lennard_jones¶
All data and functions for computing the Lennard-Jones molecular diameter.
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thermosteam.properties.lennard_jones.
Stockmayer
(Tm=None, Tb=None, Tc=None, Zc=None, omega=None, CASRN='', AvailableMethods=False, Method=None)[source]¶ This function handles the retrieval or calculation a chemical’s Stockmayer parameter. Values are available from one source with lookup based on CASRNs, or can be estimated from 7 CSP methods. Will automatically select a data source to use if no Method is provided; returns None if the data is not available.
Prefered sources are ‘Magalhães, Lito, Da Silva, and Silva (2013)’ for common chemicals which had valies listed in that source, and the CSP method Tee, Gotoh, and Stewart CSP with Tc, omega (1966) for chemicals which don’t.
Examples
>>> Stockmayer(CASRN='64-17-5') 1291.41
- Parameters
Tm (float, optional) – Melting temperature of fluid [K]
Tb (float, optional) – Boiling temperature of fluid [K]
Tc (float, optional) – Critical temperature, [K]
Zc (float, optional) – Critical compressibility, [-]
omega (float, optional) – Acentric factor of compound, [-]
CASRN (string, optional) – CASRN [-]
- Returns
epsilon_k (float) – Lennard-Jones depth of potential-energy minimum over k, [K]
methods (list, only returned if AvailableMethods == True) – List of methods which can be used to obtain epsilon with the given inputs
- Other Parameters
Method (string, optional) – A string for the method name to use, as defined by constants in Stockmayer_methods
AvailableMethods (bool, optional) – If True, function will determine which methods can be used to obtain epsilon for the desired chemical, and will return methods instead of epsilon
Notes
These values are somewhat rough, as they attempt to pigeonhole a chemical into L-J behavior.
The tabulated data is from [2]_, for 322 chemicals.
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
- 2
Magalhães, Ana L., Patrícia F. Lito, Francisco A. Da Silva, and Carlos M. Silva. “Simple and Accurate Correlations for Diffusion Coefficients of Solutes in Liquids and Supercritical Fluids over Wide Ranges of Temperature and Density.” The Journal of Supercritical Fluids 76 (April 2013): 94-114. doi:10.1016/j.supflu.2013.02.002.
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thermosteam.properties.lennard_jones.
molecular_diameter
(Tc=None, Pc=None, Vc=None, Zc=None, omega=None, Vm=None, Vb=None, CASRN='', AvailableMethods=False, Method=None)[source]¶ This function handles the retrieval or calculation a chemical’s L-J molecular diameter. Values are available from one source with lookup based on CASRNs, or can be estimated from 9 CSP methods. Will automatically select a data source to use if no Method is provided; returns None if the data is not available.
Prefered sources are ‘Magalhães, Lito, Da Silva, and Silva (2013)’ for common chemicals which had valies listed in that source, and the CSP method Tee, Gotoh, and Stewart CSP with Tc, Pc, omega (1966) for chemicals which don’t.
Examples
>>> molecular_diameter(CASRN='64-17-5') 4.23738
- Parameters
Tc (float, optional) – Critical temperature, [K]
Pc (float, optional) – Critical pressure, [Pa]
Vc (float, optional) – Critical volume, [m^3/mol]
Zc (float, optional) – Critical compressibility, [-]
omega (float, optional) – Acentric factor of compound, [-]
Vm (float, optional) – Molar volume of liquid at the melting point of the fluid [K]
Vb (float, optional) – Molar volume of liquid at the boiling point of the fluid [K]
CASRN (string, optional) – CASRN [-]
- Returns
sigma (float) – Lennard-Jones molecular diameter, [Angstrom]
methods (list, only returned if AvailableMethods == True) – List of methods which can be used to obtain epsilon with the given inputs
- Other Parameters
Method (string, optional) – A string for the method name to use, as defined by constants in molecular_diameter_methods
AvailableMethods (bool, optional) – If True, function will determine which methods can be used to obtain sigma for the desired chemical, and will return methods instead of sigma
Notes
These values are somewhat rough, as they attempt to pigeonhole a chemical into L-J behavior.
The tabulated data is from [2]_, for 322 chemicals.
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
- 2
Magalhães, Ana L., Patrícia F. Lito, Francisco A. Da Silva, and Carlos M. Silva. “Simple and Accurate Correlations for Diffusion Coefficients of Solutes in Liquids and Supercritical Fluids over Wide Ranges of Temperature and Density.” The Journal of Supercritical Fluids 76 (April 2013): 94-114. doi:10.1016/j.supflu.2013.02.002.
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thermosteam.properties.lennard_jones.
sigma_Flynn
(Vc)[source]¶ Calculates Lennard-Jones molecular diameter. Uses critical volume. CSP method by [1]_ as reported in [2]_.
\[\sigma = 0.561(V_c^{1/3})^{5/4}\]- Parameters
Vc (float) – Critical volume of fluid [m^3/mol]
- Returns
sigma – Lennard-Jones molecular diameter, [Angstrom]
- Return type
float
Notes
Vc is originally in units of mL/mol.
Examples
>>> sigma_Flynn(0.000268) 5.2506948422196285
References
- 1
Flynn, L.W., M.S. thesis, Northwestern Univ., Evanston, Ill. (1960).
- 2
Stiel, L. I., and George Thodos. “Lennard-Jones Force Constants Predicted from Critical Properties.” Journal of Chemical & Engineering Data 7, no. 2 (April 1, 1962): 234-36. doi:10.1021/je60013a023
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thermosteam.properties.lennard_jones.
sigma_Bird_Stewart_Lightfoot_critical_2
(Tc, Pc)[source]¶ Calculates Lennard-Jones molecular diameter. Uses critical temperature and pressure. CSP method by [1]_.
\[\sigma = 2.44(T_c/P_c)^{1/3}\]- Parameters
Tc (float) – Critical temperature of fluid [K]
Pc (float) – Critical pressure of fluid [Pa]
- Returns
sigma – Lennard-Jones molecular diameter, [Angstrom]
- Return type
float
Notes
Original units of critical pressure are atmospheres.
Examples
>>> sigma_Bird_Stewart_Lightfoot_critical_2(560.1, 4550000) 5.658657684653222
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
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thermosteam.properties.lennard_jones.
sigma_Bird_Stewart_Lightfoot_critical_1
(Vc)[source]¶ Calculates Lennard-Jones molecular diameter. Uses critical volume. CSP method by [1]_.
\[\sigma = 0.841 V_c^{1/3}\]- Parameters
Vc (float) – Critical volume of fluid [m^3/mol]
- Returns
sigma – Lennard-Jones molecular diameter, [Angstrom]
- Return type
float
Notes
Original units of Vc are mL/mol.
Examples
>>> sigma_Bird_Stewart_Lightfoot_critical_1(0.000268) 5.422184116631474
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
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thermosteam.properties.lennard_jones.
sigma_Bird_Stewart_Lightfoot_boiling
(Vb)[source]¶ Calculates Lennard-Jones molecular diameter. Uses molar volume of liquid at boiling. CSP method by [1]_.
\[\sigma = 1.166V_{b,liq}^{1/3}\]- Parameters
Vb (float) – Boiling molar volume of liquid [m^3/mol]
- Returns
sigma – Lennard-Jones collision integral, [Angstrom]
- Return type
float
Notes
Original units of Vb are mL/mol.
Examples
>>> sigma_Bird_Stewart_Lightfoot_boiling(0.0001015) 5.439018856944655
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
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thermosteam.properties.lennard_jones.
sigma_Bird_Stewart_Lightfoot_melting
(Vm)[source]¶ Calculates Lennard-Jones molecular diameter. Uses molar volume of a liquid at its melting point. CSP method by [1]_.
\[\sigma = 1.222 V_{m,sol}^{1/3}\]- Parameters
Vm (float) – Melting molar volume of a liquid at its melting point [m^3/mol]
- Returns
sigma – Lennard-Jones molecular diameter, [Angstrom]
- Return type
float
Notes
Original units of Vm are mL/mol.
Examples
>>> sigma_Bird_Stewart_Lightfoot_melting(8.8e-05) 5.435407341351406
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
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thermosteam.properties.lennard_jones.
sigma_Stiel_Thodos
(Vc, Zc)[source]¶ Calculates Lennard-Jones molecular diameter. Uses critical volume and compressibility. CSP method by [1]_.
\[\sigma = 0.1866 V_c^{1/3} Z_c^{-6/5}\]- Parameters
Vc (float) – Critical volume of fluid [m^3/mol]
Zc (float) – Critical compressibility of fluid, [-]
- Returns
sigma – Lennard-Jones molecular diameter, [Angstrom]
- Return type
float
Notes
Vc is originally in units of mL/mol.
Examples
Monofluorobenzene
>>> sigma_Stiel_Thodos(0.000271, 0.265) 5.94300853971033
References
- 1
Stiel, L. I., and George Thodos. “Lennard-Jones Force Constants Predicted from Critical Properties.” Journal of Chemical & Engineering Data 7, no. 2 (April 1, 1962): 234-36. doi:10.1021/je60013a023
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thermosteam.properties.lennard_jones.
sigma_Tee_Gotoh_Steward_1
(Tc, Pc)[source]¶ Calculates Lennard-Jones molecular diameter. Uses critical temperature and pressure. CSP method by [1]_.
\[\sigma = 2.3647 \left(\frac{T_c}{P_c}\right)^{1/3}\]- Parameters
Tc (float) – Critical temperature of fluid [K]
Pc (float) – Critical pressure of fluid [Pa]
- Returns
sigma – Lennard-Jones molecular diameter, [Angstrom]
- Return type
float
Notes
Original units of Pc are atm. Further regressions with other parameters were performed in [1]_ but are not included here, except for sigma_Tee_Gotoh_Steward_2.
Examples
>>> sigma_Tee_Gotoh_Steward_1(560.1, 4550000) 5.48402779790962
References
- 1
Tee, L. S., Sukehiro Gotoh, and W. E. Stewart. “Molecular Parameters for Normal Fluids. Lennard-Jones 12-6 Potential.” Industrial & Engineering Chemistry Fundamentals 5, no. 3 (August 1, 1966): 356-63. doi:10.1021/i160019a011
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thermosteam.properties.lennard_jones.
sigma_Tee_Gotoh_Steward_2
(Tc, Pc, omega)[source]¶ Calculates Lennard-Jones molecular diameter. Uses critical temperature, pressure, and acentric factor. CSP method by [1]_.
\[\sigma = (2.3551 - 0.0874\omega)\left(\frac{T_c}{P_c}\right)^{1/3}\]- Parameters
Tc (float) – Critical temperature of fluid [K]
Pc (float) – Critical pressure of fluid [Pa]
omega (float) – Acentric factor for fluid, [-]
- Returns
sigma – Lennard-Jones molecular diameter, [Angstrom]
- Return type
float
Notes
Original units of Pc are atm. Further regressions with other parameters were performed in [1]_ but are not included here, except for sigma_Tee_Gotoh_Steward_1.
Examples
>>> sigma_Tee_Gotoh_Steward_2(560.1, 4550000, 0.245) 5.412104867264477
References
- 1
Tee, L. S., Sukehiro Gotoh, and W. E. Stewart. “Molecular Parameters for Normal Fluids. Lennard-Jones 12-6 Potential.” Industrial & Engineering Chemistry Fundamentals 5, no. 3 (August 1, 1966): 356-63. doi:10.1021/i160019a011
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thermosteam.properties.lennard_jones.
sigma_Silva_Liu_Macedo
(Tc, Pc)[source]¶ Calculates Lennard-Jones molecular diameter. Uses critical temperature and pressure. CSP method by [1]_.
\[\sigma_{LJ}^3 = 0.17791 + 11.779 \left( \frac{T_c}{P_c}\right) - 0.049029\left( \frac{T_c}{P_c}\right)^2\]- Parameters
Tc (float) – Critical temperature of fluid [K]
Pc (float) – Critical pressure of fluid [Pa]
- Returns
sigma – Lennard-Jones molecular diameter, [Angstrom]
- Return type
float
Notes
Pc is originally in bar. An excellent paper. None is returned if the polynomial returns a negative number, as in the case of 1029.13 K and 3.83 bar.
Examples
>>> sigma_Silva_Liu_Macedo(560.1, 4550000) 5.164483998730177
References
- 1
Silva, Carlos M., Hongqin Liu, and Eugenia A. Macedo. “Models for Self-Diffusion Coefficients of Dense Fluids, Including Hydrogen-Bonding Substances.” Chemical Engineering Science 53, no. 13 (July 1, 1998): 2423-29. doi:10.1016/S0009-2509(98)00037-2
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thermosteam.properties.lennard_jones.
epsilon_Flynn
(Tc)[source]¶ Calculates Lennard-Jones depth of potential-energy minimum. Uses critical temperature. CSP method by [1]_ as reported in [2]_.
\[\epsilon/k = 1.77 T_c^{5/6}\]- Parameters
Tc (float) – Critical temperature of fluid [K]
- Returns
epsilon_k – Lennard-Jones depth of potential-energy minimum over k, [K]
- Return type
float
Notes
Examples
>>> epsilon_Flynn(560.1) 345.2984087011443
References
- 1
Flynn, L.W., M.S. thesis, Northwestern Univ., Evanston, Ill. (1960).
- 2
Stiel, L. I., and George Thodos. “Lennard-Jones Force Constants Predicted from Critical Properties.” Journal of Chemical & Engineering Data 7, no. 2 (April 1, 1962): 234-36. doi:10.1021/je60013a023
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thermosteam.properties.lennard_jones.
epsilon_Bird_Stewart_Lightfoot_critical
(Tc)[source]¶ Calculates Lennard-Jones depth of potential-energy minimum. Uses critical temperature. CSP method by [1]_.
\[\epsilon/k = 0.77T_c\]- Parameters
Tc (float) – Critical temperature of fluid [K]
- Returns
epsilon_k – Lennard-Jones depth of potential-energy minimum over k, [K]
- Return type
float
Notes
Examples
>>> epsilon_Bird_Stewart_Lightfoot_critical(560.1) 431.27700000000004
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
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thermosteam.properties.lennard_jones.
epsilon_Bird_Stewart_Lightfoot_boiling
(Tb)[source]¶ Calculates Lennard-Jones depth of potential-energy minimum. Uses boiling temperature. CSP method by [1]_.
\[\epsilon/k = 1.15 T_b\]- Parameters
Tb (float) – Boiling temperature [K]
- Returns
epsilon_k – Lennard-Jones depth of potential-energy minimum over k, [K]
- Return type
float
Notes
Examples
>>> epsilon_Bird_Stewart_Lightfoot_boiling(357.85) 411.5275
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
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thermosteam.properties.lennard_jones.
epsilon_Bird_Stewart_Lightfoot_melting
(Tm)[source]¶ Calculates Lennard-Jones depth of potential-energy minimum. Uses melting temperature. CSP method by [1]_.
\[\epsilon/k = 1.92T_m\]- Parameters
Tm (float) – Melting temperature [K]
- Returns
epsilon_k – Lennard-Jones depth of potential-energy minimum over k, [K]
- Return type
float
Notes
Examples
>>> epsilon_Bird_Stewart_Lightfoot_melting(231.15) 443.808
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006
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thermosteam.properties.lennard_jones.
epsilon_Stiel_Thodos
(Tc, Zc)[source]¶ Calculates Lennard-Jones depth of potential-energy minimum. Uses Critical temperature and critical compressibility. CSP method by [1]_.
\[\epsilon/k = 65.3 T_c Z_c^{3.6}\]- Parameters
Tc (float) – Critical temperature of fluid [K]
Zc (float) – Critical compressibility of fluid, [-]
- Returns
epsilon_k – Lennard-Jones depth of potential-energy minimum over k, [K]
- Return type
float
Notes
Examples
Fluorobenzene
>>> epsilon_Stiel_Thodos(358.5, 0.265) 196.3755830305783
References
- 1
Stiel, L. I., and George Thodos. “Lennard-Jones Force Constants Predicted from Critical Properties.” Journal of Chemical & Engineering Data 7, no. 2 (April 1, 1962): 234-36. doi:10.1021/je60013a023
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thermosteam.properties.lennard_jones.
epsilon_Tee_Gotoh_Steward_1
(Tc)[source]¶ Calculates Lennard-Jones depth of potential-energy minimum. Uses Critical temperature. CSP method by [1]_.
\[\epsilon/k = 0.7740T_c\]- Parameters
Tc (float) – Critical temperature of fluid [K]
- Returns
epsilon_k – Lennard-Jones depth of potential-energy minimum over k, [K]
- Return type
float
Notes
Further regressions with other parameters were performed in [1]_ but are not included here, except for epsilon_Tee_Gotoh_Steward_2.
Examples
>>> epsilon_Tee_Gotoh_Steward_1(560.1) 433.5174
References
- 1
Tee, L. S., Sukehiro Gotoh, and W. E. Stewart. “Molecular Parameters for Normal Fluids. Lennard-Jones 12-6 Potential.” Industrial & Engineering Chemistry Fundamentals 5, no. 3 (August 1, 1966): 356-63. doi:10.1021/i160019a011
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thermosteam.properties.lennard_jones.
epsilon_Tee_Gotoh_Steward_2
(Tc, omega)[source]¶ Calculates Lennard-Jones depth of potential-energy minimum. Uses critical temperature and acentric factor. CSP method by [1]_.
\[\epsilon/k = (0.7915 + 0.1693 \omega)T_c\]- Parameters
Tc (float) – Critical temperature of fluid [K]
omega (float) – Acentric factor for fluid, [-]
- Returns
epsilon_k – Lennard-Jones depth of potential-energy minimum over k, [K]
- Return type
float
Notes
Further regressions with other parameters were performed in [1]_ but are not included here, except for epsilon_Tee_Gotoh_Steward_1.
Examples
>>> epsilon_Tee_Gotoh_Steward_2(560.1, 0.245) 466.55125785
References
- 1
Tee, L. S., Sukehiro Gotoh, and W. E. Stewart. “Molecular Parameters for Normal Fluids. Lennard-Jones 12-6 Potential.” Industrial & Engineering Chemistry Fundamentals 5, no. 3 (August 1, 1966): 356-63. doi:10.1021/i160019a011
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thermosteam.properties.lennard_jones.
collision_integral_Neufeld_Janzen_Aziz
(Tstar, l=1, s=1)[source]¶ Calculates Lennard-Jones collision integral for any of 16 values of (l,j) for the wide range of 0.3 < Tstar < 100. Values are accurate to 0.1 % of actual values, but the calculation of actual values is computationally intensive and so these simplifications are used, developed in [1]_.
\[\Omega_D = \frac{A}{T^{*B}} + \frac{C}{\exp(DT^*)} + \frac{E}{\exp(FT^{*})} + \frac{G}{\exp(HT^*)} + RT^{*B}\sin(ST^{*W}-P)\]- Parameters
Tstar (float) – Reduced temperature of the fluid [-]
l (int) – term
s (int) – term
- Returns
Omega – Collision integral of A and B
- Return type
float
Notes
Acceptable pairs of (l,s) are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), and (4, 4).
\[T^* = \frac{k_b T}{\epsilon}\]Results are very similar to those of the more modern formulation, collision_integral_Kim_Monroe.
Calculations begin to yield overflow errors in some values of (l, 2) after Tstar = 75, beginning with (1, 7). Also susceptible are (1, 5) and (1, 6).
Examples
>>> collision_integral_Neufeld_Janzen_Aziz(100, 1, 1) 0.516717697672334
References
- 1
Neufeld, Philip D., A. R. Janzen, and R. A. Aziz. “Empirical Equations to Calculate 16 of the Transport Collision Integrals Omega(l, S)* for the Lennard-Jones (12-6) Potential.” The Journal of Chemical Physics 57, no. 3 (August 1, 1972): 1100-1102. doi:10.1063/1.1678363
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thermosteam.properties.lennard_jones.
collision_integral_Kim_Monroe
(Tstar, l=1, s=1)[source]¶ Calculates Lennard-Jones collision integral for any of 16 values of (l,j) for the wide range of 0.3 < Tstar < 400. Values are accurate to 0.007 % of actual values, but the calculation of actual values is computationally intensive and so these simplifications are used, developed in [1]_.
\[\Omega^{(l,s)*} = A^{(l,s)} + \sum_{k=1}^6 \left[ \frac{B_k^{(l,s)}} {(T^*)^k} + C_k^{(l,s)} (\ln T^*)^k \right]\]- Parameters
Tstar (float) – Reduced temperature of the fluid [-]
l (int) – term
s (int) – term
- Returns
Omega – Collision integral of A and B
- Return type
float
Notes
Acceptable pairs of (l,s) are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), and (4, 4).
\[T^* = \frac{k_b T}{\epsilon}\]Examples
>>> collision_integral_Kim_Monroe(400, 1, 1) 0.4141818082392228
References
- 1
Kim, Sun Ung, and Charles W. Monroe. “High-Accuracy Calculations of Sixteen Collision Integrals for Lennard-Jones (12-6) Gases and Their Interpolation to Parameterize Neon, Argon, and Krypton.” Journal of Computational Physics 273 (September 15, 2014): 358-73. doi:10.1016/j.jcp.2014.05.018.
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thermosteam.properties.lennard_jones.
Tstar
(T, epsilon_k=None, epsilon=None)[source]¶ This function calculates the parameter Tstar as needed in performing collision integral calculations.
\[T^* = \frac{kT}{\epsilon}\]Examples
>>> Tstar(T=318.2, epsilon_k=308.43) 1.0316765554582887
- Parameters
epsilon_k (float, optional) – Lennard-Jones depth of potential-energy minimum over k, [K]
epsilon (float, optional) – Lennard-Jones depth of potential-energy minimum [J]
- Returns
Tstar – Dimentionless temperature for calculating collision integral, [-]
- Return type
float
Notes
Tabulated values are normally listed as epsilon/k. k is the Boltzman constant, with units of J/K.
References
- 1
Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena, Revised 2nd Edition. New York: John Wiley & Sons, Inc., 2006