From bee14d514db4d04538a01ba6163d103a8a9f329b Mon Sep 17 00:00:00 2001
From: Ian Bell <ian.bell@nist.gov>
Date: Thu, 7 Jul 2022 10:43:50 -0400
Subject: [PATCH] More derivatives
---
doc/source/derivs/derivs.ipynb | 37 +++++++++++++++++++++++++++++++++-
1 file changed, 36 insertions(+), 1 deletion(-)
diff --git a/doc/source/derivs/derivs.ipynb b/doc/source/derivs/derivs.ipynb
index c621e71..a2015a9 100644
--- a/doc/source/derivs/derivs.ipynb
+++ b/doc/source/derivs/derivs.ipynb
@@ -24,7 +24,42 @@
"\n",
"$$ p^r = \\rho R T \\Lambda^r_{01}$$\n",
"\n",
- "Similar definitions apply for all the other residual thermodynamic properties"
+ "Similar definitions apply for all the other thermodynamic properties, with the tot superscript indicating it is the sum of the residual and ideal-gas (not included in teqp) contributions:\n",
+ "\n",
+ "$$\n",
+ "\\frac{p}{\\rho R T} = 1 + \\Lambda^r_{01}\n",
+ "$$\n",
+ "Internal energy ($u= a+Ts$):\n",
+ "$$\n",
+ "\t\\frac{u}{RT} = \\Lambda^{\\rm tot}_{10}\n",
+ "$$\n",
+ "Enthalpy ($h= u+p/\\rho$):\n",
+ "$$\n",
+ "\\frac{h}{RT} = 1+\\Lambda^r_{01} + \\Lambda^{\\rm tot}_{10}\n",
+ "$$\n",
+ "Entropy ($s\\equiv -(\\partial a/\\partial T)_v$):\n",
+ "$$\n",
+ "\\frac{s}{R} = \\Lambda^{\\rm tot}_{10}-\\Lambda^{\\rm tot}_{00}\n",
+ "$$\n",
+ "Gibbs energy ($g= h-Ts$):\n",
+ "$$\n",
+ "\t\\frac{g}{RT} = 1+\\Lambda^r_{01}+\\Lambda^{\\rm tot}_{00}\n",
+ "$$\n",
+ "Derivatives of pressure:\n",
+ "$$\n",
+ "\t\\left(\\frac{\\partial p}{\\partial \\rho}\\right)_{T} = RT\\left(1+2\\Lambda^r_{01}+\\Lambda^r_{02}\\right)\n",
+ "$$\n",
+ "$$\n",
+ "\t\\left(\\frac{\\partial p}{\\partial T}\\right)_{\\rho} = R\\rho\\left(1+\\Lambda^r_{01}-\\Lambda^r_{11}\\right)\n",
+ "$$\n",
+ "Isochoric specific heat ($c_v\\equiv (\\partial u/\\partial T)_v$):\n",
+ "$$\n",
+ "\\frac{c_v}{R} = -\\Lambda^{\\rm tot}_{20}\n",
+ "$$\n",
+ "Isobaric specific heat ($c_p\\equiv (\\partial h/\\partial T)_p$; see Eq. 3.56 from Span \\cite{Span-BOOK-2000} for the derivation):\n",
+ "$$\n",
+ "\\frac{c_p}{R} = -\\Lambda^{\\rm tot}_{20}+\\frac{(1+\\Lambda^r_{01}-\\Lambda^r_{11})^2}{1+2\\Lambda^r_{01}+\\Lambda^r_{02}}\n",
+ "$$"
]
},
{
--
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