NOTE: The following information is for Pure Compounds only. We are working on similar information for Binary Mixtures.

Fitted Equations for Specific Properties

Listed below are the properties for which evaluated data is generated by TDE. Each property is linked to a list showing the set of possible equations that can be fit to the data. The equation that is used for a specific query is the one that provides the best fit of the data. This equation is then used to provide evaluated data.

NOTE: All of this information is displayed here in an individual file so that you can do text searches by using the Find funtion from the Edit menu of your browser.

Purpose: Provide definitions of equations and equation parameters used for output of evaluated data.

Select a property to see all associated equations. Properties represented with equations in TDE output are:


Vapor Pressure: Liquid-Gas Phase Boundary Pressure

Wagner 25 (Vapor Pressure: Output Details)

ln(p/po) ln(pc/po) = Tc/T (A1 + A2×t1.5 + A3×t2.5 + A4×t5); where t = 1 - T/Tc and po = 1 kPa

Evaluation Results:

The example is for fitted vapor pressures for benzene.

Antoine (Vapor Pressure: Output Details)

ln(p/po) = A + B/(T + C); where po = 1 kPa

Evaluation Results:

The example is for fitted vapor pressures for benzene.

Yaws (Vapor Pressure: Output Details)

lg(p/po) = a + b/T + c×lg(T) + d×T + e/T2 ; where po = 1 kPa and lg = log10

Evaluation Results:

The example is for fitted vapor pressures for benzene.

DIPPR 115 (Vapor Pressure: Output Details)

ln(p/po) = a + b/T + c×ln(T) + d×T2 + e/T2 ; where po = 1 kPa

Evaluation Results:

The example is for fitted vapor pressures for benzene.

DIPPR 101 (Vapor Pressure: Output Details)

ln(p/po) = a + b/T + c×ln(T) + d×Te ; where po = 1 kPa

Evaluation Results:

The example is for fitted vapor pressures for benzene.

Wagner36 (Vapor Pressure: Output Details)

ln(p/po) ln(pc/po) = Tc/T (A1 + A2×t1.5 + A3×t3 + A4×t6); where t = 1 - T/Tc and po = 1 kPa

Evaluation Results:

The example is for fitted vapor pressures for benzene.


Sublimation Pressure: Crystal-Gas Phase Boundary Pressure

PV Expansion: Sublimation Pressure

ln(p/po) = a1 + a2/T + a3×ln(T) + a4×T + a5×T2 + a6×T6+ a7/T4

NOTE: The TDE program truncates this equation based upon the extent and quality of the fitted data.


Condensed Phase boundary pressure

PolynomialExpansion: Phase boundary pressure for the crystal/liquid boundary

ln(p/po) = å ai× T i, where the summation is from i = 0 to nTerms - 1

Evaluation Results:

The example is for fitted phase-boundary pressures for benzene.


Density of the Liquid (on the Liquid/Gas phase boundary): dsat

VDNS Expansion: For dsat of the Liquid or Gas phase

dsat = dc + a1×t0.35 + åai+1×ti ; where the summation is from i = 1 to nTerms -1.

dc = the critical density and t = 1 - T/Tc, where Tc is the critical temperature.

NOTE: The TDE program truncates this equation based upon the extent and quality of the fitted data.

Rackett Equation: For dsat of the Liquid phase

dsat = dc×B (1-T/Tc)N; where Tc and dc are the critical temperature and critical density, respectively.

PPDS 10: For dsat of the Liquid phase

dsat = dc + a1×t0.35 + a2×t2/3 + a3×t + a4×t4/3;

dc = the critical density and t = 1 - T/Tc, where Tc is the critical temperature.

Evaluation Results:

The example is for fitted densities at vapor saturation for benzene.

PPDS 17: For dsat of the Liquid phase

dsat = (a1 + a2×t) -1 - t-2/7/a0 ; where t = 1 - T/Tc, and Tc is the critical temperature.

Evaluation Results:

The example is for fitted densities at vapor saturation for benzene.


Density of the Gas (on the Liquid/Gas phase boundary)


Density (Liquid Phase)

Tait Equation: Density (Liquid Phase)

d = dsat / [1 - c×ln{(b + p) / (b + psat)}] ; where

b = åBi+1×t i, c = åCi+1×t i, and t = (T-Tcenter)/100, where Tcenter is a constant parameter.
Summations are from i = 0 to (nTerms -1), where nTerms is the number of B or C terms.
dsat = the density of the saturated liquid and psat = the saturation vapor pressure.


Density (Gas Phase)

VirialV: For density of the gas phase.

d = 1000×Mw / Vm; where Mw is the molar mass and Vm is the molar volume.

Z = 1000×p×Vm/(R×T) = 1 + B/Vm + C/Vm2, where B = åbi+1/T i and C = åci+1/T i

Evaluation Results:

The example is for fitted gas densities of pentane.


Enthalpy of Vaporization (Liquid/Gas)

HVPExpansion: For Hvap for the liquid-gas phase boundary

ln(Hvap/Hvapo) = a1 + åai ×Tri-1×ln(1-Tr) , where the summation is from i = 2 to nTerms -1

Tr = T/Tc, Tc is the critical temperature, and Hvapo = 1 kJ/mol

Evaluation Results:

The example is for fitted enthalpies of vaporization for benzene.

Yaws.VaporizationH: For Hvap for the liquid-gas phase boundary

Hvap = A×{1 - ( T / Tc )}n

Evaluation Results:

The example is for fitted enthalpies of vaporization for pentane.

PPDS12: For Hvap for the liquid-gas phase boundary

Hvap/R = a1×t1/3 + a2×t2/3 + a3×t + a4×t2 + a5×t6

where t = 1 - T/Tc, Tc is the critical temperature, and R is the gas constant.

Evaluation Results:

The example is for fitted enthalpies of vaporization for benzene.


Csat (Liquid Phase)

CSExpansion: For Csat of the Liquid phase

Csat = (åai+1× ti) + b/t , where the summation is from i = 0 to nTerms -1.

Evaluation Results:

The example is for fitted heat capacities at vapor saturation for benzene.

Yaws.PolynomialExpansion: For Csat of the liquid phase

Csat = å ai× T i, where the summation is from i = 0 to nTerms - 1

Evaluation Results:

The example is for fitted heat capacities at vapor saturation for benzene.

DIPPR.PolynomialExpansion: For Csat of the liquid phase

Csat = å ai× T i, where the summation is from i = 0 to nTerms - 1

Evaluation Results:

The example is for fitted heat capacities at vapor saturation for benzene.

PPDS 15: For Csat of the liquid phase

Csat / R = a0/t + a1 + a2×t + a3×t2 + a4×t3 + a5×t4

where t = 1 - T/Tc, Tc is the critical temperature, and R is the gas constant.

Evaluation Results:

The example is for fitted heat capacities at vapor saturation for benzene.


Cpo(Ideal Gas)

Cpo(Ideal Gas)

Cpo = å ai× T i, where the summation is from i = 0 to nTerms - 1

The example is for fitted heat capacities in the ideal-gas state at p = 100 kPa for pentane.

Aly & Lee Equation (same as DIPPR 107):
Cpo(Ideal Gas)

Cpo = a + b×{(c/T)/sinh(c/T)}2 + d×{(e/T)/cosh(e/T)}2

Reference: Aly, F. A.; Lee, L. L. Fluid Phase Equil. 1981, 6, 169-179.

The example is for fitted heat capacities in the ideal-gas state at p = 100 kPa for pentane.

PPDS 2: Cpo(Ideal Gas)

Cpo/R = Clow + (Clow - C¥)×y2 ×{1 + (y - 1) å(ai × yi)} ; where the summation is from i = 0 to 4.

Clow and C¥ are equation constants, and y = T / (T + TS), where TS is a constant.

Evaluation Results:

The example is for fitted heat capacities in the ideal-gas state at p = 100 kPa for pentane.

Helmholtz: Cpo(Ideal Gas)

Cpo/R = 1 + t - {åai×ni×(ni - 1)×tni}(ni¹ 0 or 1) + åbi×(ci×t)2×exp(ci×t) / {exp(ci×t) - 1}2;
where t = Tc/T, Tc = the critical temperature, and the summations are from i = 1 to nTerms.

The example is for fitted heat capacities in the ideal-gas state at p = 100 kPa for 2-methylpyrrole.


Speed of Sound (Liquid Phase)

Speed of Sound (Liquid Phase)

u = A + B×T + C×(d - dsat) + D×d 2,

where d is the density of the liquid and dsat is the density of the saturated liquid.

The example is for fitted speeds of sound for benzene.


Speed of Sound (Gas Phase)

Speed of Sound (Gas Phase)

u = A + B×T + C×p + D×p/T ;

where T is the temperature and p is pressure.

The example is for fitted speeds of sound for pentane in the gas phase.


Refractive Index nD (Liquid)

RIXExpansion: Refractive Index nD (Liquid)

nD = A + B×t + å Ci×wi ;the summation is from i = 1 to nTerms

where t = T - 298.15 K and w = WL - 589.26 (WL = wavelength in nm)

Evaluation Results:

The example is for fitted surface tensions for pentane.


Surface Tension s (Liquid/Gas)

PPDS14: For surface tension s for the liquid/gas interface

s = a0× ta1×(1 + a2 ×t) , where t = 1 - T/Tc and Tc is the critical temperature.

Evaluation Results:

The example is for fitted surface tensions for benzene.

Yaws.SurfaceTension: For surface tension s for the liquid/gas interface

  • Alternative 1: Yaws.SurfaceTension (sample parameter output)

    s = exp(A)×{1 - ( T / Tc )}n

    Evaluation Results:

    The example is for fitted surface tensions for benzene.

    HVPExpansion: For surface tension s for the liquid/gas interface

    ln(s/so) = a1 + åai ×Tri-1×ln(1-Tr) , where the summation is from i = 2 to nTerms -1

    Tr = T/Tc, Tc is the critical temperature, and so = 1 N/m

    The example is for fitted surface tensions for benzene.


    Viscosity (Saturated Liquid)

    PPDS9: Viscosity h of the saturated liquid

    ln(h/ho) = a1 ×X1/3 + a2 ×X4/3 + ln(a5) , where X = (a3 - T) / (T - a4) and ho = 1 Pa×s.

    Evaluation Results:

    The example is for fitted viscosities for the saturated liquid phase of benzene.

    Yaws.Viscosity: Viscosity h of the saturated liquid

    lg(h/ho) = A + B/T + C×T + D×T 2

    Evaluation Results:

    The example is for fitted viscosities for the saturated liquid phase of benzene.

    DIPPR101: Viscosity h of the saturated liquid

    ln(h/ho) = a + b/T + c×ln(T) + d×Te ; where ho = 1 Pa×s

    Evaluation Results:

    The example is for fitted viscosities for the saturated liquid phase of benzene.


    Viscosity (Gas at low pressures; p < 6 bar)

    TransportPolynomial: For viscosity h of the gas at low pressures (p < 600 kPa)

    h = å ai× T i, where the summation is from i = 0 to nTerms - 1

    Evaluation Results:

    The example is for fitted thermal conductivities for the saturated liquid phase of pentane.

    Yaws.PolynomialExpansion: For viscosity h of the gas at low pressures (p < 600 kPa)

    h = å ai× T i, where the summation is from i = 0 to nTerms - 1

    Evaluation Results:

    The example is for fitted thermal conductivities for the saturated liquid phase of pentane.

    DIPPR 102: For viscosity h of the gas at low pressures (p < 600 kPa)

    h = A×T B / (1+ C/T + D/T 2)

    Evaluation Results:

    The example is for fitted thermal conductivities for the saturated liquid phase of pentane.

    PPDS 5: For viscosity h of the gas at low pressures (p < 600 kPa)

    h = a0×Tr / {1 + a1×(Tr - 1)× Tra2}1/6; where Tr = T/Tc and Tc is the critical temperature.

    Evaluation Results:

    The example is for fitted thermal conductivities for the saturated liquid phase of pentane.


    Thermal Conductivity l: (Liquid)

    TransportPolynomial: For thermal conductivity l of the saturated liquid

    l = å ai× T i, where the summation is from i = 0 to nTerms - 1

    Evaluation Results:

    The example is for fitted thermal conductivities for the saturated liquid phase of benzene.

    Yaws.ThermalConductivity: For thermal conductivity l of the saturated liquid

    lg(l/lo) = A + B×(1 - T/C)2/7

  • Evaluation Results:

    The example is for fitted thermal conductivities for the saturated liquid phase of benzene.

    Yaws.PolynomialExpansion: For thermal conductivity l of the saturated liquid

    l = å ai× T i, where the summation is from i = 0 to nTerms - 1

    Evaluation Results:

    The example is for fitted thermal conductivities for the saturated liquid phase of benzene.

    DIPPR.PolynomialExpansion: For thermal conductivity l of the saturated liquid

    l = å ai× T i, where the summation is from i = 0 to nTerms - 1

    Evaluation Results:

    The example is for fitted thermal conductivities for the saturated liquid phase of benzene.

    PPDS8: For thermal conductivity l of the saturated liquid

    l = a1 + å(ai+1 ×ti/3) , where the summation is from i = 1 to nTerms -1 and t = 1 - T/Tc

    Evaluation Results:

    The example is for fitted thermal conductivities for the liquid phase of benzene.


    Thermal Conductivity (Gas at low pressures; p < 6 bar)

    TransportPolynomial: For thermal conductivity l of the gas at low pressure (p < 600 kPa)

    l = å ai× T i, where the summation is from i = 0 to nTerms - 1

    Evaluation Results:

    The example is for fitted thermal conductivities for the saturated liquid phase of pentane.

    Yaws.PolynomialExpansion: For thermal conductivity l of the gas at low pressure (p < 600 kPa)

    l = å ai× T i, where the summation is from i = 0 to nTerms - 1

    Evaluation Results:

    The example is for fitted thermal conductivities for the saturated liquid phase of pentane.

    PPDS 3: For thermal conductivity l of the gas at low pressure (p < 600 kPa)

    l = Tr0.5 (åai / Tri)-1 , where the summation is from i = 1 to 3,

    and Tr = T/Tc, where Tc is the critical temperature.

    Evaluation Results:

    The example is for fitted thermal conductivities for the saturated liquid phase of pentane.