 4.0 1. 0. -0.0319923148922 0.0 2. 0. 0.333278228743 1.0 2. 0. 0.0219652478083 2.0 2. 0. 0.0751994891628 0.0 3. 0. -0.212109737251 1.0 3. 0. -0.00645185506524 0.0 4. 0. 0.04091756102 1.0 4. 0. 0.00169416098754 1.0 5. 0. 0.402218741560 3.0 0. 2. -0.679250544381 4.0 0. 2. 0.187886980286 5.0 0. 2. 0.108265263587 3.0 2. 2. -0.137102675805 4.0 2. 2. -0.110549803007 5.0 2. 2. @AUX !---Auxiliary function for Cp0 CP1 !Ideal gas heat capacity function for krypton. ? ?``````````````````````````````````````````````````````````````````````````````` ?Polt, A., Platzer, B., and Maurer, G., ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 1.0 83.7 !Reducing parameters for T, Cp0 1 0 0 0 0 0 0 !Nterms: polynomial, exponential, cosh, sinh 0.2483363 0.0 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ #TRN !---ECS Transport--- ECS !Extended Corresponding States model (Nitrogen reference); predictive mode for krypton. :DOI: 10.6028/NIST.IR.8209 ? ?``````````````````````````````````````````````````````````````````````````````` ?*** ESTIMATION METHOD *** NOT STANDARD REFERENCE QUALITY *** ?Huber, M.L., "Models for the Viscosity, Thermal Conductivity, and Surface Tension ? of Selected Pure Fluids as Implemented in REFPROP v10.0," NISTIR 8209, 2018. ? doi: 10.6028/NIST.IR.8209 ? ?Uncertainty of viscosity in the liquid phase is 30%, data unavailable. ? Uncertainty of viscosity in the gas phase at atmospheric pressure is 3%. ? ?Uncertainty of thermal conductivity is 4% at pressures to 50 MPa. ? ?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. ? !``````````````````````````````````````````````````````````````````````````````` 115.775 !Lower temperature limit [K] 750.0 !Upper temperature limit [K] 100000.0 !Upper pressure limit [kPa] 33.42 !Maximum density [mol/L] FEQ NITROGEN.FLD VS1 !Model for reference fluid viscosity TC1 !Model for reference fluid thermal conductivity BIG !Large molecule identifier 1.008291 0. 0. 0. !Large molecule parameters 1 !Lennard-Jones flag (0 or 1) (0 => use estimates) 0.3655 !Lennard-Jones coefficient sigma [nm] for ECS method 178.9 !Lennard-Jones coefficient epsilon/kappa [K] for ECS method 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; dummy value - term is zero 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 2 0 0 !Number of terms in chi (t.c. shape factor): poly,spare1,spare2 0.962573 0. 0. 0. !Coefficient, power of Tr, power of Dr, spare -0.0118156 0. 1. 0. !Coefficient, power of Tr, power of Dr, spare TK3 !Pointer to critical enhancement auxiliary function #AUX !---Auxiliary function for the thermal conductivity critical enhancement TK3 !Simplified thermal conductivity critical enhancement for krypton of Perkins et al. (2013). ? ?``````````````````````````````````````````````````````````````````````````````` ?Perkins, R.A., Sengers, J.V., Abdulagatov, I.M., and Huber, M.L., ? "Simplified Model for the Critical Thermal-Conductivity Enhancement in Molecular Fluids," ? Int. J. Thermophys., 34(2):191-212, 2013. doi: 10.1007/s10765-013-1409-z ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 9 0 0 0 !# terms: CO2-terms, spare, spare, spare 1.0 1.0 1.0 !Reducing parameters for T, rho, tcx [mW/(m-K)] 0.63 !Nu (universal exponent) 1.239 !Gamma (universal exponent) 1.02 !R0 (universal amplitude) 0.063 !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) 0.168e-9 !Xi0 (amplitude) [m] 0.058 !Gam0 (amplitude) [-] 0.437e-9 !Qd_inverse (modified effective cutoff parameter) [m] 314.22 !Tref (reference temperature)=1.5*Tc [K] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #STN !---Surface tension--- ST1 !Surface tension model for krypton of Mulero et al. (2012). :DOI: 10.1063/1.4768782 ? ?``````````````````````````````````````````````````````````````````````````````` ?Mulero, A., Cachadiņa, 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 209.48 !Critical temperature used in fit (dummy) 0.0447 1.245 !Sigma0 and n #DE !---Dielectric constant--- DE3 !Dielectric constant model for krypton 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 ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 10000. ! 0. ! 0. ! 273.16 1000.0 1.0 !Reducing parameters for T and D 0 1 4 0 0 0 !Number of terms in dielectric constant model 6.273 0. 1. 0. !Coefficient, T exp, D exp 6.485 0. 2. 0. 13.48 1. 2. 0. -82.51 0. 2.7 0. -170.4 1. 2.7 0. #MLT !---Melting line--- ML1 !Melting line model for krypton of Michels and Prins (1962). :DOI: 10.1016/0031-8914(62)90096-4 ? ?``````````````````````````````````````````````````````````````````````````````` ?Michels, A. and Prins, C., ? "The Melting Lines of Argon, Krypton and Xenon up to 1500 Atm; ? Representation of the Results by a Law of Corresponding States," ? Physica, 28:101-116, 1962. ? !``````````````````````````````````````````````````````````````````````````````` 115.775 !Lower temperature limit [K] 800.0 !Upper temperature limit [K] 0. ! 0. ! 1. 101.325 !Reducing temperature and pressure 2 0 0 0 0 0 !Number of terms in melting line equation -2345.921 0.0 !Coefficients and exponents 1.080476685 1.6169841 #SBL !---Sublimation line--- SB3 !Sublimation line model for krypton of Lemmon (2002). :DOI: ? ?``````````````````````````````````````````````````````````````````````````````` ?Lemmon, E.W., 2002. ? !``````````````````````````````````````````````````````````````````````````````` 0. ! 115.775 !Upper temperature limit [K] 0. ! 0. ! 115.775 73.197 !Reducing temperature and pressure 0 1 0 0 0 0 !Number of terms in sublimation line equation -11.5616 1. !Coefficients and exponents #PS !---Vapor pressure--- PS5 !Vapor pressure equation for krypton of Lemmon (2010). ? ?``````````````````````````````````````````````````````````````````````````````` ?Lemmon, C.K. and Lemmon, E.W., 2010. ? ?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. ! 209.48 5525.0 !Reducing parameters 5 0 0 0 0 0 !Number of terms in equation -5.9697 1.0 1.2673 1.5 -0.95609 2.95 -35.630 9.3 56.884 10.4 #DL !---Saturated liquid density--- DL1 !Saturated liquid density equation for krypton of Lemmon (2010). ? ?``````````````````````````````````````````````````````````````````````````````` ?Lemmon, C.K. and Lemmon, E.W., 2010. ? ?Functional Form: D=Dc*[1+SUM(Ni*Theta^ti)] 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. ! 209.48 10.85 !Reducing parameters 5 0 0 0 0 0 !Number of terms in equation 20.593 0.62 -65.490 0.84 94.407 1.07 -69.678 1.34 22.810 1.6 #DV !---Saturated vapor density--- DV3 !Saturated vapor density equation for krypton of Lemmon (2010). ? ?``````````````````````````````````````````````````````````````````````````````` ?Lemmon, C.K. and Lemmon, E.W., 2010. ? ?Functional Form: D=Dc*EXP[SUM(Ni*Theta^ti)] 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. ! 209.48 10.85 !Reducing parameters 6 0 0 0 0 0 !Number of terms in equation -6.4163 0.525 8.9956 0.77 -10.216 1.04 -13.477 3.2 -211.52 8.3 213.75 9.0 @END c 1 2 3 4 5 6 7 8 c2345678901234567890123456789012345678901234567890123456789012345678901234567890