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

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(PdewPj)=(TjT)i8Niθi/2\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(PbubblePj)=(TjT)i8Niθi/2\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(ρdewρj)=N1θ0.41+N2θ+N3θ2.8+N4θ6.5\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).

(ρbubblerhoj1)=N1θ0.65+N2θ0.85+N3θ0.95+N4θ1.1+N5lnTTj\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).

ϕ=lnδ+i=15Niτi4+N6τ1.5+N7lnτ+N8ln[1exp(N11τ)]+N9ln[1exp(N12τ)]+N10ln[2/3+exp(N13τ)]\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].

Baw(T)=1ρˉi=13ci(θ)diB_{aw}(T) = \frac{1}{\bar \rho^*}\sum_{i=1}^3 c_i(\theta)^{d_i}

Where θ=T/T\theta = T/T^* and T=100T^* = 100 K and ρˉ=106\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].

Caaw(T)=1(ρˉ)2i=15ci(θ)1iC_{aaw}(T) = \frac{1}{(\bar \rho^*)^2}\sum_{i=1}^5 c_i(\theta)^{1-i}

Where θ=T/T\theta = T/T^* and T=100T^* = 100 K and ρˉ=106\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].

Caww(T)=1(ρˉ)2exp[i=14di(θ)1i]C_{aww}(T) = \frac{1}{(\bar \rho^*)^2}\exp\left[\sum_{i=1}^4 d_i(\theta)^{1-i}\right]

Where θ=T/T\theta = T/T^* and T=100T^* = 100 K and ρˉ=106\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)