CoolProp
CoolProp::BaseHelmholtzTerm Class Referenceabstract

## Detailed Description

The base class class for the Helmholtz energy terms.

Residual Helmholtz Energy Terms:

Term Helmholtz Energy Contribution
ResidualHelmholtzPower $$\alpha^r=\left\lbrace\begin{array}{cc}\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} & l_i=0\\ \displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\delta^{l_i}) & l_i\neq 0\end{array}\right.$$
ResidualHelmholtzExponential $$\alpha^r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\gamma_i\delta^{l_i})$$
ResidualHelmholtzLemmon2005 $$\alpha^r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\delta^{l_i}-\tau^{m_i})$$
ResidualHelmholtzGaussian $$\alpha^r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\eta_i(\delta-\epsilon_i)^2-\beta_i(\tau-\gamma_i)^2)$$
ResidualHelmholtzGERG2008Gaussian $$\alpha^r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\eta_i(\delta-\epsilon_i)^2-\beta_i(\delta-\gamma_i))$$
ResidualHelmholtzNonAnalytic $$\begin{array}{c}\alpha^r&=&\displaystyle\sum_i n_i \Delta^{b_i}\delta\psi \\ \Delta & = & \theta^2+B_i[(\delta-1)^2]^{a_i}\\ \theta & = & (1-\tau)+A_i[(\delta-1)^2]^{1/(2\beta_i)}\\ \psi & = & \exp(-C_i(\delta-1)^2-D_i(\tau-1)^2) \end{array}$$
ResidualHelmholtzSAFTAssociating $$\alpha^r = am\left(\ln X-\frac{X}{2}+\frac{1}{2}\right);$$

Ideal-Gas Helmholtz Energy Terms:

Term Helmholtz Energy Contribution
IdealHelmholtzLead $$\alpha^0 = n_1 + n_2\tau + \ln\delta$$
IdealHelmholtzEnthalpyEntropyOffset $$\alpha^0 = \displaystyle\frac{\Delta s}{R_u/M}+\frac{\Delta h}{(R_u/M)T}\tau$$
IdealHelmholtzLogTau $$\alpha^0 = n_1\log\tau$$
IdealHelmholtzPower $$\alpha^0 = \displaystyle\sum_i n_i\tau^{t_i}$$
IdealHelmholtzPlanckEinsteinGeneralized $$\alpha^0 = \displaystyle\sum_i n_i\log[c_i+d_i\exp(\theta_i\tau)]$$

#include <Helmholtz.h>

Inheritance diagram for CoolProp::BaseHelmholtzTerm: ## Public Member Functions

virtual CoolPropDbl base (const CoolPropDbl &tau, const CoolPropDbl &delta) throw ()
Returns the base, non-dimensional, Helmholtz energy term (no derivatives) [-]. More...

virtual CoolPropDbl dTau (const CoolPropDbl &tau, const CoolPropDbl &delta) throw ()
Returns the first partial derivative of Helmholtz energy term with respect to tau [-]. More...

virtual CoolPropDbl dTau2 (const CoolPropDbl &tau, const CoolPropDbl &delta) throw ()
Returns the second partial derivative of Helmholtz energy term with respect to tau [-]. More...

virtual CoolPropDbl dDelta_dTau (const CoolPropDbl &tau, const CoolPropDbl &delta) throw ()
Returns the second mixed partial derivative (delta1,dtau1) of Helmholtz energy term with respect to delta and tau [-]. More...

virtual CoolPropDbl dDelta (const CoolPropDbl &tau, const CoolPropDbl &delta) throw ()
Returns the first partial derivative of Helmholtz energy term with respect to delta [-]. More...

virtual CoolPropDbl dDelta2 (const CoolPropDbl &tau, const CoolPropDbl &delta) throw ()
Returns the second partial derivative of Helmholtz energy term with respect to delta [-]. More...

virtual CoolPropDbl dDelta2_dTau (const CoolPropDbl &tau, const CoolPropDbl &delta) throw ()
Returns the third mixed partial derivative (delta2,dtau1) of Helmholtz energy term with respect to delta and tau [-]. More...

virtual CoolPropDbl dDelta_dTau2 (const CoolPropDbl &tau, const CoolPropDbl &delta) throw ()
Returns the third mixed partial derivative (delta1,dtau2) of Helmholtz energy term with respect to delta and tau [-]. More...

virtual CoolPropDbl dTau3 (const CoolPropDbl &tau, const CoolPropDbl &delta) throw ()
Returns the third partial derivative of Helmholtz energy term with respect to tau [-]. More...

virtual CoolPropDbl dDelta3 (const CoolPropDbl &tau, const CoolPropDbl &delta) throw ()
Returns the third partial derivative of Helmholtz energy term with respect to delta [-]. More...

virtual CoolPropDbl dTau4 (const CoolPropDbl &tau, const CoolPropDbl &delta) throw ()
Returns the fourth partial derivative of Helmholtz energy term with respect to tau [-]. More...

virtual CoolPropDbl dDelta_dTau3 (const CoolPropDbl &tau, const CoolPropDbl &delta) throw ()

virtual CoolPropDbl dDelta2_dTau2 (const CoolPropDbl &tau, const CoolPropDbl &delta) throw ()

virtual CoolPropDbl dDelta3_dTau (const CoolPropDbl &tau, const CoolPropDbl &delta) throw ()

virtual CoolPropDbl dDelta4 (const CoolPropDbl &tau, const CoolPropDbl &delta) throw ()

virtual void all (const CoolPropDbl &tau, const CoolPropDbl &delta, HelmholtzDerivatives &derivs)=0 throw ()

## § base()

 virtual CoolPropDbl CoolProp::BaseHelmholtzTerm::base ( const CoolPropDbl & tau, const CoolPropDbl & delta ) throw ( )
inlinevirtual

Returns the base, non-dimensional, Helmholtz energy term (no derivatives) [-].

Parameters
 tau Reciprocal reduced temperature where $$\tau=T_c / T$$ delta Reduced density where $$\delta = \rho / \rho_c$$

## § dDelta()

 virtual CoolPropDbl CoolProp::BaseHelmholtzTerm::dDelta ( const CoolPropDbl & tau, const CoolPropDbl & delta ) throw ( )
inlinevirtual

Returns the first partial derivative of Helmholtz energy term with respect to delta [-].

Parameters
 tau Reciprocal reduced temperature where $$\tau=T_c / T$$ delta Reduced density where $$\delta = \rho / \rho_c$$

## § dDelta2()

 virtual CoolPropDbl CoolProp::BaseHelmholtzTerm::dDelta2 ( const CoolPropDbl & tau, const CoolPropDbl & delta ) throw ( )
inlinevirtual

Returns the second partial derivative of Helmholtz energy term with respect to delta [-].

Parameters
 tau Reciprocal reduced temperature where $$\tau=T_c / T$$ delta Reduced density where $$\delta = \rho / \rho_c$$

## § dDelta2_dTau()

 virtual CoolPropDbl CoolProp::BaseHelmholtzTerm::dDelta2_dTau ( const CoolPropDbl & tau, const CoolPropDbl & delta ) throw ( )
inlinevirtual

Returns the third mixed partial derivative (delta2,dtau1) of Helmholtz energy term with respect to delta and tau [-].

Parameters
 tau Reciprocal reduced temperature where $$\tau=T_c / T$$ delta Reduced density where $$\delta = \rho / \rho_c$$

## § dDelta3()

 virtual CoolPropDbl CoolProp::BaseHelmholtzTerm::dDelta3 ( const CoolPropDbl & tau, const CoolPropDbl & delta ) throw ( )
inlinevirtual

Returns the third partial derivative of Helmholtz energy term with respect to delta [-].

Parameters
 tau Reciprocal reduced temperature where $$\tau=T_c / T$$ delta Reduced density where $$\delta = \rho / \rho_c$$

## § dDelta_dTau()

 virtual CoolPropDbl CoolProp::BaseHelmholtzTerm::dDelta_dTau ( const CoolPropDbl & tau, const CoolPropDbl & delta ) throw ( )
inlinevirtual

Returns the second mixed partial derivative (delta1,dtau1) of Helmholtz energy term with respect to delta and tau [-].

Parameters
 tau Reciprocal reduced temperature where $$\tau=T_c / T$$ delta Reduced density where $$\delta = \rho / \rho_c$$

## § dDelta_dTau2()

 virtual CoolPropDbl CoolProp::BaseHelmholtzTerm::dDelta_dTau2 ( const CoolPropDbl & tau, const CoolPropDbl & delta ) throw ( )
inlinevirtual

Returns the third mixed partial derivative (delta1,dtau2) of Helmholtz energy term with respect to delta and tau [-].

Parameters
 tau Reciprocal reduced temperature where $$\tau=T_c / T$$ delta Reduced density where $$\delta = \rho / \rho_c$$

## § dTau()

 virtual CoolPropDbl CoolProp::BaseHelmholtzTerm::dTau ( const CoolPropDbl & tau, const CoolPropDbl & delta ) throw ( )
inlinevirtual

Returns the first partial derivative of Helmholtz energy term with respect to tau [-].

Parameters
 tau Reciprocal reduced temperature where $$\tau=T_c / T$$ delta Reduced density where $$\delta = \rho / \rho_c$$

## § dTau2()

 virtual CoolPropDbl CoolProp::BaseHelmholtzTerm::dTau2 ( const CoolPropDbl & tau, const CoolPropDbl & delta ) throw ( )
inlinevirtual

Returns the second partial derivative of Helmholtz energy term with respect to tau [-].

Parameters
 tau Reciprocal reduced temperature where $$\tau=T_c / T$$ delta Reduced density where $$\delta = \rho / \rho_c$$

## § dTau3()

 virtual CoolPropDbl CoolProp::BaseHelmholtzTerm::dTau3 ( const CoolPropDbl & tau, const CoolPropDbl & delta ) throw ( )
inlinevirtual

Returns the third partial derivative of Helmholtz energy term with respect to tau [-].

Parameters
 tau Reciprocal reduced temperature where $$\tau=T_c / T$$ delta Reduced density where $$\delta = \rho / \rho_c$$

## § dTau4()

 virtual CoolPropDbl CoolProp::BaseHelmholtzTerm::dTau4 ( const CoolPropDbl & tau, const CoolPropDbl & delta ) throw ( )
inlinevirtual

Returns the fourth partial derivative of Helmholtz energy term with respect to tau [-].

Parameters
 tau Reciprocal reduced temperature where $$\tau=T_c / T$$ delta Reduced density where $$\delta = \rho / \rho_c$$

Reimplemented in CoolProp::ResidualHelmholtzSAFTAssociating.

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