Following modifications in the code are performed:

1. Fixing typos
2. Adding more detailed documentation
3. Deleting redundant variables

include/cantera/thermo/PengRobinsonMFTP.h

@@ -1,7 +1,7 @@
 //! @file PengRobinsonMFTP.h
 
 // This file is part of Cantera. See License.txt in the top-level directory or
-// at http://www.cantera.org/license.txt for license and copyright information.
+// at https://cantera.org/license.txt for license and copyright information.
 
 #ifndef CT_PENGROBINSONMFTP_H
 #define CT_PENGROBINSONMFTP_H
@@ -73,9 +73,33 @@ class PengRobinsonMFTP : public MixtureFugacityTP
      *  where:
      *
      * \f[
-     *    \alpha = \left[ 1 + \left(0.37464 + 1.54226\omega - 0.26992\omega^2\right)\left(1-T_r^{0.5}\right)\right]^2
+     *    \alpha = \left[ 1 + \kappa \left(1-T_r^{0.5}\right)\right]^2
      * \f]
+     *
+     *  and
+     *
+     * \f[
+     *    \kappa = \left(0.37464 + 1.54226\omega - 0.26992\omega^2\right)                              for omega <= 0.491
+     *    \kappa = \left(0.379642 + 1.487503\omega - 0.164423\omega^2 +  0.016667\omega^3 \right)      for omega > 0.491
+     * \f]
+     *
+     *Coefficients a_mix, b_mix and (a \alpha)_{mix} are caclulated as
+     *
+     *\f[
+     *a_{mix} = \sum_i \sum_j X_i X_j a_{i, j} = \sum_i \sum_j X_i X_j sqrt{a_i a_j}
+     *\f]
+     *
+     *\f[
+     *   b_{mix} = \sum_i X_i b_i
+     *\f]
+     *
+     *\f[
+     *   {a \alpha}_{mix} = \sum_i \sum_j X_i X_j {a \alpha}_{i, j} = \sum_i \sum_j X_i X_j sqrt{a_i a_j} sqrt{\alpha_i \alpha_j}
+     *\f]
+     *
+     *
      */
+
     virtual double pressure() const;
 
     // @}
@@ -112,8 +136,9 @@ class PengRobinsonMFTP : public MixtureFugacityTP
     /*!
      * This is defined as the concentration by which the generalized
      * concentration is normalized to produce the activity. In many cases, this
-     * quantity will be the same for all species in a phase. Since the activity
-     * for an ideal gas mixture is simply the mole fraction, for an ideal gas
+     * quantity will be the same for all species in a phase. 
+     * The ideal gas mixture is considered as the standard or reference state here. 
+     * Since the activity for an ideal gas mixture is simply the mole fraction, for an ideal gas
      * \f$ C^0_k = P/\hat R T \f$.
      *
      * @param k Optional parameter indicating the species. The default is to
@@ -143,7 +168,7 @@ class PengRobinsonMFTP : public MixtureFugacityTP
      * \f$ \mu_k / \hat R T \f$.
      * Units: unitless
      *
-     * We close the loop on this function, here, calling getChemPotentials() and
+     * We close the loop on this function here calling getChemPotentials() and
      * then dividing by RT. No need for child classes to handle.
      *
      * @param mu    Output vector of non-dimensional species chemical potentials
@@ -158,7 +183,13 @@ class PengRobinsonMFTP : public MixtureFugacityTP
     virtual void getPartialMolarCp(double* cpbar) const;
     virtual void getPartialMolarVolumes(double* vbar) const;
 
-
+    //! Calculate the temperature dependent interaction parameter alpha needed for P-R EoS
+    /*
+    *  The temperature dependent parameter in P-R EoS is calculated as
+    *       \alpha = [1 + \kappa(1 - sqrt{T/T_crit}]^2
+    *  kappa is a function calulated based on the accentric factor.
+    *  Units: unitless
+    */
     virtual void calculateAlpha(const std::string& species, double a, double b, double w);
     //@}
     /// @name Critical State Properties.
@@ -190,7 +221,7 @@ class PengRobinsonMFTP : public MixtureFugacityTP
     //! Retrieve a and b coefficients by looking up tabulated critical parameters
     /*!
     *  If pureFluidParameters are not provided for any species in the phase,
-    *  consult the critical properties tabulated in /thermo/critProperties.xml.
+    *  consult the critical properties tabulated in /build/data/thermo/critProperties.xml.
     *  If the species is found there, calculate pure fluid parameters a_k and b_k as:
     *  \f[ a_k = 0.4278*R**2*T_c^2/P_c \f]
     *
@@ -223,10 +254,10 @@ class PengRobinsonMFTP : public MixtureFugacityTP
     /*!
      *  The "a" parameter for interactions between species *i* and *j* is
      *  assumed by default to be computed as:
-     *  \f[ a_{ij} = \sqrt(a_{i,0} a_{j,0}) + \sqrt(a_{i,1} a_{j,1}) T \f]
+     *  \f[ a_{ij} = \sqrt(a_{i, 0} a_{j, 0}) + \sqrt(a_{i, 1} a_{j, 1}) T \f]
      *
      *  This function overrides the defaults with the specified parameters:
-     *  \f[ a_{ij} = a_{ij,0} + a_{ij,1} T \f]
+     *  \f[ a_{ij} = a_{ij, 0} + a_{ij, 1} T \f]
      *
      *  @param species_i   Name of one species
      *  @param species_j   Name of the other species
@@ -316,20 +347,20 @@ class PengRobinsonMFTP : public MixtureFugacityTP
 protected:
     //! Form of the temperature parameterization
     /*!
-     *  - 0 = There is no temperature parameterization of a or b
-     *  - 1 = The a_ij parameter is a linear function of the temperature
+     *  0 = There is no temperature parameterization of a or b
+     *  1 = The a_ij parameter is a linear function of the temperature
      */
     int m_formTempParam;
 
     //! Value of b in the equation of state
     /*!
-     *  m_b is a function of the temperature and the mole fraction.
+     *  m_b_current is a function of the temperature and the mole fractions.
      */
     double m_b_current;
 
-    //! Value of a in the equation of state
+    //! Value of a and alpha in the equation of state
     /*!
-     *  a_b is a function of the temperature and the mole fraction.
+     *  m_aAlpha_current is a function of the temperature and the mole fractions. m_a_current depends only on the mole fractions.
      */
     double m_a_current;
     double m_aAlpha_current;
@@ -358,31 +389,31 @@ class PengRobinsonMFTP : public MixtureFugacityTP
     // Partial molar volumes of the species
     mutable vector_fp m_partialMolarVolumes;
 
-    //! The derivative of the pressure wrt the volume
+    //! The derivative of the pressure with respect to the volume
     /*!
      * Calculated at the current conditions. temperature and mole number kept
      * constant
      */
     mutable double dpdV_;
 
-    //! The derivative of the pressure wrt the temperature
+    //! The derivative of the pressure with respect to the temperature
     /*!
      *  Calculated at the current conditions. Total volume and mole number kept
      *  constant
      */
     mutable double dpdT_;
 
-    //! Vector of derivatives of pressure wrt mole number
+    //! Vector of derivatives of pressure with respect to mole number
     /*!
      *  Calculated at the current conditions. Total volume, temperature and
      *  other mole number kept constant
      */
     mutable vector_fp dpdni_;
 
 public:
-    //! Omega constant for a -> value of a in terms of critical properties
+    //! Omega constants: a0 (= omega_a) and b0 (= omega_b) values used in Peng-Robinson equation of state
     /*!
-     *  this was calculated from a small nonlinear solve
+     *  These values are calculated by solving P-R cubic equation at the critical point.
      */
     static const double omega_a;