def BVirial_Abbott(T, Tc, Pc, omega, order=0):
    r'''Calculates the second virial coefficient using the model in [1]_.
    Simple fit to the Lee-Kesler equation.

    .. math::
        B_r=B^{(0)}+\omega B^{(1)}

        B^{(0)}=0.083+\frac{0.422}{T_r^{1.6}}

        B^{(1)}=0.139-\frac{0.172}{T_r^{4.2}}

    Parameters
    ----------
    T : float
        Temperature of fluid [K]
    Tc : float
        Critical temperature of fluid [K]
    Pc : float
        Critical pressure of the fluid [Pa]
    omega : float
        Acentric factor for fluid, [-]
    order : int, optional
        Order of the calculation. 0 for the calculation of B itself; for 1/2/3, 
        the first/second/third derivative of B with respect to temperature; and  
        for -1/-2, the first/second indefinite integral of B with respect to 
        temperature. No other integrals or derivatives are implemented, and an 
        exception will be raised if any other order is given.

    Returns
    -------
    B : float
        Second virial coefficient in density form or its integral/derivative if
        specified, [m^3/mol or m^3/mol/K^order]

    Notes
    -----
    Analytical models for derivatives and integrals are available for orders
    -2, -1, 1, 2, and 3, all obtained with SymPy.

    For first temperature derivative of B:
    
    .. math::
        \frac{d B^{(0)}}{dT} = \frac{0.6752}{T \left(\frac{T}{Tc}\right)^{1.6}}

        \frac{d B^{(1)}}{dT} = \frac{0.7224}{T \left(\frac{T}{Tc}\right)^{4.2}}

    For the second temperature derivative of B:
    
    .. math::
        \frac{d^2 B^{(0)}}{dT^2} = - \frac{1.75552}{T^{2} \left(\frac{T}{Tc}\right)^{1.6}}

        \frac{d^2 B^{(1)}}{dT^2} = - \frac{3.75648}{T^{2} \left(\frac{T}{Tc}\right)^{4.2}}

    For the third temperature derivative of B:
    
    .. math::
        \frac{d^3 B^{(0)}}{dT^3} = \frac{6.319872}{T^{3} \left(\frac{T}{Tc}\right)^{1.6}}

        \frac{d^3 B^{(1)}}{dT^3} = \frac{23.290176}{T^{3} \left(\frac{T}{Tc}\right)^{4.2}}
    
    For the first indefinite integral of B:
    
    .. math::
        \int{B^{(0)}} dT = 0.083 T + \frac{\frac{211}{300} Tc}{\left(\frac{T}{Tc}\right)^{0.6}}
        
        \int{B^{(1)}} dT = 0.139 T + \frac{0.05375 Tc}{\left(\frac{T}{Tc}\right)^{3.2}}
    
    For the second indefinite integral of B:

    .. math::
        \int\int B^{(0)} dT dT = 0.0415 T^{2} + \frac{211}{120} Tc^{2} \left(\frac{T}{Tc}\right)^{0.4}
    
        \int\int B^{(1)} dT dT = 0.0695 T^{2} - \frac{\frac{43}{1760} Tc^{2}}{\left(\frac{T}{Tc}\right)^{2.2}}
    
    Examples
    --------
    Example is from [1]_, p. 93, and matches the result exactly, for isobutane.

    >>> BVirial_Abbott(510., 425.2, 38E5, 0.193)
    -0.00020570178037383633

    References
    ----------
    .. [1] Smith, H. C. Van Ness Joseph M. Introduction to Chemical Engineering
       Thermodynamics 4E 1987.
    '''
    Tr = T/Tc
    if order == 0:
        B0 = 0.083 - 0.422/Tr**1.6
        B1 = 0.139 - 0.172/Tr**4.2
    elif order == 1:
        B0 = 0.6752*Tr**(-1.6)/T
        B1 = 0.7224*Tr**(-4.2)/T
    elif order == 2:
        B0 = -1.75552*Tr**(-1.6)/T**2
        B1 = -3.75648*Tr**(-4.2)/T**2
    elif order == 3:
        B0 = 6.319872*Tr**(-1.6)/T**3
        B1 = 23.290176*Tr**(-4.2)/T**3
    elif order == -1:
        B0 = 0.083*T + 211/300.*Tc*(Tr)**(-0.6)
        B1 = 0.139*T + 0.05375*Tc*Tr**(-3.2)
    elif order == -2:
        B0 = 0.0415*T**2 + 211/120.*Tc**2*Tr**0.4
        B1 = 0.0695*T**2 - 43/1760.*Tc**2*Tr**(-2.2)
    else: 
        raise Exception('Only orders -2, -1, 0, 1, 2 and 3 are supported.')
    Br = B0 + omega*B1
    return Br*R*Tc/Pc
def BVirial_Abbott(T, Tc, Pc, omega, order=0):
    r'''Calculates the second virial coefficient using the model in [1]_.
    Simple fit to the Lee-Kesler equation.

    .. math::
        B_r=B^{(0)}+\omega B^{(1)}

        B^{(0)}=0.083+\frac{0.422}{T_r^{1.6}}

        B^{(1)}=0.139-\frac{0.172}{T_r^{4.2}}

    Parameters
    ----------
    T : float
        Temperature of fluid [K]
    Tc : float
        Critical temperature of fluid [K]
    Pc : float
        Critical pressure of the fluid [Pa]
    omega : float
        Acentric factor for fluid, [-]
    order : int, optional
        Order of the calculation. 0 for the calculation of B itself; for 1/2/3, 
        the first/second/third derivative of B with respect to temperature; and  
        for -1/-2, the first/second indefinite integral of B with respect to 
        temperature. No other integrals or derivatives are implemented, and an 
        exception will be raised if any other order is given.

    Returns
    -------
    B : float
        Second virial coefficient in density form or its integral/derivative if
        specified, [m^3/mol or m^3/mol/K^order]

    Notes
    -----
    Analytical models for derivatives and integrals are available for orders
    -2, -1, 1, 2, and 3, all obtained with SymPy.

    For first temperature derivative of B:
    
    .. math::
        \frac{d B^{(0)}}{dT} = \frac{0.6752}{T \left(\frac{T}{Tc}\right)^{1.6}}

        \frac{d B^{(1)}}{dT} = \frac{0.7224}{T \left(\frac{T}{Tc}\right)^{4.2}}

    For the second temperature derivative of B:
    
    .. math::
        \frac{d^2 B^{(0)}}{dT^2} = - \frac{1.75552}{T^{2} \left(\frac{T}{Tc}\right)^{1.6}}

        \frac{d^2 B^{(1)}}{dT^2} = - \frac{3.75648}{T^{2} \left(\frac{T}{Tc}\right)^{4.2}}

    For the third temperature derivative of B:
    
    .. math::
        \frac{d^3 B^{(0)}}{dT^3} = \frac{6.319872}{T^{3} \left(\frac{T}{Tc}\right)^{1.6}}

        \frac{d^3 B^{(1)}}{dT^3} = \frac{23.290176}{T^{3} \left(\frac{T}{Tc}\right)^{4.2}}
    
    For the first indefinite integral of B:
    
    .. math::
        \int{B^{(0)}} dT = 0.083 T + \frac{\frac{211}{300} Tc}{\left(\frac{T}{Tc}\right)^{0.6}}
        
        \int{B^{(1)}} dT = 0.139 T + \frac{0.05375 Tc}{\left(\frac{T}{Tc}\right)^{3.2}}
    
    For the second indefinite integral of B:

    .. math::
        \int\int B^{(0)} dT dT = 0.0415 T^{2} + \frac{211}{120} Tc^{2} \left(\frac{T}{Tc}\right)^{0.4}
    
        \int\int B^{(1)} dT dT = 0.0695 T^{2} - \frac{\frac{43}{1760} Tc^{2}}{\left(\frac{T}{Tc}\right)^{2.2}}
    
    Examples
    --------
    Example is from [1]_, p. 93, and matches the result exactly, for isobutane.

    >>> BVirial_Abbott(510., 425.2, 38E5, 0.193)
    -0.00020570178037383633

    References
    ----------
    .. [1] Smith, H. C. Van Ness Joseph M. Introduction to Chemical Engineering
       Thermodynamics 4E 1987.
    '''
    Tr = T/Tc
    if order == 0:
        B0 = 0.083 - 0.422/Tr**1.6
        B1 = 0.139 - 0.172/Tr**4.2
    elif order == 1:
        B0 = 0.6752*Tr**(-1.6)/T
        B1 = 0.7224*Tr**(-4.2)/T
    elif order == 2:
        B0 = -1.75552*Tr**(-1.6)/T**2
        B1 = -3.75648*Tr**(-4.2)/T**2
    elif order == 3:
        B0 = 6.319872*Tr**(-1.6)/T**3
        B1 = 23.290176*Tr**(-4.2)/T**3
    elif order == -1:
        B0 = 0.083*T + 211/300.*Tc*(Tr)**(-0.6)
        B1 = 0.139*T + 0.05375*Tc*Tr**(-3.2)
    elif order == -2:
        B0 = 0.0415*T**2 + 211/120.*Tc**2*Tr**0.4
        B1 = 0.0695*T**2 - 43/1760.*Tc**2*Tr**(-2.2)
    else: 
        raise Exception('Only orders -2, -1, 0, 1, 2 and 3 are supported.')
    Br = B0 + omega*B1
    return Br*R*Tc/Pc
def BVirial_Abbott ( T , Tc , Pc , omega , order = 0 ) : Tr = T / Tc if order == 0 : B0 = 0.083 - 0.422 / Tr ** 1.6 B1 = 0.139 - 0.172 / Tr ** 4.2 elif order == 1 : B0 = 0.6752 * Tr ** ( - 1.6 ) / T B1 = 0.7224 * Tr ** ( - 4.2 ) / T elif order == 2 : B0 = - 1.75552 * Tr ** ( - 1.6 ) / T ** 2 B1 = - 3.75648 * Tr ** ( - 4.2 ) / T ** 2 elif order == 3 : B0 = 6.319872 * Tr ** ( - 1.6 ) / T ** 3 B1 = 23.290176 * Tr ** ( - 4.2 ) / T ** 3 elif order == - 1 : B0 = 0.083 * T + 211 / 300. * Tc * ( Tr ) ** ( - 0.6 ) B1 = 0.139 * T + 0.05375 * Tc * Tr ** ( - 3.2 ) elif order == - 2 : B0 = 0.0415 * T ** 2 + 211 / 120. * Tc ** 2 * Tr ** 0.4 B1 = 0.0695 * T ** 2 - 43 / 1760. * Tc ** 2 * Tr ** ( - 2.2 ) else : raise Exception ( 'Only orders -2, -1, 0, 1, 2 and 3 are supported.' ) Br = B0 + omega * B1 return Br * R * Tc / Pc
r'''Calculates the second virial coefficient using the model in [1]_.
    Simple fit to the Lee-Kesler equation.

    .. math::
        B_r=B^{(0)}+\omega B^{(1)}

        B^{(0)}=0.083+\frac{0.422}{T_r^{1.6}}

        B^{(1)}=0.139-\frac{0.172}{T_r^{4.2}}

    Parameters
    ----------
    T : float
        Temperature of fluid [K]
    Tc : float
        Critical temperature of fluid [K]
    Pc : float
        Critical pressure of the fluid [Pa]
    omega : float
        Acentric factor for fluid, [-]
    order : int, optional
        Order of the calculation. 0 for the calculation of B itself; for 1/2/3, 
        the first/second/third derivative of B with respect to temperature; and  
        for -1/-2, the first/second indefinite integral of B with respect to 
        temperature. No other integrals or derivatives are implemented, and an 
        exception will be raised if any other order is given.

    Returns
    -------
    B : float
        Second virial coefficient in density form or its integral/derivative if
        specified, [m^3/mol or m^3/mol/K^order]

    Notes
    -----
    Analytical models for derivatives and integrals are available for orders
    -2, -1, 1, 2, and 3, all obtained with SymPy.

    For first temperature derivative of B:
    
    .. math::
        \frac{d B^{(0)}}{dT} = \frac{0.6752}{T \left(\frac{T}{Tc}\right)^{1.6}}

        \frac{d B^{(1)}}{dT} = \frac{0.7224}{T \left(\frac{T}{Tc}\right)^{4.2}}

    For the second temperature derivative of B:
    
    .. math::
        \frac{d^2 B^{(0)}}{dT^2} = - \frac{1.75552}{T^{2} \left(\frac{T}{Tc}\right)^{1.6}}

        \frac{d^2 B^{(1)}}{dT^2} = - \frac{3.75648}{T^{2} \left(\frac{T}{Tc}\right)^{4.2}}

    For the third temperature derivative of B:
    
    .. math::
        \frac{d^3 B^{(0)}}{dT^3} = \frac{6.319872}{T^{3} \left(\frac{T}{Tc}\right)^{1.6}}

        \frac{d^3 B^{(1)}}{dT^3} = \frac{23.290176}{T^{3} \left(\frac{T}{Tc}\right)^{4.2}}
    
    For the first indefinite integral of B:
    
    .. math::
        \int{B^{(0)}} dT = 0.083 T + \frac{\frac{211}{300} Tc}{\left(\frac{T}{Tc}\right)^{0.6}}
        
        \int{B^{(1)}} dT = 0.139 T + \frac{0.05375 Tc}{\left(\frac{T}{Tc}\right)^{3.2}}
    
    For the second indefinite integral of B:

    .. math::
        \int\int B^{(0)} dT dT = 0.0415 T^{2} + \frac{211}{120} Tc^{2} \left(\frac{T}{Tc}\right)^{0.4}
    
        \int\int B^{(1)} dT dT = 0.0695 T^{2} - \frac{\frac{43}{1760} Tc^{2}}{\left(\frac{T}{Tc}\right)^{2.2}}
    
    Examples
    --------
    Example is from [1]_, p. 93, and matches the result exactly, for isobutane.

    >>> BVirial_Abbott(510., 425.2, 38E5, 0.193)
    -0.00020570178037383633

    References
    ----------
    .. [1] Smith, H. C. Van Ness Joseph M. Introduction to Chemical Engineering
       Thermodynamics 4E 1987.
r Calculates the second virial coefficient using the model in [ 1 ] _ . Simple fit to the Lee - Kesler equation .