[cig-commits] [commit] doc_updates: Added stub for thermodynamics background to manual (1bddbf9)

[cig_noreply at geodynamics.org]

Repository : https://github.com/geodynamics/burnman

On branch  : doc_updates
Link       : https://github.com/geodynamics/burnman/compare/d0fbf8ecb96ee63aaab75a291b47de002616afab...1bddbf92f327ecb65fdf1c11b0695bbc569510ea

>---------------------------------------------------------------

commit 1bddbf92f327ecb65fdf1c11b0695bbc569510ea
Author: Bob Myhill <myhill.bob at gmail.com>
Date:   Mon Dec 29 23:18:44 2014 +0000

    Added stub for thermodynamics background to manual


>---------------------------------------------------------------

1bddbf92f327ecb65fdf1c11b0695bbc569510ea
 sphinx/background_thermodynamics.txt | 28 ++++++++++++++++++++++++++++
 1 file changed, 28 insertions(+)

diff --git a/sphinx/background_thermodynamics.txt b/sphinx/background_thermodynamics.txt
new file mode 100644
index 0000000..1c8230d
--- /dev/null
+++ b/sphinx/background_thermodynamics.txt
@@ -0,0 +1,28 @@
+Calculating Thermodynamic Properties
+------------------------------------
+
+At any given pressure and temperature, the equilibrium assemblage of minerals is that which minimises the Gibbs Free Energy of the system. The Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a closed system. For each phase, the Gibbs free energy is equal to 
+
+.. math::
+    \mathcal{G}= \mathcal{U} - T\mathcal{S} + PV = \mathcal{H} - TS = \mathcal{F} + PV
+    :label: gibbs
+
+where :math:`P` is the pressure, :math:`T` is the temperature and :math:`\mathcal{U}`, :math:`\mathcal{F}`, :math:`\mathcal{H}`, :math:`\mathcal{S}` and :math:`V` are the molar internal energy, Helmholtz Free Energy, enthalpy, entropy and volume respectively. The total energy of the system is then
+
+.. math::
+    \mathcal{G}_{\textrm{system}}= \sum_i n_i \mathcal{G}_i
+    :label: gibbstotal
+
+HP2011
+^^^^^^
+
+.. math::
+    \mathcal{G}(P,T) = \mathcal{H}_{\textrm{1 bar, T}} - T\mathcal{S}_{\textrm{1 bar, T}} + \int_{\textrm{1 bar}}^P V(P,T)~dP
+    :label: gibbs_hp2011  
+
+.. math::
+    \mathcal{G}(P,T) = \left( \Delta_f\mathcal{H}_{\textrm{1 bar, 298 K}} + \int_{298}^T C_P~dT \right) - T\left(\mathcal{S}_{\textrm{1 bar, 298 K}} + \int_{298}^T \frac{C_P}{T}~dT \right) + \int_{\textrm{1 bar}}^P V(P,T)~dP
+    :label: gibbs_hp2011_2   
+
+SLB2005
+^^^^^^^