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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _prop(self, T, rho, fav):
 """Thermodynamic properties of humid air Parameters T : float Temperature, [K] rho : float Density, [kg/m³] fav : dict dictionary with helmholtz energy and derivatives Returns ------- prop : dict Dictionary with thermodynamic properties of humid air: * P: Pressure, [MPa] * s: Specific entropy, [kJ/kgK] * cp: Specific isobaric heat capacity, [kJ/kgK] * h: Specific enthalpy, [kJ/kg] * g: Specific gibbs energy, [kJ/kg] * alfav: Thermal expansion coefficient, [1/K] * betas: Isentropic T-P coefficient, [K/MPa] * xkappa: Isothermal compressibility, [1/MPa] * ks: Isentropic compressibility, [1/MPa] * w: Speed of sound, [m/s] References IAPWS, Guideline on an Equation of State for Humid Air in Contact with Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the Thermodynamic Properties of Seawater, Table 5, http://www.iapws.org/relguide/SeaAir.html """

        prop = {}
        prop["P"] = rho**2*fav["fird"]/1000                             # Eq T1
        prop["s"] = -fav["firt"]                                        # Eq T2
        prop["cp"] = -T*fav["firtt"]+T*rho*fav["firdt"]**2/(            # Eq T3
            2*fav["fird"]+rho*fav["firdd"])
        prop["h"] = fav["fir"]-T*fav["firt"]+rho*fav["fird"]            # Eq T4
        prop["g"] = fav["fir"]+rho*fav["fird"]                          # Eq T5
        prop["alfav"] = fav["firdt"]/(2*fav["fird"]+rho*fav["firdd"])   # Eq T6
        prop["betas"] = 1000*fav["firdt"]/rho/(                         # Eq T7
            rho*fav["firdt"]**2-fav["firtt"]*(2*fav["fird"]+rho*fav["firdd"]))
        prop["xkappa"] = 1e3/(rho**2*(2*fav["fird"]+rho*fav["firdd"]))  # Eq T8
        prop["ks"] = 1000*fav["firtt"]/rho**2/(                         # Eq T9
            fav["firtt"]*(2*fav["fird"]+rho*fav["firdd"])-rho*fav["firdt"]**2)
        prop["w"] = (rho**2*1000*(fav["firtt"]*fav["firdd"]-fav["firdt"]**2) /
                     fav["firtt"]+2*rho*fav["fird"]*1000)**0.5         # Eq T10
        return prop