Description of the Software FLUIDCAL (Dynamic Link Library

RUHR-UNIVERSITÄT BOCHUM

Prof. em. Dr.-Ing. Wolfgang Wagner Lehrstuhl für Thermodynamik Fakultät für Maschinenbau

UNIVERSITÄTSSTRASSE 150 • GEBÄUDE IB • RAUM 5/36

TH ERM D YN A M I KOTH ERM D YN A M I KO

Description of the Software FLUIDCAL (Dynamic Link Library) for the Calculation of Thermodynamic and Transport Properties

of a Great Number of Fluids

Contents 1 References and range of validity ………………………………..……………… 2 2 Calculable states ………….……………………………………………………….. 2 2.1 List of integrated fluids …………………………………..…………………….. 2 2.2 Calculable thermodynamic and transport properties ….……………………….. 4 2.3 Combinations of input variables ………………..……………………………… 6 3 Calculating the several thermodynamic and transport properties ………… 7 3.1 Functions depending on temperature and pressure …….……………………… 7 3.2 Functions depending on temperature and density ……..………………………. 10 3.3 Functions depending on pressure and specific entropy ……………………… 13 3.4 Functions depending on pressure and specific enthalpy …….………………… 14 3.5 Functions depending on specific enthalpy and specific entropy ………………. 14 3.6 Further functions for the calculation of the density depending on temperature and specific entropy or on temperature and specific enthalpy………..15 3.7 Further functions for the calculation of the temperature depending on density and pressure, density and specific entropy, or on density and specific enthalpy …. 15 3.8 Functions depending on temperature …………………………………..…….. 16 3.9 Functions for the calculation of the vapour fraction depending on temperature and specific volume or spec. enthalpy or spec. entropy or spec. internal energy …16 3.10 Functions for the calculation of properties on the saturated-liquid and saturated- vapour phase boundary depending on temperature or pressure or density and the function ρ (T, x) …… 17 3.11 Functions for the output of critical values and the limits of the range of validity ……………………………………….……………………… 21 4 Installation and integration of the software ……………..……………………. 23 5 Terms of use …………………………………………………..………………….. 25 5.1 Developers of the software and copyright ……………………………………… 25 5.2 Exclusion of liability ……………………………………………..…………… 26 6 References of the used equations ……………………………………………. 27 7 Ranges of validity ……………………………………………………..…………. 35 8 Reference points for the specific enthalpy and specific entropy………….. 38 This software description contains 42 pages.

D-44780 Bochum • Tel: +49-234-32-29033 • Fax: +49-234-32-14945 [email protected] • www.ruhr-uni-bochum.de/thermo

Status: 19.07.2012

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1 References and range of validity The calculation of thermodynamic and transport properties by using the functions given in the dynamic link library FLUIDCAL.DLL is based on the corresponding equations of state, of which the references are listed in Section 6. The equations used for the calculation of thermodynamic and transport properties of the implemented fluids cover different ranges of validity*

2 Calculable states

, which are listed in Section 7 of this manual.

2.1 List of integrated substances From the delivered software package the thermodynamic and transport properties of the following substances can be calculated. The table contains the names of the integrated fluids with the corresponding substantial numbers (SUBNR), which have to be used in the call of the functions listed in Section 3 and an information about the possibility of the transport property calculation (TPC / VIS = viscosity, TCON = thermal conductivity).

Table 1 Integrated substances

TPC Substance SUBNR VIS TCON

Methane 1 Yes Yes Ethane 2 Yes Yes Propane 3 Yes Yes Butane 4 Yes Yes Pentane 5 Yes Yes Hexane 6 Yes No Heptane 7 Yes No Octane 8 Yes No Nonane 9 Yes No Decane 10 Yes No Ethanol 11 No No n-Dodecane 12 No No Acetone 13 No No Isobutene 14 No No Isobutane 15 Yes Yes

*When considering larger uncertainties, some equations of state can be extrapolated beyond the range of

validity, for details see the corresponding references given in Section 7.

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Table 1 continued


Ethene 16 Yes Yes Propene 17 No No Cyclohexane 18 No No Methanol 19 No No Benzene 20 No No Toluene 21 No No Ethylbenzene 22 No No Propylbenzene 23 No No Cyclopentane 25 No No Neopentane 26 No No Isopentane 27 No No Isohexane 28 No No Diisopropyl (2,3 Dimethylbutane) 29 No No 1-Butene 30 No No Diethylether 32 No No Neon 40 No No Argon 41 Yes Yes Nitrogen 42 Yes Yes Oxygen 43 Yes Yes Chlorine 44 No No Hydrogen 45 No No Fluorine 46 No No Krypton 47 No No Xenon 48 No No Helium 49 No No Water 50 Yes Yes Carbon dioxide 51 Yes Yes Sulfur hexafluoride 52 No No Ammonia 53 Yes Yes Nitrous oxide 54 No No Hydrogen sulfide 55 No No Carbon monoxide 56 No No Carbonyl sulfide 57 No No

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Table 1 continued


Sulfur dioxide 58 No No R116 59 No No R11 60 Yes No R12 61 Yes No R22 62 Yes Yes R23 63 No No R32 64 Yes Yes R41 65 No No R113 66 No No R123 67 Yes Yes R124 68 Yes Yes R125 69 Yes Yes R134a 70 Yes Yes R141b 71 No No R142b 72 No No R143a 73 Yes Yes R152a 74 Yes Yes R218 75 No No R227ea 76 No No trans-2-Butene 77 No No cis-2-Butene 78 No No R245fa 79 No No R1234yf 80 No No Hydrogen chloride 81 No No

2.2 Calculable thermodynamic and transport properties Based on the corresponding equations mentioned in Section 6, the thermodynamic and transport properties listed in Table 2 of the substances listed in Table 1 can be calculated with the help of this software package. The units of the different properties, which are valid for all input and output variables of the functions listed in Sections 2.3 and 3, are given in the last column of Table 2. The reference points for the calculated specific enthalpy h and specific entropy s are given in Section 8.

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Table 2 Calculable thermodynamic and transport properties

Property Symbol Symbol in the software Unit

Thermodynamic properties

Pressure p P MPa

Temperature T T K

Density ρ D kg m−3 Specific volume* v , v = 1/ρ − m3 kg−1

Specific enthalpy h H kJ kg−1 Specific entropy s S kJ kg−1 K−1 Specific isobaric heat capacity cp CP kJ kg−1 K−1 Specific isochoric heat capacity cv CV kJ kg−1 K−1 Speed of sound w W m s−1 Specific internal energy u U kJ kg−1 Specific Helmholtz free energy, f = u – Ts f F kJ kg−1 Specific Gibbs free energy, g = h – Ts g G kJ kg−1 Isentropic exponent, κ = – (v /p)(∂p/∂v)s κ CAP − Fugacity f + FUG MPa

Isothermal throttling coefficient, δT = (∂h/∂p)T δT THC kJ kg−1 MPa−1

Second virial coefficient B B m3 kg−1 Third virial coefficient C C m6 kg−2 Joule-Thomson coefficient, µ = (∂T/∂p)h µ RJT K MPa−1 Compression factor, Z = (RTρ) Z Z – Vapour fraction x X – Partial derivative (∂ρ/∂Τ )p DDDT kg m−3 K−1 Partial derivative (∂p/∂T )ρ DPD MPa K−1 Partial derivative (∂p/∂ρ)T DPDD MPa m3 kg−1

Transport properties

Dynamic viscosity η VIS N s m−2 Kinematic viscosity ν VKI m2 s−1 Thermal conductivity λ TCON W m−1 K−1 Prandtl number, Pr = η cp λ−1 Pr PRN – Specific gas constant R RCONST J kg−1 K−1 Molar mass M MOLM g mol−1 *Although there is no function for the direct calculation of the specific volume, this property is listed because it is used in the definition of the isentropic exponent κ.

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2.3 Combinations of input variables The thermodynamic and transport properties listed in Section 2.2 can be calculated depending on different input variables. It is also possible to calculate directly different properties on the saturated liquid (′) and saturated vapour (″) line, as well as the saturation pressure ps and the

Density ρ Specific enthalpy h Specific entropy s Temperature T

ρ(T, p) h(T, p) s(T, p) T(ρ, p) ρ(T, s) h(T,ρ) s(T,ρ) T(ρ,s) ρ(T,h) h(p, s) s(p,h) T(ρ,h) ρ(p, s) h′(T) s ′(T) T(p,s) ρ(p,h) h″(T) s″(T) T(p,h) ρ(h, s) T(h,s) ρ(T , x) Compression factor Vapour fraction Ts(p) ρ′(T) Z(T,p) x(T ,ρ) Ts(ρ) ρ″(T) Z(T,ρ) x(T , v) Ts(s) ρ′(p) x(T , h) ρ″(p) x(T , s) ρ′(h) x(T ,u) ρ″(h)

Isothermal throttling coefficient δ T

Specific Gibbs free energy g

Specific Helmholtz free energy f Fugacity f *

δ T (T, p) g(T, p) f(T, p) f *(T, p) δ T (T,ρ) g(T,ρ) f(T,ρ) f *(T,ρ )

Specific isochoric heat capacity cv

Specific isobaric heat capacity cp

Specific internal energy u Pressure p

cv(T, p) cp(T, p) u(T, p) p(T,ρ) cv(T,ρ) cp(T,ρ) u(T,ρ) ps(T) cv′ (T) cp′ (T) u′(T) ps(ρ) cv″(T) cp″(T) u″(T) pmelt(T)

Speed of sound w Isentropic exponent κ

Joule-Thomson coefficient µ

Second and third virial coefficient

B and C w(T, p) κ(T, p) µ(T, p) B(T) w(T,ρ) κ(T,ρ) µ(T,ρ) C(T) w′(T) w″(T)

Partial derivatives Transport properties

( )pTTp ,

ρ

∂∂ ( )ρ

ρ

,TTp

∂∂

η(T, p) λ(Τ, p)

η(Τ,ρ) λ(Τ,ρ)

( )pTp

T

,

∂∂ρ

( )ρρ

,Tp

T

∂∂

ν(Τ,p) Pr(Τ, p)

ν(Τ,ρ) Pr(Τ,ρ)

( )pTT p

,

∂∂ρ ( )ρρ ,T

T p

∂∂

Substance parameters: Tc , pc , ρc, Tt , p t , Tmin, Tmax, pmin, pmax, M , and R

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saturation temperature Ts. Furthermore, the program is able to give out the critical parameters Tc , pc , ρc, the triple-point parameters, the upper and lower limits of the ranges of validity of the corresponding equation of state, the molar mass, the specific gas constant, and the enthalpy and entropy values at their reference points (see fluidcal.xlsm).

3 Calculating the several thermodynamic and transport properties

The following list of functions, that are already mentioned in Section 2.3, gives a detailed description of the functions that are implemented in the dynamic link library FLUIDCAL.DLL. All functions, input, and output values are defined as DOUBLEPRECISION. The arguments are transferred BY REFERENCE, whereas the values of the functions are given back BY VALUE.

The call of a function with incorrect input values (e.g. negative temperature or values outside the area of validity of the used equation) will return the value – 9999, whereas the return of the value – 5555 indicates a wrong substantial number (SUBNR) as an input value.

3.1 Functions depending on temperature and pressure If for a certain calculation the saturation pressure and the corresponding saturation temperature should be chosen exactly as input parameters, the functions will return the value - 999 due to the ambiguity at these points.

DOTP Function for the calculation of the density (DCALC) depending on given values of temperature T and pressure P.

Example: DCALC = DOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: DCALC [kg m−3] HOTP Function for the calculation of the specific enthalpy (HCALC) depending on

given values of temperature T and pressure P. Example: HCALC = HOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: HCALC [kJ kg−1] SOTP Function for the calculation of the specific entropy (SCALC) depending on

given values of temperature T and pressure P. Example: SCALC = SOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: SCALC [kJ kg−1 K−1] FOTP Function for the calculation of the specific free energy (FCALC) depending on

given values of temperature T and pressure P. Example: FCALC = FOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: FCALC [kJ kg−1]

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UOTP Function for the calculation of the specific internal energy (UCALC) depending on given values of temperature T and pressure P.

Example: UCALC = UOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: UCALC [kJ kg−1] DPDTOTP Function for the calculation of the partial derivative (∂p/∂T)ρ (DPDTCALC)

depending on given values of temperature T and pressure P. Example: DPDTCALC = DPDTOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: DPDTCALC [MPa K−1] DPDDOTP Function for the calculation of the partial derivative (∂p/∂)T (DPDDCALC)

depending on given values of temperature T and pressure P. Example: DPDDCALC = DPDDOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: DPDDCALC [MPa kg−1 m3] DDDTOTP Function for the calculation of the partial derivative (∂ρ/∂T)p (DDDTCALC)

depending on given values of temperature T and pressure P. Example: DDDTCALC = DDDTOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: DDDTCALC [kg m−3 K−1] FUGOTP Function for the calculation of the fugacity (FUGCALC) depending on given

values of temperature T and pressure P. Example: FUGCALC = FUGOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: FUGCALC [MPa] CVOTP Function for the calculation of the specific isochoric heat capacity (CVCALC)

depending on given values of temperature T and pressure P. Example: CVCALC = CVOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: CVCALC [kJ kg−1 K−1] CPOTP Function for the calculation of the specific isobaric heat capacity (CPCALC)

depending on given values of temperature T and pressure P. Example: CPCALC = CPOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: CPCALC [kJ kg−1 K−1]

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WOTP Function for the calculation of the speed of sound (WCALC) depending on given values of temperature T and pressure P.

Example: WCALC = WOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: WCALC [m s−1] GOTP Function for the calculation of the specific free enthalpy (GCALC) depending

on given values of temperature T and pressure P. Example: GCALC = GOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: GCALC [kJ kg−1] RJTOTP Function for the calculation of the Joule-Thomson coefficient (RJTCALC)

depending on given values of temperature T and pressure P. Example: RJTCALC = RJTOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: RJTCALC [K MPa−1] THCOTP Function for the calculation of the isothermal throttling coefficient

(THCCALC) depending on given values of temperature T and pressure P. Example: THCCALC = THCOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: THCCALC [kJ kg−1

MPa−1] CAPOTP Function for the calculation of the isentropic exponent (CAPCALC) depending

on given values of temperature T and pressure P. Example: CAPCALC = CAPOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: CAPCALC [-] VISOTP Function for the calculation of the dynamic viscosity (VISCALC) depending

on given values of temperature T and pressure P. Example: VISCALC = VISOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: VISCALC [N m−2 s] VKIOTP Function for the calculation of the kinematic viscosity (VKICALC) depending

on given values of temperature T and pressure P. Example: VKICALC = VKIOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: VKICALC [m2 s−1]

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TCONOTP Function for the calculation of the thermal conductivity (TCONCALC) depending on given values of temperature T and pressure P.

Example: TCONCALC = TCONOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: TCONCALC [W m−1 K−1] PRNOTP Function for the calculation of the Prandtl number (PRNCALC) depending on

given values of temperature T and pressure P. Example: PRNCALC = PRNOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: PRNCALC [-] ZOTP Function for the calculation of the compression factor (ZCALC) depending on

given values of temperature T and pressure P. Example: ZCALC = ZOTP(T,P,SUBNR) Input: T [K], P [MPa], SUBNR [-] Output: ZCALC [ - ]

3.2 Functions depending on temperature and density Properties that are calculable in the two-phase region (condition: ρ″(T) < ρ < ρ′(T)) are calculated as stable two-phase-system properties (valid for: h, s, u, f, p). For all other properties, that are not defined in the two phase region, the value –9999 will be returned.

POTD Function for the calculation of the pressure (PCALC) depending on given values of temperature T and density D.

Example: PCALC = POTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: PCALC [MPa] HOTD Function for the calculation of the specific enthalpy (HCALC) depending on

given values of temperature T and density D. Example: HCALC = HOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: HCALC [kJ kg−1] SOTD Function for the calculation of the specific entropy (SCALC) depending on

given values of temperature T and density D. Example: SCALC = SOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: SCALC [kJ kg−1 K−1]

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FOTD Function for the calculation of the specific Helmholtz free energy (FCALC) depending on given values of temperature T and density D.

Example: FCALC = FOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: FCALC [kJ kg−1] UOTD Function for the calculation of the specific internal energy (UCALC)

depending on given values of temperature T and density D. Example: UCALC = UOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: UCALC [kJ kg−1] DPDTOTD Function for the calculation of the partial derivative (∂p/∂T)ρ (DPDTCALC)

depending on given values of temperature T and density D. Example: DPDTCALC = DPDTOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: DPDTCALC [MPa K−1] DPDDOTD Function for the calculation of the partial derivative (∂p/∂)T (DPDDCALC)

depending on given values of temperature T and density D. Example: DPDDCALC = DPDDOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: DPDDCALC [MPa kg−1 m3] DDDTOTD Function for the calculation of the partial derivative (∂ρ/∂T)p (DDDTCALC)

depending on given values of temperature T and density D Example: DDDTCALC = DDDTOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: DDDTCALC [kg m−3 K−1] FUGOTD Function for the calculation of the fugacity (FUGCALC) depending on given

values of temperature T and density D. Example: FUGCALC = FUGOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: FUGCALC [MPa] CVOTD Function for the calculation of the specific isochoric heat capacity (CVCALC)

depending on given values of temperature T and density D. Example: CVCALC = CVOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: CVCALC [kJ kg−1 K−1]

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CPOTD Function for the calculation of the specific isobaric heat capacity (CPCALC) depending on given values of temperature T and density D.

Example: CPCALC = CPOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: CPCALC [kJ kg−1 K−1] WOTD Function for the calculation of the speed of sound (WCALC) depending on

given values of temperature T and density D. Example: WCALC = WOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: WCALC [m s−1] GOTD Function for the calculation of the specific Gibbs free energy (GCALC)

depending on given values of temperature T and density D. Example: GCALC = GOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: GCALC [kJ kg−1] RJTOTD Function for the calculation of the Joule-Thomson coefficient RJT depending

on given values of temperature T and density D. Example: RJTCALC = RJTOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: RJTCALC [K MPa−1] THCOTD Function for the calculation of the isothermal throttling coefficient

(THCCALC) depending on given values of temperature T and density D. Example: THCCALC = THCOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: THCCALC [kJ kg−1 MPa−1] CAPOTD Function for the calculation of the isentropic exponent (CAPCALC) depending

on given values of temperature T and density D. Example: CAPCALC = CAPOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: CAPCALC [-] VISOTD Function for the calculation of the dynamic viscosity (VISCALC) depending

on given values of temperature T and density D. Example: VISCALC = VISOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: VISCALC [N m−2 s]

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VKIOTD Function for the calculation of the kinematic viscosity (VKICALC) depending on given values of temperature T and density D.

Example: VKICALC = VKIOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: VKICALC [m2 s−1] TCONOTD Function for the calculation of the thermal conductivity (TCONCALC)

depending on given values of temperature T and density D. Example: TCONCALC = TCONOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: TCONCALC [W m−1 K−1] PRNOTD Function for the calculation of the Prandtl number (PRNCALC) depending on

given values of temperature T and density D. Example: PRNCALC = PRNOTD(D,P,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: PRNCALC [-] ZOTD Function for the calculation of the compression factor (ZCALC) depending on

given values of temperature T and density D. Example: ZCALC = ZOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: ZCALC [ - ] XOTD Function for the calculation of the vapour fraction (XCALC) depending on

given values of temperature T and density D. Example: XCALC = XOTD(T,D,SUBNR) Input: T [K], D [kg m−3], SUBNR [-] Output: XCALC [ - ]

3.3 Functions depending on pressure and specific entropy Values in the two phase region (condition: s″(p) < s < s ′(p)) are calculated as stable two-phase-system properties. The function TOPS calculates the saturation temperature. TOPS Function for the calculation of the temperature (TCALC) depending on given

values of pressure P and specific entropy S. Example: TCALC = TOPS(P,S,SUBNR) Input: P [MPa], S [kJ kg−1 K−1], SUBNR [-] Output: TCALC [K]

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DOPS Function for the calculation of the density (DCALC) depending on given values of pressure P and specific entropy S.

Example: DCALC = DOPS(P,S,SUBNR) Input: P [MPa], S [kJ kg−1 K−1], SUBNR [-] Output: DCALC [kg m−3] HOPS Function for the calculation of the specific enthalpy (HCALC) depending on

given values of pressure P and specific entropy S. Example: HCALC = HOPS(P,S,SUBNR) Input: P [MPa], S [kJ kg−1 K−1], SUBNR [-] Output: HCALC [kJ kg−1]

3.4 Functions depending on pressure and specific enthalpy Values in the two phase region (condition: h″(p) < h < h ′(p)) are calculated as stable two-phase-system properties. The function TOPH calculates the saturation temperature.

TOPH Function for the calculation of the temperature (TCALC) depending on given values of pressure P and specific enthalpy H.

Example: TCALC = TOPH(P,H,SUBNR) Input: P [MPa], H [kJ kg−1], SUBNR [-] Output: TCALC [K] DOPH Function for the calculation of the density (DCALC) depending on given

values of pressure P and specific enthalpy H. Example: DCALC = DOPH(P,H,SUBNR) Input: P [MPa], H [kJ kg−1], SUBNR [-] Output: DCALC [kg m−3] SOPH Function for the calculation of the specific entropy (SCALC) depending on

given values of pressure P and specific enthalpy H. Example: SCALC = SOPH(P,H,SUBNR) Input: P [MPa], H [kJ kg−1], SUBNR [-] Output: SCALC [kJ kg−1 K−1]

3.5 Functions depending on specific enthalpy and specific entropy Within the two-phase region, the function DOHS calculates the stable two-phase-system density.

TOHS Function for the calculation of the temperature (TCALC) depending on given values of specific enthalpy H and specific entropy S.

Example: TCALC = TOHS(H,S,SUBNR) Input: H [kJ kg−1], S [kJ kg−1 K−1], SUBNR [-] Output: TCALC [K]

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DOHS Function for the calculation of the density (DCALC) depending on given

values of specific enthalpy H and specific entropy S. Example: DCALC = DOHS(H,S,SUBNR) Input: H [kJ kg−1], S [kJ kg−1 K−1], SUBNR [-] Output: DCALC [kg m−3]

3.6 Further functions for the calculation of the density depending on temperature and specific entropy or on temperature and specific enthalpy

With the help of the following three functions, all other properties can be calculated depending on temperature and specific entropy or on temperature and specific enthalpy. First, the density can be calculated with the functions in this section and secondly all other properties listed in Section 2.1 can be calculated with this density and the given temperature.

DOTS Function for the calculation of the density (DCALC) depending on given values of temperature T and specific entropy S.

Example: DCALC = DOTS(T,S,SUBNR) Input: T [K], S [kJ kg−1 K−1], SUBNR [-] Output: DCALC [kg m−3] DOTH Function for the calculation of the density (DCALC) depending on given

values of temperature T and specific enthalpy H. Example: DCALC = DOTH(T,H,SUBNR) Input: T [K], H [kJ kg−1], SUBNR [-] Output: DCALC [kg m−3] DOTHZ*

Example: DCALC = DOTHZ(T,H,SUBNR)

Function for the calculation of the density (DCALC) depending on given values of temperature T and specific enthalpy H (additional upper value).

Input: T [K], H [kJ kg−1], SUBNR [-] Output: DCALC [kg m−3]

3.7 Further functions for the calculation of the temperature depending on density and pressure, density and specific entropy, or on density and specific enthalpy

With the help of the following three functions, all other properties can be calculated depending on density and pressure, density and specific entropy or on density and specific enthalpy. First, the temperature can be calculated with the functions in this section and

*Due to the fact, that in some cases two different densities can be assigned to a set of input values of temperature and

enthalpy, it might be necessary to use both functions, DOTH (for the usual calculation) and DOTHZ (for the region above the Joule-Thomson inversion curve).

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secondly all other properties listed in Section 2.1 can be calculated with this temperature and the given density.

TODP Function for the calculation of the temperature (TCALC) depending on given values of density D and pressure P.

Example: TCALC = TODP(D,P,SUBNR) Input: D [kg m−3], P[MPa], SUBNR [-] Output: TCALC [K] TODS Function for the calculation of the temperature (TCALC) depending on given

values of density D and specific entropy S. Example: TCALC = TODS(D,S,SUBNR) Input: D [kg m−3], S [kJ kg−1 K−1], SUBNR [-] Output: TCALC [K] TODH Function for the calculation of the temperature (TCALC) depending on given

values of density D and specific enthalpy H. Example: TCALC = TODH(D,H,SUBNR) Input: D [kg m−3], H [kJ kg−1], SUBNR [-] Output: TCALC [K]

3.8 Functions depending on temperature

BOT Function for the calculation of the second virial coefficient (BCALC) depending on a given value of temperature T.

Example: BCALC = BOT(T,SUBNR) Input: T [K], SUBNR [-] Output: BCALC [m3 kg−1] COT Function for the calculation of the third virial coefficient (CCALC) depending

on a given value of temperature T. Example: CCALC = COT(T,SUBNR) Input: T [K], SUBNR [-] Output: CCALC [m6 kg−2]

3.9 Functions for the calculation of the vapour fraction depending on temperature and specific volume or specific enthalpy or specific entropy or specific internal energy

XOTV Function for the calculation of the vapour fraction (XCALC) depending on given values of temperature T and specific volume V.

Example: XCALC = XOTV(T,V,SUBNR) Input: T [K], V [m−3 kg], SUBNR [-] Output: XCALC [ - ]

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XOTH Function for the calculation of the vapour fraction (XCALC) depending on

given values of temperature T and specific enthalpy H. Example: XCALC = XOTH(T,H,SUBNR) Input: T [K], H [kJ kg−1], SUBNR [-] Output: XCALC [ - ] XOTS Function for the calculation of the vapour fraction (XCALC) depending on

given values of temperature T and specific entropy S. Example: XCALC = XOTS(T,S,SUBNR) Input: T [K], S [kJ kg−1 K−1], SUBNR [-] Output: XCALC [ - ] XOTU Function for the calculation of the vapour fraction (XCALC) depending on

given values of temperature T and specific internal energy U. Example: XCALC = XOTU(T,U,SUBNR) Input: T [K], U [kJ kg−1], SUBNR [-] Output: XCALC [ - ]

3.10 Functions for the calculation of properties on the saturated liquid and saturated vapour phase boundary depending on temperature, pressure, or density and the function ρ (T,x)

All of the properties in this section will be calculated by solving the phase-equilibrium condition (Maxwell criterion) using the corresponding equation of state.

DLOT Function for the calculation of the density on the saturated liquid line (DLCALC) depending on a given value of temperature T.

Example: DLCALC = DLOT(T,SUBNR) Input: T [K], SUBNR [-] Output: DLCALC [kg m−3] DVOT Function for the calculation of the density on the saturated vapour line

(DVCALC) depending on a given value of temperature T. Example: DVCALC = DVOT(T,SUBNR) Input: T [K], SUBNR [-] Output: DVCALC [kg m−3]

HLOT Function for the calculation of the specific specific enthalpy on the saturated liquid line (HLCALC) depending on a given value of temperature T.

Example: HLCALC = HLOT(T,SUBNR) Input: T [K], SUBNR [-] Output: HLCALC [kJ kg−1]

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HVOT Function for the calculation of the specific specific enthalpy on the saturated vapour line (HVCALC) depending on a given value of temperature T.

Example: HVCALC = HVOT(T,SUBNR) Input: T [K], SUBNR [-] Output: HVCALC [kJ kg−1]

SLOT Function for the calculation of the specific specific entropy on the saturated liquid line (SLCALC) depending on a given value of temperature T.

Example: SLCALC = SLOT(T,SUBNR) Input: T [K], SUBNR [-] Output: SLCALC [kJ kg−1 K−1]

SVOT Function for the calculation of the specific specific entropy on the saturated vapour line (SVCALC) depending on a given value of temperature T.

Example: SVCALC = SVOT(T,SUBNR) Input: T [K], SUBNR [-] Output: SVCALC [kJ kg−1 K−1]

ULOT Function for the calculation of the specific internal energy on the saturated liquid line (ULCALC) depending on a given value of temperature T.

Example: ULCALC = ULOT(T,SUBNR) Input: T [K], SUBNR [-] Output: ULCALC [kJ kg−1]

UVOT Function for the calculation of the specific internal energy on the saturated vapour line (UVCALC) depending on a given value of temperature T.

Example: UVCALC = UVOT(T,SUBNR) Input: T [K], SUBNR [-] Output: UVCALC [kJ kg−1]

CVLOT Function for the calculation of the specific isochoric heat capacity on the saturated liquid line (CVLCALC) depending on a given value of temperature T.

Example: CVLCALC = CVLOT(T,SUBNR) Input: T [K], SUBNR [-] Output: CVLCALC [kJ kg−1 K−1]

CVVOT Function for the calculation of the specific isochoric heat capacity on the saturated vapour line (CVVCALC) depending on a given value of temperature T.

Example: CVVCALC = CVVOT(T,SUBNR) Input: T [K], SUBNR [-] Output: CVVCALC [kJ kg−1 K−1]

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CPLOT Function for the calculation of the specific isobaric heat capacity on the saturated liquid line (CPLCALC) depending on a given value of temperature T.

Example: CPLCALC = CPLOT(T,SUBNR) Input: T [K], SUBNR [-] Output: CPLCALC [kJ kg−1 K−1] CPVOT Function for the calculation of the specific isobaric heat capacity on the

saturated vapour line (CPVCALC) depending on a given value of temperature T.

Example: CPVCALC = CPVOT(T,SUBNR) Input: T [K], SUBNR [-] Output: CPVCALC [kJ kg−1 K−1] WLOT Function for the calculation of the speed of sound on the saturated liquid line

(WLCALC) depending on a given value of temperature T. Example: WLCALC = WLOT(T,SUBNR) Input: T [K], SUBNR [-] Output: WLCALC [m s−1] WVOT Function for the calculation of the speed of sound on the saturated vapour line

WV depending on a given value of temperature T. Example: WVCALC = WVOT(T,SUBNR) Input: T [K], SUBNR [-] Output: WVCALC [m s−1] PSATOT Function for the calculation of the vapour pressure (PSATCALC) depending

on a given value of temperature T. Example: PSATCALC = PSATOT(T,SUBNR) Input: T [K], SUBNR [-] Output: PSATCALC [MPa] PMELTOT Function for the calculation of the melting pressure (PMELTCALC) depending

on a given value of temperature T. Example: PMELTCALC = PMELTOT(T,SUBNR) Input: T [K], SUBNR [-] Output: PMELTCALC [MPa]

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DLOP Function for the calculation of the density on the saturated liquid line (DLCALC) depending on a given value of pressure P.

Example: DLCALC = DLOP(P,SUBNR) Input: P [MPa], SUBNR [-] Output: DLCALC [kg m−3] DVOP Function for the calculation of the density on the saturated vapour line

(DVCALC) depending on a given value of pressure P. Example: DVCALC = DVOP(P,SUBNR) Input: P [MPa], SUBNR [-] Output: DVCALC [kg m−3] DLOH Function for the calculation of the density on the saturated liquid line

(DLCALC) depending on a given value of specific enthalpy H. Example: DLCALC = DLOH(H,SUBNR) Input: H [kJ kg−1], SUBNR [-] Output: DLCALC [kg m−3] DVOH Function for the calculation of the density on the saturated vapour line

(DLCALC) depending on a given value of specific enthalpy H. Example: DVCALC = DVOH(H,SUBNR) Input: H [kJ kg−1], SUBNR [-] Output: DVCALC [kg m−3] DVOHZ*

Example: DVCALC = DVOHZ(H,SUBNR)

Function for the calculation of the density on the saturated vapour line (DLCALC) depending on a given value of specific enthalpy H.

Input: H [kJ kg−1], SUBNR [-] Output: DVCALC [kg m−3] TSATOP Function for the calculation of the boiling temperature (TSATCALC)

depending on a given value of pressure P. Example: TSATCALC = TSATOP(P,SUBNR) Input: P [MPa], SUBNR [-] Output: TSATCALC [K]

*Due to the fact, that in some cases two different densities on the saturated vapour line can be assigned to one value

enthalpy, it might be necessary to use both functions, DVOH (for the usual calculation) and DVOHZ, which will return the lower value.

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TSATOD Function for the calculation of the boiling temperature (TSATCALC) depending on a given value of density D.

Example: TSATCALC = TSATOD(D,SUBNR) Input: D [kg m−3], SUBNR [-] Output: TSATCALC [K] TSATOS Function for the calculation of the boiling temperature (TSATCALC)

depending on a given value of specific entropy S. Example: TSATCALC = TSATOS(S,SUBNR) Input: S [kJ kg−1 K−1], SUBNR [-] Output: TSATCALC [K] PSATOD Function for the calculation of the vapour pressure (PSATCALC) depending

on a given value of density D. Example: PSATCALC = PSATOD(D,SUBNR) Input: D [kg m−3], SUBNR [-] Output: PSATCALC [MPa] DOTX Function for the calculation of the density in the two-phase region (DCALC)

depending on temperature T and vapour fraction X. Example: DCALC = DOTX(T,X,SUBNR) Input: T [K], X [–], SUBNR [-] Output: DCALC [kg m−3]

3.11 Functions for the output of critical values and the limits of the range of validity

The functions for the output of the critical parameters return values calculated from the corresponding equation of state. The functions for the limits of the range of validity return the values valid for the corresponding equation of state listed in Section 7.

TCRIT Function for the output of the critical temperature (TCRIT) calculated from the equation of state.

Example: TCRIT = TCRIT(SUBNR) Input: SUBNR [-] Output: TCRIT [K]

PCRIT Function for the output of the critical pressure (PCRIT) calculated from the equation of state.

Example: PCRIT = PCRIT(SUBNR) Input: SUBNR [-] Output: PCRIT [MPa]

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DCRIT Function for the output of the critical density (DCRIT) calculated from the equation of state.

Example: DCRIT = DCRIT(SUBNR) Input: SUBNR [-] Output: DCRIT [kg m−3]

PTRIPLE Function for the output of the triple-point pressure (PTRIPLE) calculated from the equation of state.

Example: PTRIPLE = PTRIPLE(SUBNR) Input: SUBNR [-] Output: PTRIPLE [MPa]

TTRIPLE Function for the output of the triple-point temperature (TTRIPLE) calculated from the equation of state.

Example: TTRIPLE = TTRIPLE(SUBNR) Input: SUBNR [-] Output: TTRIPLE [K]

TMIN Function for the output of the lower temperature limit (TMIN) of the range of validity of the equation of state.

Example: TMIN = TMIN(SUBNR) Input: SUBNR [-] Output: TMIN [K]

TMAX Function for the output of the upper temperature limit (TMAX) of the range of validity of the equation of state.

Example: TMAX = TMAX(SUBNR) Input: SUBNR [-] Output: TMAX [K]

PMIN Function for the output of the lower pressure limit (PMIN) of the range of validity of the equation of state.

Example: PMIN = PMIN(SUBNR) Input: SUBNR [-] Output: PMIN [MPa]

PMAX Function for the output of the upper pressure limit (PMAX) of the range of validity of the equation of state.

Example: PMAX = PMAX(SUBNR) Input: SUBNR [-] Output: PMAX [MPa]

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RCONST Function for the output of the specific gas constant (RCONST) of the range of validity of the equation of state.

Example: RCONST = RCONST(SUBNR) Input: SUBNR [-] Output: RCONST [J kg−1 K−1]

MOLM Function for the output of the molar mass (MOLM) of the considered substance.

Example: MOLM = MOLM(SUBNR) Input: SUBNR [-] Output: MOLM [g mol−1]

4 Installation and integration of the software FLUIDCAL First of all, the content of the FLUIDCAL software package has to be unpacked or copied into an installation directory of your hard disc like C:\AddIns\FLUIDCAL. Then you have to manage that your executable program or Microsoft Excel has path access to the files FLUIDCAL.DLL and LICENCE.FLC, libmmd.dll, libifcoremd.dll and svml_dispmd.dll of the Intel Visual Fortran Composer XE runtime library, and msvcr100.dll of the Visual Studio 2010 runtime library. This can easily be done by Right-Click and run as administrator the enclosed file FLUIDCAL_env.bat, which will make the necessary environment entries for you. Alternatively, with temporary administrator rights this can be done by select “Start”, Right-Click "Computer", select "Properties", select "Advanced System Settings", select Environment Variables, and add the directory C:\AddIns\FLUIDCAL to the entries of the system variable Path. Be careful not to override the existing entries and to separate the entries using a semicolon ";".Another possibility is to copy the files FLUIDCAL.DLL, LICENCE.FLC, libmmd.dll, libifcoremd.dll, svml_dispmd.dll and msvcr100.dll into a directory with path access like C:\WINDOWS\system32 or C:\WINDOWS\SysWOW64, which likewise requires temporary administrator rights.

User-specific programs (32 Bit) For the calculation of the several thermodynamic properties by means of an user-specific executable program, it is required to link FLUIDCAL.DLL to the main program of this application. This is usually handled by linking to the import library FLUIDCAL.LIB when building or linking to create an executable file.

The exported property functions and subroutines of FLUIDCAL.DLL use the Compaq Visual Fortran (CVF) default calling convention, which conforms to the standard calling convention (STDCALL), except that routine names are converted to UPPERCASE and arguments are passed BY REFERENCE (and CHARACTER variables are passed as address/length pairs). It should be noted that the default calling convention used by Intel Visual Fortran Composer XE, which is the successor to CVF, differs from the CVF default behaviour; for more infor-mation see the attached document Migration_CVF_Intel.pdf. However, also for the successor Intel Visual Fortran Composer XE the same behaviour like the CVF can be accomplished by choosing CVF for the calling convention (/iface:cvf) under the item external procedures in the compiler options.

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Microsoft Excel (32 Bit) With the Add-In file FLUIDCAL.XLA , the functions imported can be added to the standard function volume of Microsoft Excel 97-2003. For preventing of any compatibility mode, it may be more convenient, for Excel 2007-2010 to use the Add-In file FLUIDCAL.XLAM. In this way, all functions of FLUIDCAL.DLL can be used as easily as standard Excel functions. For the installation of this Add-In, it is recommended not to use the different Add-Ins installation directories as given by default by the different versions of Microsoft Windows (XP, Vista or Windows 7, each 32 or 64-Bit) but to use a common Add-Ins installation directory as given above. Then, the Add-In can be installed by using the Add-Ins-Manager of Microsoft Excel as follows: in Excel 2010 select “File”, select “Options” , select “Add-Ins”, manage “Excel-Add-Ins”, select “Go…”, select “Browse” and search for the path C:\AddIns\FLUIDCAL\FLUIDCAL.xlam; in Excel 2007 select “Office”, select “Excel-Options”, select “Add-Ins”, manage “Excel-Add-Ins”, select “Go…”, select “Browse”, and search for the path C:\AddIns\FLUIDCAL\FLUIDCALxlam; in Excel 97-2003 select “Tools”, select “Add-Ins”, and search for the path C:\AddIns\FLUIDCAL\FLUIDCAL.xla. In this way, the same Excel spreadsheet with FLUIDCAL function calls can easily be used in different versions of Excel and on different operating systems of Microsoft. If older versions of one or all of these files exist, at first it is necessary to close Microsoft Excel and to remove all of these files from the hard disk. In the case of Excel 97-2003 you have to restart Excel, to call the Add-Ins manager and to delete the no longer available FLUIDCAL Add-In from the Add-Ins list. Following a log off and back in from the operating system, the necessary files may then be installed as follows. In the case of Excel 2007-2010 the necessary files may be installed directly. If you have preferred another installation directory as the default path C:\AddIns\Fluidcal\, however, you have to change the default path of the file LICENCE.FLC, where the Excel Add-In is searching for. Therefore you have to open the Visual Basic Editor inside Microsoft Excel, choose the Module “new_category” inside the project “Fluidcal” on the left side and to change the expression “Datei = C:\AddIns\Fluidcal\LICENCE.FLC” to your preferred installation path. Save your changes and restart Excel. By opening a Microsoft Excel spreadsheet with a different link to the FLUIDCAL Add-In possibly you have to agree to “Enable Contents”, to select “Update”, to select “Edit links” and to select “Change Source” to the installation path of the FLUIDCAL Add-In in your operating system. If this update does not work, it is recommended to delete the links to a different installation directory by the “find and replace” function of Microsoft Excel.

The functions that are implemented in FLUIDCAL.DLL can be used by selecting the category FLUIDCAL in the listing of the different function categories listed by Microsoft Excel. Then, for example, the density of one of the fluids listed in Table 1 depending on temperature and pressure can be calculated by assigning the following command to one cell in the Excel spread sheet

=DOTP(cell1,cell2,cell3),

where cell1 contains a numerical value of the temperature, (“,” is the country-specific list separator), cell2 contains a numerical value for the pressure, and cell 3 contains a numerical value for the substantial number (SUBNR). It is recommended, however, to use the Microsoft Excel function assistant for such function calls, which will give you some useful assistance

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(see the attached document “Screenshots for the installation of the FLUIDCAL software package.pdf”).

Examples for all function calls supported by FLUIDCAL can easily be seen by opening the Excel spreadsheet FLUIDCAL.XLS in Microsoft Excel 97-2003 and FLUIDCAL.XLSM in Microsoft Excel 2007-2010, respectively.

Example screenshot: The figure below shows an example screenshot of calculations carried out with the software package described above.

5 Terms of use

5.1 Developers of the software and copyright The developers of the software,

Dr.-Ing. Urs Overhoff and Prof. em. Dr.-Ing. Wolfgang Wagner ([email protected]),

reserve all rights regarding the distributed software. The license for the use of the delivered software is restricted for

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• universities to the chair, institute or scientific group that ordered the software and their co-workers

• scientific institutes to the whole institute that ordered the software

• companies at the specified location

unless different regulations are explicitly stated. The software must not be passed on to third parties without explicit permission. Within the groups defined above, the software can be installed on different computers to any desired extent.

The same regulations apply to software that contains subroutines or functions taken from any of our software packages.

5.2 Exclusion of liability The developers of the software have made their best efforts to deliver a reliable version of this software and to verify the corresponding equation of state contained herein on the basis of sound scientific judgement. However, we make no warranties to that effect and shall not be liable for any damage that may result from any possible errors either in the delivered software or in the equation of state. Additionally, we shall not be liable for any damage that may result from any wrong use of the software.

By receiving or using the delivered software, the user accepts all terms of the agreements given in Sections 5.1 and 5.2.

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6 References of the used equations

Equations of state Acetone Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20

Industrial Fluids. J. Chem. Eng. Data 51 (2004), 785 – 850. Ammonia Tillner-Roth, R., Harms-Watzenberg, F., Baehr, H.D.: Eine neue

Fundamentalgleichung für Ammoniak. DKV-Tagungsbericht 20 (1993), 167 – 181.

Argon Tegeler, Ch., Span, R., 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 (1999), 779 – 850.

Benzene Bonsen, C.: Entwicklung von Verfahren und entsprechender Software zur einfachen Berechnung thermodynamischer Eigenschaften fluider Stoffe für industrielle Anwendungen. Dissertation am Lehrstuhl für Thermodynamik, Ruhr-Universität Bochum (2002).

Butane Bücker, D., Wagner, W.: Reference equation of state for the thermodynamic properties of fluid phase n-butane and isobutane. J. Phys. Chem. Ref. Data 35, 2 (2006), 929 – 1020.

Butene Lemmon, E.W., Ihmels, E.C: Thermodynamic properties of the butenes Part (1-Butene) II. Short fundamental equations of state. Fluid Phase Equilibria 228 – 229 (2004), 173 – 187.

Butene Lemmon, E.W., Ihmels, E.C: Thermodynamic properties of the butenes Part (cis-2-Butene) II. Short fundamental equations of state. Fluid Phase Equilibria 228 – 229 (2004), 173 – 187. Butene Lemmon, E.W., Ihmels, E.C: Thermodynamic properties of the butenes Part (trans-2- II. Short fundamental equations of state. Fluid Phase Equilibria 228 - 229 Butene) (2004), 173 – 187. Carbon Span, R., Wagner, W.: A new equation of state for carbon dioxide covering dioxide the fluid region from the triple-point temperature to 1100 K at pressures up to 800 MPa. J. Phys. Chem. Ref. Data 25 (1996), 1509 – 1596.

Carbon Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20 monoxide Industrial Fluids. J. Chem. Eng. Data 51, 3 (2006), 785 – 850.

Carbonyl- Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20 sulfide Industrial Fluids. J. Chem. Eng. Data 51, 3 (2006), 785 – 850. Chlorine Angus, S., Amstrong, B., de Reuck, K.M.: International thermodynamic

tables of the fluid state: Vol. 8 – chlorine. Pergamon Press, Oxford (1985).

Cyclohexane Penoncello, S.G., Jacobsen, R.T., Goodwin, A.R.H.: Thermodynamic property formulation for cyclohexane. Int. J. Thermophys. 16 (1995), 519 – 531.

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Cyclopentane Bonsen, C.: Entwicklung von Verfahren und entsprechender Software zur einfachen Berechnung thermodynamischer Eigenschaften fluider Stoffe für industrielle Anwendungen. Dissertation am Lehrstuhl für Thermodynamik, Ruhr-Universität Bochum (2002).

Decane Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20 Industrial Fluids. J. Chem. Eng. Data 51, 3 (2006), 785 – 850.

Diethylether Bonsen, C.:Entwicklung von Verfahren und entsprechender Software zur einfachen Berechnung thermodynamischer Eigenschaften fluider Stoffe für industrielle Anwendungen. Dissertation am Lehrstuhl für Thermodynamik, Ruhr-Universität Bochum (2002).

Diisopropyl Bonsen, C.: Entwicklung von Verfahren und entsprechender Software zur (2,3 Dimethyl- einfachen Berechnung thermodynamischer Eigenschaften fluider Stoffe butane) für industrielle Anwendungen. Dissertation am Lehrstuhl für Thermo-

dynamik, Ruhr-Universität Bochum (2002). Dodecane Lemmon, E.W., Huber, M.L.: Thermodynamic Properties of n-Dodecane. (n-Dodecane) Energy & Fuels 18 (2004), 960 – 967.

Ethane Bücker, D., Wagner, W.: Reference equation of state for the thermodynamic properties of fluid phase n-butane and isobutane. J. Phys. Chem. Ref. Data 35, 1 (2006), 205 – 266.

Ethanol Dillon, H.E., Penoncello, S.G.: A fundamental equation for the calculation of the thermodynamix properties of ethanol. Paper at the Fifteenth Symposium on Thermophysical Properties, Boulder, USA, 2003.

Ethylbenzene Bonsen, C.:Entwicklung von Verfahren und entsprechender Software zur einfachen Berechnung thermodynamischer Eigenschaften fluider Stoffe für industrielle Anwendungen. Dissertation am Lehrstuhl für Thermodynamik, Ruhr-Universität Bochum (2002).

Ethene Smukala, J., Span, R., Wagner, W.: New equation of state for ethylene covering the fluid region from the melting line to 450 K at pressures up to 300 MPa. J. Phys. Chem. Ref. Data 29 (2000), 1053 – 1121.

Fluorine de Reuck, K.M.: International thermodynamic tables of the fluid state: Vol. 11 – fluorine. Pergamon Press, Oxford (1990).

Helium McCarty, R.D., Arp, V.D: A new wide range equation of state for helium. Adv. Cryo. Eng. 35 (1990), 1465 – 1475.

Heptane Span, R., Wagner, W.: Equations of state for technical applications. II. Results for nonpolar fluids. Int. J. Thermophys. 24 (2003), 41 – 109.

Hexane Span, R., Wagner, W.: Equations of state for technical applications. II. Results for nonpolar fluids. Int. J. Thermophys. 24 (2003), 41 – 109.

Hydrogen Leachman, J.W., Jacobsen, R.T., Penoncello, S.G., Lemmon, E.W.: Fundamental Equations of State for Parahydrogen, Normal Hydrogen, and

Orthohydrogen. J. Phys. Chem. Ref. Data, Vol. 38, No. 3, (2009), 721 – 748.

Hydrogen Thol M., Piazza L., Span R.: A New Functional Form for Equations of State chloride for Some Polar and Weakly Associating Fluids, Int. J. Thermophys., to be submitted 2012

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Hydrogen Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20 sulfide Industrial Fluids. J. Chem. Eng. Data 51, 3 (2006), 785 – 850. Isobutane Bücker, D., Wagner, W.: Reference equation of state for the thermodynamic

properties of fluid phase n-butane and isobutane. J. Phys. Chem. Ref. Data 35, 2 (2004), 929 – 1020.

Isobutene Lemmon, E.W., Ihmels, E.C: Thermodynamic properties of the butenes Part II. Short fundamental equations of state. Fluid Phase Equilibria 228 – 229 (2004), 173 – 187. Isohexane Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20

Industrial Fluids. J. Chem. Eng. Data 51, 3 (2006), 785 – 850. Isopentane Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20

Industrial Fluids. J. Chem. Eng. Data 51, 3 (2006), 785 – 850.

Krypton Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20 Industrial Fluids. J. Chem. Eng. Data 51, 3 (2006), 785 – 850.

Methane Setzmann, U., Wagner, W.: A new equation of state and tables of the thermodynamic properties for methane covering the range from the melting line to 625 K at pressures up to 1000 MPa. J. Phys. Chem. Ref. Data 20 (1991), 1061 – 1155.

Methanol de Reuck, K.M., Craven, R.J.B.: International thermodynamic tables of the fluid state: Vol. 12 – methanol. Blackwell Scientific, London (1993).

Neon Katti, R.S., Jacobsen, R.T, Stewart, R.B., Jahangiri, M.: Thermodynamic properties for neon for temperatures from the triple point to 700 K at pressures up to 700 MPa. Adv. Cryo. Eng. 31 (1986), 1189 – 1197.

Neopentane Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20 Industrial Fluids. J. Chem. Eng. Data 51, 3 (2006), 785 – 850.

Nitrogen Span, R., Lemmon, E.W., Jacobsen, R.T, Wagner, W., Yokozeki, A.: A Reference Equation of State for the Thermodynamic Properties of Nitrogen for Temperatures from 63.151 to 1000 K and Pressures to 2200 MPa. J. Phys. Chem. Ref. Data 29 (2000), 1361 – 1433.

Nitrous oxide Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20 Industrial Fluids. J. Chem. Eng. Data 51, 3 (2006), 785 – 850.

Nonane Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20 Industrial Fluids. J. Chem. Eng. Data 51, 3 (2006), 785 – 850.

Octane Span, R., Wagner, W.: Equations of state for technical applications. II. Results for nonpolar fluids. Int. J. Thermophys. 24 (2003), 41 – 109..

Oxygen Schmidt, R., Wagner, W.: A new form of the equation of state for pure substances and its application to oxygen. Fluid Phase Equilibria. 19 (1985), 175 – 200.

Pentane Span, R., Wagner, W.: Equations of state for technical applications. II. Results for nonpolar fluids. Int. J. Thermophys. 24 (2003), 41 – 109.

Propane Lemmon, E.W., McLinden, M.O., Wagner, W.: Thermodynamic Properties of Propane. III. A Reference Equation of State for Temperatures from the Melting Line to 650 K and Pressures up to 1000 MPa. J. Chem. Eng. Data 54, 12 (2009), 3141 – 3180.

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Propene Lemmon, E.W., McLinden, M.O., Wagner, W., Overhoff, U.: to be submitted to J. Phys. Chem. Ref. Data 2010.

Propylbenzene Bonsen, C., Span, R., Wagner, W.: Automatic generation of equations of state for technical applications. To be submitted to Ind. Eng. Chem. Res..

R11 Marx, V., Pruß, A., Wagner, W.: Neue Zustandsgleichungen für R12, R22, R11 und R113 – Beschreibung des thermodynamischen Zustandsverhaltens bei Temperaturen bis 525 K und Drücken bis 200 MPa. VDI-Fortschritt-Berichte, Reihe 19, Nr. 57, VDI-Verlag, Düsseldorf (1992).


R22 Wagner, W., Marx, V., Pruß, A.: A new equation of state for chlorodifluoromethane (R22) covering the fluid region from 116 K to 1100 K at pressures up to 200 MPa. Int. J. Refrigeration 16 (1993), 373 - 389.

R23 Penoncello, S.G., Shah, Z., Jacobsen, R.T.: A fundamental equation for the calculation of the thermodynamic properties of trifluoromethane (R-23). ASHRAE Transact. 106 (2000), 739 – 756.

R32 Tillner-Roth, R., Yokozeki, A.: An international standard equation of state for difluoromethane (R-32) for temperatures from the triple point at 136.4 K to 435 K at pressures up to 70 MPa. J. Phys. Chem. Ref. Data 26 (1997), 1273 - 1328.

R41 Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20 Industrial Fluids. J. Chem. Eng. Data 51, 3 (2006), 785 – 850.



R123 Younglove, B.A., McLinden, M.O.: An international standard equation of state for the thermodynamic properties of refrigerant 123 (2,2-dichlor-1,1,1-trifluoroethane). J. Phys. Chem. Ref. Data 23 (1994), 731 – 779.

R124 de Vries, B., Tillner-Roth, R., Baehr, H.D.: The thermodynamic properties of HFC-124. 19 th International Congress of Refrigeration, Den Haag, The Netherlands (1995), 582 – 589.

R125 Piao, C.C., Noguchi, M.: An international standard equation of state for the thermodynamic properties of HFC-125 (pentafluoroethane). J. Phys. Chem. Ref. Data 27 (1998), 775 – 806.

R134a Tillner-Roth, R., Baehr, H.D.: An international standard equation of state for the thermodynamic properties of 1,1,1,2-tetrafluoroethane (HFC-134a) for temperatures from 170 K to 455 K at pressures up to 70 MPa. J. Phys. Chem. Ref. Data 23 (1994), 657 – 729.

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R141b Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20 Industrial Fluids. J. Chem. Eng. Data 51, 3 (2006), 785 – 850.

R142b Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20 Industrial Fluids. J. Chem. Eng. Data 51, 3 (2006), 785 – 850.

R143a Lemmon, E.W., Jacobsen, R.T: An international standard equation of state for the thermodynamic properties of 1,1,1-trifluoroethane (HFC-143a) for temperatures from 161 K to 450 K at pressures up to 50 MPa. J. Phys. Chem. Ref. Data 29 (2000), 521 – 552.

R152a Outcalc, S.L.; Mc Linden, M.O.: A modified Benedict-Webb-Rubin equation of state for the thermodynamic properties of R152a (1,1-difluoroethane). J. Phys. Chem. Ref. Data 25, 2 (1996), 605 – 636.


R227ea Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20 Industrial Fluids. J. Chem. Eng. Data (2004).

R245fa Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20 Industrial Fluids. J. Chem. Eng. Data 51, 3 (2006), 785 – 850.

R1234yf Richter, M., McLinden, M.O., Lemmon, E.W.: Journal of Chemical and Engineering Data, (to be submitted) 2010

Sulfur dioxide Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20 Industrial Fluids. J. Chem. Eng. Data 51, 3 (2006), 785 – 850.

Sulfur Guder, C.; Wagner, W.: A Reference Equation of State for the hexafluoride Thermodynamic Properties of Sulfur Hexafluoride (SF6) for Temperatures from the Melting Line to 625 K and Pressures up to 150 Mpa. J. Phys. Chem Ref. Data 38, 1 (2009). Toluene Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20

Industrial Fluids. J. Chem. Eng. Data 51, 3 (2006), 785 – 850. Water Wagner, W., Pruß, A.: The IAPWS formulation 1995 for the

thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 31 (2002), 387 – 535.

Xenon Lemmon, E.W., Span, R.: Short Fundamental Equations of State for 20 Industrial Fluids. J. Chem. Eng. Data 51, 3 (2006), 785 – 850.

Equations for the calculation of the transport properties Viscosity

Ammonia Fenghour, A., Wakeham, W.A., Vesovic, V., Watson, J.T.R., Millat, J., Vogel, E.: The viscosity of ammonia. J. Phys. Chem. Ref. Data 24 (1995), 1649-1667.

Argon Younglove, B.A., Hanley, H.J.M.: The viscosity and thermal conductivity coefficients of gaseous and liquid argon. J. Phys. Chem. Ref. Data 15 (1986), 1323-1337.

Butane Vogel, E., Küchenmeister, C., Bich, E.: Viscosity correlation for n-butane in the fluid region. High Temperatures – High Pressures 31 (1999), 173-186.

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Carbon Fenghour, A., Wakeham, W.A., Vesovic, V.: The viscosity of carbon dioxide. dioxide J. Phys. Chem. Ref. Data 27 (1998), 31-44.

Decane Klein, S.A., McLinden, M.O., Laesecke, A.: An improved extended corresponding states method for estimation of viscosity of pure refrigerants and mixtures. Int. J. Refrigeration 20 (1997), 208-217.

Ethane Hendl, S., Millat, J., Vogel, E., Vesovic, V., Wakeham, W.A., Luettmer-Stratmann, J., Sengers, J.V., Assael, M. J.: The transport properties of ethane. I. Viscosity. Int. J. Thermophys. 15 (1994), 1-31.

Ethylene Holland, P.M., Eaton, B.E., Hanley, H.J.M.: A correlation of the viscosity and thermal conductivity data of gaseous and liquid ethylene. J. Phys. Chem. Ref. Data 12 (1983), 917-932.

Heptane Klein, S.A., McLinden, M.O., Laesecke, A.: An improved extended corresponding states method for estimation of viscosity of pure refrigerants and mixtures. Int. J. Refrigeration 20 (1997), 208-217.

Hexane Klein, S.A., McLinden, M.O., Laesecke, A.: An improved extended corresponding states method for estimation of viscosity of pure refrigerants and mixtures. Int. J. Refrigeration 20 (1997), 208-217.

Isobutane Vogel, E., Küchenmeister, C., Bich, E.: Viscosity correlation for isobutane over wide ranges of the fluid region. Int. J. Thermophys. 21 (2000), 343-356.

Methane Friend, D.G., Ely, J.F., Ingham, H.: Thermophysical properties of methane. J. Phys. Chem. Ref. Data 18 (1989), 583-638.

Nitrogen Stephan, K., Krauss, R., Laesecke, A.: Viscosity and thermal conductivity of nitrogen for a wide range of fluid states. J. Phys. Chem. Ref. Data 16 (1987), 993-1023.

Nonane Klein, S.A., McLinden, M.O., Laesecke, A.: An improved extended corresponding states method for estimation of viscosity of pure refrigerants and mixtures. Int. J. Refrigeration 20 (1997), 208-217.

Octane Klein, S.A., McLinden, M.O., Laesecke, A.: An improved extended corresponding states method for estimation of viscosity of pure refrigerants and mixtures. Int. J. Refrigeration 20 (1997), 208-217.

Oxygen Laesecke, A., Krauss, R., Stephan, K., Wagner, W.: Transport properties of fluid oxygen. J. Phys. Chem. Ref. Data 19 (1990), 1089-1122.

Pentane Klein, S. A., McLinden, M. O., Laesecke, A. (1997): An improved extended corresponding states method for estimation of viscosity fo pure refrigerants and mixtures. Int. J. Refrigeration 20 (1997), 208 – 217.

Propane Vogel, E., Küchenmeister, C., Bich, E., Laesecke, A.: Reference correlation of the viscosity of Propane. J. Phys. Chem. Ref. Data 27 (1998), 947-970.

R11 Klein, S.A., McLinden, M.O., Laesecke, A.: An improved extended corresponding states method for estimation of viscosity of pure refrigerants and mixtures. Int. J. Refrigeration 20 (1997), 208-217.


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R123 Tanaka, Y., Sotani, T.: Thermal conductivity and viscosity of 2,2-dichloro-1,1,1-trifluoroethane (HCFC-123). Int. J. Thermophys. 17 (1996), 293-328.



R134a Klein, S.A., McLinden, M.O., Laesecke, A.: An improved extended corresponding states method for estimation of viscosity of pure refrigerants and mixtures. Int. J. Refrigeration 20 (1997), 208-217.

R143a Klein, S.A., McLinden, M.O., Laesecke, A.: An improved extended corresponding states method for estimation of viscosity of pure refrigerants and mixtures. Int. J. Refrigeration 20 (1997), 208-217.

R152a Krauss, R., Weiss, V.C., Edison, T.A., Sengers, J.V., Stephan, K.: Transport properties of 1,1-difluoroethane (R-152a). Int. J. Thermophys. 17 (1996), 731-757.



Water Sengers, J.V., Kamgar-Parsi, B.: Representative equations for the viscosity of water substance. J. Phys. Chem. Ref. Data 13 (1984), 185-205.

Thermal conductivity

Ammonia Tufeu, R., Ivanov, D.Y., Garrabos, Y., Le Neindre, B.: Thermal conductivity of Ammonia in a large temperature and pressure range including the critical region. Ber. Bunsenges. Phys. Chem. 88 (1984), 422-427.

Argon Perkins, R.A., Friend, D.G., Roder, H. M., Nieto de Castro, C.A.: Thermal conductivity surface of argon: A fresh analysis. Int. J. Thermophys. 12 (1991), 965-984.

Butane Younglove, B.A., Ely, J.F.: Thermophysical properties of fluids. II. Methane, ethane, propane, isobutane, and normal butane. J. Phys. Chem. Ref. Data 16 (1987), 577-798.

Carbon Vesovic, V., Wakeham, W.A., Olchowy, G.A., Sengers, J.V., Watson, J.T.R., dioxide Millat, J.: The transport properties of carbon dioxide. J. Phys. Chem. Ref. Data 19 (1990), 763-808.

Ethane Friend, D.G., Ingham, H., Ely, J.F.: Thermophysical properties of ethane. J. Phys. Chem. Ref. Data 20 (1991), 275-347.

Ethylene Holland, P.M., Eaton, B.E., Hanley, H.J.M.: A correlation of the viscosity and thermal conductivity data of gaseous and liquid ethylene. J. Phys. Chem. Ref. Data 12 (1983), 917-932.

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Isobutane Younglove, B.A., Ely, J.F.: Thermophysical properties of fluids. II. Methane, ethane, propane, isobutane, and normal butane. J. Phys. Chem. Ref. Data 16 (1987), 577-798.

Methane Friend, D.G., Ely, J.F., Ingham, H.: Thermophysical properties of methane. J. Phys. Chem. Ref. Data 18 (1989), 583-638.

Nitrogen Stephan, K., Krauss, R., Laesecke, A.: Viscosity and thermal conductivity of nitrogen for a wide range of fluid states. J. Phys. Chem. Ref. Data 16 (1987), 993-1023.

Oxygen Laesecke, A., Krauss, R., Stephan, K., Wagner, W.: Transport properties of fluid oxygen. J. Phys. Chem. Ref. Data 19 (1990), 1089-1122.

Pentane McLinden, M.O., Klein, S.A., Perkins, R.A.: An extended corresponding states method for the thermal conductivity of pure refrigerants and refrigerant mixtures. Int. J. Refrigeration 23 (2000), 43-63.

Propane Ramires, M.L.V., Nieto de Castro, C.A., Perkins, R.A.: An improved empirical correlation for the thermal conductivity of propane. Int. J. Therm. 21 (2000), 639-650.

R123 Laesecke, A., Perkins, R.A., Howley, J.B.: An improved correlation for the thermal conductivity of HCFC 123 (2,2-dichloro-1,1,1-triluoroethane). Int. J. Refrigeration 19 (1996), 231-238.

R124 McLinden, M.O., Klein, S.A., Perkins, R.A.: An extended corresponding states method for the thermal conductivity of pure refrigerants and refrigerant mixtures. Int. J. Refrigeration 23 (2000), 43-63.


R134a McLinden, M.O., Klein, S.A., Perkins, R.A.: An extended corresponding states method for the thermal conductivity of pure refrigerants and refrigerant mixtures. Int. J. Refrigeration 23 (2000), 43-63.

R143a McLinden, M.O., Klein, S.A., Perkins, R.A.: An extended corresponding states method for the thermal conductivity of pure refrigerants and refrigerant mixtures. Int. J. Refrigeration 23 (2000), 43-63.

R152a Krauss, R., Weiss, V.C., Edison, T.A., Sengers, J.V., Stephan, K.: Transport properties of 1,1-difluoroethane (R-152a). Int. J. Thermophys. 17 (1996), 731-757.



Water Sengers, J.V., Watson, J.T.R., Basu, R.S., Kamgar-Parsi, B., Hendricks, R.C.: Representative equations for the thermal conductivity of water substance. J. Phys. Chem. Ref. Data 13 (1984), 893-933.

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7 Ranges of validity

Ranges of validity of the equations of state

Substance Minimum temperature

Maximum temperature

Maximum pressure

Acetone 178.5 K 538 K 65 MPa Ammonia 195.5 K 600 K 1000 MPa Argon 84 K 700 K 1000 MPa Benzene 278.7 K 700 K 100 MPa Butane 134.9 K 573 K 69 MPa Butylene (1-Butylene)

87.8 K 525 K 50 MPa

Butylene (cis-2-Butylene)

134.3 K 525 K 50 MPa

Butylene (trans-2-Butylene)

167.6 K 525 K 50 MPa

Butylene 87.8 K 525 K 50 MPa Carbon dioxide 216.6 K 1100 K 800 MPa Carbon monoxide 68.1 K 1000 K 100 MPa Chlorine 180 K 900 K 25 MPa Cyclohexane 279.5 K 700 K 80 MPa Cyclopentane 179.3 K 500 K 100 MPa Decane 200 K 800 K 100 MPa Diethylether 156.9 K 600 K 100 MPa

Diisopropyl (2,3 Dimethylbutane)

145.2 K 500 K 100 MPa

Dodecane (n-Dodecane)

263.6 K 700 K 500 MPa

Ethane 90 K 673 K 900 MPa Ethanol 250 K 650 K 280 MPa Ethylbenzene 178.2 K 700 K 80 MPa Ethylene 104 K 450 K 300 MPa Fluorine 54 K 300 K 20 MPa Helium 2.2 K 1500 K 100 MPa Heptane 182.6 K 523 K 100 MPa Hexane 177.8 K 548 K 92 MPa Hydrogen 13.957 K 1000 K 2000 MPa Hydrogen sulfide 187.7 K 760 K 170 MPa Hydrogen chloride 131.4 K 5000 K 20 MPa Isobutane 113.6 K 573 K 35 MPa Isobutene 132.4 K 525 K 50 MPa Isohexane 119.5 K 500 K 30 MPa Isopentane 112.7 K 600 K 1000 MPa Krypton 115.8 K 800 K 300 MPa Methane 90.7 K 625 K 1000 MPa Methanol 175 K 570 K 800 MPa Neon 24.6 K 700 K 700 MPa Neopentane 256.6 K 450 K 30 MPa

- 36 -



Maximum temperature

Maximum pressure

Nitrogen 63.151 K 1000 K 2200 MPa Nitrous oxide 182.4 K 600 K 50 MPa Nonane 200 K 800 K 120 MPa Octane 258 K 548 K 96 MPa Oxygen 54 K 300 K 82 MPa Pentane 143.5 K 573 K 69 MPa Propane 85.5 K 650 K 1000 MPa Propene 87.953 K 575 K 1000 MPa Propylbenzene 173.7 K 600 K 50 MPa R11 162.7 K 525 K 200 MPa R113 236.9 K 525 K 200 MPa R116 173.1 K 475 K 55MPa R12 116.1 K 525 K 200 MPa R123 166 K 500 K 40 MPa R1234yf 220 K 410 K 30 MPa R124 120 K 470 K 40 MPa R125 172.5 K 475 K 68 MPa R134a 170 K 455 K 70 MPa R141b 169.9 K 500 K 100 MPa R142b 142.7 K 500 K 60 MPa R143a 161.3 K 450 K 50 MPa R152a 154.56 K 500 K 60 MPa R218 113 K 500 K 30 MPa R22 115.7 K 525 K 200 MPa R227ea 146.35 K 473 K 65 MPa R23 158 K 473.2 K 120 MPa R32 136.3 K 435 K 70 MPa R41 129.8 K 500 K 60 MPa R245fa 171.05 K 440 K 200 MPa Sulfur dioxide 197.7 K 523 K 35 MPa Sulfur hexafluoride 222.4 K 525 K 55 MPa Toluol 179 K 750 K 100 MPa Water 273.2 K 1273.15 K 1000 MPa Xenon 160.4 K 800 K 350 MPa

Ranges of validity for the calculation of the transport properties Viscosity


Maximum temperature

Maximum pressure / Maximum density

Ammonia 195.5 K 700 K 1000 MPa Argon 86 K 500 K 400 MPa Butane 134.9 K 500 K 70 MPa Carbon dioxide 216.6 K 1000 K 300 MPa

- 37 -



Maximum temperature


1000 K 1500 K 30 MPa Decane 200 K 500 K 55 MPa Ethane 100 K 500 K 60 MPa

500 K 1000 K 2 MPa Ethylene 110 K 500 K 50 MPa Heptane 182.6 K 490 K 100 MPa Hexane 177.8 K 450 K 65 MPa Isobutane 113.6 K 600 K 35 MPa Methane 91 K 700 K 100 MPa Nitrogen 70 K 1100 K 100 MPa Nonane 200 K 325 K 70 MPa Octane 216.4 K 500 K 50 MPa Oxygen 70 K 1400 K 0.01 – 100 MPa Pentane 143.4 K 400 K 100 MPa Propane 54 K 600 K 100 MPa R11 162.7 K 350 K 20 MPa R12 116.1 K 350 K 15 MPa R123 166 K 600 K 80 MPa R124 170 K 500 K 1740 kg/m³ R125 170 K 500 K 1740 kg/m³ R134a 170 K 500 K 1740 kg/m³ R143a 170 K 500 K 1740 kg/m³ R152a 155 K 500 K 60 MPa R22 170 K 500 K 1740 kg/m³ R32 170 K 500 K 1740 kg/m³ Water 273.15 K 423.15 K 500 MPa

423.15 K 873.15 K 350 Mpa 873.15 K 1173.15 K 300 MPa

Thermal conductivity


Maximum temperature


Ammonia 195.5 K 700 K 1000 MPa Argon 100 K 700 K 70 MPa Butane 134.9 K 500 K 70 MPa Carbon dioxide 216.6 K 1000 K 100 MPa Ethane 100 K 500 K 60 MPa

500 K 600 K 2 MPa Ethylene 110 K 500 K 50 MPa Isobutane 113.6 K 600 K 70 MPa Methane 91 K 700 K 100 MPa Nitrogen 70 K 1100 K 100 MPa Oxygen 70 K 1400 K 0.01 – 100 MPa

- 38 -



Maximum temperature


Pentane 143.4 K 500 K 70 MPa Propane 110 K 700 K 0.1 – 70 MPa R123 180 K 480 K 67 MPa R124 169.9 K 455 K 70 MPa R125 169.9 K 455 K 70 MPa R134a 169.9 K 455 K 70 MPa R143a 169.9 K 455 K 70 MPa R152a 240 K 550 K 60 MPa R22 169.9 K 455 K 70 MPa R32 169.9 K 455 K 70 MPa Water 273.15 K 773.15 K 100 MPa

773.15 K 923.15 K 70 MPa 923.15 K 1073.15 K 40 MPa

8 Reference points for the specific enthalpy and specific entropy Depending on the several equations of state, different reference points for the specific enthalpy h and specific entropy s are used. The table lists the reference values for enthalpy and entropy calculated with this software at the three reference states mostly used. These values are based exactly on the reference points given in the publication on the considered equation of state. However, if the reference points selected by the authors of the equation of state do not correspond to one of the three points shown in the table, the values for enthalpy and entropy were calculated at the reference point given in the third column of the table. For this reference point, the values for enthalpy and entropy are not given at T0 and p0 for the ideal-gas part of the Helmholtz free energy (as usual), but for the real-gas state. In this way, the user can calculate with the software the enthalpy and entropy values at this point, for example, to compare these values with those from other software, from own computer programs, or from property tables.

The values for enthalpy and entropy in this table make sure that the values of the caloric properties h, s, u, f, and g are exactly the same when calculating them with this software or with a program developed by the user for the same equation of state.

For each of the reference points two values are given; the first value is the specific enthalpy in kJ kg−1 and the second one the specific entropy in kJ kg−1 K−1. The h and s values in the third column were calculated from the functions HOTP and SOTP for T0 and p0, in the fourth column from the functions HLOT and SLOT for T0, and in the fifth column T0 from the function TSATOP for p0, and then HLOT and SLOT for the calculated value of T0.

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Substance

SUBNR

Reference point at T0 = 298.15 K, p0 = 0.1 MPa (real-gas state)

Reference point for refrigerants at T0 = 273.15 K, saturated-liquid line

Reference point at the normal-boiling point, p0 =0.101325 MPa, saturated-liquid line

Methane 1 -0.976 200 685 0.004 444 605

Ethane 2 -1.901 034 762 -0.000 667 635

Propane 3 630.372 956 1 2.847 041 254

Butane 4 -4.233 074 197 -0.008 140 233

Pentane 5 -370.328 984 5 -1.193 076 654

Hexane 6 -367.130 100 7 -1.074 624 588

Heptane 7 -365.710 918 8 0.993 185 714

Octane 8 -364.716 9550 -0.932 414 714

Nonane 9 -309.560 122 5 -0.860 841 520

Decane 10 0.000 000 000 0.000 000 000

Ethanol 11 110.597 983 7 0.575 761 534

n-Dodecane 12 -361.362 009 5 -0.790 597 094

Acetone 13 200.000 000 0 1.000 000 000

Isobutene 14 0.000 002 689 0.000 000 000

Isobutane 15 -3.586 287 065 -0.006 460 648

Ethene 16 -1.556 423 808 0.000 358 415

Propene 17 200.000 000 0 1.000 000 000

Cyclohexane 18 -392.684 753 7 -1.114 068 366

Methanol 19 -1189.069 169 -3.524 371 071

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Substance

SUBNR




Benzene 20 -433.876 929 5 -1.233 521 501

Toluene 21 -158.164 016 8 -0.464 747 974

Ethylbenzene 22 -397.409 960 0 -0.990 912 632

Propylbenzene 23 -383.202 617 7 -0.913 038 650

Cyclopentane 25 -407.950 680 0 -0.443 697 668

Neopentane 26 0.000 000 000 0.000 000 000

Isopentane 27 0.000 000 001 0.000 000 000

Isohexane 28 0.000 000 000 0.000 000 000

Diisopropyl

(2,3 Dimethylbutane)

29 -340.367 461 8 -0.359 894 699

1-Butene 30 0.000 000 876 0.000 000 000

Diethylether 32 -370.589 466 0 -1.200 173 897

Neon 40 0.031 064 663 0.005 332 387

Argon 41 −0.190 795 452 0.002 230 536

Nitrogen 42 309.270 539 8 6.839 229 250

Oxygen 43 -0.246 956 808 0.002 757 939

Chlorine 44 -1.222 9471 68 -0.001 118 603

Hydrogen 45 448.711 439 6 22.029 238 77

Fluorine 46 -0.156 762 149 -0.000 437 352

Krypton 47 0.000 000 001 0.000 000 000

- 41 -


Substance

SUBNR




Xenon 48 117.399 212 5 0.677 235 489

Helium 49 -5.204 872 208 34.086 902 67

Water * 50

Carbon dioxide 51 -0.926 133 395 0.000 319 627

Sulfur hexafluoride

52 -0.617 703 697 -0.000 688 629

Ammonia 53 200.000 067 0 1.000 000 392

Nitrous oxide 54 468.564 461 6 2.425 272 037

Hydrogen sulfide

55 0.000 000 004 0.000 000 000

Carbon monoxide 56 442.402 801 0 4.003 355 647

Carbonyl sulfide 57 359.628951026 1.582 770 739

Sulfur dioxide 58 412.383 731 1 1.563 493 621

R116 59 200.000 000 0 1.000 000 000

R11 60 -1.595 489 330 -0.002 682 045

R12 61 -1.225 718 113 -0.001 920 197

R22 62 199.999 994 1 0.999 999 992

R23 63 200.000 000 0 1.000 000 000

R32 64 200.000 013 4 1.000000006

R41 65 200.000 000 0 1.000 000 000

R113 66 -152.349 933 8 -0.473 933 128

R123 67 200.000 000 0 1.000 000 000

- 42 -


Substance

SUBNR




R124 68 200.000 002 5 1.000 000 028

R125 69 200.000 000 0 1.000 000 000

R134a 70 199.999 988 4 1.000 000 036

R141b 71 200.000 000 0 1.000 000 000

R142b 72 200.000 000 0 1.000 000 000

R143a 73 200.000 088 3 0.999 996 256

R152a 74 200.000 003 7 1.000 000 013

R218 75 200.000 000 0 1.000 000 000

R227ea 76 -1.431 004 902 -0.002 854 367

trans-2-Butene 77 0.000 002 800 0.000 000 005

cis-2-Butene 78 445.418 613 4 1.606 480 029

R245fa 79 200.000 000 0 1.000 000 000

R1234yf 80 200.000 000 0 1.000 000 000

Hydrogen chloride 81 -1,496912803 -0.000 560 883

*The reference state of water is internationally defined at the triple point (subscript t) for u and s on the

saturated-liquid line: Tt = 273.16 K, pt = 0.000 611 655 MPa: ut′ = 0.000 000 000 kJ kg−1 (corresponding to ht′ = 0.000 611 782 kJ kg−1), st′ = 0.000 000 000 kJ kg−1 K−1.

Documents

Description of the Software FLUIDCAL (Dynamic Link Library