[Thermo] Add real gas compressibility functions

Add `isothermalCompressibility` and `thermalExpansionCoeff` definitions to the `RedlichKwongMFTP` and `PengRobinson` models

Author: corykinney

include/cantera/thermo/PengRobinson.h

@@ -205,6 +205,22 @@ class PengRobinson : public MixtureFugacityTP
 
 public:
 
+    //! Returns the isothermal compressibility (\f$\beta_T\f$). Units: 1/Pa.
+    /*!
+     *  \f[ 
+     *    \beta_T = -\frac{1}{v} \left(\frac{\partial v}{\partial p}\right)_T
+     *  \f]
+     */
+    virtual double isothermalCompressibility() const;
+
+    //! Return the volumetric thermal expansion coefficient (\f$\alpha_V\f$). Units: 1/K.
+    /*!
+     *  \f[ 
+     *    \alpha_V = \frac{1}{v} \left(\frac{\partial v}{\partial T}\right)_p
+     *  \f]
+     */
+    virtual double thermalExpansionCoeff() const;
+
     //! Calculate \f$dp/dV\f$ and \f$dp/dT\f$ at the current conditions
     /*!
      *  These are stored internally.
@@ -248,7 +264,7 @@ class PengRobinson : public MixtureFugacityTP
      */
     double m_a;
 
-    //! Value of \f$\alpha\f$ in the equation of state
+    //! Value of \f$a \alpha\f$ in the equation of state
     /*!
      *  `m_aAlpha_mix` is a function of the temperature and the mole fractions.
      */

include/cantera/thermo/RedlichKwongMFTP.h

@@ -173,6 +173,22 @@ class RedlichKwongMFTP : public MixtureFugacityTP
     virtual doublereal densSpinodalGas() const;
     virtual doublereal dpdVCalc(doublereal TKelvin, doublereal molarVol, doublereal& presCalc) const;
 
+    //! Returns the isothermal compressibility (\f$\beta_T\f$). Units: 1/Pa.
+    /*!
+     *  \f[ 
+     *    \beta_T = -\frac{1}{v} \left(\frac{\partial v}{\partial p}\right)_T
+     *  \f]
+     */
+    virtual double isothermalCompressibility() const;
+
+    //! Return the volumetric thermal expansion coefficient (\f$\alpha_V\f$). Units: 1/K.
+    /*!
+     *  \f[ 
+     *    \alpha_V = \frac{1}{v} \left(\frac{\partial v}{\partial T}\right)_p
+     *  \f]
+     */
+    virtual double thermalExpansionCoeff() const;
+
     //! Calculate dpdV and dpdT at the current conditions
     /*!
      *  These are stored internally.

src/thermo/PengRobinson.cpp

@@ -630,6 +630,18 @@ double PengRobinson::dpdVCalc(double T, double molarVol, double& presCalc) const
     return -GasConstant * T / (vmb * vmb) + 2 * m_aAlpha_mix * vpb / (denom*denom);
 }
 
+double PengRobinson::isothermalCompressibility() const
+{
+    calculatePressureDerivatives();
+    return -1 / (molarVolume() * m_dpdV);
+}
+
+double PengRobinson::thermalExpansionCoeff() const
+{
+    calculatePressureDerivatives();
+    return -m_dpdT / (molarVolume() * m_dpdV);
+}
+
 void PengRobinson::calculatePressureDerivatives() const
 {
     double T = temperature();

src/thermo/RedlichKwongMFTP.cpp

@@ -707,6 +707,18 @@ doublereal RedlichKwongMFTP::dpdVCalc(doublereal TKelvin, doublereal molarVol, d
     return dpdv;
 }
 
+double RedlichKwongMFTP::isothermalCompressibility() const
+{
+    pressureDerivatives();
+    return -1 / (molarVolume() * dpdV_);
+}
+
+double RedlichKwongMFTP::thermalExpansionCoeff() const
+{
+    pressureDerivatives();
+    return -dpdT_ / (molarVolume() * dpdV_);
+}
+
 void RedlichKwongMFTP::pressureDerivatives() const
 {
     doublereal TKelvin = temperature();