Final edits - typos, clarity, formatting, etc.

Update pages/science/thermodynamics.rst

Explaining the ideal gas law.
- Fix math formatting.
- Link to info on Maxwell relations.

Update pages/science/species-thermo.rst
- Grammar
- Fix math formatting.

Typo fix on pages/science/transport.rst

pages/science/species-thermo.rst

@@ -73,7 +73,7 @@ defined to be composed solely of electrons.
 Thermodynamic Properties
 ------------------------
 
-The phase models discussed in the `Phases section </science/phases.html>`__
+The phase models discussed in the `Phases section </science/phases-thermo.html>`__
 implement specific models for the thermodynamic properties appropriate for the
 type of phase or interface they represent. Although each one may use different
 expressions to compute the properties, they all require thermodynamic property
@@ -86,7 +86,7 @@ present, the properties needed are:
    temperature :math:`T^\circ`;
 3. the absolute molar entropy :math:`\hat{s}(T^\circ, p^\circ)` at :math:`(T^\circ, p^\circ)`.
 
-See: :ref:`the Thermodynamic Models section <sec-thermo-models>`
+The superscript :math:`^\circ` here represents the *reference state*--a specified state (i.e. set of conditions :math:`T^\circ` and :math:`p^\circ` and fixed chemical composition) at which thermodynamic properties are known.
 
 .. _sec-thermo-models:
 
@@ -204,12 +204,12 @@ thermodynamic properties:
 
    \hat{c}_p^\circ(T) = \hat{c}_p^\circ(T^\circ)
 
-   \hat{h}^\circ(T) = \hat{h}^\circ(T_0) + \hat{c}_p^\circ\cdot(T-T^\circ)
+   \hat{h}^\circ(T) = \hat{h}^\circ\left(T_0\right) + \hat{c}_p^\circ \left(T-T^\circ\right)
 
-   \hat{s}^\circ(T) = \hat{s}^\circ(T_0) + \hat{c}_p^\circ \ln (T/T^\circ)
+   \hat{s}^\circ(T) = \hat{s}^\circ(T_0) + \hat{c}_p^\circ \ln{\left(\frac{T}{T^\circ}\right)}
 
 The parameterization uses four constants: :math:`T^\circ, \hat{c}_p^\circ(T^\circ),
-\hat{h}^\circ(T^\circ), \hat{s}^\circ(T)`. The default value of :math:`T^\circ` is 298.15 K; the
+\hat{h}^\circ(T^\circ), and \hat{s}^\circ(T)`. The default value of :math:`T^\circ` is 298.15 K; the
 default value for the other parameters is 0.0.
 
 A constant heat capacity parameterization can be defined in the CTI format using

pages/science/thermodynamics.rst

@@ -15,18 +15,18 @@
    Thermodynamic properties typically depend on information at both the species and phase levels. The user must specify thermodynamic models for both levels, and these selections must be compatible with one another. For instance: one cannot pair certain non-ideal species thermodyamic models with an ideal phase model.
 
    - The user must specify a thermodynamic model for each species and provide inputs that inform how species properties are calculated. For example, the user specifies how the reference enthalpy and entropy values for each species are calcualted, as a function of temperature.
-   - The user also selects a phase model. This model describes how the species interact with one another to determine phase properties and species specific properties, for a given thermodynamic state. This includes general :math:`P-\hat{v}-T` behavior (for example, calculate the phase pressure for a given molar volume, temperature, and chemical composition), as well as how species-specific properties, such as internal energy, entropy, and others depend on the state variables
+   - The user also selects a phase model. This model describes how the species interact with one another to determine phase properties and species specific properties, for a given thermodynamic state. This includes general :math:`p`-:math:`\hat{v}`-:math:`T` behavior (for example, calculate the phase pressure for a given molar volume, temperature, and chemical composition), as well as how species-specific properties, such as internal energy, entropy, and others depend on the state variables
 
 Example: The Ideal Gas Model
 ============================
 For a simple example: in the Ideal Gas model, one might use 7-parameter NASA polynomials to specify the species reference thermodynamic quantities.  These would be used to calculate the reference molar enthalpy :math:`\hat{h}_k^\circ(T)` and entropy :math:`\hat{s}_k^\circ(T)` for a given species :math:`k` as a function of temperature :math:`T`. See the `NASA Polynomials Species Thermo entry </science/science-species.html#the-nasa-7-coefficient-polynomial-parameterization>`__ for more information.
 
-At the phase level, the Ideal Gas Law provides the P-v-T relationship, called an equation of state. This is used, for example, to calculate the pressure as a function of molar volume :math:`\hat{v}` and temperature :math:`T`:
+At the phase level, the Ideal Gas Law provides the :math:`P`-:math:`\hat{v}`-:math:`T` relationship. The ideal gas law is an example of an equation of state. This is used, for example, to calculate the pressure as a function of molar volume :math:`\hat{v}`, and temperature, :math:`T`:
 
 .. math::
    p = \frac{\overline{R}T}{\hat{v}}
 
-where :math:`\overline{R}` is the Universal Gas Constant. Maxwell's relations are used to derive other thermodynamic properties from the equation of state. With the Ideal Gas phase model, these reduce to rather simple forms. For example, for a species :math:`k`, the Ideal Gas molar internal energy :math:`\hat{u}_k` and entropy :math:`\hat{s}_k` are:
+where :math:`\overline{R}` is the Universal Gas Constant. The `Maxwell relations <https://en.wikipedia.org/wiki/Maxwell_relations>`__ are used to derive other thermodynamic properties from the equation of state. With the Ideal Gas phase model, these reduce to rather simple forms. For example, for a species :math:`k`, the Ideal Gas molar internal energy :math:`\hat{u}_k` and entropy :math:`\hat{s}_k` are:
 
 .. math::
    \hat{u}_k = \hat{h}^\circ_k(T) - p\hat{v}
@@ -58,7 +58,7 @@ Please click either of the cards below for details on the species and phase mode
 
             .. container:: card-text
 
-               The models and equations that Cantera uses to calculate species thermodynamic properties.
+               The models and equations that Cantera uses to calculate species thermodynamic properties, such as the NASA 7-parameter polynomial form.
 
       .. container:: card
 
@@ -76,6 +76,6 @@ Please click either of the cards below for details on the species and phase mode
 
             .. container:: card-text
 
-               The theory behind some of Cantera's phase models.
+               The theory behind some of Cantera's phase models, such as the Ideal Gas Law.
 
 

pages/science/transport.rst

@@ -12,7 +12,7 @@
 
       Here, we describe how Cantera uses species and phase information to calculate transport properties and rates.
 
-   Similar to Cantera's approach to `thermodynamic properties </science/thermodynamics.html>`__, transport property calcualtions in Cantera depend on information at both the species and phase levels. The user must specify transport models for both levels, and these selections must be compatible with one another. 
+   Similar to Cantera's approach to `thermodynamic properties </science/thermodynamics.html>`__, transport property calculations in Cantera depend on information at both the species and phase levels. The user must specify transport models for both levels, and these selections must be compatible with one another. 
 
    - The user must specify a transport model for each species and provide inputs that inform how species properties are calculated. For example, the user provides inputs that allow Cantera to calculate species collision integrals based on species-specific Lennard-Jones parameters.
    - The user also selects a phase model. This model describes how the species interact with one another to determine phase-averaged properties (such viscosity or thermal conductivity) and species specific properties (such as diffusion coefficients), for a given thermodynamic state.