Instruction:
Can you tell what is the following Python 3 function doing
def decrypt(self, text, appid):
        try:
            cryptor = AES.new(self.key, self.mode, self.key[:16])
            # 使用BASE64对密文进行解码，然后AES-CBC解密
            plain_text = cryptor.decrypt(base64.b64decode(text))
        except Exception as e:
            raise DecryptAESError(e)

        try:
            if six.PY2:
                pad = ord(plain_text[-1])
            else:
                pad = plain_text[-1]
            # 去掉补位字符串
            # pkcs7 = PKCS7Encoder()
            # plain_text = pkcs7.encode(plain_text)
            # 去除16位随机字符串
            content = plain_text[16:-pad]
            xml_len = socket.ntohl(struct.unpack("I", content[: 4])[0])
            xml_content = content[4: xml_len + 4]
            from_appid = content[xml_len + 4:]
        except Exception as e:
            raise IllegalBuffer(e)
        if from_appid != appid:
            raise ValidateAppIDError()
        return xml_content

Response: Decrypt a text and return the XML content.


Instruction:
How would you explain what the following Python 3 function does
def _check_signature(self, msg_signature, timestamp, nonce, echostr):
        signature = get_sha1_signature(self.__token, timestamp, nonce, echostr)
        if not signature == msg_signature:
            raise ValidateSignatureError()
        try:
            return self.__pc.decrypt(echostr, self.__id)
        except DecryptAESError as e:
            raise ValidateSignatureError(e)

Response: Check if the message signature is correct.


Instruction:
Can you generate a brief explanation for the following Python 3 code
def _decrypt_message(self, msg, msg_signature, timestamp, nonce):
        timestamp = to_binary(timestamp)
        nonce = to_binary(nonce)
        if isinstance(msg, six.string_types):
            try:
                msg = xmltodict.parse(to_text(msg))['xml']
            except Exception as e:
                raise ParseError(e)

        encrypt = msg['Encrypt']
        signature = get_sha1_signature(self.__token, timestamp, nonce, encrypt)
        if signature != msg_signature:
            raise ValidateSignatureError()
        return self.__pc.decrypt(encrypt, self.__id)

Response:
检验消息的真实性，并且获取解密后的明文

        :param msg: 密文，对应POST请求的数据
        :param msg_signature: 签名串，对应URL参数的msg_signature
        :param timestamp: 时间戳，对应URL参数的timestamp
        :param nonce: 随机串，对应URL参数的nonce
        :return: 解密后的原文


Instruction:
Here you have a function in Python 3, explain what it does
def Lastovka_Shaw(T, similarity_variable, cyclic_aliphatic=False):
    r'''Calculate ideal-gas constant-pressure heat capacitiy with the similarity
    variable concept and method as shown in [1]_.

    .. math::
        C_p^0 = \left(A_2 + \frac{A_1 - A_2}{1 + \exp(\frac{\alpha-A_3}{A_4})}\right)
        + (B_{11} + B_{12}\alpha)\left(-\frac{(C_{11} + C_{12}\alpha)}{T}\right)^2
        \frac{\exp(-(C_{11} + C_{12}\alpha)/T)}{[1-\exp(-(C_{11}+C_{12}\alpha)/T)]^2}\\
        + (B_{21} + B_{22}\alpha)\left(-\frac{(C_{21} + C_{22}\alpha)}{T}\right)^2
        \frac{\exp(-(C_{21} + C_{22}\alpha)/T)}{[1-\exp(-(C_{21}+C_{22}\alpha)/T)]^2}

    Parameters
    ----------
    T : float
        Temperature of gas [K]
    similarity_variable : float
        similarity variable as defined in [1]_, [mol/g]

    Returns
    -------
    Cpg : float
        Gas constant-pressure heat capacitiy, [J/kg/K]

    Notes
    -----
    Original model is in terms of J/g/K. Note that the model is for predicting
    mass heat capacity, not molar heat capacity like most other methods!

    A1 = 0.58, A2 = 1.25, A3 = 0.17338003, A4 = 0.014, B11 = 0.73917383,
    B12 = 8.88308889, C11 = 1188.28051, C12 = 1813.04613, B21 = 0.0483019,
    B22 = 4.35656721, C21 = 2897.01927, C22 = 5987.80407.

    Examples
    --------
    >>> Lastovka_Shaw(1000.0, 0.1333)
    2467.113309084757

    References
    ----------
    .. [1] Lastovka, Vaclav, and John M. Shaw. "Predictive Correlations for
       Ideal Gas Heat Capacities of Pure Hydrocarbons and Petroleum Fractions."
       Fluid Phase Equilibria 356 (October 25, 2013): 338-370.
       doi:10.1016/j.fluid.2013.07.023.
    '''
    a = similarity_variable
    if cyclic_aliphatic:
        A1 = -0.1793547
        A2 = 3.86944439
        first = A1 + A2*a
    else:
        A1 = 0.58
        A2 = 1.25
        A3 = 0.17338003 # 803 instead of 8003 in another paper
        A4 = 0.014
        first = A2 + (A1-A2)/(1. + exp((a - A3)/A4))
        # Personal communication confirms the change

    B11 = 0.73917383
    B12 = 8.88308889
    C11 = 1188.28051
    C12 = 1813.04613
    B21 = 0.0483019
    B22 = 4.35656721
    C21 = 2897.01927
    C22 = 5987.80407
    Cp = first + (B11 + B12*a)*((C11+C12*a)/T)**2*exp(-(C11 + C12*a)/T)/(1.-exp(-(C11+C12*a)/T))**2
    Cp += (B21 + B22*a)*((C21+C22*a)/T)**2*exp(-(C21 + C22*a)/T)/(1.-exp(-(C21+C22*a)/T))**2
    return Cp*1000.

Response: Calculate ideal - gas constant - pressure heat capacitiy with the similarity variable concept and method as shown in [ 1 ] _.


Instruction:
Explain what the following Python 3 code does
def Lastovka_Shaw_integral_over_T(T, similarity_variable, cyclic_aliphatic=False):
    r'''Calculate the integral over temperature of ideal-gas constant-pressure
    heat capacitiy with the similarity variable concept and method as shown in
    [1]_.

    Parameters
    ----------
    T : float
        Temperature of gas [K]
    similarity_variable : float
        similarity variable as defined in [1]_, [mol/g]

    Returns
    -------
    S : float
        Difference in entropy from 0 K, [J/kg/K]

    Notes
    -----
    Original model is in terms of J/g/K. Note that the model is for predicting
    mass heat capacity, not molar heat capacity like most other methods!
    Integral was computed with SymPy.

    See Also
    --------
    Lastovka_Shaw
    Lastovka_Shaw_integral

    Examples
    --------
    >>> Lastovka_Shaw_integral_over_T(300.0, 0.1333)
    3609.791928945323

    References
    ----------
    .. [1] Lastovka, Vaclav, and John M. Shaw. "Predictive Correlations for
       Ideal Gas Heat Capacities of Pure Hydrocarbons and Petroleum Fractions."
       Fluid Phase Equilibria 356 (October 25, 2013): 338-370.
       doi:10.1016/j.fluid.2013.07.023.
    '''
    from cmath import log, exp
    a = similarity_variable
    if cyclic_aliphatic:
        A1 = -0.1793547
        A2 = 3.86944439
        first = A1 + A2*a
    else:
        A1 = 0.58
        A2 = 1.25
        A3 = 0.17338003 # 803 instead of 8003 in another paper
        A4 = 0.014
        first = A2 + (A1-A2)/(1. + exp((a - A3)/A4))

    a2 = a*a
    B11 = 0.73917383
    B12 = 8.88308889
    C11 = 1188.28051
    C12 = 1813.04613
    B21 = 0.0483019
    B22 = 4.35656721
    C21 = 2897.01927
    C22 = 5987.80407
    S = (first*log(T) + (-B11 - B12*a)*log(exp((-C11 - C12*a)/T) - 1.)
        + (-B11*C11 - B11*C12*a - B12*C11*a - B12*C12*a2)/(T*exp((-C11
        - C12*a)/T) - T) - (B11*C11 + B11*C12*a + B12*C11*a + B12*C12*a2)/T)
    S += ((-B21 - B22*a)*log(exp((-C21 - C22*a)/T) - 1.) + (-B21*C21 - B21*C22*a
        - B22*C21*a - B22*C22*a2)/(T*exp((-C21 - C22*a)/T) - T) - (B21*C21
        + B21*C22*a + B22*C21*a + B22*C22*a**2)/T)
    # There is a non-real component, but it is only a function of similariy
    # variable and so will always cancel out.
    return S.real*1000.

Response: r Calculates the integral over temperature of ideal - gas constant - pressure vector with the similarity variable concept and method as shown in SymPy.


Instruction:
Make a summary of the following Python 3 code
def TRCCp_integral(T, a0, a1, a2, a3, a4, a5, a6, a7, I=0):
    r'''Integrates ideal gas heat capacity using the model developed in [1]_.
    Best used as a delta only.

    The difference in enthalpy with respect to 0 K is given by:

    .. math::
        \frac{H(T) - H^{ref}}{RT} = a_0 + a_1x(a_2)/(a_2T) + I/T + h(T)/T

        h(T) = (a_5 + a_7)\left[(2a_3 + 8a_4)\ln(1-y)+ \left\{a_3\left(1 +
        \frac{1}{1-y}\right) + a_4\left(7 + \frac{1}{1-y}\right)\right\}y
        + a_4\left\{3y^2 + (5/3)y^3 + y^4 + (3/5)y^5 + (1/3)y^6\right\}
        + (1/7)\left\{a_4 - \frac{a_5}{(a_6+a_7)^2}\right\}y^7\right]

        h(T) = 0 \text{ for } T \le a_7

        y = \frac{T-a_7}{T+a_6} \text{ for } T > a_7 \text{ otherwise } 0

    Parameters
    ----------
    T : float
        Temperature [K]
    a1-a7 : float
        Coefficients
    I : float, optional
        Integral offset

    Returns
    -------
    H-H(0) : float
        Difference in enthalpy from 0 K , [J/mol]

    Notes
    -----
    Analytical integral as provided in [1]_ and verified with numerical
    integration.

    Examples
    --------
    >>> TRCCp_integral(298.15, 4.0, 7.65E5, 720., 3.565, -0.052, -1.55E6, 52.,
    ... 201., 1.2)
    10802.532600592816

    References
    ----------
    .. [1] Kabo, G. J., and G. N. Roganov. Thermodynamics of Organic Compounds
       in the Gas State, Volume II: V. 2. College Station, Tex: CRC Press, 1994.
    '''
    if T <= a7:
        y = 0.
    else:
        y = (T - a7)/(T + a6)
    y2 = y*y
    y4 = y2*y2
    if T <= a7:
        h = 0.0
    else:
        first = a6 + a7
        second = (2.*a3 + 8.*a4)*log(1. - y)
        third = (a3*(1. + 1./(1. - y)) + a4*(7. + 1./(1. - y)))*y
        fourth = a4*(3.*y2 + 5./3.*y*y2 + y4 + 0.6*y4*y + 1/3.*y4*y2)
        fifth = 1/7.*(a4 - a5/((a6 + a7)**2))*y4*y2*y
        h = first*(second + third + fourth + fifth)
    return (a0 + a1*exp(-a2/T)/(a2*T) + I/T + h/T)*R*T

Response: Integrates ideal gas heat capacity using the model developed in [ 1 ] _.


Instruction:
Can you create a Python 3 function that
returns a base class for a rowlinson - bonded liquid with the CSP method

Response:
def Rowlinson_Bondi(T, Tc, omega, Cpgm):
    r'''Calculate liquid constant-pressure heat capacitiy with the CSP method
    shown in [1]_.

    The heat capacity of a liquid is given by:

    .. math::
        \frac{Cp^L - Cp^{ig}}{R} = 1.45 + 0.45(1-T_r)^{-1} + 0.25\omega
        [17.11 + 25.2(1-T_r)^{1/3}T_r^{-1} + 1.742(1-T_r)^{-1}]

    Parameters
    ----------
    T : float
        Temperature of fluid [K]
    Tc : float
        Critical temperature of fluid [K]
    omega : float
        Acentric factor for fluid, [-]
    Cpgm : float
        Constant-pressure gas heat capacity, [J/mol/K]

    Returns
    -------
    Cplm : float
        Liquid constant-pressure heat capacitiy, [J/mol/K]

    Notes
    -----
    Less accurate than `Rowlinson_Poling`.

    Examples
    --------
    >>> Rowlinson_Bondi(T=373.28, Tc=535.55, omega=0.323, Cpgm=119.342)
    175.39760730048116

    References
    ----------
    .. [1] Poling, Bruce E. The Properties of Gases and Liquids. 5th edition.
       New York: McGraw-Hill Professional, 2000.
    .. [2] Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition.
       Berlin; New York:: Springer, 2010.
    .. [3] J.S. Rowlinson, Liquids and Liquid Mixtures, 2nd Ed.,
       Butterworth, London (1969).
    '''
    Tr = T/Tc
    Cplm = Cpgm + R*(1.45 + 0.45/(1.-Tr) + 0.25*omega*(17.11
    + 25.2*(1-Tr)**(1/3.)/Tr + 1.742/(1.-Tr)))
    return Cplm


Instruction:
Here you have a function in Python 3, explain what it does
def Dadgostar_Shaw(T, similarity_variable):
    r'''Calculate liquid constant-pressure heat capacitiy with the similarity
    variable concept and method as shown in [1]_.

    .. math::
        C_{p} = 24.5(a_{11}\alpha + a_{12}\alpha^2)+ (a_{21}\alpha
        + a_{22}\alpha^2)T +(a_{31}\alpha + a_{32}\alpha^2)T^2

    Parameters
    ----------
    T : float
        Temperature of liquid [K]
    similarity_variable : float
        similarity variable as defined in [1]_, [mol/g]

    Returns
    -------
    Cpl : float
        Liquid constant-pressure heat capacitiy, [J/kg/K]

    Notes
    -----
    Many restrictions on its use.

    Original model is in terms of J/g/K. Note that the model is for predicting
    mass heat capacity, not molar heat capacity like most other methods!

    a11 = -0.3416; a12 = 2.2671; a21 = 0.1064; a22 = -0.3874l;
    a31 = -9.8231E-05; a32 = 4.182E-04

    Examples
    --------
    >>> Dadgostar_Shaw(355.6, 0.139)
    1802.5291501191516

    References
    ----------
    .. [1] Dadgostar, Nafiseh, and John M. Shaw. "A Predictive Correlation for
       the Constant-Pressure Specific Heat Capacity of Pure and Ill-Defined
       Liquid Hydrocarbons." Fluid Phase Equilibria 313 (January 15, 2012):
       211-226. doi:10.1016/j.fluid.2011.09.015.
    '''
    a = similarity_variable
    a11 = -0.3416
    a12 = 2.2671
    a21 = 0.1064
    a22 = -0.3874
    a31 = -9.8231E-05
    a32 = 4.182E-04

    # Didn't seem to improve the comparison; sum of errors on some
    # points included went from 65.5  to 286.
    # Author probably used more precision in their calculation.
#    theta = 151.8675
#    constant = 3*R*(theta/T)**2*exp(theta/T)/(exp(theta/T)-1)**2
    constant = 24.5

    Cp = (constant*(a11*a + a12*a**2) + (a21*a + a22*a**2)*T
          + (a31*a + a32*a**2)*T**2)
    Cp = Cp*1000 # J/g/K to J/kg/K
    return Cp

Response: r A Predictive Correlation for a Liquid constant - pressure heat capacitiy with the similarity variable concept and method as shown in [ 1 ] _.


Instruction:
How would you explain what the following Python 3 function does
def Zabransky_quasi_polynomial(T, Tc, a1, a2, a3, a4, a5, a6):
    r'''Calculates liquid heat capacity using the model developed in [1]_.

    .. math::
        \frac{C}{R}=A_1\ln(1-T_r) + \frac{A_2}{1-T_r}
        + \sum_{j=0}^m A_{j+3} T_r^j

    Parameters
    ----------
    T : float
        Temperature [K]
    Tc : float
        Critical temperature of fluid, [K]
    a1-a6 : float
        Coefficients

    Returns
    -------
    Cp : float
        Liquid heat capacity, [J/mol/K]

    Notes
    -----
    Used only for isobaric heat capacities, not saturation heat capacities.
    Designed for reasonable extrapolation behavior caused by using the reduced
    critical temperature. Used by the authors of [1]_ when critical temperature
    was available for the fluid.
    Analytical integrals are available for this expression.

    Examples
    --------
    >>> Zabransky_quasi_polynomial(330, 591.79, -3.12743, 0.0857315, 13.7282, 1.28971, 6.42297, 4.10989)
    165.4728226923247

    References
    ----------
    .. [1] Zabransky, M., V. Ruzicka Jr, V. Majer, and Eugene S. Domalski.
       Heat Capacity of Liquids: Critical Review and Recommended Values.
       2 Volume Set. Washington, D.C.: Amer Inst of Physics, 1996.
    '''
    Tr = T/Tc
    return R*(a1*log(1-Tr) + a2/(1-Tr) + a3 + a4*Tr + a5*Tr**2 + a6*Tr**3)

Response: r Zabransky - quasi - polarized version of the formula.


Instruction:
Explain what the following Python 3 code does
def Zabransky_quasi_polynomial_integral_over_T(T, Tc, a1, a2, a3, a4, a5, a6):
    r'''Calculates the integral of liquid heat capacity over T using the
    quasi-polynomial model  developed in [1]_.

    Parameters
    ----------
    T : float
        Temperature [K]
    a1-a6 : float
        Coefficients

    Returns
    -------
    S : float
        Difference in entropy from 0 K, [J/mol/K]

    Notes
    -----
    The analytical integral was derived with Sympy. It requires the
    Polylog(2,x) function, which is unimplemented in SciPy. A very accurate
    numerical approximation was implemented as :obj:`thermo.utils.polylog2`.
    Relatively slow due to the use of that special function.

    Examples
    --------
    >>> S2 = Zabransky_quasi_polynomial_integral_over_T(300, 591.79, -3.12743,
    ... 0.0857315, 13.7282, 1.28971, 6.42297, 4.10989)
    >>> S1 = Zabransky_quasi_polynomial_integral_over_T(200, 591.79, -3.12743,
    ... 0.0857315, 13.7282, 1.28971, 6.42297, 4.10989)
    >>> S2 - S1
    59.16997291893654

    References
    ----------
    .. [1] Zabransky, M., V. Ruzicka Jr, V. Majer, and Eugene S. Domalski.
       Heat Capacity of Liquids: Critical Review and Recommended Values.
       2 Volume Set. Washington, D.C.: Amer Inst of Physics, 1996.
    '''
    term = T - Tc
    logT = log(T)
    Tc2 = Tc*Tc
    Tc3 = Tc2*Tc
    return R*(a3*logT -a1*polylog2(T/Tc) - a2*(-logT + 0.5*log(term*term))
              + T*(T*(T*a6/(3.*Tc3) + a5/(2.*Tc2)) + a4/Tc))

Response: r Calculates the integral of liquid heat capacity over T using the Zabransky - quasi - polar model developed in [ 1 ].


Instruction:
Can you tell what is the following Python 3 function doing
def Zabransky_cubic_integral(T, a1, a2, a3, a4):
    r'''Calculates the integral of liquid heat capacity using the model
    developed in [1]_.

    Parameters
    ----------
    T : float
        Temperature [K]
    a1-a4 : float
        Coefficients

    Returns
    -------
    H : float
        Difference in enthalpy from 0 K, [J/mol]

    Notes
    -----
    The analytical integral was derived with Sympy; it is a simple polynomial.

    Examples
    --------
    >>> Zabransky_cubic_integral(298.15, 20.9634, -10.1344, 2.8253, -0.256738)
    31051.679845520586

    References
    ----------
    .. [1] Zabransky, M., V. Ruzicka Jr, V. Majer, and Eugene S. Domalski.
       Heat Capacity of Liquids: Critical Review and Recommended Values.
       2 Volume Set. Washington, D.C.: Amer Inst of Physics, 1996.
    '''
    T = T/100.
    return 100*R*T*(T*(T*(T*a4*0.25 + a3/3.) + a2*0.5) + a1)

Response:
r Calculates the integral of liquid heat capacity using the model
    developed in [ 1 ].


Instruction:
How would you explain what the following Python 3 function does
def Zabransky_cubic_integral_over_T(T, a1, a2, a3, a4):
    r'''Calculates the integral of liquid heat capacity over T using the model
    developed in [1]_.

    Parameters
    ----------
    T : float
        Temperature [K]
    a1-a4 : float
        Coefficients

    Returns
    -------
    S : float
        Difference in entropy from 0 K, [J/mol/K]

    Notes
    -----
    The analytical integral was derived with Sympy; it is a simple polynomial,
    plus a logarithm

    Examples
    --------
    >>> Zabransky_cubic_integral_over_T(298.15, 20.9634, -10.1344, 2.8253,
    ... -0.256738)
    24.73245695987246

    References
    ----------
    .. [1] Zabransky, M., V. Ruzicka Jr, V. Majer, and Eugene S. Domalski.
       Heat Capacity of Liquids: Critical Review and Recommended Values.
       2 Volume Set. Washington, D.C.: Amer Inst of Physics, 1996.
    '''
    T = T/100.
    return R*(T*(T*(T*a4/3 + a3/2) + a2) + a1*log(T))

Response: r Calculates the integral of liquid heat capacity over T using the Zabransky model.


Instruction:
Explain what the following Python 3 code does
def Lastovka_solid_integral(T, similarity_variable):
    r'''Integrates solid constant-pressure heat capacitiy with the similarity
    variable concept and method as shown in [1]_.

    Uses a explicit form as derived with Sympy.

    Parameters
    ----------
    T : float
        Temperature of solid [K]
    similarity_variable : float
        similarity variable as defined in [1]_, [mol/g]

    Returns
    -------
    H : float
        Difference in enthalpy from 0 K, [J/kg]

    Notes
    -----
    Original model is in terms of J/g/K. Note that the model is for predicting
    mass heat capacity, not molar heat capacity like most other methods!

    See Also
    --------
    Lastovka_solid

    Examples
    --------
    >>> Lastovka_solid_integral(300, 0.2139)
    283246.1242170376

    References
    ----------
    .. [1] Laštovka, Václav, Michal Fulem, Mildred Becerra, and John M. Shaw.
       "A Similarity Variable for Estimating the Heat Capacity of Solid Organic
       Compounds: Part II. Application: Heat Capacity Calculation for
       Ill-Defined Organic Solids." Fluid Phase Equilibria 268, no. 1-2
       (June 25, 2008): 134-41. doi:10.1016/j.fluid.2008.03.018.
    '''
    A1 = 0.013183
    A2 = 0.249381
    theta = 151.8675
    C1 = 0.026526
    C2 = -0.024942
    D1 = 0.000025
    D2 = -0.000123
    similarity_variable2 = similarity_variable*similarity_variable

    return (T*T*T*(1000.*D1*similarity_variable/3.
        + 1000.*D2*similarity_variable2/3.) + T*T*(500.*C1*similarity_variable
        + 500.*C2*similarity_variable2)
        + (3000.*A1*R*similarity_variable*theta
        + 3000.*A2*R*similarity_variable2*theta)/(exp(theta/T) - 1.))

Response: Integrates solid constant - pressure heat capacitiy with the similarity variable as derived with Sympy.


Instruction:
Explain what the following Python 3 code does
def Lastovka_solid_integral_over_T(T, similarity_variable):
    r'''Integrates over T solid constant-pressure heat capacitiy with the
    similarity variable concept and method as shown in [1]_.

    Uses a explicit form as derived with Sympy.

    Parameters
    ----------
    T : float
        Temperature of solid [K]
    similarity_variable : float
        similarity variable as defined in [1]_, [mol/g]

    Returns
    -------
    S : float
        Difference in entropy from 0 K, [J/kg/K]

    Notes
    -----
    Original model is in terms of J/g/K. Note that the model is for predicting
    mass heat capacity, not molar heat capacity like most other methods!

    See Also
    --------
    Lastovka_solid

    Examples
    --------
    >>> Lastovka_solid_integral_over_T(300, 0.2139)
    1947.553552666818

    References
    ----------
    .. [1] Laštovka, Václav, Michal Fulem, Mildred Becerra, and John M. Shaw.
       "A Similarity Variable for Estimating the Heat Capacity of Solid Organic
       Compounds: Part II. Application: Heat Capacity Calculation for
       Ill-Defined Organic Solids." Fluid Phase Equilibria 268, no. 1-2
       (June 25, 2008): 134-41. doi:10.1016/j.fluid.2008.03.018.
    '''
    A1 = 0.013183
    A2 = 0.249381
    theta = 151.8675
    C1 = 0.026526
    C2 = -0.024942
    D1 = 0.000025
    D2 = -0.000123

    sim2 = similarity_variable*similarity_variable
    exp_theta_T = exp(theta/T)

    return (-3000.*R*similarity_variable*(A1 + A2*similarity_variable)*log(exp_theta_T - 1.)
    + T**2*(500.*D1*similarity_variable + 500.*D2*sim2)
    + T*(1000.*C1*similarity_variable + 1000.*C2*sim2)
    + (3000.*A1*R*similarity_variable*theta
    + 3000.*A2*R*sim2*theta)/(T*exp_theta_T - T)
    + (3000.*A1*R*similarity_variable*theta
    + 3000.*A2*R*sim2*theta)/T)

Response: Integrates over T solid constant - pressure heat capacitiy with the given similarity variable.


Instruction:
Can you generate a brief explanation for the following Python 3 code
def calculate(self, T, method):
        r'''Method to calculate surface tension of a liquid at temperature `T`
        with a given method.

        This method has no exception handling; see `T_dependent_property`
        for that.

        Parameters
        ----------
        T : float
            Temperature at which to calculate heat capacity, [K]
        method : str
            Method name to use

        Returns
        -------
        Cp : float
            Calculated heat capacity, [J/mol/K]
        '''
        if method == TRCIG:
            Cp = TRCCp(T, *self.TRCIG_coefs)
        elif method == COOLPROP:
            Cp = PropsSI('Cp0molar', 'T', T,'P', 101325.0, self.CASRN)
        elif method == POLING:
            Cp = R*(self.POLING_coefs[0] + self.POLING_coefs[1]*T
            + self.POLING_coefs[2]*T**2 + self.POLING_coefs[3]*T**3
            + self.POLING_coefs[4]*T**4)
        elif method == POLING_CONST:
            Cp = self.POLING_constant
        elif method == CRCSTD:
            Cp = self.CRCSTD_constant
        elif method == LASTOVKA_SHAW:
            Cp = Lastovka_Shaw(T, self.similarity_variable)
            Cp = property_mass_to_molar(Cp, self.MW)
        elif method in self.tabular_data:
            Cp = self.interpolate(T, method)
        return Cp

Response: r Method to calculate surface tension of a liquid at temperature T with a given method.


Instruction:
Given the following Python 3 function, write the documentation
def calculate_integral_over_T(self, T1, T2, method):
        r'''Method to calculate the integral of a property over temperature
        with respect to temperature, using a specified method. Implements the
        analytical integrals of all available methods except for tabular data.

        Parameters
        ----------
        T1 : float
            Lower limit of integration, [K]
        T2 : float
            Upper limit of integration, [K]
        method : str
            Method for which to find the integral

        Returns
        -------
        integral : float
            Calculated integral of the property over the given range,
            [`units`]
        '''
        if method == TRCIG:
            S2 = TRCCp_integral_over_T(T2, *self.TRCIG_coefs)
            S1 = TRCCp_integral_over_T(T1, *self.TRCIG_coefs)
            return S2 - S1
        elif method == CRCSTD:
            return self.CRCSTD_constant*log(T2/T1)
        elif method == POLING_CONST:
            return self.POLING_constant*log(T2/T1)
        elif method == POLING:
            A, B, C, D, E = self.POLING_coefs
            S2 = ((((0.25*E)*T2 + D/3.)*T2 + 0.5*C)*T2 + B)*T2
            S1 = ((((0.25*E)*T1 + D/3.)*T1 + 0.5*C)*T1 + B)*T1
            return R*(S2-S1 + A*log(T2/T1))
        elif method == LASTOVKA_SHAW:
            dS = (Lastovka_Shaw_integral_over_T(T2, self.similarity_variable)
                 - Lastovka_Shaw_integral_over_T(T1, self.similarity_variable))
            return property_mass_to_molar(dS, self.MW)
        elif method in self.tabular_data or method == COOLPROP:
            return float(quad(lambda T: self.calculate(T, method)/T, T1, T2)[0])
        else:
            raise Exception('Method not valid')

Response: r Calculates the integral of a property over a given temperature.


Instruction:
Can you generate a brief explanation for the following Python 3 code
def calculate_integral(self, T1, T2):
        r'''Method to compute the enthalpy integral of heat capacity from
         `T1` to `T2`.

        Parameters
        ----------
        T1 : float
            Initial temperature, [K]
        T2 : float
            Final temperature, [K]

        Returns
        -------
        dH : float
            Enthalpy difference between `T1` and `T2`, [J/mol]
        '''
        return (Zabransky_quasi_polynomial_integral(T2, self.Tc, *self.coeffs)
               - Zabransky_quasi_polynomial_integral(T1, self.Tc, *self.coeffs))

Response:
r Method to compute the enthalpy integral of heat capacity from
         T1 to T2.


Instruction:
Can you write a function in Python 3 where it
calls internally during the parsing of the Zabransky database add coefficients as they are read one per line

Response:
def add_coeffs(self, Tmin, Tmax, coeffs):
        '''Called internally during the parsing of the Zabransky database, to
        add coefficients as they are read one per line'''
        self.n += 1
        if not self.Ts:
            self.Ts = [Tmin, Tmax]
            self.coeff_sets = [coeffs]
        else:
            for ind, T in enumerate(self.Ts):
                if Tmin < T:
                    # Under an existing coefficient set - assume Tmax will come from another set
                    self.Ts.insert(ind, Tmin)
                    self.coeff_sets.insert(ind, coeffs)
                    return
            # Must be appended to end instead
            self.Ts.append(Tmax)
            self.coeff_sets.append(coeffs)


Instruction:
Create a Python 3 function for
determining the index at which the coefficients for the current temperature are stored in thecoeff_sets.

Response:
def _coeff_ind_from_T(self, T):
        '''Determines the index at which the coefficients for the current
        temperature are stored in `coeff_sets`.
        '''
        # DO NOT CHANGE
        if self.n == 1:
            return 0
        for i in range(self.n):
            if T <= self.Ts[i+1]:
                return i
        return self.n - 1


Instruction:
Make a summary of the following Python 3 code
def calculate_integral_over_T(self, T1, T2):
        r'''Method to compute the entropy integral of heat capacity from
        `T1` to `T2`. Analytically integrates across the piecewise spline
        as necessary.

        Parameters
        ----------
        T1 : float
            Initial temperature, [K]
        T2 : float
            Final temperature, [K]

        Returns
        -------
        dS : float
            Entropy difference between `T1` and `T2`, [J/mol/K]
        '''
        # Simplify the problem so we can assume T2 >= T1
        if T2 < T1:
            flipped = True
            T1, T2 = T2, T1
        else:
            flipped = False

        # Fastest case - only one coefficient set, occurs surprisingly often
        if self.n == 1:
            dS = (Zabransky_cubic_integral_over_T(T2, *self.coeff_sets[0])
                  - Zabransky_cubic_integral_over_T(T1, *self.coeff_sets[0]))
        else:
            ind_T1, ind_T2 = self._coeff_ind_from_T(T1), self._coeff_ind_from_T(T2)
            # Second fastest case - both are in the same coefficient set
            if ind_T1 == ind_T2:
                dS = (Zabransky_cubic_integral_over_T(T2, *self.coeff_sets[ind_T2])
                        - Zabransky_cubic_integral_over_T(T1, *self.coeff_sets[ind_T1]))
            # Fo through the loop if we need to - inevitably slow
            else:
                dS = (Zabransky_cubic_integral_over_T(self.Ts[ind_T1], *self.coeff_sets[ind_T1])
                      - Zabransky_cubic_integral_over_T(T1, *self.coeff_sets[ind_T1]))
                for i in range(ind_T1, ind_T2):
                    diff =(Zabransky_cubic_integral_over_T(self.Ts[i+1], *self.coeff_sets[i])
                          - Zabransky_cubic_integral_over_T(self.Ts[i], *self.coeff_sets[i]))
                    dS += diff
                end = (Zabransky_cubic_integral_over_T(T2, *self.coeff_sets[ind_T2])
                      - Zabransky_cubic_integral_over_T(self.Ts[ind_T2], *self.coeff_sets[ind_T2]))
                dS += end
        return -dS if flipped else dS

Response: r Method to compute the entropy integral of heat capacity from a piecewise spline system from a set of temperature T1 to T2. Analytically integrates across the piecewise spline system and returns the result.


Instruction:
Here you have a function in Python 3, explain what it does
def calculate_integral(self, T1, T2, method):
        r'''Method to calculate the integral of a property with respect to
        temperature, using a specified method.  Implements the
        analytical integrals of all available methods except for tabular data,
        the case of multiple coefficient sets needed to encompass the temperature
        range of any of the ZABRANSKY methods, and the CSP methods using the
        vapor phase properties.

        Parameters
        ----------
        T1 : float
            Lower limit of integration, [K]
        T2 : float
            Upper limit of integration, [K]
        method : str
            Method for which to find the integral

        Returns
        -------
        integral : float
            Calculated integral of the property over the given range,
            [`units*K`]
        '''
        if method == ZABRANSKY_SPLINE:
            return self.Zabransky_spline.calculate_integral(T1, T2)
        elif method == ZABRANSKY_SPLINE_C:
            return self.Zabransky_spline_iso.calculate_integral(T1, T2)
        elif method == ZABRANSKY_SPLINE_SAT:
            return self.Zabransky_spline_sat.calculate_integral(T1, T2)
        elif method == ZABRANSKY_QUASIPOLYNOMIAL:
            return self.Zabransky_quasipolynomial.calculate_integral(T1, T2)
        elif method == ZABRANSKY_QUASIPOLYNOMIAL_C:
            return self.Zabransky_quasipolynomial_iso.calculate_integral(T1, T2)
        elif method == ZABRANSKY_QUASIPOLYNOMIAL_SAT:
            return self.Zabransky_quasipolynomial_sat.calculate_integral(T1, T2)
        elif method == POLING_CONST:
            return (T2 - T1)*self.POLING_constant
        elif method == CRCSTD:
            return (T2 - T1)*self.CRCSTD_constant
        elif method == DADGOSTAR_SHAW:
            dH = (Dadgostar_Shaw_integral(T2, self.similarity_variable)
                    - Dadgostar_Shaw_integral(T1, self.similarity_variable))
            return property_mass_to_molar(dH, self.MW)
        elif method in self.tabular_data or method == COOLPROP or method in [ROWLINSON_POLING, ROWLINSON_BONDI]:
            return float(quad(self.calculate, T1, T2, args=(method))[0])
        else:
            raise Exception('Method not valid')

Response: r Calculates the integral of a property with respect to a given temperature.


Instruction:
Can you generate the documentation for the following Python 3 function
def calculate_integral_over_T(self, T1, T2, method):
        r'''Method to calculate the integral of a property over temperature
        with respect to temperature, using a specified method.   Implements the
        analytical integrals of all available methods except for tabular data,
        the case of multiple coefficient sets needed to encompass the temperature
        range of any of the ZABRANSKY methods, and the CSP methods using the
        vapor phase properties.

        Parameters
        ----------
        T1 : float
            Lower limit of integration, [K]
        T2 : float
            Upper limit of integration, [K]
        method : str
            Method for which to find the integral

        Returns
        -------
        integral : float
            Calculated integral of the property over the given range,
            [`units`]
        '''
        if method == ZABRANSKY_SPLINE:
            return self.Zabransky_spline.calculate_integral_over_T(T1, T2)
        elif method == ZABRANSKY_SPLINE_C:
            return self.Zabransky_spline_iso.calculate_integral_over_T(T1, T2)
        elif method == ZABRANSKY_SPLINE_SAT:
            return self.Zabransky_spline_sat.calculate_integral_over_T(T1, T2)
        elif method == ZABRANSKY_QUASIPOLYNOMIAL:
            return self.Zabransky_quasipolynomial.calculate_integral_over_T(T1, T2)
        elif method == ZABRANSKY_QUASIPOLYNOMIAL_C:
            return self.Zabransky_quasipolynomial_iso.calculate_integral_over_T(T1, T2)
        elif method == ZABRANSKY_QUASIPOLYNOMIAL_SAT:
            return self.Zabransky_quasipolynomial_sat.calculate_integral_over_T(T1, T2)
        elif method == POLING_CONST:
            return self.POLING_constant*log(T2/T1)
        elif method == CRCSTD:
            return self.CRCSTD_constant*log(T2/T1)
        elif method == DADGOSTAR_SHAW:
            dS = (Dadgostar_Shaw_integral_over_T(T2, self.similarity_variable)
                    - Dadgostar_Shaw_integral_over_T(T1, self.similarity_variable))
            return property_mass_to_molar(dS, self.MW)
        elif method in self.tabular_data or method == COOLPROP or method in [ROWLINSON_POLING, ROWLINSON_BONDI]:
            return float(quad(lambda T: self.calculate(T, method)/T, T1, T2)[0])
        else:
            raise Exception('Method not valid')

Response: r Calculates the integral of a property over a given temperature.


Instruction:
Here you have a function in Python 3, explain what it does
def load_all_methods(self):
        r'''Method which picks out coefficients for the specified chemical
        from the various dictionaries and DataFrames storing it. All data is
        stored as attributes. This method also sets :obj:`Tmin`, :obj:`Tmax`,
        and :obj:`all_methods` as a set of methods for which the data exists for.

        Called on initialization only. See the source code for the variables at
        which the coefficients are stored. The coefficients can safely be
        altered once the class is initialized. This method can be called again
        to reset the parameters.
        '''
        methods = []
        Tmins, Tmaxs = [], []
        if self.CASRN and self.CASRN in _PerryI and 'c' in _PerryI[self.CASRN]:
            self.PERRY151_Tmin = _PerryI[self.CASRN]['c']['Tmin'] if _PerryI[self.CASRN]['c']['Tmin'] else 0
            self.PERRY151_Tmax = _PerryI[self.CASRN]['c']['Tmax'] if _PerryI[self.CASRN]['c']['Tmax'] else 2000
            self.PERRY151_const = _PerryI[self.CASRN]['c']['Const']
            self.PERRY151_lin = _PerryI[self.CASRN]['c']['Lin']
            self.PERRY151_quad = _PerryI[self.CASRN]['c']['Quad']
            self.PERRY151_quadinv = _PerryI[self.CASRN]['c']['Quadinv']
            methods.append(PERRY151)
            Tmins.append(self.PERRY151_Tmin); Tmaxs.append(self.PERRY151_Tmax)
        if self.CASRN in CRC_standard_data.index and not np.isnan(CRC_standard_data.at[self.CASRN, 'Cpc']):
            self.CRCSTD_Cp = float(CRC_standard_data.at[self.CASRN, 'Cpc'])
            methods.append(CRCSTD)
        if self.MW and self.similarity_variable:
            methods.append(LASTOVKA_S)
            Tmins.append(1.0); Tmaxs.append(10000)
            # Works above roughly 1 K up to 10K.
        self.all_methods = set(methods)
        if Tmins and Tmaxs:
            self.Tmin, self.Tmax = min(Tmins), max(Tmaxs)

Response: r This method loads all methods for the specified chemicalical hierarchy from the various dictionaries and DataFrames storing them as attributes.


Instruction:
Can you generate a brief explanation for the following Python 3 code
def calculate_integral(self, T1, T2, method):
        r'''Method to calculate the integral of a property with respect to
        temperature, using a specified method. Implements the analytical
        integrals of all available methods except for tabular data.

        Parameters
        ----------
        T1 : float
            Lower limit of integration, [K]
        T2 : float
            Upper limit of integration, [K]
        method : str
            Method for which to find the integral

        Returns
        -------
        integral : float
            Calculated integral of the property over the given range,
            [`units*K`]
        '''
        if method == PERRY151:
            H2 = (self.PERRY151_const*T2 + 0.5*self.PERRY151_lin*T2**2
                  - self.PERRY151_quadinv/T2 + self.PERRY151_quad*T2**3/3.)
            H1 = (self.PERRY151_const*T1 + 0.5*self.PERRY151_lin*T1**2
                  - self.PERRY151_quadinv/T1 + self.PERRY151_quad*T1**3/3.)
            return (H2-H1)*calorie
        elif method == CRCSTD:
            return (T2-T1)*self.CRCSTD_Cp
        elif method == LASTOVKA_S:
            dH = (Lastovka_solid_integral(T2, self.similarity_variable)
                    - Lastovka_solid_integral(T1, self.similarity_variable))
            return property_mass_to_molar(dH, self.MW)
        elif method in self.tabular_data:
            return float(quad(self.calculate, T1, T2, args=(method))[0])
        else:
            raise Exception('Method not valid')

Response:
r Method to calculate the integral of a property with respect to
            temperature T1 T2 using a specified method.


Instruction:
Can you generate the documentation for the following Python 3 function
def calculate_integral_over_T(self, T1, T2, method):
        r'''Method to calculate the integral of a property over temperature
        with respect to temperature, using a specified method. Implements the
        analytical integrals of all available methods except for tabular data.

        Parameters
        ----------
        T1 : float
            Lower limit of integration, [K]
        T2 : float
            Upper limit of integration, [K]
        method : str
            Method for which to find the integral

        Returns
        -------
        integral : float
            Calculated integral of the property over the given range,
            [`units`]
        '''
        if method == PERRY151:
            S2 = (self.PERRY151_const*log(T2) + self.PERRY151_lin*T2
                  - self.PERRY151_quadinv/(2.*T2**2) + 0.5*self.PERRY151_quad*T2**2)
            S1 = (self.PERRY151_const*log(T1) + self.PERRY151_lin*T1
                  - self.PERRY151_quadinv/(2.*T1**2) + 0.5*self.PERRY151_quad*T1**2)
            return (S2 - S1)*calorie
        elif method == CRCSTD:
            S2 = self.CRCSTD_Cp*log(T2)
            S1 = self.CRCSTD_Cp*log(T1)
            return (S2 - S1)
        elif method == LASTOVKA_S:
            dS = (Lastovka_solid_integral_over_T(T2, self.similarity_variable)
                    - Lastovka_solid_integral_over_T(T1, self.similarity_variable))
            return property_mass_to_molar(dS, self.MW)
        elif method in self.tabular_data:
            return float(quad(lambda T: self.calculate(T, method)/T, T1, T2)[0])
        else:
            raise Exception('Method not valid')

Response: r Calculates the integral of a property over a given temperature.


Instruction:
Can you generate a brief explanation for the following Python 3 code
def calculate(self, T, P, zs, ws, method):
        r'''Method to calculate heat capacity of a gas mixture at
        temperature `T`, pressure `P`, mole fractions `zs` and weight fractions
        `ws` with a given method.

        This method has no exception handling; see `mixture_property`
        for that.

        Parameters
        ----------
        T : float
            Temperature at which to calculate the property, [K]
        P : float
            Pressure at which to calculate the property, [Pa]
        zs : list[float]
            Mole fractions of all species in the mixture, [-]
        ws : list[float]
            Weight fractions of all species in the mixture, [-]
        method : str
            Name of the method to use

        Returns
        -------
        Cpgm : float
            Molar heat capacity of the gas mixture at the given conditions,
            [J/mol]
        '''
        if method == SIMPLE:
            Cpgms = [i(T) for i in self.HeatCapacityGases]
            return mixing_simple(zs, Cpgms)
        else:
            raise Exception('Method not valid')

Response:
r Method to calculate the heat capacity of a gas mixture at
 temperature pressure mole fractions and weight fractions of all species in the mixture at a given temperature.


Instruction:
Explain what the following Python 3 code does
def Rachford_Rice_flash_error(V_over_F, zs, Ks):
    r'''Calculates the objective function of the Rachford-Rice flash equation.
    This function should be called by a solver seeking a solution to a flash
    calculation. The unknown variable is `V_over_F`, for which a solution
    must be between 0 and 1.

    .. math::
        \sum_i \frac{z_i(K_i-1)}{1 + \frac{V}{F}(K_i-1)} = 0

    Parameters
    ----------
    V_over_F : float
        Vapor fraction guess [-]
    zs : list[float]
        Overall mole fractions of all species, [-]
    Ks : list[float]
        Equilibrium K-values, [-]

    Returns
    -------
    error : float
        Deviation between the objective function at the correct V_over_F
        and the attempted V_over_F, [-]

    Notes
    -----
    The derivation is as follows:

    .. math::
        F z_i = L x_i + V y_i

        x_i = \frac{z_i}{1 + \frac{V}{F}(K_i-1)}

        \sum_i y_i = \sum_i K_i x_i = 1

        \sum_i(y_i - x_i)=0

        \sum_i \frac{z_i(K_i-1)}{1 + \frac{V}{F}(K_i-1)} = 0

    Examples
    --------
    >>> Rachford_Rice_flash_error(0.5, zs=[0.5, 0.3, 0.2],
    ... Ks=[1.685, 0.742, 0.532])
    0.04406445591174976

    References
    ----------
    .. [1] Rachford, H. H. Jr, and J. D. Rice. "Procedure for Use of Electronic
       Digital Computers in Calculating Flash Vaporization Hydrocarbon
       Equilibrium." Journal of Petroleum Technology 4, no. 10 (October 1,
       1952): 19-3. doi:10.2118/952327-G.
    '''
    return sum([zi*(Ki-1.)/(1.+V_over_F*(Ki-1.)) for Ki, zi in zip(Ks, zs)])

Response: r Calculates the objective function of the Rachford - Rice flash equation.


Instruction:
Explain what the following Python 3 code does
def flash_inner_loop(zs, Ks, AvailableMethods=False, Method=None):
    r'''This function handles the solution of the inner loop of a flash
    calculation, solving for liquid and gas mole fractions and vapor fraction
    based on specified overall mole fractions and K values. As K values are
    weak functions of composition, this should be called repeatedly by an outer
    loop. Will automatically select an algorithm to use if no Method is
    provided. Should always provide a solution.

    The automatic algorithm selection will try an analytical solution, and use
    the Rachford-Rice method if there are 4 or more components in the mixture.

    Parameters
    ----------
    zs : list[float]
        Overall mole fractions of all species, [-]
    Ks : list[float]
        Equilibrium K-values, [-]

    Returns
    -------
    V_over_F : float
        Vapor fraction solution [-]
    xs : list[float]
        Mole fractions of each species in the liquid phase, [-]
    ys : list[float]
        Mole fractions of each species in the vapor phase, [-]
    methods : list, only returned if AvailableMethods == True
        List of methods which can be used to obtain a solution with the given
        inputs

    Other Parameters
    ----------------
    Method : string, optional
        The method name to use. Accepted methods are 'Analytical',
        'Rachford-Rice', and 'Li-Johns-Ahmadi'. All valid values are also held
        in the list `flash_inner_loop_methods`.
    AvailableMethods : bool, optional
        If True, function will determine which methods can be used to obtain
        a solution for the desired chemical, and will return methods instead of
        `V_over_F`, `xs`, and `ys`.

    Notes
    -----
    A total of three methods are available for this function. They are:

        * 'Analytical', an exact solution derived with SymPy, applicable only
          only to mixtures of two or three components
        * 'Rachford-Rice', which numerically solves an objective function
          described in :obj:`Rachford_Rice_solution`.
        * 'Li-Johns-Ahmadi', which numerically solves an objective function
          described in :obj:`Li_Johns_Ahmadi_solution`.

    Examples
    --------
    >>> flash_inner_loop(zs=[0.5, 0.3, 0.2], Ks=[1.685, 0.742, 0.532])
    (0.6907302627738537, [0.3394086969663437, 0.36505605903717053, 0.29553524399648573], [0.5719036543882892, 0.2708715958055805, 0.1572247498061304])
    '''
    l = len(zs)
    def list_methods():
        methods = []
        if l in [2,3]:
            methods.append('Analytical')
        if l >= 2:
            methods.append('Rachford-Rice')
        if l >= 3:
            methods.append('Li-Johns-Ahmadi')
        return methods
    if AvailableMethods:
        return list_methods()
    if not Method:
        Method = 'Analytical' if l < 4 else 'Rachford-Rice'
    if Method == 'Analytical':
        if l == 2:
            z1, z2 = zs
            K1, K2 = Ks
            V_over_F = (-K1*z1 - K2*z2 + z1 + z2)/(K1*K2*z1 + K1*K2*z2 - K1*z1 - K1*z2 - K2*z1 - K2*z2 + z1 + z2)
        elif l == 3:
            z1, z2, z3 = zs
            K1, K2, K3 = Ks
            V_over_F = (-K1*K2*z1/2 - K1*K2*z2/2 - K1*K3*z1/2 - K1*K3*z3/2 + K1*z1 + K1*z2/2 + K1*z3/2 - K2*K3*z2/2 - K2*K3*z3/2 + K2*z1/2 + K2*z2 + K2*z3/2 + K3*z1/2 + K3*z2/2 + K3*z3 - z1 - z2 - z3 - (K1**2*K2**2*z1**2 + 2*K1**2*K2**2*z1*z2 + K1**2*K2**2*z2**2 - 2*K1**2*K2*K3*z1**2 - 2*K1**2*K2*K3*z1*z2 - 2*K1**2*K2*K3*z1*z3 + 2*K1**2*K2*K3*z2*z3 - 2*K1**2*K2*z1*z2 + 2*K1**2*K2*z1*z3 - 2*K1**2*K2*z2**2 - 2*K1**2*K2*z2*z3 + K1**2*K3**2*z1**2 + 2*K1**2*K3**2*z1*z3 + K1**2*K3**2*z3**2 + 2*K1**2*K3*z1*z2 - 2*K1**2*K3*z1*z3 - 2*K1**2*K3*z2*z3 - 2*K1**2*K3*z3**2 + K1**2*z2**2 + 2*K1**2*z2*z3 + K1**2*z3**2 - 2*K1*K2**2*K3*z1*z2 + 2*K1*K2**2*K3*z1*z3 - 2*K1*K2**2*K3*z2**2 - 2*K1*K2**2*K3*z2*z3 - 2*K1*K2**2*z1**2 - 2*K1*K2**2*z1*z2 - 2*K1*K2**2*z1*z3 + 2*K1*K2**2*z2*z3 + 2*K1*K2*K3**2*z1*z2 - 2*K1*K2*K3**2*z1*z3 - 2*K1*K2*K3**2*z2*z3 - 2*K1*K2*K3**2*z3**2 + 4*K1*K2*K3*z1**2 + 4*K1*K2*K3*z1*z2 + 4*K1*K2*K3*z1*z3 + 4*K1*K2*K3*z2**2 + 4*K1*K2*K3*z2*z3 + 4*K1*K2*K3*z3**2 + 2*K1*K2*z1*z2 - 2*K1*K2*z1*z3 - 2*K1*K2*z2*z3 - 2*K1*K2*z3**2 - 2*K1*K3**2*z1**2 - 2*K1*K3**2*z1*z2 - 2*K1*K3**2*z1*z3 + 2*K1*K3**2*z2*z3 - 2*K1*K3*z1*z2 + 2*K1*K3*z1*z3 - 2*K1*K3*z2**2 - 2*K1*K3*z2*z3 + K2**2*K3**2*z2**2 + 2*K2**2*K3**2*z2*z3 + K2**2*K3**2*z3**2 + 2*K2**2*K3*z1*z2 - 2*K2**2*K3*z1*z3 - 2*K2**2*K3*z2*z3 - 2*K2**2*K3*z3**2 + K2**2*z1**2 + 2*K2**2*z1*z3 + K2**2*z3**2 - 2*K2*K3**2*z1*z2 + 2*K2*K3**2*z1*z3 - 2*K2*K3**2*z2**2 - 2*K2*K3**2*z2*z3 - 2*K2*K3*z1**2 - 2*K2*K3*z1*z2 - 2*K2*K3*z1*z3 + 2*K2*K3*z2*z3 + K3**2*z1**2 + 2*K3**2*z1*z2 + K3**2*z2**2)**0.5/2)/(K1*K2*K3*z1 + K1*K2*K3*z2 + K1*K2*K3*z3 - K1*K2*z1 - K1*K2*z2 - K1*K2*z3 - K1*K3*z1 - K1*K3*z2 - K1*K3*z3 + K1*z1 + K1*z2 + K1*z3 - K2*K3*z1 - K2*K3*z2 - K2*K3*z3 + K2*z1 + K2*z2 + K2*z3 + K3*z1 + K3*z2 + K3*z3 - z1 - z2 - z3)
        else:
            raise Exception('Only solutions of one or two variables are available analytically')
        xs = [zi/(1.+V_over_F*(Ki-1.)) for zi, Ki in zip(zs, Ks)]
        ys = [Ki*xi for xi, Ki in zip(xs, Ks)]
        return V_over_F, xs, ys
    elif Method == 'Rachford-Rice':
        return Rachford_Rice_solution(zs=zs, Ks=Ks)
    elif Method == 'Li-Johns-Ahmadi':
        return Li_Johns_Ahmadi_solution(zs=zs, Ks=Ks)
    else:
        raise Exception('Incorrect Method input')

Response: r This function handles the inner loop of a flash base of a flash base of a mixture of species and K values.


Instruction:
Can you generate the documentation for the following Python 3 function
def NRTL(xs, taus, alphas):
    r'''Calculates the activity coefficients of each species in a mixture
    using the Non-Random Two-Liquid (NRTL) method, given their mole fractions,
    dimensionless interaction parameters, and nonrandomness constants. Those
    are normally correlated with temperature in some form, and need to be
    calculated separately.

    .. math::
        \ln(\gamma_i)=\frac{\displaystyle\sum_{j=1}^{n}{x_{j}\tau_{ji}G_{ji}}}
        {\displaystyle\sum_{k=1}^{n}{x_{k}G_{ki}}}+\sum_{j=1}^{n}
        {\frac{x_{j}G_{ij}}{\displaystyle\sum_{k=1}^{n}{x_{k}G_{kj}}}}
        {\left ({\tau_{ij}-\frac{\displaystyle\sum_{m=1}^{n}{x_{m}\tau_{mj}
        G_{mj}}}{\displaystyle\sum_{k=1}^{n}{x_{k}G_{kj}}}}\right )}

        G_{ij}=\text{exp}\left ({-\alpha_{ij}\tau_{ij}}\right )

    Parameters
    ----------
    xs : list[float]
        Liquid mole fractions of each species, [-]
    taus : list[list[float]]
        Dimensionless interaction parameters of each compound with each other,
        [-]
    alphas : list[list[float]]
        Nonrandomness constants of each compound interacting with each other, [-]

    Returns
    -------
    gammas : list[float]
        Activity coefficient for each species in the liquid mixture, [-]

    Notes
    -----
    This model needs N^2 parameters.

    One common temperature dependence of the nonrandomness constants is:

    .. math::
        \alpha_{ij}=c_{ij}+d_{ij}T

    Most correlations for the interaction parameters include some of the terms
    shown in the following form:

    .. math::
        \tau_{ij}=A_{ij}+\frac{B_{ij}}{T}+\frac{C_{ij}}{T^{2}}+D_{ij}
        \ln{\left ({T}\right )}+E_{ij}T^{F_{ij}}

    Examples
    --------
    Ethanol-water example, at 343.15 K and 1 MPa:

    >>> NRTL(xs=[0.252, 0.748], taus=[[0, -0.178], [1.963, 0]],
    ... alphas=[[0, 0.2974],[.2974, 0]])
    [1.9363183763514304, 1.1537609663170014]

    References
    ----------
    .. [1] Renon, Henri, and J. M. Prausnitz. "Local Compositions in
       Thermodynamic Excess Functions for Liquid Mixtures." AIChE Journal 14,
       no. 1 (1968): 135-144. doi:10.1002/aic.690140124.
    .. [2] Gmehling, Jurgen, Barbel Kolbe, Michael Kleiber, and Jurgen Rarey.
       Chemical Thermodynamics for Process Simulation. 1st edition. Weinheim:
       Wiley-VCH, 2012.
    '''
    gammas = []
    cmps = range(len(xs))
    Gs = [[exp(-alphas[i][j]*taus[i][j]) for j in cmps] for i in cmps]
    for i in cmps:
        tn1, td1, total2 = 0., 0., 0.
        for j in cmps:
            # Term 1, numerator and denominator
            tn1 += xs[j]*taus[j][i]*Gs[j][i]
            td1 +=  xs[j]*Gs[j][i]
            # Term 2
            tn2 = xs[j]*Gs[i][j]
            td2 = td3 = sum([xs[k]*Gs[k][j] for k in cmps])
            tn3 = sum([xs[m]*taus[m][j]*Gs[m][j] for m in cmps])
            total2 += tn2/td2*(taus[i][j] - tn3/td3)
        gamma = exp(tn1/td1 + total2)
        gammas.append(gamma)
    return gammas

Response: r Returns the non - random two - liquid mixture with the same number of non - random parameters.


Instruction:
Can you tell what is the following Python 3 function doing
def Wilson(xs, params):
    r'''Calculates the activity coefficients of each species in a mixture
    using the Wilson method, given their mole fractions, and
    dimensionless interaction parameters. Those are normally correlated with
    temperature, and need to be calculated separately.

    .. math::
        \ln \gamma_i = 1 - \ln \left(\sum_j^N \Lambda_{ij} x_j\right)
        -\sum_j^N \frac{\Lambda_{ji}x_j}{\displaystyle\sum_k^N \Lambda_{jk}x_k}

    Parameters
    ----------
    xs : list[float]
        Liquid mole fractions of each species, [-]
    params : list[list[float]]
        Dimensionless interaction parameters of each compound with each other,
        [-]

    Returns
    -------
    gammas : list[float]
        Activity coefficient for each species in the liquid mixture, [-]

    Notes
    -----
    This model needs N^2 parameters.

    The original model correlated the interaction parameters using the standard
    pure-component molar volumes of each species at 25°C, in the following form:

    .. math::
        \Lambda_{ij} = \frac{V_j}{V_i} \exp\left(\frac{-\lambda_{i,j}}{RT}\right)

    However, that form has less flexibility and offered no advantage over
    using only regressed parameters.

    Most correlations for the interaction parameters include some of the terms
    shown in the following form:

    .. math::
        \ln \Lambda_{ij} =a_{ij}+\frac{b_{ij}}{T}+c_{ij}\ln T + d_{ij}T
        + \frac{e_{ij}}{T^2} + h_{ij}{T^2}

    The Wilson model is not applicable to liquid-liquid systems.

    Examples
    --------
    Ethanol-water example, at 343.15 K and 1 MPa:

    >>> Wilson([0.252, 0.748], [[1, 0.154], [0.888, 1]])
    [1.8814926087178843, 1.1655774931125487]

    References
    ----------
    .. [1] Wilson, Grant M. "Vapor-Liquid Equilibrium. XI. A New Expression for
       the Excess Free Energy of Mixing." Journal of the American Chemical
       Society 86, no. 2 (January 1, 1964): 127-130. doi:10.1021/ja01056a002.
    .. [2] Gmehling, Jurgen, Barbel Kolbe, Michael Kleiber, and Jurgen Rarey.
       Chemical Thermodynamics for Process Simulation. 1st edition. Weinheim:
       Wiley-VCH, 2012.
    '''
    gammas = []
    cmps = range(len(xs))
    for i in cmps:
        tot1 = log(sum([params[i][j]*xs[j] for j in cmps]))
        tot2 = 0.
        for j in cmps:
            tot2 += params[j][i]*xs[j]/sum([params[j][k]*xs[k] for k in cmps])

        gamma = exp(1. - tot1 - tot2)
        gammas.append(gamma)
    return gammas

Response: r Returns the activity coefficients of each species in a mixture of liquid - liquid systems.


Instruction:
Explain what the following Python 3 code does
def UNIQUAC(xs, rs, qs, taus):
    r'''Calculates the activity coefficients of each species in a mixture
    using the Universal quasi-chemical (UNIQUAC) equation, given their mole
    fractions, `rs`, `qs`, and dimensionless interaction parameters. The
    interaction parameters are normally correlated with temperature, and need
    to be calculated separately.

    .. math::
        \ln \gamma_i = \ln \frac{\Phi_i}{x_i} + \frac{z}{2} q_i \ln
        \frac{\theta_i}{\Phi_i}+ l_i - \frac{\Phi_i}{x_i}\sum_j^N x_j l_j
        - q_i \ln\left( \sum_j^N \theta_j \tau_{ji}\right)+ q_i - q_i\sum_j^N
        \frac{\theta_j \tau_{ij}}{\sum_k^N \theta_k \tau_{kj}}

        \theta_i = \frac{x_i q_i}{\displaystyle\sum_{j=1}^{n} x_j q_j}

         \Phi_i = \frac{x_i r_i}{\displaystyle\sum_{j=1}^{n} x_j r_j}

         l_i = \frac{z}{2}(r_i - q_i) - (r_i - 1)

    Parameters
    ----------
    xs : list[float]
        Liquid mole fractions of each species, [-]
    rs : list[float]
        Van der Waals volume parameters for each species, [-]
    qs : list[float]
        Surface area parameters for each species, [-]
    taus : list[list[float]]
        Dimensionless interaction parameters of each compound with each other,
        [-]

    Returns
    -------
    gammas : list[float]
        Activity coefficient for each species in the liquid mixture, [-]

    Notes
    -----
    This model needs N^2 parameters.

    The original expression for the interaction parameters is as follows:

    .. math::
        \tau_{ji} = \exp\left(\frac{-\Delta u_{ij}}{RT}\right)

    However, it is seldom used. Most correlations for the interaction
    parameters include some of the terms shown in the following form:

    .. math::
        \ln \tau{ij} =a_{ij}+\frac{b_{ij}}{T}+c_{ij}\ln T + d_{ij}T
        + \frac{e_{ij}}{T^2}

    This model is recast in a slightly more computationally efficient way in
    [2]_, as shown below:

    .. math::
        \ln \gamma_i = \ln \gamma_i^{res} + \ln \gamma_i^{comb}

        \ln \gamma_i^{res} = q_i \left(1 - \ln\frac{\sum_j^N q_j x_j \tau_{ji}}
        {\sum_j^N q_j x_j}- \sum_j \frac{q_k x_j \tau_{ij}}{\sum_k q_k x_k
        \tau_{kj}}\right)

        \ln \gamma_i^{comb} = (1 - V_i + \ln V_i) - \frac{z}{2}q_i\left(1 -
        \frac{V_i}{F_i} + \ln \frac{V_i}{F_i}\right)

        V_i = \frac{r_i}{\sum_j^N r_j x_j}

        F_i = \frac{q_i}{\sum_j q_j x_j}

    Examples
    --------
    Ethanol-water example, at 343.15 K and 1 MPa:

    >>> UNIQUAC(xs=[0.252, 0.748], rs=[2.1055, 0.9200], qs=[1.972, 1.400],
    ... taus=[[1.0, 1.0919744384510301], [0.37452902779205477, 1.0]])
    [2.35875137797083, 1.2442093415968987]

    References
    ----------
    .. [1] Abrams, Denis S., and John M. Prausnitz. "Statistical Thermodynamics
       of Liquid Mixtures: A New Expression for the Excess Gibbs Energy of
       Partly or Completely Miscible Systems." AIChE Journal 21, no. 1 (January
       1, 1975): 116-28. doi:10.1002/aic.690210115.
    .. [2] Gmehling, Jurgen, Barbel Kolbe, Michael Kleiber, and Jurgen Rarey.
       Chemical Thermodynamics for Process Simulation. 1st edition. Weinheim:
       Wiley-VCH, 2012.
    .. [3] Maurer, G., and J. M. Prausnitz. "On the Derivation and Extension of
       the Uniquac Equation." Fluid Phase Equilibria 2, no. 2 (January 1,
       1978): 91-99. doi:10.1016/0378-3812(78)85002-X.
    '''
    cmps = range(len(xs))
    rsxs = sum([rs[i]*xs[i] for i in cmps])
    phis = [rs[i]*xs[i]/rsxs for i in cmps]
    qsxs = sum([qs[i]*xs[i] for i in cmps])
    vs = [qs[i]*xs[i]/qsxs for i in cmps]

    Ss = [sum([vs[j]*taus[j][i] for j in cmps]) for i in cmps]

    loggammacs = [log(phis[i]/xs[i]) + 1 - phis[i]/xs[i]
    - 5*qs[i]*(log(phis[i]/vs[i]) + 1 - phis[i]/vs[i]) for i in cmps]

    loggammars = [qs[i]*(1 - log(Ss[i]) - sum([taus[i][j]*vs[j]/Ss[j]
                  for j in cmps])) for i in cmps]

    return [exp(loggammacs[i] + loggammars[i]) for i in cmps]

Response: r Returns the composition of the liquid mixture that is a mixture of the same type as the mixture of the liquid mixture.


Instruction:
Given the following Python 3 function, write the documentation
def bubble_at_T(zs, Psats, fugacities=None, gammas=None):
    '''
    >>> bubble_at_T([0.5, 0.5], [1400, 7000])
    4200.0
    >>> bubble_at_T([0.5, 0.5], [1400, 7000], gammas=[1.1, .75])
    3395.0
    >>> bubble_at_T([0.5, 0.5], [1400, 7000], gammas=[1.1, .75], fugacities=[.995, 0.98])
    3452.440775305097
    '''
    if not fugacities:
        fugacities = [1 for i in range(len(Psats))]
    if not gammas:
        gammas = [1 for i in range(len(Psats))]
    if not none_and_length_check((zs, Psats, fugacities, gammas)):
        raise Exception('Input dimentions are inconsistent or some input parameters are missing.')
    P = sum(zs[i]*Psats[i]*gammas[i]/fugacities[i] for i in range(len(zs)))
    return P

Response: This function calculates the bubble frequency at the given dimentions.


Instruction:
Here you have a function in Python 3, explain what it does
def identify_phase_mixture(T=None, P=None, zs=None, Tcs=None, Pcs=None,
                           Psats=None, CASRNs=None,
                           AvailableMethods=False, Method=None):  # pragma: no cover
    '''
    >>> identify_phase_mixture(T=280, P=5000., zs=[0.5, 0.5], Psats=[1400, 7000])
    ('l', [0.5, 0.5], None, 0)
    >>> identify_phase_mixture(T=280, P=3000., zs=[0.5, 0.5], Psats=[1400, 7000])
    ('two-phase', [0.7142857142857143, 0.2857142857142857], [0.33333333333333337, 0.6666666666666666], 0.5625000000000001)
    >>> identify_phase_mixture(T=280, P=800., zs=[0.5, 0.5], Psats=[1400, 7000])
    ('g', None, [0.5, 0.5], 1)
    >>> identify_phase_mixture(T=280, P=800., zs=[0.5, 0.5])
    (None, None, None, None)
    '''
    def list_methods():
        methods = []
        if Psats and none_and_length_check((Psats, zs)):
            methods.append('IDEAL_VLE')
        if Tcs and none_and_length_check([Tcs]) and all([T >= i for i in Tcs]):
            methods.append('SUPERCRITICAL_T')
        if Pcs and none_and_length_check([Pcs]) and all([P >= i for i in Pcs]):
            methods.append('SUPERCRITICAL_P')
        if Tcs and none_and_length_check([zs, Tcs]) and any([T > Tc for Tc in Tcs]):
            methods.append('IDEAL_VLE_SUPERCRITICAL')
        methods.append('NONE')
        return methods
    if AvailableMethods:
        return list_methods()
    if not Method:
        Method = list_methods()[0]
    # This is the calculate, given the method section
    xs, ys, phase, V_over_F = None, None, None, None
    if Method == 'IDEAL_VLE':
        Pdew = dew_at_T(zs, Psats)
        Pbubble = bubble_at_T(zs, Psats)
        if P >= Pbubble:
            phase = 'l'
            ys = None
            xs = zs
            V_over_F = 0
        elif P <= Pdew:
            phase = 'g'
            ys = zs
            xs = None
            V_over_F = 1
        elif Pdew < P < Pbubble:
            xs, ys, V_over_F = flash(P, zs, Psats)
            phase = 'two-phase'
    elif Method == 'SUPERCRITICAL_T':
        if all([T >= i for i in Tcs]):
            phase = 'g'
        else: # The following is nonsensical
            phase = 'two-phase'
    elif Method == 'SUPERCRITICAL_P':
        if all([P >= i for i in Pcs]):
            phase = 'g'
        else: # The following is nonsensical
            phase = 'two-phase'
    elif Method == 'IDEAL_VLE_SUPERCRITICAL':
        Psats = list(Psats)
        for i in range(len(Psats)):
            if not Psats[i] and Tcs[i] and Tcs[i] <= T:
                Psats[i] = 1E8
        Pdew = dew_at_T(zs, Psats)
        Pbubble = 1E99
        if P >= Pbubble:
            phase = 'l'
            ys = None
            xs = zs
            V_over_F = 0
        elif P <= Pdew:
            phase = 'g'
            ys = zs
            xs = None
            V_over_F = 1
        elif Pdew < P < Pbubble:
            xs, ys, V_over_F = flash(P, zs, Psats)
            phase = 'two-phase'

    elif Method == 'NONE':
        pass
    else:
        raise Exception('Failure in in function')
    return phase, xs, ys, V_over_F

Response: Identify the phase of a single object.


Instruction:
Here you have a function in Python 3, explain what it does
def Pbubble_mixture(T=None, zs=None, Psats=None, CASRNs=None,
                   AvailableMethods=False, Method=None):  # pragma: no cover
    '''
    >>> Pbubble_mixture(zs=[0.5, 0.5], Psats=[1400, 7000])
    4200.0
    '''
    def list_methods():
        methods = []
        if none_and_length_check((Psats, zs)):
            methods.append('IDEAL_VLE')
        methods.append('NONE')
        return methods
    if AvailableMethods:
        return list_methods()
    if not Method:
        Method = list_methods()[0]
    # This is the calculate, given the method section
    if Method == 'IDEAL_VLE':
        Pbubble = bubble_at_T(zs, Psats)
    elif Method == 'NONE':
        Pbubble = None
    else:
        raise Exception('Failure in in function')
    return Pbubble

Response: This function calculates the bubble at T with the given Zs Psats CASRNs and Method.


Instruction:
Can you implement a function in Python 3 that
calculates the bubble point at a given pressure.

Response:
def bubble_at_P(P, zs, vapor_pressure_eqns, fugacities=None, gammas=None):
    '''Calculates bubble point for a given pressure

    Parameters
    ----------
    P : float
        Pressure, [Pa]
    zs : list[float]
        Overall mole fractions of all species, [-]
    vapor_pressure_eqns : list[functions]
        Temperature dependent function for each specie, Returns Psat, [Pa]
    fugacities : list[float], optional
        fugacities of each species, defaults to list of ones, [-]
    gammas : list[float], optional
        gammas of each species, defaults to list of ones, [-]

    Returns
    -------
    Tbubble : float, optional
        Temperature of bubble point at pressure `P`, [K]

    '''

    def bubble_P_error(T):
        Psats = [VP(T) for VP in vapor_pressure_eqns]
        Pcalc = bubble_at_T(zs, Psats, fugacities, gammas)

        return P - Pcalc

    T_bubble = newton(bubble_P_error, 300)

    return T_bubble


Instruction:
Can you generate the documentation for the following Python 3 function
def Pdew_mixture(T=None, zs=None, Psats=None, CASRNs=None,
                 AvailableMethods=False, Method=None):  # pragma: no cover
    '''
    >>> Pdew_mixture(zs=[0.5, 0.5], Psats=[1400, 7000])
    2333.3333333333335
    '''
    def list_methods():
        methods = []
        if none_and_length_check((Psats, zs)):
            methods.append('IDEAL_VLE')
        methods.append('NONE')
        return methods
    if AvailableMethods:
        return list_methods()
    if not Method:
        Method = list_methods()[0]
    # This is the calculate, given the method section
    if Method == 'IDEAL_VLE':
        Pdew = dew_at_T(zs, Psats)
    elif Method == 'NONE':
        Pdew = None
    else:
        raise Exception('Failure in in function')
    return Pdew

Response: This function calculates the Pdew of a mixture of the Ideal VLE and a set of CASRNs.


Instruction:
Can you generate the documentation for the following Python 3 function
def draw_2d(self, width=300, height=300, Hs=False): # pragma: no cover
        r'''Interface for drawing a 2D image of the molecule.
        Requires an HTML5 browser, and the libraries RDKit and
        IPython. An exception is raised if either of these libraries is
        absent.

        Parameters
        ----------
        width : int
            Number of pixels wide for the view
        height : int
            Number of pixels tall for the view
        Hs : bool
            Whether or not to show hydrogen

        Examples
        --------
        >>> Chemical('decane').draw_2d() # doctest: +ELLIPSIS
        <PIL.Image.Image image mode=RGBA size=300x300 at 0x...>
        '''
        try:
            from rdkit.Chem import Draw
            from rdkit.Chem.Draw import IPythonConsole
            if Hs:
                mol = self.rdkitmol_Hs
            else:
                mol = self.rdkitmol
            return Draw.MolToImage(mol, size=(width, height))
        except:
            return 'Rdkit is required for this feature.'

Response: Interface for drawing a 2D image of the molecule.


Instruction:
Implement a Python 3 function for
interfacing for drawing an interactive 3D view of the molecule.

Response:
def draw_3d(self, width=300, height=500, style='stick', Hs=True): # pragma: no cover
        r'''Interface for drawing an interactive 3D view of the molecule.
        Requires an HTML5 browser, and the libraries RDKit, pymol3D, and
        IPython. An exception is raised if all three of these libraries are
        not installed.

        Parameters
        ----------
        width : int
            Number of pixels wide for the view
        height : int
            Number of pixels tall for the view
        style : str
            One of 'stick', 'line', 'cross', or 'sphere'
        Hs : bool
            Whether or not to show hydrogen

        Examples
        --------
        >>> Chemical('cubane').draw_3d()
        <IPython.core.display.HTML object>
        '''
        try:
            import py3Dmol
            from IPython.display import display
            if Hs:
                mol = self.rdkitmol_Hs
            else:
                mol = self.rdkitmol
            AllChem.EmbedMultipleConfs(mol)
            mb = Chem.MolToMolBlock(mol)
            p = py3Dmol.view(width=width,height=height)
            p.addModel(mb,'sdf')
            p.setStyle({style:{}})
            p.zoomTo()
            display(p.show())
        except:
            return 'py3Dmol, RDKit, and IPython are required for this feature.'


Instruction:
Here you have a function in Python 3, explain what it does
def Um(self):
        r'''Internal energy of the chemical at its current temperature and
        pressure, in units of [J/mol].

        This property requires that :obj:`thermo.chemical.set_thermo` ran
        successfully to be accurate.
        It also depends on the molar volume of the chemical at its current
        conditions.
        '''
        return self.Hm - self.P*self.Vm if (self.Vm and self.Hm is not None) else None

Response:
Internal energy of the chemical at its current temperature and
        pressure in units of [ J / mol ]


Instruction:
Implement a function in Python 3 to
return the total energy in units of [ J / mol ]

Response:
def Am(self):
        r'''Helmholtz energy of the chemical at its current temperature and
        pressure, in units of [J/mol].

        This property requires that :obj:`thermo.chemical.set_thermo` ran
        successfully to be accurate.
        It also depends on the molar volume of the chemical at its current
        conditions.
        '''
        return self.Um - self.T*self.Sm if (self.Um is not None and self.Sm is not None) else None


Instruction:
Can you tell what is the following Python 3 function doing
def A(self):
        r'''Helmholtz energy of the chemical at its current temperature and
        pressure, in units of [J/kg].

        This property requires that :obj:`thermo.chemical.set_thermo` ran
        successfully to be accurate.
        It also depends on the molar volume of the chemical at its current
        conditions.
        '''
        return self.U - self.T*self.S if (self.U is not None and self.S is not None) else None

Response:
A property that returns the Helmholtz energy of the chemical at its current temperature and
        pressure in units of [ J / k ].


Instruction:
Here you have a function in Python 3, explain what it does
def charge(self):
        r'''Charge of a chemical, computed with RDKit from a chemical's SMILES.
        If RDKit is not available, holds None.

        Examples
        --------
        >>> Chemical('sodium ion').charge
        1
        '''
        try:
            if not self.rdkitmol:
                return charge_from_formula(self.formula)
            else:
                return Chem.GetFormalCharge(self.rdkitmol)
        except:
            return charge_from_formula(self.formula)

Response: Returns the charge of a chemical in the SMILES system.


Instruction:
Make a summary of the following Python 3 code
def rdkitmol(self):
        r'''RDKit object of the chemical, without hydrogen. If RDKit is not
        available, holds None.

        For examples of what can be done with RDKit, see
        `their website <http://www.rdkit.org/docs/GettingStartedInPython.html>`_.
        '''
        if self.__rdkitmol:
            return self.__rdkitmol
        else:
            try:
                self.__rdkitmol = Chem.MolFromSmiles(self.smiles)
                return self.__rdkitmol
            except:
                return None

Response: RDKit object of the chemical without hydrogen.


Instruction:
Explain what the following Python 3 code does
def rdkitmol_Hs(self):
        r'''RDKit object of the chemical, with hydrogen. If RDKit is not
        available, holds None.

        For examples of what can be done with RDKit, see
        `their website <http://www.rdkit.org/docs/GettingStartedInPython.html>`_.
        '''
        if self.__rdkitmol_Hs:
            return self.__rdkitmol_Hs
        else:
            try:
                self.__rdkitmol_Hs = Chem.AddHs(self.rdkitmol)
                return self.__rdkitmol_Hs
            except:
                return None

Response: r'''RDKit object of the chemical with hydrogen.


Instruction:
Given the following Python 3 function, write the documentation
def atom_fractions(self):
        r'''Dictionary of atom:fractional occurence of the elements in a
        chemical. Useful when performing element balances. For mass-fraction
        occurences, see :obj:`mass_fractions`.

        Examples
        --------
        >>> Chemical('Ammonium aluminium sulfate').atom_fractions
        {'H': 0.25, 'S': 0.125, 'Al': 0.0625, 'O': 0.5, 'N': 0.0625}
        '''
        if self.__atom_fractions:
            return self.__atom_fractions
        else:
            self.__atom_fractions = atom_fractions(self.atoms)
            return self.__atom_fractions

Response:
Dictionary of atom : fraction occurence of the elements in a
        chemical. Useful when performing element balances.


Instruction:
Given the following Python 3 function, write the documentation
def legal_status(self):
        r'''Dictionary of legal status indicators for the chemical.

        Examples
        --------
        >>> pprint(Chemical('benzene').legal_status)
        {'DSL': 'LISTED',
         'EINECS': 'LISTED',
         'NLP': 'UNLISTED',
         'SPIN': 'LISTED',
         'TSCA': 'LISTED'}
        '''
        if self.__legal_status:
            return self.__legal_status
        else:
            self.__legal_status = legal_status(self.CAS, Method='COMBINED')
            return self.__legal_status

Response: Dictionary of legal status indicators for the chemical.


Instruction:
Write a Python 3 script for
returning a dictionary of economic status indicators for the chemical.

Response:
def economic_status(self):
        r'''Dictionary of economic status indicators for the chemical.

        Examples
        --------
        >>> pprint(Chemical('benzene').economic_status)
        ["US public: {'Manufactured': 6165232.1, 'Imported': 463146.474, 'Exported': 271908.252}",
         u'1,000,000 - 10,000,000 tonnes per annum',
         u'Intermediate Use Only',
         'OECD HPV Chemicals']
        '''
        if self.__economic_status:
            return self.__economic_status
        else:
            self.__economic_status = economic_status(self.CAS, Method='Combined')
            return self.__economic_status


Instruction:
Can you generate a brief explanation for the following Python 3 code
def PSRK_groups(self):
        r'''Dictionary of PSRK subgroup: count groups for the PSRK subgroups,
        as determined by `DDBST's online service <http://www.ddbst.com/unifacga.html>`_.

        Examples
        --------
        >>> pprint(Chemical('Cumene').PSRK_groups)
        {1: 2, 9: 5, 13: 1}
        '''
        if self.__PSRK_groups:
            return self.__PSRK_groups
        else:
            load_group_assignments_DDBST()
            if self.InChI_Key in DDBST_PSRK_assignments:
                self.__PSRK_groups = DDBST_PSRK_assignments[self.InChI_Key]
                return self.__PSRK_groups
            else:
                return None

Response: Dictionary of PSRK subgroup names for the PSRK subgroups.


Instruction:
Write a Python 3 function for
returning the Hvap property of the chemical at its current temperature.

Response:
def Hvap(self):
        r'''Enthalpy of vaporization of the chemical at its current temperature,
        in units of [J/kg].

        This property uses the object-oriented interface
        :obj:`thermo.phase_change.EnthalpyVaporization`, but converts its
        results from molar to mass units.

        Examples
        --------
        >>> Chemical('water', T=320).Hvap
        2389540.219347256
        '''
        Hvamp = self.Hvapm
        if Hvamp:
            return property_molar_to_mass(Hvamp, self.MW)
        return None


Instruction:
Here you have a function in Python 3, explain what it does
def Cpl(self):
        r'''Liquid-phase heat capacity of the chemical at its current temperature,
        in units of [J/kg/K]. For calculation of this property at other
        temperatures, or specifying manually the method used to calculate it,
        and more - see the object oriented interface
        :obj:`thermo.heat_capacity.HeatCapacityLiquid`; each Chemical instance
        creates one to actually perform the calculations. Note that that
        interface provides output in molar units.

        Examples
        --------
        >>> Chemical('water', T=320).Cpl
        4177.518996988284

        Ideal entropy change of water from 280 K to 340 K, output converted
        back to mass-based units of J/kg/K.

        >>> dSm = Chemical('water').HeatCapacityLiquid.T_dependent_property_integral_over_T(280, 340)
        >>> property_molar_to_mass(dSm, Chemical('water').MW)
        812.1024585274956
        '''
        Cplm = self.HeatCapacityLiquid(self.T)
        if Cplm:
            return property_molar_to_mass(Cplm, self.MW)
        return None

Response: Liquid - phase heat capacity of the chemical at the current temperature.


Instruction:
Can you implement a function in Python 3 that
returns the property of the chemical at the current temperature and the mass of the chemical at the current temperature.

Response:
def Cpg(self):
        r'''Gas-phase heat capacity of the chemical at its current temperature,
        in units of [J/kg/K]. For calculation of this property at other
        temperatures, or specifying manually the method used to calculate it,
        and more - see the object oriented interface
        :obj:`thermo.heat_capacity.HeatCapacityGas`; each Chemical instance
        creates one to actually perform the calculations. Note that that
        interface provides output in molar units.

        Examples
        --------
        >>> w = Chemical('water', T=520)
        >>> w.Cpg
        1967.6698314620658
        '''
        Cpgm = self.HeatCapacityGas(self.T)
        if Cpgm:
            return property_molar_to_mass(Cpgm, self.MW)
        return None


Instruction:
Make a summary of the following Python 3 code
def Cvgm(self):
        r'''Gas-phase ideal-gas contant-volume heat capacity of the chemical at
        its current temperature, in units of [J/mol/K]. Subtracts R from
        the ideal-gas heat capacity; does not include pressure-compensation
        from an equation of state.

        Examples
        --------
        >>> w = Chemical('water', T=520)
        >>> w.Cvgm
        27.13366316134193
        '''
        Cpgm = self.HeatCapacityGas(self.T)
        if Cpgm:
            return Cpgm - R
        return None

Response:
Returns the gas - phase ideal - gas contant - volume heat capacity of the chemical at
        s current temperature in units of [ J / mol / K ].


Instruction:
Make a summary of the following Python 3 code
def Cvg(self):
        r'''Gas-phase ideal-gas contant-volume heat capacity of the chemical at
        its current temperature, in units of [J/kg/K]. Subtracts R from
        the ideal-gas heat capacity; does not include pressure-compensation
        from an equation of state.

        Examples
        --------
        >>> w = Chemical('water', T=520)
        >>> w.Cvg
        1506.1471795798861
        '''
        Cvgm = self.Cvgm
        if Cvgm:
            return property_molar_to_mass(Cvgm, self.MW)
        return None

Response:
Returns the chemical contant - volume heat capacity of the chemical at
       .


Instruction:
Can you tell what is the following Python 3 function doing
def isentropic_exponent(self):
        r'''Gas-phase ideal-gas isentropic exponent of the chemical at its
        current temperature, [dimensionless]. Does not include
        pressure-compensation from an equation of state.

        Examples
        --------
        >>> Chemical('hydrogen').isentropic_exponent
        1.405237786321222
        '''
        Cp, Cv = self.Cpg, self.Cvg
        if all((Cp, Cv)):
            return isentropic_exponent(Cp, Cv)
        return None

Response:
Returns the ideal gas isentropic exponent of the chemical at its
        current temperature.


Instruction:
Explain what the following Python 3 code does
def rhol(self):
        r'''Liquid-phase mass density of the chemical at its current
        temperature and pressure, in units of [kg/m^3]. For calculation of this
        property at other temperatures and pressures, or specifying manually
        the method used to calculate it, and more - see the object oriented
        interface :obj:`thermo.volume.VolumeLiquid`; each Chemical instance
        creates one to actually perform the calculations. Note that that
        interface provides output in molar units.

        Examples
        --------
        >>> Chemical('o-xylene', T=297).rhol
        876.9946785618097
        '''
        Vml = self.Vml
        if Vml:
            return Vm_to_rho(Vml, self.MW)
        return None

Response:
Returns the liquid mass density of the chemical at its current
        temperature and pressure in units of [ km ].


Instruction:
Given the following Python 3 function, write the documentation
def rhog(self):
        r'''Gas-phase mass density of the chemical at its current temperature
        and pressure, in units of [kg/m^3]. For calculation of this property at
        other temperatures or pressures, or specifying manually the method used
        to calculate it, and more - see the object oriented interface
        :obj:`thermo.volume.VolumeGas`; each Chemical instance
        creates one to actually perform the calculations. Note that that
        interface provides output in molar units.

        Examples
        --------
        Estimate the density of the core of the sun, at 15 million K and
        26.5 PetaPascals, assuming pure helium (actually 68% helium):

        >>> Chemical('helium', T=15E6, P=26.5E15).rhog
        8329.27226509739

        Compared to a result on
        `Wikipedia <https://en.wikipedia.org/wiki/Solar_core>`_ of 150000
        kg/m^3, the fundamental equation of state performs poorly.

        >>> He = Chemical('helium', T=15E6, P=26.5E15)
        >>> He.VolumeGas.set_user_methods_P(['IDEAL']); He.rhog
        850477.8065477367

        The ideal-gas law performs somewhat better, but vastly overshoots
        the density prediction.
        '''
        Vmg = self.Vmg
        if Vmg:
            return Vm_to_rho(Vmg, self.MW)
        return None

Response: Returns the gas mass of the chemical at the current temperature and pressure.


Instruction:
Make a summary of the following Python 3 code
def Zs(self):
        r'''Compressibility factor of the chemical in the solid phase at the
        current temperature and pressure, [dimensionless].

        Utilizes the object oriented interface and
        :obj:`thermo.volume.VolumeSolid` to perform the actual calculation of
        molar volume.

        Examples
        --------
        >>> Chemical('palladium').Z
        0.00036248477437931853
        '''
        Vms = self.Vms
        if Vms:
            return Z(self.T, self.P, Vms)
        return None

Response: Return the compressibility factor of the chemical in the solid phase at the current temperature and pressure.


Instruction:
Here you have a function in Python 3, explain what it does
def Zl(self):
        r'''Compressibility factor of the chemical in the liquid phase at the
        current temperature and pressure, [dimensionless].

        Utilizes the object oriented interface and
        :obj:`thermo.volume.VolumeLiquid` to perform the actual calculation of
        molar volume.

        Examples
        --------
        >>> Chemical('water').Zl
        0.0007385375470263454
        '''
        Vml = self.Vml
        if Vml:
            return Z(self.T, self.P, Vml)
        return None

Response: Return the Zl value of the chemical in the liquid phase at the current temperature and pressure.


Instruction:
Can you generate a brief explanation for the following Python 3 code
def Zg(self):
        r'''Compressibility factor of the chemical in the gas phase at the
        current temperature and pressure, [dimensionless].

        Utilizes the object oriented interface and
        :obj:`thermo.volume.VolumeGas` to perform the actual calculation of
        molar volume.

        Examples
        --------
        >>> Chemical('sulfur hexafluoride', T=700, P=1E9).Zg
        11.140084184207813
        '''
        Vmg = self.Vmg
        if Vmg:
            return Z(self.T, self.P, Vmg)
        return None

Response:
Return the compressibility factor of the chemical in the gas phase at the
        current temperature and pressure.


Instruction:
Can you generate the documentation for the following Python 3 function
def SGg(self):
        r'''Specific gravity of the gas phase of the chemical, [dimensionless].
        The reference condition is air at 15.6 °C (60 °F) and 1 atm
        (rho=1.223 kg/m^3). The definition for gases uses the compressibility
        factor of the reference gas and the chemical both at the reference
        conditions, not the conditions of the chemical.

        Examples
        --------
        >>> Chemical('argon').SGg
        1.3795835970877504
        '''
        Vmg = self.VolumeGas(T=288.70555555555552, P=101325)
        if Vmg:
            rho = Vm_to_rho(Vmg, self.MW)
            return SG(rho, rho_ref=1.2231876628642968) # calculated with Mixture
        return None

Response: Specific gravity of the gas phase of the chemical.


Instruction:
Can you generate a brief explanation for the following Python 3 code
def API(self):
        r'''API gravity of the liquid phase of the chemical, [degrees].
        The reference condition is water at 15.6 °C (60 °F) and 1 atm
        (rho=999.016 kg/m^3, standardized).

        Examples
        --------
        >>> Chemical('water').API
        9.999752435378895
        '''
        Vml = self.VolumeLiquid(T=288.70555555555552, P=101325)
        if Vml:
            rho = Vm_to_rho(Vml, self.MW)
        sg = SG(rho, rho_ref=999.016)
        return SG_to_API(sg)

Response: A simple API for the chemical.


Instruction:
Can you generate a brief explanation for the following Python 3 code
def Bvirial(self):
        r'''Second virial coefficient of the gas phase of the chemical at its
        current temperature and pressure, in units of [mol/m^3].

        This property uses the object-oriented interface
        :obj:`thermo.volume.VolumeGas`, converting its result with
        :obj:`thermo.utils.B_from_Z`.

        Examples
        --------
        >>> Chemical('water').Bvirial
        -0.0009596286322838357
        '''
        if self.Vmg:
            return B_from_Z(self.Zg, self.T, self.P)
        return None

Response:
Second virial coefficient of the chemical at its
        current temperature and pressure in units of [mol / m^3 ]


Instruction:
Implement a function in Python 3 to
return the isobaric expansion of the liquid phase of the current cluster.

Response:
def isobaric_expansion_l(self):
        r'''Isobaric (constant-pressure) expansion of the liquid phase of the
        chemical at its current temperature and pressure, in units of [1/K].

        .. math::
            \beta = \frac{1}{V}\left(\frac{\partial V}{\partial T} \right)_P

        Utilizes the temperature-derivative method of
        :obj:`thermo.volume.VolumeLiquid` to perform the actual calculation.
        The derivatives are all numerical.

        Examples
        --------
        >>> Chemical('dodecane', T=400).isobaric_expansion_l
        0.0011617555762469477
        '''
        dV_dT = self.VolumeLiquid.TP_dependent_property_derivative_T(self.T, self.P)
        Vm = self.Vml
        if dV_dT and Vm:
            return isobaric_expansion(V=Vm, dV_dT=dV_dT)


Instruction:
Can you tell what is the following Python 3 function doing
def isobaric_expansion_g(self):
        r'''Isobaric (constant-pressure) expansion of the gas phase of the
        chemical at its current temperature and pressure, in units of [1/K].

        .. math::
            \beta = \frac{1}{V}\left(\frac{\partial V}{\partial T} \right)_P

        Utilizes the temperature-derivative method of
        :obj:`thermo.VolumeGas` to perform the actual calculation.
        The derivatives are all numerical.

        Examples
        --------
        >>> Chemical('Hexachlorobenzene', T=900).isobaric_expansion_g
        0.001151869741981048
        '''
        dV_dT = self.VolumeGas.TP_dependent_property_derivative_T(self.T, self.P)
        Vm = self.Vmg
        if dV_dT and Vm:
            return isobaric_expansion(V=Vm, dV_dT=dV_dT)

Response: A simple isobaric expansion of the gas phase of the current chemical at its current temperature and pressure.


Instruction:
Create a Python 3 function to
return the Joule Thomson coefficient of the chemical in the liquid phase at .

Response:
def JTl(self):
        r'''Joule Thomson coefficient of the chemical in the liquid phase at
        its current temperature and pressure, in units of [K/Pa].

        .. math::
            \mu_{JT} = \left(\frac{\partial T}{\partial P}\right)_H = \frac{1}{C_p}
            \left[T \left(\frac{\partial V}{\partial T}\right)_P - V\right]
            = \frac{V}{C_p}\left(\beta T-1\right)

        Utilizes the temperature-derivative method of
        :obj:`thermo.volume.VolumeLiquid` and the temperature-dependent heat
        capacity method :obj:`thermo.heat_capacity.HeatCapacityLiquid` to
        obtain the properties required for the actual calculation.

        Examples
        --------
        >>> Chemical('dodecane', T=400).JTl
        -3.0827160465192742e-07
        '''
        Vml, Cplm, isobaric_expansion_l = self.Vml, self.Cplm, self.isobaric_expansion_l
        if all((Vml, Cplm, isobaric_expansion_l)):
            return Joule_Thomson(T=self.T, V=Vml, Cp=Cplm, beta=isobaric_expansion_l)
        return None


Instruction:
Given the following Python 3 function, write the documentation
def JTg(self):
        r'''Joule Thomson coefficient of the chemical in the gas phase at
        its current temperature and pressure, in units of [K/Pa].

        .. math::
            \mu_{JT} = \left(\frac{\partial T}{\partial P}\right)_H = \frac{1}{C_p}
            \left[T \left(\frac{\partial V}{\partial T}\right)_P - V\right]
            = \frac{V}{C_p}\left(\beta T-1\right)

        Utilizes the temperature-derivative method of
        :obj:`thermo.volume.VolumeGas` and the temperature-dependent heat
        capacity method :obj:`thermo.heat_capacity.HeatCapacityGas` to
        obtain the properties required for the actual calculation.

        Examples
        --------
        >>> Chemical('dodecane', T=400, P=1000).JTg
        5.4089897835384913e-05
        '''
        Vmg, Cpgm, isobaric_expansion_g = self.Vmg, self.Cpgm, self.isobaric_expansion_g
        if all((Vmg, Cpgm, isobaric_expansion_g)):
            return Joule_Thomson(T=self.T, V=Vmg, Cp=Cpgm, beta=isobaric_expansion_g)
        return None

Response:
Returns the Joule Thomson coefficient of the chemical in the gas phase at
       .


Instruction:
Write a Python 3 function that can
return the nu of the chemical at its current temperature and pressure in units of [ m^2 / s ].

Response:
def nul(self):
        r'''Kinematic viscosity of the liquid phase of the chemical at its
        current temperature and pressure, in units of [m^2/s].

        .. math::
            \nu = \frac{\mu}{\rho}

        Utilizes the temperature and pressure dependent object oriented
        interfaces :obj:`thermo.volume.VolumeLiquid`,
        :obj:`thermo.viscosity.ViscosityLiquid`  to calculate the
        actual properties.

        Examples
        --------
        >>> Chemical('methane', T=110).nul
        2.858088468937331e-07
        '''
        mul, rhol = self.mul, self.rhol
        if all([mul, rhol]):
            return nu_mu_converter(mu=mul, rho=rhol)
        return None


Instruction:
Can you implement a function in Python 3 that
returns the nu of the chemical at its current temperature and pressure in units of [ m^2 / s ) if the chemical is in the nug phase otherwise None.

Response:
def nug(self):
        r'''Kinematic viscosity of the gas phase of the chemical at its
        current temperature and pressure, in units of [m^2/s].

        .. math::
            \nu = \frac{\mu}{\rho}

        Utilizes the temperature and pressure dependent object oriented
        interfaces :obj:`thermo.volume.VolumeGas`,
        :obj:`thermo.viscosity.ViscosityGas`  to calculate the
        actual properties.

        Examples
        --------
        >>> Chemical('methane', T=115).nug
        2.5056924327995865e-06
        '''
        mug, rhog = self.mug, self.rhog
        if all([mug, rhog]):
            return nu_mu_converter(mu=mug, rho=rhog)
        return None


Instruction:
Make a summary of the following Python 3 code
def alphal(self):
        r'''Thermal diffusivity of the liquid phase of the chemical at its
        current temperature and pressure, in units of [m^2/s].

        .. math::
            \alpha = \frac{k}{\rho Cp}

        Utilizes the temperature and pressure dependent object oriented
        interfaces :obj:`thermo.volume.VolumeLiquid`,
        :obj:`thermo.thermal_conductivity.ThermalConductivityLiquid`,
        and :obj:`thermo.heat_capacity.HeatCapacityLiquid` to calculate the
        actual properties.

        Examples
        --------
        >>> Chemical('nitrogen', T=70).alphal
        9.444949636299626e-08
        '''
        kl, rhol, Cpl = self.kl, self.rhol, self.Cpl
        if all([kl, rhol, Cpl]):
            return thermal_diffusivity(k=kl, rho=rhol, Cp=Cpl)
        return None

Response:
Returns the thermal diffusivity of the liquid phase of the chemical at its
        current temperature and pressure in units of [ m^2 / s ].


Instruction:
Given the following Python 3 function, write the documentation
def alphag(self):
        r'''Thermal diffusivity of the gas phase of the chemical at its
        current temperature and pressure, in units of [m^2/s].

        .. math::
            \alpha = \frac{k}{\rho Cp}

        Utilizes the temperature and pressure dependent object oriented
        interfaces :obj:`thermo.volume.VolumeGas`,
        :obj:`thermo.thermal_conductivity.ThermalConductivityGas`,
        and :obj:`thermo.heat_capacity.HeatCapacityGas` to calculate the
        actual properties.

        Examples
        --------
        >>> Chemical('ammonia').alphag
        1.6931865425158556e-05
        '''
        kg, rhog, Cpg = self.kg, self.rhog, self.Cpg
        if all([kg, rhog, Cpg]):
            return thermal_diffusivity(k=kg, rho=rhog, Cp=Cpg)
        return None

Response:
Returns the thermal diffusivity of the gas phase of the chemical at its
        current temperature and pressure in units of [ m^2 / s ).


Instruction:
Write a Python 3 script for
returning the Prandtl number of the liquid phase of the chemical at its current temperature and pressure.

Response:
def Prl(self):
        r'''Prandtl number of the liquid phase of the chemical at its
        current temperature and pressure, [dimensionless].

        .. math::
            Pr = \frac{C_p \mu}{k}

        Utilizes the temperature and pressure dependent object oriented
        interfaces :obj:`thermo.viscosity.ViscosityLiquid`,
        :obj:`thermo.thermal_conductivity.ThermalConductivityLiquid`,
        and :obj:`thermo.heat_capacity.HeatCapacityLiquid` to calculate the
        actual properties.

        Examples
        --------
        >>> Chemical('nitrogen', T=70).Prl
        2.7828214501488886
        '''
        Cpl, mul, kl = self.Cpl, self.mul, self.kl
        if all([Cpl, mul, kl]):
            return Prandtl(Cp=Cpl, mu=mul, k=kl)
        return None


Instruction:
Write a Python 3 function for
calculating the gas phase of the chemical at its current temperature and pressure and returns the Prandtl number of the gas phase of the chemical at its current temperature and pressure and pressure. Returns None if there is no chemical at its .

Response:
def Prg(self):
        r'''Prandtl number of the gas phase of the chemical at its
        current temperature and pressure, [dimensionless].

        .. math::
            Pr = \frac{C_p \mu}{k}

        Utilizes the temperature and pressure dependent object oriented
        interfaces :obj:`thermo.viscosity.ViscosityGas`,
        :obj:`thermo.thermal_conductivity.ThermalConductivityGas`,
        and :obj:`thermo.heat_capacity.HeatCapacityGas` to calculate the
        actual properties.

        Examples
        --------
        >>> Chemical('NH3').Prg
        0.847263731933008
        '''
        Cpg, mug, kg = self.Cpg, self.mug, self.kg
        if all([Cpg, mug, kg]):
            return Prandtl(Cp=Cpg, mu=mug, k=kg)
        return None


Instruction:
Write a Python 3 function that can
return the solubility parameter of the chemical at its current temperature and pressure.

Response:
def solubility_parameter(self):
        r'''Solubility parameter of the chemical at its
        current temperature and pressure, in units of [Pa^0.5].

        .. math::
            \delta = \sqrt{\frac{\Delta H_{vap} - RT}{V_m}}

        Calculated based on enthalpy of vaporization and molar volume.
        Normally calculated at STP. For uses of this property, see
        :obj:`thermo.solubility.solubility_parameter`.

        Examples
        --------
        >>> Chemical('NH3').solubility_parameter
        24766.329043856073
        '''
        return solubility_parameter(T=self.T, Hvapm=self.Hvapm, Vml=self.Vml,
                                    Method=self.solubility_parameter_method,
                                    CASRN=self.CAS)


Instruction:
Write a Python 3 script to
return the mass heat capacity of the chemical at its current phase and the current temperature in units of [ J / kK ].

Response:
def Cp(self):
        r'''Mass heat capacity of the chemical at its current phase and
        temperature, in units of [J/kg/K].

        Utilizes the object oriented interfaces
        :obj:`thermo.heat_capacity.HeatCapacitySolid`,
        :obj:`thermo.heat_capacity.HeatCapacityLiquid`,
        and :obj:`thermo.heat_capacity.HeatCapacityGas` to perform the
        actual calculation of each property. Note that those interfaces provide
        output in molar units (J/mol/K).

        Examples
        --------
        >>> w = Chemical('water')
        >>> w.Cp, w.phase
        (4180.597021827336, 'l')
        >>> Chemical('palladium').Cp
        234.26767209171211
        '''
        return phase_select_property(phase=self.phase, s=self.Cps, l=self.Cpl, g=self.Cpg)