[cig-commits] [commit] doc_updates: Corrected P_th term and blurb in HP2011 (bc8634d)

[cig_noreply at geodynamics.org]

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

On branch  : doc_updates
Link       : https://github.com/geodynamics/burnman/compare/72599ebd1903a1ef251b0e889b0de202e10fed51...bc8634df4edd5a0dd4f1c2592efa5a52c12a8556

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commit bc8634df4edd5a0dd4f1c2592efa5a52c12a8556
Author: Bob Myhill <myhill.bob at gmail.com>
Date:   Wed Dec 31 14:26:40 2014 +0000

    Corrected P_th term and blurb in HP2011


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bc8634df4edd5a0dd4f1c2592efa5a52c12a8556
 sphinx/background_thermoelastics.txt | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/sphinx/background_thermoelastics.txt b/sphinx/background_thermoelastics.txt
index 1f55f23..b3fa40b 100644
--- a/sphinx/background_thermoelastics.txt
+++ b/sphinx/background_thermoelastics.txt
@@ -122,12 +122,13 @@ The primary differences are in the thermal correction to the shear modulus and i
 HP2011 (thermal correction to Modified Tait)
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
-The thermal pressure can be incorporated into the Modified Tait equation of state, replacing :math:`P` with :math:`P-P_{\textrm{thermal}}` in Equation :eq:`mtait` :cite:`HP2011`. Thermal pressure here is calculated using a Mie-Grüneisen equation of state and an Einstein model for heat capacity, even though the Einstein model is not actually used for the heat capacity when calculating the enthalpy and entropy (see following section).
+The thermal pressure can be incorporated into the Modified Tait equation of state, replacing :math:`P` with :math:`P-\left(P_{\textrm{th}} - P_{\textrm{th0}}\right)` in Equation :eq:`mtait` :cite:`HP2011`. Thermal pressure is calculated using a Mie-Grüneisen equation of state and an Einstein model for heat capacity, even though the Einstein model is not actually used for the heat capacity when calculating the enthalpy and entropy (see following section).
 
 .. math::
-    P_{\textrm{th}} &= \frac{\alpha_0 K_0 E_{\textrm{th}}}{C_{V0}}, \\
-    C_{V0} &= 3 n R \frac{(\frac{\Theta}{T})^2\exp(\frac{\Theta}{T})}{(\exp(\frac{\Theta}{T})-1)^2}, \\
-    E_{\textrm{th}} &= 3 n R \Theta \left(0.5 + \frac{1}{ \exp(\frac{\Theta}{T}) - 1 }\right)
+    P_{\textrm{th}} &= \frac{\alpha_0 K_0 E_{\textrm{th}} }{C_{V0}}, \\
+    E_{\textrm{th}} &= 3 n R \Theta \left(0.5 + \frac{1}{ \exp(\frac{\Theta}{T}) - 1 }\right), \\
+    C_{V} &= 3 n R \frac{(\frac{\Theta}{T})^2\exp(\frac{\Theta}{T})}{(\exp(\frac{\Theta}{T})-1)^2}
+
 
 :math:`\Theta` is the Einstein temperature of the crystal in Kelvin, approximated for a substance :math:`i` with :math:`n_i` atoms in the unit formula and a molar entropy :math:`S_i` using the empirical formula