def _Backward3a_T_Ps(P, s):
    """Backward equation for region 3a, T=f(P,s)

    Parameters
    ----------
    P : float
        Pressure, [MPa]
    s : float
        Specific entropy, [kJ/kgK]

    Returns
    -------
    T : float
        Temperature, [K]

    References
    ----------
    IAPWS, Revised Supplementary Release on Backward Equations for the
    Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
    Industrial Formulation 1997 for the Thermodynamic Properties of Water and
    Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 6

    Examples
    --------
    >>> _Backward3a_T_Ps(20,3.8)
    628.2959869
    >>> _Backward3a_T_Ps(100,4)
    705.6880237
    """
    I = [-12, -12, -10, -10, -10, -10, -8, -8, -8, -8, -6, -6, -6, -5, -5, -5,
         -4, -4, -4, -2, -2, -1, -1, 0, 0, 0, 1, 2, 2, 3, 8, 8, 10]
    J = [28, 32, 4, 10, 12, 14, 5, 7, 8, 28, 2, 6, 32, 0, 14, 32, 6, 10, 36, 1,
         4, 1, 6, 0, 1, 4, 0, 0, 3, 2, 0, 1, 2]
    n = [0.150042008263875e10, -0.159397258480424e12, 0.502181140217975e-3,
         -0.672057767855466e2, 0.145058545404456e4, -0.823889534888890e4,
         -0.154852214233853, 0.112305046746695e2, -0.297000213482822e2,
         0.438565132635495e11, 0.137837838635464e-2, -0.297478527157462e1,
         0.971777947349413e13, -0.571527767052398e-4, 0.288307949778420e5,
         -0.744428289262703e14, 0.128017324848921e2, -0.368275545889071e3,
         0.664768904779177e16, 0.449359251958880e-1, -0.422897836099655e1,
         -0.240614376434179, -0.474341365254924e1, 0.724093999126110,
         0.923874349695897, 0.399043655281015e1, 0.384066651868009e-1,
         -0.359344365571848e-2, -0.735196448821653, 0.188367048396131,
         0.141064266818704e-3, -0.257418501496337e-2, 0.123220024851555e-2]

    Pr = P/100
    sigma = s/4.4
    suma = 0
    for i, j, ni in zip(I, J, n):
        suma += ni * (Pr+0.240)**i * (sigma-0.703)**j
    return 760*suma
Backward equation for region 3a, T=f(P,s)

    Parameters
    ----------
    P : float
        Pressure, [MPa]
    s : float
        Specific entropy, [kJ/kgK]

    Returns
    -------
    T : float
        Temperature, [K]

    References
    ----------
    IAPWS, Revised Supplementary Release on Backward Equations for the
    Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
    Industrial Formulation 1997 for the Thermodynamic Properties of Water and
    Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 6

    Examples
    --------
    >>> _Backward3a_T_Ps(20,3.8)
    628.2959869
    >>> _Backward3a_T_Ps(100,4)
    705.6880237