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:
ln(p/p^{o}) = a + b/T + c×ln(T) + d×T^{2} + e/T^{2} ; where p^{o} = 1 kPa
ln(p/p^{o}) = a + b/T + c×ln(T) + d×T^{e} ; where p^{o} = 1 kPa
ln(p/p^{o}) – ln(p_{c}/p^{o}) = T_{c}/T (A_{1} + A_{2}×t^{1.5} + A_{3}×t^{3} + A_{4}×t^{6}); where t = 1 - T/T_{c} and p^{o} = 1 kPa
Evaluation Results:
The example is for fitted vapor pressures for benzene.
Evaluation Results:
The example is for fitted vapor pressures for benzene.
Evaluation Results:
The example is for fitted vapor pressures for benzene.
Evaluation Results:
The example is for fitted vapor pressures for benzene.
Evaluation Results:
The example is for fitted vapor pressures for benzene.
Evaluation Results:
The example is for fitted vapor pressures for benzene.
ln(p/p^{o}) = a_{1} + a_{2}/T + a_{3}×ln(T) + a_{4}×T + a_{5}×T^{2} + a_{6}×T^{6}+ a_{7}/T^{4}
ln(p/p^{o}) = A + B/(T + C); where p^{o} = 1 kPa
lg(p/p^{o}) = a + b/T + c×lg(T) + d×T + e/T^{2} ; where p^{o} = 1 kPa and lg = log_{10}
ln(p/p^{o}) = a + b/T + c×ln(T) + d×T^{2} + e/T^{2} ; where p^{o} = 1 kPa
ln(p/p^{o}) = a + b/T + c×ln(T) + d×T^{e} ; where p^{o} = 1 kPa
NOTE: The TDE program truncates this equation based upon the extent and quality of the fitted data.
ln(p/p^{o}) = å a_{i}× T ^{i}, where the summation is from i = 0 to nTerms - 1
Evaluation Results:
The example is for fitted phase-boundary pressures for benzene.
d_{sat} = d_{c} + a_{1}×t^{0.35} + åa_{i+1}×t^{i} , where the summation is from i = 1 to nTerms -1.
d_{c} = the critical density and t = 1 - T/T_{c}, where T_{c} is the critical temperature.
d_{c} = the critical density and t = 1 - T/T_{c}, where T_{c} is the critical temperature.
NOTE: The TDE program truncates this equation based upon the extent and quality of the fitted data.
d_{c} = the critical density and t = 1 - T/T_{c}, where T_{c} is the critical temperature.
Evaluation Results:
The example is for fitted densities at vapor saturation for benzene.
Evaluation Results:
The example is for fitted densities at vapor saturation for benzene.
d_{sat} = d_{c} + a_{1}×t^{0.35} + åa_{i+1}×t^{i} , where the summation is from i = 1 to nTerms -1.
d_{c} = the critical density and t = 1 - T/T_{c}, where T_{c} is the critical temperature.
d = d_{sat} / [1 - c×ln{(b + p) / (b + p_{sat})}] ; where
b = åB_{i+1}×t ^{i},
c = åC_{i+1}×t ^{i}, and
t = (T-T_{center})/100, where T_{center} is a constant parameter.
Summations are from i = 0 to (nTerms -1), where nTerms is the number of B or C terms.
d_{sat} = the density of the saturated liquid and p_{sat} = the saturation vapor pressure.
b = åB_{i+1}×t ^{i},
c = åC_{i+1}×t ^{i}, and
t = (T-T_{center})/100, where T_{center} is a constant parameter.
Summations are from i = 0 to (nTerms -1), where nTerms is the number of B or C terms.
d_{sat} = the density of the saturated liquid and p_{sat} = the saturation vapor pressure.
d = 1000×Mw / V_{m}; where Mw is the molar mass and V_{m} is the molar volume.
Z = 1000×p×V_{m}/(R×T) = 1 + B/V_{m} + C/V_{m}^{2},
where B = åb_{i+1}/T^{ i} and C = åc_{i+1}/T^{ i}
Z = 1000×p×V_{m}/(R×T) = 1 + B/V_{m} + C/V_{m}^{2}, where B = åb_{i+1}/T^{ i} and C = åc_{i+1}/T^{ i}
Evaluation Results:
The example is for fitted gas densities of pentane.
ln(H_{vap}/H_{vap}^{o}) = a_{1} + åa_{i} ×T_{r}^{i-1}×ln(1-T_{r}) , where the summation is from i = 2 to nTerms -1
T_{r} = T/T_{c}, T_{c} is the critical temperature, and H_{vap}^{o} = 1 kJ/mol
H_{vap} = A×{1 - ( T / T_{c} )}^{n}
H_{vap}/R = a_{1}×t^{1/3} + a_{2}×t^{2/3} + a_{3}×t^{} + a_{4}×t^{2} + a_{5}×t^{6}
where t = 1 - T/T_{c}, T_{c} is the critical temperature, and R is the gas constant.
T_{r} = T/T_{c}, T_{c} is the critical temperature, and H_{vap}^{o} = 1 kJ/mol
Evaluation Results:
The example is for fitted enthalpies of vaporization for benzene.
Evaluation Results:
The example is for fitted enthalpies of vaporization for pentane.
where t = 1 - T/T_{c}, T_{c} is the critical temperature, and R is the gas constant.
Evaluation Results:
The example is for fitted enthalpies of vaporization for benzene.
C_{sat} = (åa_{i+1}× t^{i}) + b/t , where the summation is from i = 0 to nTerms -1.
C_{sat} = å a_{i}× T ^{i}, where the summation is from i = 0 to nTerms - 1
C_{sat} = å a_{i}× T ^{i}, where the summation is from i = 0 to nTerms - 1
C_{sat} / R = a_{0}/t + a_{1} + a_{2}×t + a_{3}×t^{2} + a_{4}×t^{3} + a_{5}×t^{4}
where t = 1 - T/T_{c}, T_{c} is the critical temperature, and R is the gas constant.
Evaluation Results:
The example is for fitted heat capacities at vapor saturation for benzene.
Evaluation Results:
The example is for fitted heat capacities at vapor saturation for benzene.
Evaluation Results:
The example is for fitted heat capacities at vapor saturation for benzene.
where t = 1 - T/T_{c}, T_{c} is the critical temperature, and R is the gas constant.
Evaluation Results:
The example is for fitted heat capacities at vapor saturation for benzene.
C_{p}^{o} / R = a_{0} + (a_{1} /T ^{2}) × exp( -a_{2} /T ) + a_{3} × y^{2} + {a_{4} - a_{5} /(T - a_{7})^{2}} × y ^{8}
where y = (T - a_{7})/(T + a_{6}) and R is the gas constant.
See Thermodynamics of Organic Compounds in the Gas State (Volumes I and II) by M. Frenkel, G. J. Kabo, K. N. Marsh, G. N. Roganov, and R. C. Wilhoit. Publsihed by the Thermodynamics Research Center (TRC), College Station: TX. 1994.
C_{p}^{o} = å a_{i}× T ^{i}, where the summation is from i = 0 to nTerms - 1
C_{p}^{o} = a + b×{(c/T)/sinh(c/T)}^{2} + d×{(e/T)/cosh(e/T)}^{2}
C_{p}^{o}/R = C_{low} + (C_{low} - C_{¥})×y^{2} ×{1 + (y - 1) å(a_{i } × y_{i})} ; where the summation is from i = 0 to 4.
C_{low} and C_{¥} are equation constants, and y = T / (T + T_{S}), where T_{S} is a constant.
C_{p}^{o}/R = 1 + t - {åa_{i}×n_{i}×(n_{i} - 1)×t^{ni}}_{(ni¹ 0 or 1)} + åb_{i}×(c_{i}×t)^{2}×exp(c_{i}×t) / {exp(c_{i}×t) - 1}^{2};
where t = T_{c}/T, T_{c} = 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 pentane.
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.
C_{low} and C_{¥} are equation constants, and y = T / (T + T_{S}), where T_{S} is a constant.
Evaluation Results:
The example is for fitted heat capacities in the ideal-gas state at p = 100 kPa for pentane.
u = A + B×T + C×(d - d_{sat}) + D×d^{ 2},
where d is the density of the liquid and d_{sat} is the density of the saturated liquid.
where d is the density of the liquid and d_{sat} is the density of the saturated liquid.
The example is for fitted speeds of sound for benzene.
u = A + B×T + C×p + D×p/T ;
where T is the temperature and p is pressure.
where T is the temperature and p is pressure.
The example is for fitted speeds of sound for pentane in the gas phase.
n_{D} = A + B×t + å C_{i}×w^{i} ;the summation is from i = 1 to nTerms
where t = T - 298.15 K and w = WL - 589.26 (WL = wavelength in nm)
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.
s = a_{0}× t^{a1}×(1 + a_{2} ×t) , where t = 1 - T/T_{c} and T_{c} is the critical temperature.
s = exp(A)×{1 - ( T / T_{c} )}^{n}
ln(s/s^{o}) = a_{1} + åa_{i} ×T_{r}^{i-1}×ln(1-T_{r}) , where the summation is from i = 2 to nTerms -1
T_{r} = T/T_{c}, T_{c} is the critical temperature, and s^{o} = 1 N/m
Evaluation Results:
The example is for fitted surface tensions for benzene.
s = exp(A)×{1 - ( T / T_{c} )}^{n}
Evaluation Results:
The example is for fitted surface tensions for benzene.
T_{r} = T/T_{c}, T_{c} is the critical temperature, and s^{o} = 1 N/m
The example is for fitted surface tensions for benzene.
ln(h/h^{o}) = a_{1} ×X^{1/3} + a_{2} ×X^{4/3} + ln(a_{5}) , where X = (a_{3} - T) / (T - a_{4}) and h^{o} = 1 Pa×s
lg(h/h^{o}) = A + B/T + C×T + D×T ^{2}
ln(h/h^{o}) = a + b/T + c×ln(T) + d×T^{e} ; where h^{o} = 1 Pa×s
Evaluation Results:
The example is for fitted viscosities for the saturated liquid phase of benzene.
Evaluation Results:
The example is for fitted viscosities for the saturated liquid phase of benzene.
Evaluation Results:
The example is for fitted viscosities for the saturated liquid phase of benzene.
h = å a_{i}× T ^{i}, where the summation is from i = 0 to nTerms - 1
h = å a_{i}× T ^{i}, where the summation is from i = 0 to nTerms - 1
h = A×T^{ B} / (1+ C/T + D/T^{ 2})
h = a_{0}×T_{r} / {1 + a_{1}×(T_{r} - 1)× T_{r}^{a2}}^{1/6}; where T_{r} = T/T_{c} and T_{c} is the critical temperature.
Evaluation Results:
The example is for fitted thermal conductivities for the saturated liquid phase of pentane.
Evaluation Results:
The example is for fitted thermal conductivities for the saturated liquid phase of pentane.
Evaluation Results:
The example is for fitted thermal conductivities for the saturated liquid phase of pentane.
Evaluation Results:
The example is for fitted thermal conductivities for the saturated liquid phase of pentane.
l = å a_{i}× T ^{i}, where the summation is from i = 0 to nTerms - 1
lg(l/l^{o}) = A + B×(1 - T/C)^{2/7}
l = å a_{i}× T ^{i}, where the summation is from i = 0 to nTerms - 1
l = å a_{i}× T ^{i}, where the summation is from i = 0 to nTerms - 1
l = a_{1} + å(a_{i+1} ×t^{i/3}) , where the summation is from i = 1 to nTerms -1 and t = 1 - T/T_{c}
Evaluation Results:
The example is for fitted thermal conductivities for the saturated liquid phase of benzene.
Evaluation Results:
The example is for fitted thermal conductivities for the saturated liquid phase of benzene.
Evaluation Results:
The example is for fitted thermal conductivities for the saturated liquid phase of benzene.
Evaluation Results:
The example is for fitted thermal conductivities for the saturated liquid phase of benzene.
Evaluation Results:
The example is for fitted thermal conductivities for the liquid phase of benzene.
l = å a_{i}× T ^{i}, where the summation is from i = 0 to nTerms - 1
l = å a_{i}× T ^{i}, where the summation is from i = 0 to nTerms - 1
l = T_{r}^{0.5} (åa_{i} / T_{r}^{i})^{-1} , where the summation is from i = 1 to 3,
and T_{r} = T/T_{c}, where T_{c} is the critical temperature.
Evaluation Results:
The example is for fitted thermal conductivities for the saturated liquid phase of pentane.
Evaluation Results:
The example is for fitted thermal conductivities for the saturated liquid phase of pentane.
and T_{r} = T/T_{c}, where T_{c} is the critical temperature.
Evaluation Results:
The example is for fitted thermal conductivities for the saturated liquid phase of pentane.