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polykin.thermo.eos¤

IdealGas ¤

Ideal gas equation of state.

This EOS is based on the following \(P(v,T)\) relationship:

\[ P = \frac{R T}{v} \]

where \(P\) is the pressure, \(T\) is the temperature, and \(v\) is the molar volume.

PARAMETER DESCRIPTION
N

Number of components.

TYPE: int

name

Name.

TYPE: str DEFAULT: ''

Source code in src/polykin/thermo/eos/idealgas.py 
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class IdealGas(GasEoS):
    r"""Ideal gas equation of state.

    This EOS is based on the following $P(v,T)$ relationship:

    $$ P = \frac{R T}{v} $$

    where $P$ is the pressure, $T$ is the temperature, and $v$ is the molar
    volume.

    Parameters
    ----------
    N : int
        Number of components.
    name : str
        Name.
    """

    def __init__(self,
                 N: int,
                 name: str = ''
                 ) -> None:

        super().__init__(N, name)

    def Z(self,
          T=None,
          P=None,
          y=None
          ) -> float:
        r"""Calculate the compressibility factor of the fluid.

        $$ Z = 1 $$

        Returns
        -------
        float
            Compressibility factor.
        """
        return 1.0

    def P(self,
          T: float,
          v: float,
          y=None
          ) -> float:
        r"""Calculate the pressure of the fluid.

        Parameters
        ----------
        T : float
            Temperature. Unit = K.
        v : float
            Molar volume. Unit = m³/mol.

        Returns
        -------
        float
             Pressure. Unit = Pa.
        """
        return R*T/v

    def phi(self,
            T=None,
            P=None,
            y=None
            ) -> FloatVector:
        r"""Calculate the fugacity coefficients of all components.

        $$ \hat{\phi}_i = 1 $$

        Returns
        -------
        FloatVector
            Fugacity coefficients of all components.
        """
        return np.ones(self.N)

    def DA(self,
           T: float,
           V: float,
           n: FloatVector,
           v0: float
           ) -> float:
        r"""Calculate the departure of Helmholtz energy.

        $$ A(T,V,n) - A^{\circ}(T,V,n)$$

        Parameters
        ----------
        T : float
            Temperature. Unit = K.
        V : float
            Volume. Unit = m³.
        n : FloatVector
            Mole amounts of all components. Unit = mol.
        v0 : float
            Molar volume in reference state. Unit = m³/mol.

        Returns
        -------
        float
            Helmholtz energy departure, $A - A^{\circ}$. Unit = J.
        """
        nT = n.sum()
        return -nT*R*T*log(V/(nT*v0))

DA ¤

DA(T: float, V: float, n: FloatVector, v0: float) -> float

Calculate the departure of Helmholtz energy.

\[ A(T,V,n) - A^{\circ}(T,V,n)\]
PARAMETER DESCRIPTION
T

Temperature. Unit = K.

TYPE: float

V

Volume. Unit = m³.

TYPE: float

n

Mole amounts of all components. Unit = mol.

TYPE: FloatVector

v0

Molar volume in reference state. Unit = m³/mol.

TYPE: float

RETURNS DESCRIPTION
float

Helmholtz energy departure, \(A - A^{\circ}\). Unit = J.
Source code in src/polykin/thermo/eos/idealgas.py 
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def DA(self,
       T: float,
       V: float,
       n: FloatVector,
       v0: float
       ) -> float:
    r"""Calculate the departure of Helmholtz energy.

    $$ A(T,V,n) - A^{\circ}(T,V,n)$$

    Parameters
    ----------
    T : float
        Temperature. Unit = K.
    V : float
        Volume. Unit = m³.
    n : FloatVector
        Mole amounts of all components. Unit = mol.
    v0 : float
        Molar volume in reference state. Unit = m³/mol.

    Returns
    -------
    float
        Helmholtz energy departure, $A - A^{\circ}$. Unit = J.
    """
    nT = n.sum()
    return -nT*R*T*log(V/(nT*v0))

N property ¤

N: int

Number of components.

P ¤

P(T: float, v: float, y=None) -> float

Calculate the pressure of the fluid.

PARAMETER DESCRIPTION
T

Temperature. Unit = K.

TYPE: float

v

Molar volume. Unit = m³/mol.

TYPE: float

RETURNS DESCRIPTION
float

Pressure. Unit = Pa.
Source code in src/polykin/thermo/eos/idealgas.py 
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def P(self,
      T: float,
      v: float,
      y=None
      ) -> float:
    r"""Calculate the pressure of the fluid.

    Parameters
    ----------
    T : float
        Temperature. Unit = K.
    v : float
        Molar volume. Unit = m³/mol.

    Returns
    -------
    float
         Pressure. Unit = Pa.
    """
    return R*T/v

Z ¤

Z(T=None, P=None, y=None) -> float

Calculate the compressibility factor of the fluid.

\[ Z = 1 \]
RETURNS DESCRIPTION
float

Compressibility factor.
Source code in src/polykin/thermo/eos/idealgas.py 
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def Z(self,
      T=None,
      P=None,
      y=None
      ) -> float:
    r"""Calculate the compressibility factor of the fluid.

    $$ Z = 1 $$

    Returns
    -------
    float
        Compressibility factor.
    """
    return 1.0

f ¤

f(T: float, P: float, y: FloatVector) -> FloatVector

Calculate the fugacity of all components.

For each component, the fugacity is given by:

\[ \hat{f}_i = \hat{\phi}_i y_i P \]

where \(\hat{\phi}_i(T,P,y)\) is the fugacity coefficient, \(P\) is the pressure, and \(y_i\) is the mole fraction.

PARAMETER DESCRIPTION
T

Temperature. Unit = K.

TYPE: float

P

Pressure. Unit = Pa.

TYPE: float

y

Mole fractions of all components. Unit = mol/mol.

TYPE: FloatVector

RETURNS DESCRIPTION
FloatVector

Fugacities of all components. Unit = Pa.
Source code in src/polykin/thermo/eos/base.py 
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def f(self,
      T: float,
      P: float,
      y: FloatVector
      ) -> FloatVector:
    r"""Calculate the fugacity of all components.

    For each component, the fugacity is given by:

    $$ \hat{f}_i = \hat{\phi}_i y_i P $$

    where $\hat{\phi}_i(T,P,y)$ is the fugacity coefficient, $P$ is the 
    pressure, and $y_i$ is the mole fraction.

    Parameters
    ----------
    T : float
        Temperature. Unit = K.
    P : float
        Pressure. Unit = Pa.
    y : FloatVector
        Mole fractions of all components. Unit = mol/mol.

    Returns
    -------
    FloatVector
        Fugacities of all components. Unit = Pa.
    """
    return self.phi(T, P, y)*y*P

phi ¤

phi(T=None, P=None, y=None) -> FloatVector

Calculate the fugacity coefficients of all components.

\[ \hat{\phi}_i = 1 \]
RETURNS DESCRIPTION
FloatVector

Fugacity coefficients of all components.
Source code in src/polykin/thermo/eos/idealgas.py 
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def phi(self,
        T=None,
        P=None,
        y=None
        ) -> FloatVector:
    r"""Calculate the fugacity coefficients of all components.

    $$ \hat{\phi}_i = 1 $$

    Returns
    -------
    FloatVector
        Fugacity coefficients of all components.
    """
    return np.ones(self.N)

v ¤

v(T: float, P: float, y: FloatVector) -> float

Calculate the molar volume the fluid.

\[ v = \frac{Z R T}{P} \]

where \(v\) is the molar volume, \(Z(T, P, y)\) is the compressibility factor, \(T\) is the temperature, \(P\) is the pressure, and \(y\) is the mole fraction vector.

PARAMETER DESCRIPTION
T

Temperature. Unit = K.

TYPE: float

P

Pressure. Unit = Pa.

TYPE: float

y

Mole fractions of all components. Unit = mol/mol.

TYPE: FloatVector

RETURNS DESCRIPTION
float

Molar volume of the fluid. Unit = m³/mol.
Source code in src/polykin/thermo/eos/base.py 
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def v(self,
      T: float,
      P: float,
      y: FloatVector
      ) -> float:
    r"""Calculate the molar volume the fluid.

    $$ v = \frac{Z R T}{P} $$

    where $v$ is the molar volume, $Z(T, P, y)$ is the compressibility
    factor, $T$ is the temperature, $P$ is the pressure, and $y$ is the
    mole fraction vector.

    Parameters
    ----------
    T : float
        Temperature. Unit = K.
    P : float
        Pressure. Unit = Pa.
    y : FloatVector
        Mole fractions of all components. Unit = mol/mol.

    Returns
    -------
    float
        Molar volume of the fluid. Unit = m³/mol.
    """
    return self.Z(T, P, y)*R*T/P

Examples¤

Estimate the molar volume of a gas at 0°C and 1 atm.

from polykin.thermo.eos import IdealGas

eos = IdealGas(1)
v = eos.v(T=273.15, P=1.01325e5, y=None)

print(f"{v:.2e} m³/mol")
2.24e-02 m³/mol