Air: Fundamental Equation of State for Air (chemicals.air)¶

This module contains various thermodynamic functions for air and humid air.

For reporting bugs, adding feature requests, or submitting pull requests, please use the GitHub issue tracker.

Dry Air Basic Solvers
Dry Air Bubble/Dew Points
Dry Air Constants
Dry Air Ideal Gas Terms
Dry Air Residual Terms
Humid Air Virial Terms
Henry’s Law for Air in Water

Dry Air Basic Solvers ¶

chemicals.air.lemmon2000_rho(T, P)[source]¶

Calculate the density of air according to the Lemmon (2000) [1] given a temperature T and pressure P.

Parameters

Tfloat: Temperature, [K]
Pfloat: Pressure, [Pa]

Returns

rhofloat: Molar density of air, [mol/m^3]

Notes

This solution is iterative due to the nature of the equation. This solver has been tested only for gas solutions.

References

1(1,2): Lemmon, Eric W., Richard T. Jacobsen, Steven G. Penoncello, and Daniel G. Friend. “Thermodynamic Properties of Air and Mixtures of Nitrogen, Argon, and Oxygen From 60 to 2000 K at Pressures to 2000 MPa.” Journal of Physical and Chemical Reference Data 29, no. 3 (May 1, 2000): 331-85. https://doi.org/10.1063/1.1285884.

Examples

>>> lemmon2000_rho(T=300.0, P=1e6)
402.046613509

2 GPa and 2000 K are suggested as upper limits of [1] although there are no hardcoded limits for temperature and pressure.

>>> lemmon2000_rho(T=2000.0, P=2e9)
32892.9327834

chemicals.air.lemmon2000_P(T, rho)[source]¶

Calculate the pressure of air according to the (2000) given a temperature T and molar density rho.

Parameters

Tfloat: Temperature, [K]
rhofloat: Molar density of air, [mol/m^3]

Returns

Pfloat: Pressure, [Pa]

Notes

Helmholtz equations of state are explicit with inputs of temperature and density, so this is a direct calculation with no iteration required.

References

1: Lemmon, Eric W., Richard T. Jacobsen, Steven G. Penoncello, and Daniel G. Friend. “Thermodynamic Properties of Air and Mixtures of Nitrogen, Argon, and Oxygen From 60 to 2000 K at Pressures to 2000 MPa.” Journal of Physical and Chemical Reference Data 29, no. 3 (May 1, 2000): 331-85. https://doi.org/10.1063/1.1285884.

Examples

>>> lemmon2000_P(330.0, lemmon2000_rho(T=330.0, P=8e5))
8e5
>>> lemmon2000_P(823.0, 40)
273973.0024911

chemicals.air.lemmon2000_T(P, rho)[source]¶

Calculate the temperature of air according to the Lemmon (2000) [1] given a pressure P and molar density rho .

Parameters

Pfloat: Pressure, [Pa]
rhofloat: Molar density of air, [mol/m^3]

Returns

Tfloat: Temperature, [K]

Notes

This solution is iterative due to the nature of the equation. This solver has been tested only for gas solutions.

References

1: Lemmon, Eric W., Richard T. Jacobsen, Steven G. Penoncello, and Daniel G. Friend. “Thermodynamic Properties of Air and Mixtures of Nitrogen, Argon, and Oxygen From 60 to 2000 K at Pressures to 2000 MPa.” Journal of Physical and Chemical Reference Data 29, no. 3 (May 1, 2000): 331-85. https://doi.org/10.1063/1.1285884.

Examples

>>> lemmon2000_T(P=1e5, rho=20.0)
601.1393854499

Dry Air Bubble/Dew Points ¶

chemicals.air.lemmon2000_air_P_dew(T)[source]¶

Calculates the dew pressure of standard dry air according to Lemmon (2000).

\ln \left(\frac{P_{dew}}{P_j} \right) = \left(\frac{T_j}{T} \right) \sum_{i}^8 N_i \theta^{i/2}

Parameters

Tfloat: Temperature, [K]

Returns

P_dewfloat: Dew pressure, [Pa]

Notes

The stated range of this ancillary equation is 59.75 K <= T <= 132.6312 K.

Examples

>>> lemmon2000_air_P_dew(100.0)
567424.1338937

chemicals.air.lemmon2000_air_P_bubble(T)[source]¶

Calculates the bubble pressure of standard dry air according to Lemmon (2000).

\ln \left(\frac{P_{bubble}}{P_j} \right) = \left(\frac{T_j}{T} \right) \sum_{i}^8 N_i \theta^{i/2}

Parameters

Tfloat: Temperature, [K]

Returns

P_bubblefloat: Bubble pressure, [Pa]

Notes

The stated range of this ancillary equation is 59.75 K <= T <= 132.6312 K.

Examples

>>> lemmon2000_air_P_bubble(100.0)
663128.589440

chemicals.air.lemmon2000_air_rho_dew(T)[source]¶

Calculates the dew molar density of standard dry air according to Lemmon (2000).

\ln \left(\frac{\rho_{dew}}{\rho_j} \right) = N_1\theta^{0.41} + N_2\theta + N_3\theta^{2.8} + N_4\theta^{6.5}

Parameters

Tfloat: Temperature, [K]

Returns

rho_dewfloat: Dew point molar density, [mol/m^3]

Notes

The stated range of this ancillary equation is 59.75 K <= T <= 132.6312 K.

Examples

>>> lemmon2000_air_rho_dew(100.0)
785.7863223794999

chemicals.air.lemmon2000_air_rho_bubble(T)[source]¶

Calculates the bubble molar density of standard dry air according to Lemmon (2000).

\left(\frac{\rho_{bubble}}{rho_j} -1 \right) = N_1\theta^{0.65} + N_2\theta^{0.85} + N_3\theta^{0.95} + N_4\theta^{1.1} + N_5\ln\frac{T}{T_j}

Parameters

Tfloat: Temperature, [K]

Returns

rho_bubblefloat: bubble point molar density, [mol/m^3]

Notes

The stated range of this ancillary equation is 59.75 K <= T <= 132.6312 K.

Examples

>>> lemmon2000_air_rho_bubble(100.0)
26530.979020427476

Dry Air Constants ¶

chemicals.air.lemmon2000_air_T_reducing = 132.6312¶: Reducing temperature in K for the Lemmon (2000) EOS for dry air

chemicals.air.lemmon2000_air_rho_reducing = 10447.7¶: Reducing molar density in mol/m^3 for the Lemmon (2000) EOS for dry air

chemicals.air.lemmon2000_air_P_reducing = 3785020.0¶: Reducing pressure in Pa for the Lemmon (2000) EOS for dry air

chemicals.air.lemmon2000_air_MW = 28.9586¶: Molecular weight of air in g/mol for the Lemmon (2000) EOS for dry air

chemicals.air.lemmon2000_air_R = 8.31451¶: Molar gas constant in Jlemmon2000_air_R/(mol*K) used in the the Lemmon (2000) EOS for dry air

chemicals.air.lemmon2000_air_T_max = 2000.0¶: Maximum temperature in K valid for the Lemmon (2000) EOS for dry air

chemicals.air.lemmon2000_air_P_max = 2000000000.0¶: Maximum pressure in Pa valid for the Lemmon (2000) EOS for dry air

Dry Air Ideal Gas Terms ¶

chemicals.air.lemmon2000_air_A0(tau, delta)[source]¶

Calculates the ideal gas Helmholtz energy of air according to Lemmon (2000).

\phi^\circ = \ln \delta + \sum_{i=1}^5 N_i\tau^{i-4} + N_6\tau^{1.5} + N_7\ln \tau + N_8\ln[1-\exp(-N_{11}\tau)] + N_9\ln[1-\exp(-N_{12}\tau)] + N_{10}\ln[2/3 + \exp(N_{13}\tau)]

Parameters

taufloat: Dimensionless temperature, (132.6312 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

A0float: Ideal gas dimensionless Helmholtz energy A0/(RT) [-]

Notes

The coefficients are as follows:

Ns = [0.605719400E-7, -0.210274769E-4, -0.158860716E-3, -13.841928076, 17.275266575, -0.195363420E-3, 2.490888032, 0.791309509, 0.212236768, -0.197938904, 25.36365, 16.90741, 37.31279]

Examples

>>> lemmon2000_air_A0(132.6312/200.0, 13000/10447.7)
-14.65173785639

chemicals.air.lemmon2000_air_dA0_dtau(tau, delta)[source]¶

Calculates the first temperature derivative of ideal gas Helmholtz energy of air according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (132.6312 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

dA0_dtaufloat: First derivative of A0/(RT) Ideal gas dimensionless Helmholtz energy with respect to tau [-]

Examples

>>> lemmon2000_air_dA0_dtau(132.6312/200.0, 13000/10447.7)
3.749095669249

chemicals.air.lemmon2000_air_d2A0_dtau2(tau, delta)[source]¶

Calculates the second temperature derivative of ideal gas Helmholtz energy of air according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (126.192 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

d2A0_dtau2float: Second derivative of A0/(RT) Ideal gas dimensionless Helmholtz energy with respect to tau [-]

Examples

>>> lemmon2000_air_d2A0_dtau2(132.6312/200.0, 13000/10447.7)
-5.66675499015

chemicals.air.lemmon2000_air_d3A0_dtau3(tau, delta)[source]¶

Calculates the third temperature derivative of ideal gas Helmholtz energy of air according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (126.192 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

d3A0_dtau3float: Third derivative of A0/(RT) Ideal gas dimensionless Helmholtz energy with respect to tau [-]

Examples

>>> lemmon2000_air_d3A0_dtau3(132.6312/200.0, 13000/10447.7)
17.10538866838

chemicals.air.lemmon2000_air_d4A0_dtau4(tau, delta)[source]¶

Calculates the fourth temperature derivative of ideal gas Helmholtz energy of air according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (132.6312 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

d4A0_dtau4float: Fourth derivative of A0/(RT) Ideal gas dimensionless Helmholtz energy with respect to tau [-]

Examples

>>> lemmon2000_air_d4A0_dtau4(126.192/200.0, 13000/10447.7)
-94.815532727

Dry Air Residual Terms ¶

chemicals.air.lemmon2000_air_Ar(tau, delta)[source]¶

Calculates the residual Helmholtz energy of air according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (132.6312 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

Arfloat: Residual dimensionless Helmholtz energy Ar/(RT) [-]

Notes

The cost of this function is 1 power, 3 exp, 2 sqrt and many multiplies/adds.

Examples

>>> lemmon2000_air_Ar(132.6312/200.0, 13000/10447.7)
-0.34683017661
>>> lemmon2000_air_Ar(0.36842, 0.15880050154579475)
0.0047988122806

chemicals.air.lemmon2000_air_dAr_dtau(tau, delta)[source]¶

Calculates the first derivative of residual Helmholtz energy of air with respect to tau according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (132.6312 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

dAr_dtaufloat: First derivative of residual dimensionless Helmholtz energy Ar/(RT) with respect to tau, [-]

Notes

The cost of this function is 1 power, 3 exp, 2 sqrt, 1 divisions and the necessary adds/multiplies.

Examples

>>> lemmon2000_air_dAr_dtau(132.6312/200.0, 13000/10447.7)
-1.8112257495223263

chemicals.air.lemmon2000_air_d2Ar_dtau2(tau, delta)[source]¶

Calculates the second derivative of residual Helmholtz energy of air with respect to tau according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (132.6312 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

d2Ar_dtau2float: Second derivative of residual dimensionless Helmholtz energy Ar/(RT) with respect to tau, [-]

Notes

The cost of this function is 1 power, 3 exp, 2 sqrt, 2 divisions and the necessary adds/multiplies.

Examples

>>> lemmon2000_air_d2Ar_dtau2(132.6312/200.0, 13000/10447.7)
-0.7632109061747

chemicals.air.lemmon2000_air_d3Ar_dtau3(tau, delta)[source]¶

Calculates the third derivative of residual Helmholtz energy of air with respect to tau according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (132.6312 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

d3Ar_dtau3float: Third derivative of residual dimensionless Helmholtz energy Ar/(RT) with respect to tau, [-]

Notes

The cost of this function is 1 power, 3 exp, 2 sqrt, 4 divisions and the necessary adds/multiplies.

Examples

>>> lemmon2000_air_d3Ar_dtau3(132.6312/200.0, 13000/10447.7)
0.27922007457420

chemicals.air.lemmon2000_air_d4Ar_dtau4(tau, delta)[source]¶

Calculates the fourth derivative of residual Helmholtz energy of air with respect to tau according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (132.6312 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

d4Ar_dtau4float: Fourth derivative of residual dimensionless Helmholtz energy Ar/(RT) with respect to tau, [-]

Notes

The cost of this function is 1 power, 3 exp, 2 sqrt, 4 divisions and the necessary adds/multiplies.

Examples

>>> lemmon2000_air_d4Ar_dtau4(132.6312/200.0, 13000/10447.7)
-8.197368061417

chemicals.air.lemmon2000_air_dAr_ddelta(tau, delta)[source]¶

Calculates the first derivative of residual Helmholtz energy of air with respect to delta according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (132.6312 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

dAr_ddeltafloat: First derivative of residual dimensionless Helmholtz energy Ar/(RT) with respect to delta, [-]

Notes

The cost of this function is 1 power, 3 exp, 2 sqrt, and the necessary adds/multiplies.

Examples

>>> lemmon2000_air_dAr_ddelta(132.6312/200.0, 13000/10447.7)
-0.1367917666005

chemicals.air.lemmon2000_air_d2Ar_ddelta2(tau, delta)[source]¶

Calculates the second derivative of residual Helmholtz energy of air with respect to delta according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (132.6312 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

d2Ar_ddelta2float: Second derivative of residual dimensionless Helmholtz energy Ar/(RT) with respect to delta, [-]

Notes

The cost of this function is 1 power, 3 exp, 2 sqrt, and the necessary adds/multiplies.

Examples

>>> lemmon2000_air_d2Ar_ddelta2(132.6312/200.0, 13000/10447.7)
0.27027259528316

chemicals.air.lemmon2000_air_d3Ar_ddelta3(tau, delta)[source]¶

Calculates the third derivative of residual Helmholtz energy of air with respect to delta according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (132.6312 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

d3Ar_ddelta3float: Third derivative of residual dimensionless Helmholtz energy Ar/(RT) with respect to delta, [-]

Notes

The cost of this function is 1 power, 3 exp, 2 sqrt, and the necessary adds/multiplies.

Examples

>>> lemmon2000_air_d3Ar_ddelta3(132.6312/200.0, 13000/10447.7)
0.1849386546766

chemicals.air.lemmon2000_air_d4Ar_ddelta4(tau, delta)[source]¶

Calculates the fourth derivative of residual Helmholtz energy of air with respect to delta according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (132.6312 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

d4Ar_ddelta4float: Fourth derivative of residual dimensionless Helmholtz energy Ar/(RT) with respect to delta, [-]

Notes

The cost of this function is 1 power, 3 exp, 2 sqrt, and the necessary adds/multiplies.

Examples

>>> lemmon2000_air_d4Ar_ddelta4(132.6312/200.0, 13000/10447.7)
0.37902213262258

chemicals.air.lemmon2000_air_d2Ar_ddeltadtau(tau, delta)[source]¶

Calculates the second derivative of residual Helmholtz energy of air with respect to delta and tau according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (132.6312 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

d2Ar_ddeltadtaufloat: Second derivative of residual dimensionless Helmholtz energy Ar/(RT) with respect to delta and tau, [-]

Notes

The cost of this function is 1 power, 3 exp, 2 sqrt, and the necessary adds/multiplies.

Examples

>>> lemmon2000_air_d2Ar_ddeltadtau(132.6312/200.0, 13000/10447.7)
-1.359976184125

chemicals.air.lemmon2000_air_d3Ar_ddeltadtau2(tau, delta)[source]¶

Calculates the third derivative of residual Helmholtz energy of air with respect to delta once and tau twice according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (132.6312 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

d3Ar_ddeltadtau2float: Third derivative of residual dimensionless Helmholtz energy Ar/(RT) with respect to delta once and tau twice, [-]

Notes

The cost of this function is 1 power, 3 exp, 2 sqrt, 3 divisions, and the necessary adds/multiplies.

Examples

>>> lemmon2000_air_d3Ar_ddeltadtau2(132.6312/200.0, 13000/10447.7)
-0.19089212184849

chemicals.air.lemmon2000_air_d3Ar_ddelta2dtau(tau, delta)[source]¶

Calculates the third derivative of residual Helmholtz energy of air with respect to delta twice and tau once according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (132.6312 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

d3Ar_ddelta2dtaufloat: Third derivative of residual dimensionless Helmholtz energy Ar/(RT) with respect to delta twice and once twice, [-]

Notes

The cost of this function is 1 power, 3 exp, 2 sqrt, 3 divisions, and the necessary adds/multiplies.

Examples

>>> lemmon2000_air_d3Ar_ddelta2dtau(132.6312/200.0, 13000/10447.7)
0.01441788198940

chemicals.air.lemmon2000_air_d4Ar_ddelta2dtau2(tau, delta)[source]¶

Calculates the fourth derivative of residual Helmholtz energy of air with respect to delta twice and tau twice according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (132.6312 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

d4Ar_ddelta2dtau2float: Fourth derivative of residual dimensionless Helmholtz energy Ar/(RT) with respect to delta twice and tau twice, [-]

Notes

The cost of this function is 1 power, 3 exp, 2 sqrt, 2 divisions, and the necessary adds/multiplies.

Examples

>>> lemmon2000_air_d4Ar_ddelta2dtau2(132.6312/200.0, 13000/10447.7)
0.1196873112730

chemicals.air.lemmon2000_air_d4Ar_ddeltadtau3(tau, delta)[source]¶

Calculates the fourth derivative of residual Helmholtz energy of air with respect to delta once and tau thrice according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (132.6312 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

d4Ar_ddeltadtau3float: Fourth derivative of residual dimensionless Helmholtz energy Ar/(RT) with respect to delta once and tau thrice, [-]

Notes

The cost of this function is 1 power, 3 exp, 2 sqrt, 1 division, and the necessary adds/multiplies.

Examples

>>> lemmon2000_air_d4Ar_ddeltadtau3(132.6312/200.0, 13000/10447.7)
2.077739387492

chemicals.air.lemmon2000_air_d4Ar_ddelta3dtau(tau, delta)[source]¶

Calculates the fourth derivative of residual Helmholtz energy of air with respect to delta thrice and tau once according to Lemmon (2000).

Parameters

taufloat: Dimensionless temperature, (132.6312 K)/T [-]
deltafloat: Dimensionless density, rho/(10447.7 mol/m^3), [-]

Returns

d4Ar_ddelta3dtaufloat: Fourth derivative of residual dimensionless Helmholtz energy Ar/(RT) with respect to delta thrice and tau once, [-]

Notes

The cost of this function is 1 power, 3 exp, 2 sqrt, 1 division, and the necessary adds/multiplies.

Examples

>>> lemmon2000_air_d4Ar_ddelta3dtau(132.6312/200.0, 13000/10447.7)
-0.26039336747

Humid Air Virial Terms ¶

chemicals.air.TEOS10_BAW_derivatives(T)[source]¶

Calculates the second molar virial cross coefficient between air and water according to [1].

B_{aw}(T) = \frac{1}{\bar \rho^*}\sum_{i=1}^3 c_i(\theta)^{d_i}

Where $\theta = T/T^*$ and $T^* = 100$ K and $\bar \rho = 10^6$ mol/m^3.

Parameters

Tfloat: Temperature, [K]

Returns

Bawfloat: Air-water second molar virial cross coefficient [m^3/mol]
dBaw_dTfloat: First temperature derivative of air-water second molar virial cross coefficient [m^3/(mol*K)]
d2Baw_dT2float: Second temperature derivative of air-water second molar virial cross coefficient [m^3/(mol*K^2)]
d3Baw_dT3float: Third temperature derivative of air-water second molar virial cross coefficient [m^3/(mol*K^3)]

Notes

The coefficients are as follows:

cis = [0.665687E2, -0.238834E3, -0.176755E3]

dis = [-0.237, -1.048, -3.183]

References

1: Herrmann, Sebastian, Hans-Joachim Kretzschmar, and Donald P. Gatley. “Thermodynamic Properties of Real Moist Air, Dry Air, Steam, Water, and Ice (RP-1485).” HVAC&R Research 15, no. 5 (September 1, 2009): 961-986. https://doi.org/10.1080/10789669.2009.10390874.

Examples

>>> TEOS10_BAW_derivatives(300.0)
(-2.956727474282386e-05, 2.8009736043809844e-07, -2.425992413058737e-09,  3.0736974302787557e-11)

chemicals.air.TEOS10_CAAW_derivatives(T)[source]¶

Calculates the third molar virial cross coefficient between air and air-water according to [1].

C_{aaw}(T) = \frac{1}{(\bar \rho^*)^2}\sum_{i=1}^5 c_i(\theta)^{1-i}

Where $\theta = T/T^*$ and $T^* = 100$ K and $\bar \rho = 10^6$ mol/m^3.

Parameters

Tfloat: Temperature, [K]

Returns

Caawfloat: Air air-water second molar virial cross coefficient [m^6/mol^2]
dCaaw_dTfloat: First temperature derivative of air air-water third molar virial cross coefficient [m^6/(mol^2*K)]
d2Caaw_dT2float: Second temperature derivative of air air-water third molar virial cross coefficient [m^6/(mol^2*K^2)]
d3Caaw_dT3float: Third temperature derivative of air air-water third molar virial cross coefficient [m^6/(mol^2*K^3)]

Notes

The coefficients are as follows:

cis = [0.482737E-9, 1.05678E-7, -6.56394E-5, 0.294442E-1, -3.19317]

References

1: Herrmann, Sebastian, Hans-Joachim Kretzschmar, and Donald P. Gatley. “Thermodynamic Properties of Real Moist Air, Dry Air, Steam, Water, and Ice (RP-1485).” HVAC&R Research 15, no. 5 (September 1, 2009): 961-986. https://doi.org/10.1080/10789669.2009.10390874.

Examples

>>> TEOS10_CAAW_derivatives(300.0)
(8.019777407407409e-10, -1.9610345679012353e-12, 1.700556378600824e-14, -1.0129827160493832e-16)

chemicals.air.TEOS10_CAWW_derivatives(T)[source]¶

Calculates the third molar virial cross coefficient between air and water-water according to [1].

C_{aww}(T) = \frac{1}{(\bar \rho^*)^2}\exp\left[\sum_{i=1}^4 d_i(\theta)^{1-i}\right]

Where $\theta = T/T^*$ and $T^* = 100$ K and $\bar \rho = 10^6$ mol/m^3.

Parameters

Tfloat: Temperature, [K]

Returns

Cawwfloat: Air water-water second molar virial cross coefficient [m^6/mol^2]
dCaww_dTfloat: First temperature derivative of air water-water third molar virial cross coefficient [m^6/(mol^2*K)]
d2Caww_dT2float: Second temperature derivative of air water-water third molar virial cross coefficient [m^6/(mol^2*K^2)]
d3Caww_dT3float: Third temperature derivative of air water-water third molar virial cross coefficient [m^6/(mol^2*K^3)]

Notes

The coefficients are as follows:

dis = [-0.10728876E2, 0.347802E2, -0.383383E2, 0.334060E2]

References

1: Herrmann, Sebastian, Hans-Joachim Kretzschmar, and Donald P. Gatley. “Thermodynamic Properties of Real Moist Air, Dry Air, Steam, Water, and Ice (RP-1485).” HVAC&R Research 15, no. 5 (September 1, 2009): 961-986. https://doi.org/10.1080/10789669.2009.10390874.

Examples

>>> TEOS10_CAWW_derivatives(300.0)
(-1.1555278368039349e-07, 2.6136327775413448e-09, -7.513345818045024e-11, 2.601834967770415e-12)

Henry’s Law for Air in Water ¶

chemicals.air.iapws04_Henry_air(T)[source]¶

Calculate the Henry’s law constant of air in water according to the IAPWS-04 standard.

Parameters

Tfloat: Temperature, [K]

Returns

Hfloat: Henry’s law constant, [1/Pa]

Notes

The mole fractions of air in this model are 0.7812 N2, 0.2095 O2 and 0.0093 Ar.

References

1: Fernández-Prini, Roberto, Jorge L. Alvarez, and Allan H. Harvey. “Henry’s Constants and Vapor-Liquid Distribution Constants for Gaseous Solutes in H2O and D2O at High Temperatures.” Journal of Physical and Chemical Reference Data 32, no. 2 (June 2003): 903-16. https://doi.org/10.1063/1.1564818.

Examples

>>> iapws04_Henry_air(320.0)
1.0991553689889531e-10

chemicals.air.iapws04_dHenry_air_dT(T)[source]¶

Calculate the temperature derivative of Henry’s law constant of air in water according to the IAPWS-04 standard. As the actual Henry’s law constant must be calculated as well, it is also returned.

Parameters

Tfloat: Temperature, [K]

Returns

dH_dTfloat: First temperature derivative of Henry’s law constant, [1/(Pa*K)]
Hfloat: Henry’s law constant, [1/Pa]

Notes

The mole fractions of air in this model are 0.7812 N2, 0.2095 O2 and 0.0093 Ar.

References

1: Fernández-Prini, Roberto, Jorge L. Alvarez, and Allan H. Harvey. “Henry’s Constants and Vapor-Liquid Distribution Constants for Gaseous Solutes in H2O and D2O at High Temperatures.” Journal of Physical and Chemical Reference Data 32, no. 2 (June 2003): 903-16. https://doi.org/10.1063/1.1564818.

Examples

>>> iapws04_dHenry_air_dT(320.0)
(-8.680064421141611e-13, 1.0991553689889561e-10)

Air: Fundamental Equation of State for Air (chemicals.air)¶

Dry Air Basic Solvers ¶

Dry Air Bubble/Dew Points ¶

Dry Air Constants ¶

Dry Air Ideal Gas Terms ¶

Dry Air Residual Terms ¶

Humid Air Virial Terms ¶

Henry’s Law for Air in Water ¶

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