CoolProp::MixtureDerivatives Class Reference

Detailed Description

This class is a friend class of HelmholtzEOSMixtureBackend, therefore the static methods contained in it have access to the private and protected variables in the HelmholtzEOSMixtureBackend instance.

In this way the derivative routines can be kept in their own separate file and not pollute the HelmholtzEOSMixtureBackend namespace

Definition at line 33 of file MixtureDerivatives.h.

#include <MixtureDerivatives.h>

Static Public Member Functions
static CoolPropDbl	ndpdV__constT_n (HelmholtzEOSMixtureBackend &HEOS)
	GERG 2004 Monograph equation 7.62. More...
static CoolPropDbl	dpdT__constV_n (HelmholtzEOSMixtureBackend &HEOS)
	GERG 2004 Monograph equation 7.61. More...
static CoolPropDbl	dpdrho__constT_n (HelmholtzEOSMixtureBackend &HEOS)
static CoolPropDbl	ndpdni__constT_V_nj (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	GERG 2004 Monograph equation 7.63. More...
static CoolPropDbl	partial_molar_volume (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	GERG 2004 monograph Eqn. 7.32. More...
static CoolPropDbl	fugacity_i (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	Fugacity of the i-th component. More...
static CoolPropDbl	ln_fugacity_coefficient (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	Natural logarithm of the fugacity coefficient. More...
static CoolPropDbl	dln_fugacity_i_dT__constrho_n (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	Derivative of the natural logarithm of the fugacity with respect to T. More...
static CoolPropDbl	dln_fugacity_i_drho__constT_n (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	Derivative of the natural logarithm of the fugacity with respect to T. More...
static CoolPropDbl	dln_fugacity_coefficient_dT__constp_n (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	GERG 2004 Monograph Eqn. 7.29. More...
static CoolPropDbl	dln_fugacity_i_dT__constp_n (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
static CoolPropDbl	dln_fugacity_i_dp__constT_n (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
static CoolPropDbl	dln_fugacity_dxj__constT_p_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	dln_fugacity_i_dtau__constdelta_x (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
static CoolPropDbl	dln_fugacity_i_ddelta__consttau_x (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
static CoolPropDbl	dln_fugacity_dxj__constT_rho_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	ndln_fugacity_i_dnj__constT_V_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d_ndln_fugacity_i_dnj_dtau__constdelta_x (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2_ndln_fugacity_i_dnj_dtau2__constdelta_x (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2_ndln_fugacity_i_dnj_ddelta_dtau__constx (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2_ndln_fugacity_i_dnj_ddelta2__consttau_x (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d_ndln_fugacity_i_dnj_ddelta__consttau_x (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d_ndln_fugacity_i_dnj_ddxk__consttau_delta (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2_ndln_fugacity_i_dnj_dxk_dTau__constdelta (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2_ndln_fugacity_i_dnj_dxk_dDelta__consttau (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag)
static CoolPropDbl	nd_ndln_fugacity_i_dnj_dnk__constT_V_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag)
static CoolPropDbl	nAij (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	n2Aijk (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag)
static CoolPropDbl	d_nAij_dTau (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d_nAij_dDelta (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d_nAij_dX (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag, parameters WRT)
static CoolPropDbl	d_n2Aijk_dTau (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag)
static CoolPropDbl	d_n2Aijk_dDelta (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag)
static CoolPropDbl	d_n2Aijk_dX (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag, parameters WRT)
static Eigen::MatrixXd	Lstar (HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag)
static Eigen::MatrixXd	dLstar_dX (HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag, parameters WRT)
static Eigen::MatrixXd	d2Lstar_dX2 (HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag, parameters WRT1, parameters WRT2)
static Eigen::MatrixXd	Mstar (HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag, Eigen::MatrixXd &L)
static Eigen::MatrixXd	dMstar_dX (HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag, parameters WRT, Eigen::MatrixXd &L, Eigen::MatrixXd &dL_dX)
static CoolPropDbl	ndalphar_dni__constT_V_nj (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	Table B4, Kunz, JCED, 2012 for the original term and the subsequent substitutions. More...
static CoolPropDbl	dnalphar_dni__constT_V_nj (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	GERG Equation 7.42. More...
static CoolPropDbl	dln_fugacity_coefficient_dp__constT_n (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	GERG 2004 Monograph Eqn. 7.30. More...
static CoolPropDbl	ndln_fugacity_coefficient_dnj__constT_p (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
	GERG 2004 Monograph Equation 7.31. More...
static CoolPropDbl	dln_fugacity_coefficient_dxj__constT_p_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
	Gernert Equation 3.115. More...
static CoolPropDbl	dpdxj__constT_V_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t j, x_N_dependency_flag xN_flag)
	Gernert Equation 3.130. More...
static CoolPropDbl	d2nalphar_dxj_dni__constT_V (HelmholtzEOSMixtureBackend &HEOS, std::size_t j, std::size_t i, x_N_dependency_flag xN_flag)
	Gernert Equation 3.117. More...
static CoolPropDbl	dalphar_dxj__constT_V_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d_ndalphardni_dxj__constT_V_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d_dalpharddelta_dxj__constT_V_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	ddelta_dxj__constT_V_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	dtau_dxj__constT_V_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2nalphar_dni_dT (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	GERG 2004 Monograph, equations 7.44 and 7.51. More...
static CoolPropDbl	d_ndalphardni_dTau (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	GERG 2004 Monograph Equation 7.51 and Table B4, Kunz, JCED, 2012. More...
static CoolPropDbl	d2_ndalphardni_dTau2 (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	\(\tau\) derivartive of GERG 2004 Monograph Equation 7.51 More...
static CoolPropDbl	d3_ndalphardni_dTau3 (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
static CoolPropDbl	d_ndalphardni_dDelta (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	GERG 2004 Monograph Equation 7.50 and Table B4, Kunz, JCED, 2012. More...
static CoolPropDbl	d2_ndalphardni_dDelta2 (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	\(\delta\) derivative of GERG 2004 Monograph Equation 7.50 More...
static CoolPropDbl	d3_ndalphardni_dDelta3 (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2_ndalphardni_dDelta_dTau (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	\(\tau\) derivative of GERG 2004 Monograph Equation 7.50 More...
static CoolPropDbl	d3_ndalphardni_dDelta2_dTau (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
static CoolPropDbl	d3_ndalphardni_dDelta_dTau2 (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2_ndalphardni_dxj_dDelta__consttau_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
	\(x_j\) derivative of GERG 2004 Monograph Equation 7.50 More...
static CoolPropDbl	d2_ndalphardni_dxj_dTau__constdelta_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
	\(x_j\) derivative of GERG 2004 Monograph Equation 7.51 More...
static CoolPropDbl	d3_ndalphardni_dxj_dTau2__constdelta_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d3_ndalphardni_dxj_dDelta2__consttau_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d3_ndalphardni_dxj_dDelta_dTau__constxi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	nd2nalphardnidnj__constT_V (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
	GERG 2004 Monograph equation 7.41. More...
static CoolPropDbl	nd_ndalphardni_dnj__constT_V (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d_nd_ndalphardni_dnj_dTau__constdelta_x (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2_nd_ndalphardni_dnj_dTau2__constdelta_x (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2_nd_ndalphardni_dnj_dDelta2__consttau_x (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2_nd_ndalphardni_dnj_dDelta_dTau__constx (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d_nd_ndalphardni_dnj_dDelta__consttau_x (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d_nd_ndalphardni_dnj_dxk__consttau_delta (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2_nd_ndalphardni_dnj_dxk_dTau__constdelta (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2_nd_ndalphardni_dnj_dxk_dDelta__consttau (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag)
static CoolPropDbl	nddeltadni__constT_V_nj (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	GERG 2004 Monograph equation 7.48. More...
static CoolPropDbl	d_nddeltadni_dDelta (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
static CoolPropDbl	d_nddeltadni_dxj__constdelta_tau (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2_nddeltadni_dxj_dDelta__consttau (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	ndtaudni__constT_V_nj (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	GERG 2004 Monograph equation 7.49. More...
static CoolPropDbl	d_ndtaudni_dTau (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
static CoolPropDbl	d_ndtaudni_dxj__constdelta_tau (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2_ndtaudni_dxj_dTau__constdelta (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	d_ndalphardni_dxj__constdelta_tau_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
	GERG 2004 Monograph equation 7.52. More...
static CoolPropDbl	d2_ndalphardni_dxj_dxk__constdelta_tau_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag)
static CoolPropDbl	d3_ndalphardni_dxj_dxk_dTau__constdelta_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag)
static CoolPropDbl	d3_ndalphardni_dxj_dxk_dDelta__consttau_xi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, x_N_dependency_flag xN_flag)
static CoolPropDbl	dalpha0_dxi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2alpha0_dxi_dTau (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2alpha0_dxi_dDelta (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2alpha0dxidxj (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
static CoolPropDbl	psi (HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag=XN_INDEPENDENT)
	Return the Helmholtz energy density \(\psi = \rho a\). More...
static CoolPropDbl	dpsi_dDelta (HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag=XN_INDEPENDENT)
	Return the first partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(\delta\). More...
static CoolPropDbl	dpsi_dTau (HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag=XN_INDEPENDENT)
	Return the first partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(\tau\). More...
static CoolPropDbl	dpsir_dTau (HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag=XN_INDEPENDENT)
	Return the first partial of residual Helmholtz energy density \(\psi^{\rm r} = \rho a^{\rm r}\) with respect to \(\tau\). More...
static CoolPropDbl	dpsi_dxi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	Return the first partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(x_i\). More...
static CoolPropDbl	dpsir_dxi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	Return the first partial of Helmholtz energy density \(\psi^{\rm r} = \rho a^{\rm r}\) with respect to \(x_i\). More...
static CoolPropDbl	d_rhorTr_dxi (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
	Return the first partial of the product \(\rho_{\rm r}T_{\rm r}\) with respect to \(x_i\). More...
static CoolPropDbl	d2_rhorTr_dxidxj (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag)
	Return the second partial of the product \(\rho_{\rm r}T_{\rm r}\) with respect to \(x_i\) and \(x_j\). More...
static CoolPropDbl	d2psi_dDelta2 (HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag=XN_INDEPENDENT)
	Return the second partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(\delta\). More...
static CoolPropDbl	d2psi_dDelta_dTau (HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag=XN_INDEPENDENT)
	Return the second cross partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(\delta\) and \(\tau\). More...
static CoolPropDbl	d2psir_dDelta_dTau (HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag=XN_INDEPENDENT)
	Return the second cross partial of Helmholtz energy density \(\psi^{\rm r} = \rho a^{\rm r} \) with respect to \(\delta\) and \(\tau\). More...
static CoolPropDbl	d2psi_dTau2 (HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag=XN_INDEPENDENT)
	Return the second partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(\tau\). More...
static CoolPropDbl	d2psir_dTau2 (HelmholtzEOSMixtureBackend &HEOS, x_N_dependency_flag xN_flag=XN_INDEPENDENT)
	Return the second partial of residual Helmholtz energy density \(\psi^{\rm r} = \rho a^{\rm r}\) with respect to \(\tau\). More...
static CoolPropDbl	d2psi_dxi_dTau (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag=XN_INDEPENDENT)
	Return the second partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(\tau\) and \(x_i\). More...
static CoolPropDbl	d2psir_dxi_dTau (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag=XN_INDEPENDENT)
	Return the second partial of residual Helmholtz energy density \(\psi^{\rm r} = \rho a^{\rm r}\) with respect to \(\tau\) and \(x_i\). More...
static CoolPropDbl	d2psi_dxi_dDelta (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag=XN_INDEPENDENT)
	Return the second partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(\delta\) and \(x_i\). More...
static CoolPropDbl	d2psi_dxi_dxj (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag=XN_INDEPENDENT)
	Return the second partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(x_i\) and \(x_j\). More...
static CoolPropDbl	d2psir_dxi_dxj (HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, x_N_dependency_flag xN_flag=XN_INDEPENDENT)
	Return the second partial of residual Helmholtz energy density \(\psi^{\rm r} = \rho a^{\rm r}\) with respect to \(x_i\) and \(x_j\). More...
static CoolPropDbl	PSI_rho (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d_PSI_rho_dxj (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d2_PSI_rho_dxj_dxk (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	PSI_T (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d_PSI_T_dxj (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d2_PSI_T_dxj_dxk (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	alpha0 (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	alphar (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag=XN_INDEPENDENT)
static CoolPropDbl	dalphar_dxi (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d2alphar_dxi_dTau (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d3alphar_dxi_dTau2 (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d4alphar_dxi_dTau3 (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d2alphar_dxi_dDelta (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d3alphar_dxi_dDelta2 (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d4alphar_dxi_dDelta3 (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d3alphar_dxi_dDelta_dTau (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d4alphar_dxi_dDelta2_dTau (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d4alphar_dxi_dDelta_dTau2 (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d2alphardxidxj (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d4alphar_dxi_dxj_dTau2 (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d4alphar_dxi_dxj_dDelta2 (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d4alphar_dxi_dxj_dDelta_dTau (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d3alphar_dxi_dxj_dDelta (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d3alphar_dxi_dxj_dTau (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d3alphardxidxjdxk (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	tau (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	Tr (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	dTrdxi__constxj (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d2Trdxi2__constxj (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d2Trdxidxj (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d3Trdxidxjdxk (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	ndTrdni__constnj (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d_ndTrdni_dxj__constxi (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d2_ndTrdni_dxj_dxk__constxi (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	dTr_dgammaT (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	dTr_dbetaT (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d2Tr_dxidgammaT (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2Tr_dxidbetaT (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
static CoolPropDbl	delta (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	rhormolar (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	drhormolardxi__constxj (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d2rhormolardxidxj (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d3rhormolardxidxjdxk (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	drhormolar_dgammaV (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	drhormolar_dbetaV (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d2rhormolar_dxidgammaV (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
static CoolPropDbl	d2rhormolar_dxidbetaV (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, x_N_dependency_flag xN_flag)
static CoolPropDbl	ndrhorbardni__constnj (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d_ndrhorbardni_dxj__constxi (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d2_ndrhorbardni_dxj_dxk__constxi (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, std::size_t k, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	p (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	dalpha0_dDelta (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag=XN_INDEPENDENT)
static CoolPropDbl	d2alpha0_dDelta2 (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag=XN_INDEPENDENT)
static CoolPropDbl	dalpha0_dTau (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag=XN_INDEPENDENT)
static CoolPropDbl	d2alpha0_dTau2 (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag=XN_INDEPENDENT)
static CoolPropDbl	dalphar_dDelta (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag=XN_INDEPENDENT)
static CoolPropDbl	d2alphar_dDelta2 (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag=XN_INDEPENDENT)
static CoolPropDbl	d2alphar_dDelta_dTau (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag=XN_INDEPENDENT)
static CoolPropDbl	dalphar_dTau (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag=XN_INDEPENDENT)
static CoolPropDbl	d2alphar_dTau2 (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag=XN_INDEPENDENT)
static CoolPropDbl	alpha (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag=XN_INDEPENDENT)
static CoolPropDbl	dalpha_dDelta (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag=XN_INDEPENDENT)
static CoolPropDbl	dalpha_dTau (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag=XN_INDEPENDENT)
static CoolPropDbl	d2alpha_dDelta2 (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag=XN_INDEPENDENT)
static CoolPropDbl	d2alpha_dDelta_dTau (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag=XN_INDEPENDENT)
static CoolPropDbl	d2alpha_dTau2 (CoolProp::HelmholtzEOSMixtureBackend &HEOS, CoolProp::x_N_dependency_flag xN_flag=XN_INDEPENDENT)
static CoolPropDbl	dalpha_dxi (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d2alpha_dxi_dDelta (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d2alpha_dxi_dTau (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	d2alphadxidxj (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, std::size_t j, CoolProp::x_N_dependency_flag xN_flag)
static CoolPropDbl	ln_fugacity (CoolProp::HelmholtzEOSMixtureBackend &HEOS, std::size_t i, CoolProp::x_N_dependency_flag xN_flag)

Member Function Documentation

alpha()

static CoolPropDbl CoolProp::MixtureDerivatives::alpha ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

inlinestatic

Definition at line 972 of file MixtureDerivatives.h.

alpha0()

static CoolPropDbl CoolProp::MixtureDerivatives::alpha0 ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 789 of file MixtureDerivatives.h.

alphar()

static CoolPropDbl CoolProp::MixtureDerivatives::alphar ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

inlinestatic

Definition at line 793 of file MixtureDerivatives.h.

d2_nd_ndalphardni_dnj_dDelta2__consttau_x()

CoolPropDbl CoolProp::MixtureDerivatives::d2_nd_ndalphardni_dnj_dDelta2__consttau_x ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 369 of file MixtureDerivatives.cpp.

d2_nd_ndalphardni_dnj_dDelta_dTau__constx()

CoolPropDbl CoolProp::MixtureDerivatives::d2_nd_ndalphardni_dnj_dDelta_dTau__constx ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 385 of file MixtureDerivatives.cpp.

d2_nd_ndalphardni_dnj_dTau2__constdelta_x()

CoolPropDbl CoolProp::MixtureDerivatives::d2_nd_ndalphardni_dnj_dTau2__constdelta_x ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 353 of file MixtureDerivatives.cpp.

d2_nd_ndalphardni_dnj_dxk_dDelta__consttau()

CoolPropDbl CoolProp::MixtureDerivatives::d2_nd_ndalphardni_dnj_dxk_dDelta__consttau ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, x_N_dependency_flag  xN_flag  )

static

Definition at line 459 of file MixtureDerivatives.cpp.

d2_nd_ndalphardni_dnj_dxk_dTau__constdelta()

CoolPropDbl CoolProp::MixtureDerivatives::d2_nd_ndalphardni_dnj_dxk_dTau__constdelta ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, x_N_dependency_flag  xN_flag  )

static

Definition at line 438 of file MixtureDerivatives.cpp.

d2_ndalphardni_dDelta2()

CoolPropDbl CoolProp::MixtureDerivatives::d2_ndalphardni_dDelta2 ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

\(\delta\) derivative of GERG 2004 Monograph Equation 7.50

The derivative term

\[ \begin{array}{ccl} \left(\dfrac{\partial^2 }{\partial \delta^2} \left( n\left(\dfrac{\partial \alpha^r}{\partial n_i} \right)_{T,V,n_j} \right)\right)_{\tau,\bar x} &=& (2\alpha_{\delta\delta}^r+\delta\alpha_{\delta\delta\delta}^r)\Psi_{\rho} +\tau\alpha^r_{\delta\delta\tau}\Psi_T+\alpha^r_{\delta\delta x_i}-\sum_{k=1}^{N}x_k\alpha^r_{\delta\delta x_k} \end{array} \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 499 of file MixtureDerivatives.cpp.

d2_ndalphardni_dDelta_dTau()

CoolPropDbl CoolProp::MixtureDerivatives::d2_ndalphardni_dDelta_dTau ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

\(\tau\) derivative of GERG 2004 Monograph Equation 7.50

The derivative term

\[ \begin{array}{ccl} \left(\dfrac{\partial^2 }{\partial \delta\partial \tau} \left( n\left(\dfrac{\partial \alpha^r}{\partial n_i} \right)_{T,V,n_j} \right)\right)_{\bar x} &=& (\alpha_{\delta\tau}^r+\delta\alpha_{\delta\delta\tau}^r)\Psi_{\rho} +(\tau\alpha^r_{\delta\tau\tau} + \alpha^r_{\delta\tau})\Psi_T +\alpha^r_{\delta\tau x_i}-\sum_{k=1}^{N}x_k\alpha^r_{\delta\tau x_k} \end{array} \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 525 of file MixtureDerivatives.cpp.

d2_ndalphardni_dTau2()

CoolPropDbl CoolProp::MixtureDerivatives::d2_ndalphardni_dTau2 ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

\(\tau\) derivartive of GERG 2004 Monograph Equation 7.51

The derivative term

\[ \dfrac{\partial^2 }{\partial \tau^2} \left( n\left(\dfrac{\partial \alpha^r}{\partial n_i} \right)_{T,V,n_j} \right) = \delta \alpha^r_{\delta\tau\tau}\Psi_{\rho}+ (2\alpha^r_{\tau\tau}+\tau\alpha^r_{\tau\tau\tau})\Psi_T+\alpha^r_{x_i\tau\tau}-\sum_{k=1}^{N}x_k\alpha^r_{x_k\tau\tau} \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 569 of file MixtureDerivatives.cpp.

d2_ndalphardni_dxj_dDelta__consttau_xi()

CoolPropDbl CoolProp::MixtureDerivatives::d2_ndalphardni_dxj_dDelta__consttau_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

\(x_j\) derivative of GERG 2004 Monograph Equation 7.50

The derivative term

\[ \begin{array}{ccl} \dfrac{\partial}{\partial x_j}\left(\dfrac{\partial }{\partial \delta} \left( n\left(\dfrac{\partial \alpha^r}{\partial n_i} \right)_{T,V,n_j} \right)_{\tau,\bar x}\right)_{\tau, \delta, x_i} &=& (\alpha_{\delta}^r+\delta\alpha_{\delta\delta}^r)\dfrac{\partial\Psi_{\rho}}{\partial x_j} + (\alpha_{\delta x_j}^r+\delta\alpha_{\delta\delta x_j}^r)\Psi_{\rho}\\ &+&\tau\alpha^r_{\delta\tau}\dfrac{\partial\Psi_{T}}{\partial x_j} + \tau\alpha^r_{\delta\tau x_j}\Psi_T\\ &+&\alpha^r_{\delta x_i x_j}-\sum_{k=1}^{N}\left[x_k\alpha^r_{\delta x_k x_j} + \dfrac{d x_k}{d x_j}\alpha^r_{\delta x_k}\right] \end{array} \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 596 of file MixtureDerivatives.cpp.

d2_ndalphardni_dxj_dTau__constdelta_xi()

CoolPropDbl CoolProp::MixtureDerivatives::d2_ndalphardni_dxj_dTau__constdelta_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

\(x_j\) derivative of GERG 2004 Monograph Equation 7.51

The derivative term

\[ \begin{array}{ccl} \dfrac{\partial}{\partial x_j}\left(\dfrac{\partial }{\partial \tau} \left( n\left(\dfrac{\partial \alpha^r}{\partial n_i} \right)_{T,V,n_j} \right)\right)_{\tau,\delta,x_i} &=& \delta \alpha^r_{\delta\tau}\dfrac{\partial \Psi_{\rho}}{\partial x_j} + \delta \alpha^r_{\delta\tau x_j}\Psi_{\rho}\\ &+& (\tau \alpha^r_{\tau\tau}+\alpha^r_{\tau})\dfrac{\partial \Psi_T}{\partial x_j}+ \left(\tau \alpha^r_{\tau\tau x_j} +\alpha^r_{\tau x_j}\right)\Psi_T\\ &+&\alpha^r_{\tau x_i x_j}-\sum_{k=1}^{N}\left[x_k\alpha^r_{\tau x_k x_j} + \dfrac{d x_k}{d x_j}\alpha^r_{\tau x_k}\right] \end{array} \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 617 of file MixtureDerivatives.cpp.

d2_ndalphardni_dxj_dxk__constdelta_tau_xi()

CoolPropDbl CoolProp::MixtureDerivatives::d2_ndalphardni_dxj_dxk__constdelta_tau_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, x_N_dependency_flag  xN_flag  )

static

Definition at line 723 of file MixtureDerivatives.cpp.

d2_nddeltadni_dxj_dDelta__consttau()

CoolPropDbl CoolProp::MixtureDerivatives::d2_nddeltadni_dxj_dDelta__consttau ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 266 of file MixtureDerivatives.cpp.

d2_ndln_fugacity_i_dnj_ddelta2__consttau_x()

CoolPropDbl CoolProp::MixtureDerivatives::d2_ndln_fugacity_i_dnj_ddelta2__consttau_x ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 112 of file MixtureDerivatives.cpp.

d2_ndln_fugacity_i_dnj_ddelta_dtau__constx()

CoolPropDbl CoolProp::MixtureDerivatives::d2_ndln_fugacity_i_dnj_ddelta_dtau__constx ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 116 of file MixtureDerivatives.cpp.

d2_ndln_fugacity_i_dnj_dtau2__constdelta_x()

CoolPropDbl CoolProp::MixtureDerivatives::d2_ndln_fugacity_i_dnj_dtau2__constdelta_x ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 108 of file MixtureDerivatives.cpp.

d2_ndln_fugacity_i_dnj_dxk_dDelta__consttau()

CoolPropDbl CoolProp::MixtureDerivatives::d2_ndln_fugacity_i_dnj_dxk_dDelta__consttau ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, x_N_dependency_flag  xN_flag  )

static

Definition at line 134 of file MixtureDerivatives.cpp.

d2_ndln_fugacity_i_dnj_dxk_dTau__constdelta()

CoolPropDbl CoolProp::MixtureDerivatives::d2_ndln_fugacity_i_dnj_dxk_dTau__constdelta ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, x_N_dependency_flag  xN_flag  )

static

Definition at line 130 of file MixtureDerivatives.cpp.

d2_ndrhorbardni_dxj_dxk__constxi()

static CoolPropDbl CoolProp::MixtureDerivatives::d2_ndrhorbardni_dxj_dxk__constxi ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 935 of file MixtureDerivatives.h.

d2_ndtaudni_dxj_dTau__constdelta()

CoolPropDbl CoolProp::MixtureDerivatives::d2_ndtaudni_dxj_dTau__constdelta ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 286 of file MixtureDerivatives.cpp.

d2_ndTrdni_dxj_dxk__constxi()

static CoolPropDbl CoolProp::MixtureDerivatives::d2_ndTrdni_dxj_dxk__constxi ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 882 of file MixtureDerivatives.h.

d2_PSI_rho_dxj_dxk()

static CoolPropDbl CoolProp::MixtureDerivatives::d2_PSI_rho_dxj_dxk ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 774 of file MixtureDerivatives.h.

d2_PSI_T_dxj_dxk()

static CoolPropDbl CoolProp::MixtureDerivatives::d2_PSI_T_dxj_dxk ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 784 of file MixtureDerivatives.h.

d2_rhorTr_dxidxj()

CoolPropDbl CoolProp::MixtureDerivatives::d2_rhorTr_dxidxj ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Return the second partial of the product \(\rho_{\rm r}T_{\rm r}\) with respect to \(x_i\) and \(x_j\).

Definition at line 1043 of file MixtureDerivatives.cpp.

d2alpha0_dDelta2()

static CoolPropDbl CoolProp::MixtureDerivatives::d2alpha0_dDelta2 ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

inlinestatic

Definition at line 946 of file MixtureDerivatives.h.

d2alpha0_dTau2()

static CoolPropDbl CoolProp::MixtureDerivatives::d2alpha0_dTau2 ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

inlinestatic

Definition at line 952 of file MixtureDerivatives.h.

d2alpha0_dxi_dDelta()

CoolPropDbl CoolProp::MixtureDerivatives::d2alpha0_dxi_dDelta ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Definition at line 863 of file MixtureDerivatives.cpp.

d2alpha0_dxi_dTau()

CoolPropDbl CoolProp::MixtureDerivatives::d2alpha0_dxi_dTau ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Definition at line 901 of file MixtureDerivatives.cpp.

d2alpha0dxidxj()

CoolPropDbl CoolProp::MixtureDerivatives::d2alpha0dxidxj ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 939 of file MixtureDerivatives.cpp.

d2alpha_dDelta2()

static CoolPropDbl CoolProp::MixtureDerivatives::d2alpha_dDelta2 ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

inlinestatic

Definition at line 981 of file MixtureDerivatives.h.

d2alpha_dDelta_dTau()

static CoolPropDbl CoolProp::MixtureDerivatives::d2alpha_dDelta_dTau ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

inlinestatic

Definition at line 984 of file MixtureDerivatives.h.

d2alpha_dTau2()

static CoolPropDbl CoolProp::MixtureDerivatives::d2alpha_dTau2 ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

inlinestatic

Definition at line 987 of file MixtureDerivatives.h.

d2alpha_dxi_dDelta()

static CoolPropDbl CoolProp::MixtureDerivatives::d2alpha_dxi_dDelta ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 993 of file MixtureDerivatives.h.

d2alpha_dxi_dTau()

static CoolPropDbl CoolProp::MixtureDerivatives::d2alpha_dxi_dTau ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 996 of file MixtureDerivatives.h.

d2alphadxidxj()

static CoolPropDbl CoolProp::MixtureDerivatives::d2alphadxidxj ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 999 of file MixtureDerivatives.h.

d2alphar_dDelta2()

static CoolPropDbl CoolProp::MixtureDerivatives::d2alphar_dDelta2 ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

inlinestatic

Definition at line 959 of file MixtureDerivatives.h.

d2alphar_dDelta_dTau()

static CoolPropDbl CoolProp::MixtureDerivatives::d2alphar_dDelta_dTau ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

inlinestatic

Definition at line 962 of file MixtureDerivatives.h.

d2alphar_dTau2()

static CoolPropDbl CoolProp::MixtureDerivatives::d2alphar_dTau2 ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

inlinestatic

Definition at line 968 of file MixtureDerivatives.h.

d2alphar_dxi_dDelta()

static CoolPropDbl CoolProp::MixtureDerivatives::d2alphar_dxi_dDelta ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 810 of file MixtureDerivatives.h.

d2alphar_dxi_dTau()

static CoolPropDbl CoolProp::MixtureDerivatives::d2alphar_dxi_dTau ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 801 of file MixtureDerivatives.h.

d2alphardxidxj()

static CoolPropDbl CoolProp::MixtureDerivatives::d2alphardxidxj ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 828 of file MixtureDerivatives.h.

d2Lstar_dX2()

static Eigen::MatrixXd CoolProp::MixtureDerivatives::d2Lstar_dX2 ( HelmholtzEOSMixtureBackend &  HEOS, x_N_dependency_flag  xN_flag, parameters  WRT1, parameters  WRT2  )

inlinestatic

Definition at line 258 of file MixtureDerivatives.h.

d2nalphar_dni_dT()

CoolPropDbl CoolProp::MixtureDerivatives::d2nalphar_dni_dT ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

GERG 2004 Monograph, equations 7.44 and 7.51.

The derivative term

\[ \left(\frac{\partial^2n\alpha^r}{\partial T\partial n_i} \right)_{V,n_j} = \left( \frac{\partial}{\partial T}\left(\frac{\partial n \alpha^r}{\partial n_i}\right)_{T,V,n_j} \right)_{V,\bar n} \]

\[ \left(\frac{\partial^2n\alpha^r}{\partial T\partial n_i} \right)_{V,n_j} = -\frac{\tau}{T}\left[\alpha_{\tau}^r +\left( \frac{\partial}{\partial \tau}\left(n\left(\frac{\partial \alpha^r}{\partial n_i}\right)_{T,V,n_j}\right)\right)_{\delta,\bar x}\right] \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The second index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 28 of file MixtureDerivatives.cpp.

d2nalphar_dxj_dni__constT_V()

static CoolPropDbl CoolProp::MixtureDerivatives::d2nalphar_dxj_dni__constT_V ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  j, std::size_t  i, x_N_dependency_flag  xN_flag  )

inlinestatic

Gernert Equation 3.117.

The derivative term

\[ \left(\frac{\partial^2n\alpha^r}{\partial x_j\partial n_i} \right)_{T,V} = \left(\frac{\partial}{\partial x_j}\left(n\left(\frac{\partial \alpha^r}{\partial n_i}\right)_{T,V,n_{j\neq i}}\right)\right)_{T,V,x_{k\neq j}} +\left(\frac{\partial \alpha^r}{\partial x_j}\right)_{T,V,x_{k\neq j}} \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
j	The first index of interest
i	The second index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 410 of file MixtureDerivatives.h.

d2psi_dDelta2()

CoolPropDbl CoolProp::MixtureDerivatives::d2psi_dDelta2 ( HelmholtzEOSMixtureBackend &  HEOS, x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

static

Return the second partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(\delta\).

Definition at line 1051 of file MixtureDerivatives.cpp.

d2psi_dDelta_dTau()

CoolPropDbl CoolProp::MixtureDerivatives::d2psi_dDelta_dTau ( HelmholtzEOSMixtureBackend &  HEOS, x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

static

Return the second cross partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(\delta\) and \(\tau\).

Definition at line 1055 of file MixtureDerivatives.cpp.

d2psi_dTau2()

CoolPropDbl CoolProp::MixtureDerivatives::d2psi_dTau2 ( HelmholtzEOSMixtureBackend &  HEOS, x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

static

Return the second partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(\tau\).

Definition at line 1065 of file MixtureDerivatives.cpp.

d2psi_dxi_dDelta()

CoolPropDbl CoolProp::MixtureDerivatives::d2psi_dxi_dDelta ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

static

Return the second partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(\delta\) and \(x_i\).

Definition at line 1075 of file MixtureDerivatives.cpp.

d2psi_dxi_dTau()

CoolPropDbl CoolProp::MixtureDerivatives::d2psi_dxi_dTau ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

static

Return the second partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(\tau\) and \(x_i\).

Definition at line 1080 of file MixtureDerivatives.cpp.

d2psi_dxi_dxj()

CoolPropDbl CoolProp::MixtureDerivatives::d2psi_dxi_dxj ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

static

Return the second partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(x_i\) and \(x_j\).

Definition at line 1090 of file MixtureDerivatives.cpp.

d2psir_dDelta_dTau()

CoolPropDbl CoolProp::MixtureDerivatives::d2psir_dDelta_dTau ( HelmholtzEOSMixtureBackend &  HEOS, x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

static

Return the second cross partial of Helmholtz energy density \(\psi^{\rm r} = \rho a^{\rm r} \) with respect to \(\delta\) and \(\tau\).

Definition at line 1060 of file MixtureDerivatives.cpp.

d2psir_dTau2()

CoolPropDbl CoolProp::MixtureDerivatives::d2psir_dTau2 ( HelmholtzEOSMixtureBackend &  HEOS, x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

static

Return the second partial of residual Helmholtz energy density \(\psi^{\rm r} = \rho a^{\rm r}\) with respect to \(\tau\).

Definition at line 1070 of file MixtureDerivatives.cpp.

d2psir_dxi_dTau()

CoolPropDbl CoolProp::MixtureDerivatives::d2psir_dxi_dTau ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

static

Return the second partial of residual Helmholtz energy density \(\psi^{\rm r} = \rho a^{\rm r}\) with respect to \(\tau\) and \(x_i\).

Definition at line 1085 of file MixtureDerivatives.cpp.

d2psir_dxi_dxj()

CoolPropDbl CoolProp::MixtureDerivatives::d2psir_dxi_dxj ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

static

Return the second partial of residual Helmholtz energy density \(\psi^{\rm r} = \rho a^{\rm r}\) with respect to \(x_i\) and \(x_j\).

Definition at line 1096 of file MixtureDerivatives.cpp.

d2rhormolar_dxidbetaV()

static CoolPropDbl CoolProp::MixtureDerivatives::d2rhormolar_dxidbetaV ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 925 of file MixtureDerivatives.h.

d2rhormolar_dxidgammaV()

static CoolPropDbl CoolProp::MixtureDerivatives::d2rhormolar_dxidgammaV ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 922 of file MixtureDerivatives.h.

d2rhormolardxidxj()

static CoolPropDbl CoolProp::MixtureDerivatives::d2rhormolardxidxj ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 908 of file MixtureDerivatives.h.

d2Tr_dxidbetaT()

static CoolPropDbl CoolProp::MixtureDerivatives::d2Tr_dxidbetaT ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 895 of file MixtureDerivatives.h.

d2Tr_dxidgammaT()

static CoolPropDbl CoolProp::MixtureDerivatives::d2Tr_dxidgammaT ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 892 of file MixtureDerivatives.h.

d2Trdxi2__constxj()

static CoolPropDbl CoolProp::MixtureDerivatives::d2Trdxi2__constxj ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 865 of file MixtureDerivatives.h.

d2Trdxidxj()

static CoolPropDbl CoolProp::MixtureDerivatives::d2Trdxidxj ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 868 of file MixtureDerivatives.h.

d3_ndalphardni_dDelta2_dTau()

CoolPropDbl CoolProp::MixtureDerivatives::d3_ndalphardni_dDelta2_dTau ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Definition at line 539 of file MixtureDerivatives.cpp.

d3_ndalphardni_dDelta3()

CoolPropDbl CoolProp::MixtureDerivatives::d3_ndalphardni_dDelta3 ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Definition at line 512 of file MixtureDerivatives.cpp.

d3_ndalphardni_dDelta_dTau2()

CoolPropDbl CoolProp::MixtureDerivatives::d3_ndalphardni_dDelta_dTau2 ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Definition at line 554 of file MixtureDerivatives.cpp.

d3_ndalphardni_dTau3()

CoolPropDbl CoolProp::MixtureDerivatives::d3_ndalphardni_dTau3 ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Definition at line 582 of file MixtureDerivatives.cpp.

d3_ndalphardni_dxj_dDelta2__consttau_xi()

CoolPropDbl CoolProp::MixtureDerivatives::d3_ndalphardni_dxj_dDelta2__consttau_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 657 of file MixtureDerivatives.cpp.

d3_ndalphardni_dxj_dDelta_dTau__constxi()

CoolPropDbl CoolProp::MixtureDerivatives::d3_ndalphardni_dxj_dDelta_dTau__constxi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 678 of file MixtureDerivatives.cpp.

d3_ndalphardni_dxj_dTau2__constdelta_xi()

CoolPropDbl CoolProp::MixtureDerivatives::d3_ndalphardni_dxj_dTau2__constdelta_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 637 of file MixtureDerivatives.cpp.

d3_ndalphardni_dxj_dxk_dDelta__consttau_xi()

CoolPropDbl CoolProp::MixtureDerivatives::d3_ndalphardni_dxj_dxk_dDelta__consttau_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, x_N_dependency_flag  xN_flag  )

static

Definition at line 791 of file MixtureDerivatives.cpp.

d3_ndalphardni_dxj_dxk_dTau__constdelta_xi()

CoolPropDbl CoolProp::MixtureDerivatives::d3_ndalphardni_dxj_dxk_dTau__constdelta_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, x_N_dependency_flag  xN_flag  )

static

Definition at line 754 of file MixtureDerivatives.cpp.

d3alphar_dxi_dDelta2()

static CoolPropDbl CoolProp::MixtureDerivatives::d3alphar_dxi_dDelta2 ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 813 of file MixtureDerivatives.h.

d3alphar_dxi_dDelta_dTau()

static CoolPropDbl CoolProp::MixtureDerivatives::d3alphar_dxi_dDelta_dTau ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 819 of file MixtureDerivatives.h.

d3alphar_dxi_dTau2()

static CoolPropDbl CoolProp::MixtureDerivatives::d3alphar_dxi_dTau2 ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 804 of file MixtureDerivatives.h.

d3alphar_dxi_dxj_dDelta()

static CoolPropDbl CoolProp::MixtureDerivatives::d3alphar_dxi_dxj_dDelta ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 844 of file MixtureDerivatives.h.

d3alphar_dxi_dxj_dTau()

static CoolPropDbl CoolProp::MixtureDerivatives::d3alphar_dxi_dxj_dTau ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 848 of file MixtureDerivatives.h.

d3alphardxidxjdxk()

static CoolPropDbl CoolProp::MixtureDerivatives::d3alphardxidxjdxk ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 852 of file MixtureDerivatives.h.

d3rhormolardxidxjdxk()

static CoolPropDbl CoolProp::MixtureDerivatives::d3rhormolardxidxjdxk ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 912 of file MixtureDerivatives.h.

d3Trdxidxjdxk()

static CoolPropDbl CoolProp::MixtureDerivatives::d3Trdxidxjdxk ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 871 of file MixtureDerivatives.h.

d4alphar_dxi_dDelta2_dTau()

static CoolPropDbl CoolProp::MixtureDerivatives::d4alphar_dxi_dDelta2_dTau ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 822 of file MixtureDerivatives.h.

d4alphar_dxi_dDelta3()

static CoolPropDbl CoolProp::MixtureDerivatives::d4alphar_dxi_dDelta3 ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 816 of file MixtureDerivatives.h.

d4alphar_dxi_dDelta_dTau2()

static CoolPropDbl CoolProp::MixtureDerivatives::d4alphar_dxi_dDelta_dTau2 ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 825 of file MixtureDerivatives.h.

d4alphar_dxi_dTau3()

static CoolPropDbl CoolProp::MixtureDerivatives::d4alphar_dxi_dTau3 ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 807 of file MixtureDerivatives.h.

d4alphar_dxi_dxj_dDelta2()

static CoolPropDbl CoolProp::MixtureDerivatives::d4alphar_dxi_dxj_dDelta2 ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 836 of file MixtureDerivatives.h.

d4alphar_dxi_dxj_dDelta_dTau()

static CoolPropDbl CoolProp::MixtureDerivatives::d4alphar_dxi_dxj_dDelta_dTau ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 840 of file MixtureDerivatives.h.

d4alphar_dxi_dxj_dTau2()

static CoolPropDbl CoolProp::MixtureDerivatives::d4alphar_dxi_dxj_dTau2 ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 832 of file MixtureDerivatives.h.

d_dalpharddelta_dxj__constT_V_xi()

CoolPropDbl CoolProp::MixtureDerivatives::d_dalpharddelta_dxj__constT_V_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Gernert Equation 3.134 Catch test provided

Definition at line 169 of file MixtureDerivatives.cpp.

d_n2Aijk_dDelta()

static CoolPropDbl CoolProp::MixtureDerivatives::d_n2Aijk_dDelta ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 189 of file MixtureDerivatives.h.

d_n2Aijk_dTau()

static CoolPropDbl CoolProp::MixtureDerivatives::d_n2Aijk_dTau ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 186 of file MixtureDerivatives.h.

d_n2Aijk_dX()

static CoolPropDbl CoolProp::MixtureDerivatives::d_n2Aijk_dX ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, x_N_dependency_flag  xN_flag, parameters  WRT  )

inlinestatic

Definition at line 192 of file MixtureDerivatives.h.

d_nAij_dDelta()

static CoolPropDbl CoolProp::MixtureDerivatives::d_nAij_dDelta ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 174 of file MixtureDerivatives.h.

d_nAij_dTau()

static CoolPropDbl CoolProp::MixtureDerivatives::d_nAij_dTau ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 171 of file MixtureDerivatives.h.

d_nAij_dX()

static CoolPropDbl CoolProp::MixtureDerivatives::d_nAij_dX ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag, parameters  WRT  )

inlinestatic

Definition at line 177 of file MixtureDerivatives.h.

d_nd_ndalphardni_dnj_dDelta__consttau_x()

CoolPropDbl CoolProp::MixtureDerivatives::d_nd_ndalphardni_dnj_dDelta__consttau_x ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 402 of file MixtureDerivatives.cpp.

d_nd_ndalphardni_dnj_dTau__constdelta_x()

CoolPropDbl CoolProp::MixtureDerivatives::d_nd_ndalphardni_dnj_dTau__constdelta_x ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 337 of file MixtureDerivatives.cpp.

d_nd_ndalphardni_dnj_dxk__consttau_delta()

CoolPropDbl CoolProp::MixtureDerivatives::d_nd_ndalphardni_dnj_dxk__consttau_delta ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, x_N_dependency_flag  xN_flag  )

static

Definition at line 419 of file MixtureDerivatives.cpp.

d_ndalphardni_dDelta()

CoolPropDbl CoolProp::MixtureDerivatives::d_ndalphardni_dDelta ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

GERG 2004 Monograph Equation 7.50 and Table B4, Kunz, JCED, 2012.

The derivative term

\begin{eqnarray*} \left(\frac{\partial }{\partial \delta} \left( n\left(\frac{\partial \alpha^r}{\partial n_i} \right)_{T,V,n_j} \right)\right)_{\tau,\bar x} &=& (\alpha_{\delta}^r+\delta\alpha_{\delta\delta}^r)\left[1-\frac{1}{\rho_r}\cdot n\left(\frac{\partial \rho_r}{\partial n_i}\right)_{n_j} \right] \\ &+&\tau\alpha^r_{\delta\tau}\frac{1}{T_r}\cdot n\left(\frac{\partial T_r}{\partial n_i}\right)_{n_j}\\ &+&\alpha^r_{\delta x_i}-\sum_{k=1}^{N}x_k\alpha^r_{\delta x_k} \end{eqnarray*}

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 479 of file MixtureDerivatives.cpp.

d_ndalphardni_dTau()

CoolPropDbl CoolProp::MixtureDerivatives::d_ndalphardni_dTau ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

GERG 2004 Monograph Equation 7.51 and Table B4, Kunz, JCED, 2012.

The derivative term

\begin{eqnarray*} \frac{\partial }{\partial \tau} \left( n\left(\frac{\partial \alpha^r}{\partial n_i} \right)_{T,V,n_j} \right) &=& \delta \alpha^r_{\delta\tau}\left[ 1-\frac{1}{\rho_r}\left[\left(\frac{\partial \rho_r}{\partial x_i}\right)_{x_j} - \sum_{k=1}^N x_k\left(\frac{\partial \rho_r}{\partial x_k}\right)_{x_j} \right]\right]\\ && +(\tau \alpha^r_{\tau\tau}+\alpha^r_{\tau})\frac{1}{T_r}\left[\left(\frac{\partial T_r}{\partial x_i}\right)_{x_j} - \sum_{k=1}^N x_k\left(\frac{\partial T_r}{\partial x_k}\right)_{x_j} \right]\\ && +\alpha^r_{x_i\tau}-\sum_{k=1}^{N}x_k\alpha^r_{x_k\tau} \end{eqnarray*}

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 702 of file MixtureDerivatives.cpp.

d_ndalphardni_dxj__constdelta_tau_xi()

CoolPropDbl CoolProp::MixtureDerivatives::d_ndalphardni_dxj__constdelta_tau_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

GERG 2004 Monograph equation 7.52.

The derivative term

\begin{eqnarray*} \left( \frac{\partial}{\partial x_j}\left(n\left(\frac{\partial\alpha^r}{\partial n_i}\right)_{T,V,n_j}\right)\right)_{\delta,\tau,x_i} &=& \delta\alpha_{\delta x_j}^{r}\left[ 1-\frac{1}{\rho_r}\cdot n\left(\frac{\partial \rho_r}{\partial n_i}\right)_{n_j}\right] \\ &-& \delta\alpha_{\delta}^{r}\frac{1}{\rho_r}\left[ \left(\frac{\partial}{\partial x_j}\left(n\left(\frac{\partial \rho_r}{\partial n_i}\right)_{n_j}\right)\right)_{x_i}-\frac{1}{\rho_r}\left(\frac{\partial \rho_r}{\partial x_j}\right)_{x_i}\cdot n\left(\frac{\partial \rho_r}{\partial n_i}\right)_{n_j}\right] \\ &+& \tau\alpha_{\tau x_j}^r\frac{1}{T_r}\cdot n\left(\frac{\partial T_r}{\partial n_i}\right)_{n_j}\\ &+& \tau\alpha_{\tau}^{r}\frac{1}{T_r}\left[ \left(\frac{\partial}{\partial x_j}\left(n\left(\frac{\partial T_r}{\partial n_i}\right)_{n_j}\right)\right)_{x_i}-\frac{1}{T_r}\left(\frac{\partial T_r}{\partial x_j}\right)_{x_i}\cdot n\left(\frac{\partial T_r}{\partial n_i}\right)_{n_j}\right] \\ &+& \alpha_{x_ix_j}^r-\alpha_{x_j}^r-\sum_{m=1}^Nx_m\alpha_{x_jx_m}^r \end{eqnarray*}

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
j	The second index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 290 of file MixtureDerivatives.cpp.

d_ndalphardni_dxj__constT_V_xi()

CoolPropDbl CoolProp::MixtureDerivatives::d_ndalphardni_dxj__constT_V_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Gernert Equation 3.118 Catch test provided

Definition at line 180 of file MixtureDerivatives.cpp.

d_nddeltadni_dDelta()

CoolPropDbl CoolProp::MixtureDerivatives::d_nddeltadni_dDelta ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Definition at line 255 of file MixtureDerivatives.cpp.

d_nddeltadni_dxj__constdelta_tau()

CoolPropDbl CoolProp::MixtureDerivatives::d_nddeltadni_dxj__constdelta_tau ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 258 of file MixtureDerivatives.cpp.

d_ndln_fugacity_i_dnj_ddelta__consttau_x()

CoolPropDbl CoolProp::MixtureDerivatives::d_ndln_fugacity_i_dnj_ddelta__consttau_x ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 121 of file MixtureDerivatives.cpp.

d_ndln_fugacity_i_dnj_ddxk__consttau_delta()

CoolPropDbl CoolProp::MixtureDerivatives::d_ndln_fugacity_i_dnj_ddxk__consttau_delta ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, x_N_dependency_flag  xN_flag  )

static

Definition at line 125 of file MixtureDerivatives.cpp.

d_ndln_fugacity_i_dnj_dtau__constdelta_x()

CoolPropDbl CoolProp::MixtureDerivatives::d_ndln_fugacity_i_dnj_dtau__constdelta_x ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 104 of file MixtureDerivatives.cpp.

d_ndrhorbardni_dxj__constxi()

static CoolPropDbl CoolProp::MixtureDerivatives::d_ndrhorbardni_dxj__constxi ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 931 of file MixtureDerivatives.h.

d_ndtaudni_dTau()

CoolPropDbl CoolProp::MixtureDerivatives::d_ndtaudni_dTau ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Definition at line 275 of file MixtureDerivatives.cpp.

d_ndtaudni_dxj__constdelta_tau()

CoolPropDbl CoolProp::MixtureDerivatives::d_ndtaudni_dxj__constdelta_tau ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 278 of file MixtureDerivatives.cpp.

d_ndTrdni_dxj__constxi()

static CoolPropDbl CoolProp::MixtureDerivatives::d_ndTrdni_dxj__constxi ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 878 of file MixtureDerivatives.h.

d_PSI_rho_dxj()

static CoolPropDbl CoolProp::MixtureDerivatives::d_PSI_rho_dxj ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 770 of file MixtureDerivatives.h.

d_PSI_T_dxj()

static CoolPropDbl CoolProp::MixtureDerivatives::d_PSI_T_dxj ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 781 of file MixtureDerivatives.h.

d_rhorTr_dxi()

CoolPropDbl CoolProp::MixtureDerivatives::d_rhorTr_dxi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Return the first partial of the product \(\rho_{\rm r}T_{\rm r}\) with respect to \(x_i\).

Definition at line 1037 of file MixtureDerivatives.cpp.

dalpha0_dDelta()

static CoolPropDbl CoolProp::MixtureDerivatives::dalpha0_dDelta ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

inlinestatic

Definition at line 943 of file MixtureDerivatives.h.

dalpha0_dTau()

static CoolPropDbl CoolProp::MixtureDerivatives::dalpha0_dTau ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

inlinestatic

Definition at line 949 of file MixtureDerivatives.h.

dalpha0_dxi()

CoolPropDbl CoolProp::MixtureDerivatives::dalpha0_dxi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Definition at line 827 of file MixtureDerivatives.cpp.

dalpha_dDelta()

static CoolPropDbl CoolProp::MixtureDerivatives::dalpha_dDelta ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

inlinestatic

Definition at line 975 of file MixtureDerivatives.h.

dalpha_dTau()

static CoolPropDbl CoolProp::MixtureDerivatives::dalpha_dTau ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

inlinestatic

Definition at line 978 of file MixtureDerivatives.h.

dalpha_dxi()

static CoolPropDbl CoolProp::MixtureDerivatives::dalpha_dxi ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 990 of file MixtureDerivatives.h.

dalphar_dDelta()

static CoolPropDbl CoolProp::MixtureDerivatives::dalphar_dDelta ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

inlinestatic

Definition at line 956 of file MixtureDerivatives.h.

dalphar_dTau()

static CoolPropDbl CoolProp::MixtureDerivatives::dalphar_dTau ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

inlinestatic

Definition at line 965 of file MixtureDerivatives.h.

dalphar_dxi()

static CoolPropDbl CoolProp::MixtureDerivatives::dalphar_dxi ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 798 of file MixtureDerivatives.h.

dalphar_dxj__constT_V_xi()

CoolPropDbl CoolProp::MixtureDerivatives::dalphar_dxj__constT_V_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Gernert Equation 3.119 Catch test provided

Definition at line 175 of file MixtureDerivatives.cpp.

ddelta_dxj__constT_V_xi()

CoolPropDbl CoolProp::MixtureDerivatives::ddelta_dxj__constT_V_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Gernert Equation 3.121 Catch test provided

Definition at line 187 of file MixtureDerivatives.cpp.

delta()

static CoolPropDbl CoolProp::MixtureDerivatives::delta ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 899 of file MixtureDerivatives.h.

dln_fugacity_coefficient_dp__constT_n()

CoolPropDbl CoolProp::MixtureDerivatives::dln_fugacity_coefficient_dp__constT_n ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

GERG 2004 Monograph Eqn. 7.30.

The derivative term

\[ \left(\frac{\partial \ln \phi_i}{\partial p} \right)_{T,\bar n} = \frac{\hat v_i}{RT}-\frac{1}{p} \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 40 of file MixtureDerivatives.cpp.

dln_fugacity_coefficient_dT__constp_n()

CoolPropDbl CoolProp::MixtureDerivatives::dln_fugacity_coefficient_dT__constp_n ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

GERG 2004 Monograph Eqn. 7.29.

The derivative term

\[ \left(\frac{\partial \ln \phi_i}{\partial T} \right)_{p,\bar n} = \left(\frac{\partial^2n\alpha^r}{\partial T\partial n_i} \right)_{V,n_j} + \frac{1}{T}-\frac{\hat v}{RT}\left(\frac{\partial p}{\partial T}\right)_{V,\bar n} \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 31 of file MixtureDerivatives.cpp.

dln_fugacity_coefficient_dxj__constT_p_xi()

CoolPropDbl CoolProp::MixtureDerivatives::dln_fugacity_coefficient_dxj__constT_p_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Gernert Equation 3.115.

The derivative term

\[ \left(\frac{\partial \ln \phi_i}{\partial x_j}\right)_{T,p,x_{k\neq j}} = \left(\frac{\partial^2n\alpha^r}{\partial x_j \partial n_i} \right)_{T,V}+\frac{1}{RT}\frac{\left(\frac{\partial p}{\partial n_i}\right)_{T,V,n_{k\neq i}}\left(\frac{\partial p}{\partial x_j}\right)_{T,V,x_{k\neq j}}}{\left(\frac{\partial p}{\partial V}\right)_{T,\bar n}} \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The first index of interest
j	The second index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 153 of file MixtureDerivatives.cpp.

dln_fugacity_dxj__constT_p_xi()

CoolPropDbl CoolProp::MixtureDerivatives::dln_fugacity_dxj__constT_p_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 54 of file MixtureDerivatives.cpp.

dln_fugacity_dxj__constT_rho_xi()

CoolPropDbl CoolProp::MixtureDerivatives::dln_fugacity_dxj__constT_rho_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 67 of file MixtureDerivatives.cpp.

dln_fugacity_i_ddelta__consttau_x()

CoolPropDbl CoolProp::MixtureDerivatives::dln_fugacity_i_ddelta__consttau_x ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Definition at line 51 of file MixtureDerivatives.cpp.

dln_fugacity_i_dp__constT_n()

CoolPropDbl CoolProp::MixtureDerivatives::dln_fugacity_i_dp__constT_n ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Definition at line 9 of file MixtureDerivatives.cpp.

dln_fugacity_i_drho__constT_n()

CoolPropDbl CoolProp::MixtureDerivatives::dln_fugacity_i_drho__constT_n ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Derivative of the natural logarithm of the fugacity with respect to T.

From Witzke, Eqn. 3.15

\[ \left(\frac{\partial \ln(f_i)}{\partial \rho} \right)_{T, x} = \frac{1}{\rho}\left(1+\delta\alpha^r_{\delta}+\delta n\left(\frac{\partial\left(\frac{\partial \alpha^r}{\partial n_i}\right)_{T,V,n_j}}{\partial \delta}\right)_{\tau,\bar x} \right) \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 21 of file MixtureDerivatives.cpp.

dln_fugacity_i_dT__constp_n()

CoolPropDbl CoolProp::MixtureDerivatives::dln_fugacity_i_dT__constp_n ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Definition at line 6 of file MixtureDerivatives.cpp.

dln_fugacity_i_dT__constrho_n()

CoolPropDbl CoolProp::MixtureDerivatives::dln_fugacity_i_dT__constrho_n ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Derivative of the natural logarithm of the fugacity with respect to T.

From Witzke, Eqn. 3.14

\[ \left(\frac{\partial \ln(f_i)}{\partial T} \right)_{\rho,x} = -\frac{1}{T}\left(1-\tau\alpha^r_{\tau}-\tau n\left(\frac{\partial\left(\frac{\partial \alpha^r}{\partial n_i}\right)_{T,V,n_j}}{\partial \tau}\right)_{\delta,\bar x} \right) \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 18 of file MixtureDerivatives.cpp.

dln_fugacity_i_dtau__constdelta_x()

CoolPropDbl CoolProp::MixtureDerivatives::dln_fugacity_i_dtau__constdelta_x ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Definition at line 48 of file MixtureDerivatives.cpp.

dLstar_dX()

static Eigen::MatrixXd CoolProp::MixtureDerivatives::dLstar_dX ( HelmholtzEOSMixtureBackend &  HEOS, x_N_dependency_flag  xN_flag, parameters  WRT  )

inlinestatic

Definition at line 241 of file MixtureDerivatives.h.

dMstar_dX()

static Eigen::MatrixXd CoolProp::MixtureDerivatives::dMstar_dX ( HelmholtzEOSMixtureBackend &  HEOS, x_N_dependency_flag  xN_flag, parameters  WRT, Eigen::MatrixXd &  L, Eigen::MatrixXd &  dL_dX  )

inlinestatic

Definition at line 298 of file MixtureDerivatives.h.

dnalphar_dni__constT_V_nj()

CoolPropDbl CoolProp::MixtureDerivatives::dnalphar_dni__constT_V_nj ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

GERG Equation 7.42.

Definition at line 24 of file MixtureDerivatives.cpp.

dpdrho__constT_n()

CoolPropDbl CoolProp::MixtureDerivatives::dpdrho__constT_n ( HelmholtzEOSMixtureBackend &  HEOS )

static

Definition at line 200 of file MixtureDerivatives.cpp.

dpdT__constV_n()

CoolPropDbl CoolProp::MixtureDerivatives::dpdT__constV_n ( HelmholtzEOSMixtureBackend &  HEOS )

static

GERG 2004 Monograph equation 7.61.

The derivative term

\[ \left(\frac{\partial p}{\partial T} \right)_{V,\bar n} = \rho R(1+\delta \alpha_{\delta}^r-\delta \tau \alpha^r_{\delta\tau}) \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used

Definition at line 196 of file MixtureDerivatives.cpp.

dpdxj__constT_V_xi()

CoolPropDbl CoolProp::MixtureDerivatives::dpdxj__constT_V_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Gernert Equation 3.130.

The derivative term

\[ \left(\frac{\partial p}{\partial x_j} \right)_{T,V,x_{k\neq j}} = \rho RT\left(-\frac{1}{\rho_r}\left(\frac{\partial \rho_r}{\partial x_j}\right)_{x_{k\neq j}} \delta\alpha_{\delta}^r + \delta\left(\frac{\partial}{\partial x_j}\left(\left( \frac{\partial \alpha^r}{\partial \delta}\right)_{\tau,\bar x}\right)\right)_{T,V,x_{k\neq j}}\right) \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
j	The index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 161 of file MixtureDerivatives.cpp.

dpsi_dDelta()

CoolPropDbl CoolProp::MixtureDerivatives::dpsi_dDelta ( HelmholtzEOSMixtureBackend &  HEOS, x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

static

Return the first partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(\delta\).

Definition at line 1013 of file MixtureDerivatives.cpp.

dpsi_dTau()

CoolPropDbl CoolProp::MixtureDerivatives::dpsi_dTau ( HelmholtzEOSMixtureBackend &  HEOS, x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

static

Return the first partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(\tau\).

Definition at line 1018 of file MixtureDerivatives.cpp.

dpsi_dxi()

CoolPropDbl CoolProp::MixtureDerivatives::dpsi_dxi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Return the first partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(x_i\).

Definition at line 1027 of file MixtureDerivatives.cpp.

dpsir_dTau()

CoolPropDbl CoolProp::MixtureDerivatives::dpsir_dTau ( HelmholtzEOSMixtureBackend &  HEOS, x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

static

Return the first partial of residual Helmholtz energy density \(\psi^{\rm r} = \rho a^{\rm r}\) with respect to \(\tau\).

Return the first partial of Helmholtz energy density \(\psi = \rho a\) with respect to \(\tau\).

Definition at line 1023 of file MixtureDerivatives.cpp.

dpsir_dxi()

CoolPropDbl CoolProp::MixtureDerivatives::dpsir_dxi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Return the first partial of Helmholtz energy density \(\psi^{\rm r} = \rho a^{\rm r}\) with respect to \(x_i\).

Definition at line 1032 of file MixtureDerivatives.cpp.

drhormolar_dbetaV()

static CoolPropDbl CoolProp::MixtureDerivatives::drhormolar_dbetaV ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 919 of file MixtureDerivatives.h.

drhormolar_dgammaV()

static CoolPropDbl CoolProp::MixtureDerivatives::drhormolar_dgammaV ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 916 of file MixtureDerivatives.h.

drhormolardxi__constxj()

static CoolPropDbl CoolProp::MixtureDerivatives::drhormolardxi__constxj ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 905 of file MixtureDerivatives.h.

dtau_dxj__constT_V_xi()

CoolPropDbl CoolProp::MixtureDerivatives::dtau_dxj__constT_V_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Gernert Equation 3.122 Catch test provided

Definition at line 191 of file MixtureDerivatives.cpp.

dTr_dbetaT()

static CoolPropDbl CoolProp::MixtureDerivatives::dTr_dbetaT ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 889 of file MixtureDerivatives.h.

dTr_dgammaT()

static CoolPropDbl CoolProp::MixtureDerivatives::dTr_dgammaT ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 886 of file MixtureDerivatives.h.

dTrdxi__constxj()

static CoolPropDbl CoolProp::MixtureDerivatives::dTrdxi__constxj ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 862 of file MixtureDerivatives.h.

fugacity_i()

CoolPropDbl CoolProp::MixtureDerivatives::fugacity_i ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Fugacity of the i-th component.

Given by the equation

\[ f_i(\delta, \tau, \bar x) = x_i\rho R T \exp\left(\frac{\partial n\alpha^r}{\partial n_i}\right)_{T,V,n_{j \neq i}} \]

Definition at line 12 of file MixtureDerivatives.cpp.

ln_fugacity()

static CoolPropDbl CoolProp::MixtureDerivatives::ln_fugacity ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 1003 of file MixtureDerivatives.h.

ln_fugacity_coefficient()

CoolPropDbl CoolProp::MixtureDerivatives::ln_fugacity_coefficient ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Natural logarithm of the fugacity coefficient.

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 15 of file MixtureDerivatives.cpp.

Lstar()

static Eigen::MatrixXd CoolProp::MixtureDerivatives::Lstar ( HelmholtzEOSMixtureBackend &  HEOS, x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 224 of file MixtureDerivatives.h.

Mstar()

static Eigen::MatrixXd CoolProp::MixtureDerivatives::Mstar ( HelmholtzEOSMixtureBackend &  HEOS, x_N_dependency_flag  xN_flag, Eigen::MatrixXd &  L  )

inlinestatic

Definition at line 279 of file MixtureDerivatives.h.

n2Aijk()

static CoolPropDbl CoolProp::MixtureDerivatives::n2Aijk ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 168 of file MixtureDerivatives.h.

nAij()

static CoolPropDbl CoolProp::MixtureDerivatives::nAij ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 165 of file MixtureDerivatives.h.

nd2nalphardnidnj__constT_V()

CoolPropDbl CoolProp::MixtureDerivatives::nd2nalphardnidnj__constT_V ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

GERG 2004 Monograph equation 7.41.

The derivative term

\[ n\left(\frac{\partial^2n\alpha^r}{\partial n_i \partial n_j} \right)_{T,V} = n\left( \frac{\partial}{\partial n_j}\left(\frac{\partial n\alpha^r}{\partial n_i}\right)_{T,V,n_j}\right)_{T,V,n_i} \]

and GERG 2004 Monograph equation 7.46:

\[ n\left( \frac{\partial}{\partial n_j}\left(\frac{\partial n\alpha^r}{\partial n_i}\right)_{T,V,n_j}\right)_{T,V,n_i} = n\left( \frac{\partial \alpha^r}{\partial n_j}\right)_{T,V,n_i} + n\left( \frac{\partial}{\partial n_j}\left(n\left(\frac{\partial \alpha^r}{\partial n_i}\right)_{T,V,n_j} \right) \right)_{T,V,n_i} \]

GERG 2004 Monograph equation 7.47:

\begin{eqnarray*} n\left( \frac{\partial}{\partial n_j}\left(n\left(\frac{\partial \alpha^r}{\partial n_i}\right)_{T,V,n_j} \right) \right)_{T,V,n_i} &=& \left( \frac{\partial}{\partial \delta}\left(n\left(\frac{\partial\alpha^r}{\partial n_i}\right)_{T,V,n_j}\right)\right)_{\tau,\bar x}\cdot n\left(\frac{\partial\delta}{\partial n_j}\right)_{T,V,n_i}\\ &+& \left( \frac{\partial}{\partial \tau}\left(n\left(\frac{\partial\alpha^r}{\partial n_i}\right)_{T,V,n_j}\right)\right)_{\tau,\bar x}\cdot n\left(\frac{\partial\tau}{\partial n_j}\right)_{T,V,n_i}\\ &+& \left( \frac{\partial}{\partial x_j}\left(n\left(\frac{\partial\alpha^r}{\partial n_i}\right)_{T,V,n_j}\right)\right)_{\delta,\tau,x_i}-\sum_{k=1}^{N}x_k \left( \frac{\partial}{\partial x_k}\left(n\left(\frac{\partial\alpha^r}{\partial n_i}\right)_{T,V,n_j}\right)\right)_{\delta,\tau,x_i}\\ \end{eqnarray*}

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
j	The second index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 317 of file MixtureDerivatives.cpp.

nd_ndalphardni_dnj__constT_V()

CoolPropDbl CoolProp::MixtureDerivatives::nd_ndalphardni_dnj__constT_V ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 323 of file MixtureDerivatives.cpp.

nd_ndln_fugacity_i_dnj_dnk__constT_V_xi()

CoolPropDbl CoolProp::MixtureDerivatives::nd_ndln_fugacity_i_dnj_dnk__constT_V_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, std::size_t  k, x_N_dependency_flag  xN_flag  )

static

Definition at line 138 of file MixtureDerivatives.cpp.

ndalphar_dni__constT_V_nj()

CoolPropDbl CoolProp::MixtureDerivatives::ndalphar_dni__constT_V_nj ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

Table B4, Kunz, JCED, 2012 for the original term and the subsequent substitutions.

The derivative term

\[ n\left(\frac{\partial \alpha^r}{\partial n_i} \right)_{T,V,n_j} \]

which is equal to

\begin{eqnarray*} n\left(\frac{\partial \alpha^r}{\partial n_i} \right)_{T,V,n_j} &=& \delta \alpha^r_{\delta}\left[ 1-\frac{1}{\rho_r}\left[\left(\frac{\partial \rho_r}{\partial x_i}\right)_{x_j} - \sum_{k=1}^N x_k\left(\frac{\partial \rho_r}{\partial x_k}\right)_{x_j} \right]\right]\\ && +\tau \alpha^r_{\tau}\frac{1}{T_r}\left[\left(\frac{\partial T_r}{\partial x_i}\right)_{x_j} - \sum_{k=1}^N x_k\left(\frac{\partial T_r}{\partial x_k}\right)_{x_j} \right]\\ && +\alpha^r_{x_i}-\sum_{k=1}^{N}x_k\alpha^r_{x_k} \end{eqnarray*}

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 230 of file MixtureDerivatives.cpp.

nddeltadni__constT_V_nj()

CoolPropDbl CoolProp::MixtureDerivatives::nddeltadni__constT_V_nj ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

GERG 2004 Monograph equation 7.48.

The derivative term

\[ n\left(\frac{\partial \delta}{\partial n_i} \right)_{T,V,n_j} = \delta - \frac{\delta}{\rho_r}\cdot n\left(\frac{\partial \rho_r}{\partial n_i} \right)_{n_j} \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 252 of file MixtureDerivatives.cpp.

ndln_fugacity_coefficient_dnj__constT_p()

CoolPropDbl CoolProp::MixtureDerivatives::ndln_fugacity_coefficient_dnj__constT_p ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

GERG 2004 Monograph Equation 7.31.

The derivative term

\[ n\left(\frac{\partial \ln \phi_i}{\partial n_j}\right)_{T,p} = n\left(\frac{\partial^2n\alpha^r}{\partial n_j \partial n_i} \right)_{T,V}+1+\frac{n}{RT}\frac{\left(\frac{\partial p}{\partial n_j}\right)_{T,V,n_i}\left(\frac{\partial p}{\partial n_i}\right)_{T,V,n_j}}{\left(\frac{\partial p}{\partial V}\right)_{T,\bar n}} \]

which is also equal to

\[ n\left(\frac{\partial \ln \phi_i}{\partial n_j}\right)_{T,p} = n\left(\frac{\partial^2n\alpha^r}{\partial n_j \partial n_i} \right)_{T,V}+1-\frac{\hat v_i}{RT}\left[n\left(\frac{\partial p}{\partial n_j}\right)_{T,V,n_i}\right] \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
j	The second index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 246 of file MixtureDerivatives.cpp.

ndln_fugacity_i_dnj__constT_V_xi()

CoolPropDbl CoolProp::MixtureDerivatives::ndln_fugacity_i_dnj__constT_V_xi ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, std::size_t  j, x_N_dependency_flag  xN_flag  )

static

Definition at line 99 of file MixtureDerivatives.cpp.

ndpdni__constT_V_nj()

CoolPropDbl CoolProp::MixtureDerivatives::ndpdni__constT_V_nj ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

GERG 2004 Monograph equation 7.63.

The derivative term

\[ n\left(\frac{\partial p}{\partial n_i} \right)_{T,V,n_j} = \rho RT\left[1+\delta\alpha_{\delta}^r\left[2- \frac{1}{\rho_r}\cdot n\left( \frac{\partial \rho_r}{\partial n_i}\right)_{n_j}\right] +\delta\cdot n\left(\frac{\partial\alpha_{\delta}^r}{\partial n_i}\right)_{T,V,n_j}\right] \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 209 of file MixtureDerivatives.cpp.

ndpdV__constT_n()

CoolPropDbl CoolProp::MixtureDerivatives::ndpdV__constT_n ( HelmholtzEOSMixtureBackend &  HEOS )

static

GERG 2004 Monograph equation 7.62.

The derivative term

\[ n\left(\frac{\partial p}{\partial V} \right)_{T,\bar n} = -\rho^2 RT(1+2\delta \alpha_{\delta}^r+\delta^2\alpha^r_{\delta\delta}) \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used

Definition at line 204 of file MixtureDerivatives.cpp.

ndrhorbardni__constnj()

static CoolPropDbl CoolProp::MixtureDerivatives::ndrhorbardni__constnj ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 928 of file MixtureDerivatives.h.

ndtaudni__constT_V_nj()

CoolPropDbl CoolProp::MixtureDerivatives::ndtaudni__constT_V_nj ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

GERG 2004 Monograph equation 7.49.

The derivative term

\[ n\left(\frac{\partial \tau}{\partial n_i} \right)_{T,V,n_j} = \frac{\tau}{T_r}\cdot n\left(\frac{\partial T_r}{\partial n_i} \right)_{n_j} \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 271 of file MixtureDerivatives.cpp.

ndTrdni__constnj()

static CoolPropDbl CoolProp::MixtureDerivatives::ndTrdni__constnj ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 875 of file MixtureDerivatives.h.

p()

static CoolPropDbl CoolProp::MixtureDerivatives::p ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 939 of file MixtureDerivatives.h.

partial_molar_volume()

CoolPropDbl CoolProp::MixtureDerivatives::partial_molar_volume ( HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, x_N_dependency_flag  xN_flag  )

static

GERG 2004 monograph Eqn. 7.32.

The partial molar volume

\[ \hat v_i = \left( \frac{\partial V}{\partial n_i}\right)_{T,p,n_j} = \frac{-\left(\dfrac{\partial p}{\partial n_i}\right)_{T,V,n_j}}{\left(\dfrac{\partial p}{\partial V}\right)_{T,\bar n}} \]

Parameters

HEOS	The HelmholtzEOSMixtureBackend to be used
i	The index of interest
xN_flag	A flag specifying whether the all mole fractions are independent or only the first N-1

Definition at line 36 of file MixtureDerivatives.cpp.

psi()

static CoolPropDbl CoolProp::MixtureDerivatives::psi ( HelmholtzEOSMixtureBackend &  HEOS, x_N_dependency_flag  xN_flag = XN_INDEPENDENT  )

inlinestatic

Return the Helmholtz energy density \(\psi = \rho a\).

Definition at line 704 of file MixtureDerivatives.h.

PSI_rho()

static CoolPropDbl CoolProp::MixtureDerivatives::PSI_rho ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

---

---

---

Shim functions for testing of derivatives

---

---

---

(these are needed because this class is a friend of HelmholtzEOSMixtureBackend and therefore has access to class private variables)

Definition at line 767 of file MixtureDerivatives.h.

PSI_T()

static CoolPropDbl CoolProp::MixtureDerivatives::PSI_T ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, std::size_t  i, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 778 of file MixtureDerivatives.h.

rhormolar()

static CoolPropDbl CoolProp::MixtureDerivatives::rhormolar ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 902 of file MixtureDerivatives.h.

tau()

static CoolPropDbl CoolProp::MixtureDerivatives::tau ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 856 of file MixtureDerivatives.h.

Tr()

static CoolPropDbl CoolProp::MixtureDerivatives::Tr ( CoolProp::HelmholtzEOSMixtureBackend &  HEOS, CoolProp::x_N_dependency_flag  xN_flag  )

inlinestatic

Definition at line 859 of file MixtureDerivatives.h.

---

The documentation for this class was generated from the following files:

• src/Backends/Helmholtz/MixtureDerivatives.h
• src/Backends/Helmholtz/MixtureDerivatives.cpp