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authorKarl Berry <karl@freefriends.org>2023-11-17 22:02:57 +0000
committerKarl Berry <karl@freefriends.org>2023-11-17 22:02:57 +0000
commitd750d4833a1999a7902080b4a55e3e89eead497d (patch)
treec5670d1d100bd424cfa1854a6713264cd21cf0ca /Master/texmf-dist/doc/latex/thermodynamics/thermodynamics-examples.tex
parent6719122c781ae5bcef2f225c8f5246f31dacf704 (diff)
thermodynamics (17nov23)
git-svn-id: svn://tug.org/texlive/trunk@68881 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/thermodynamics/thermodynamics-examples.tex')
-rw-r--r--Master/texmf-dist/doc/latex/thermodynamics/thermodynamics-examples.tex50
1 files changed, 46 insertions, 4 deletions
diff --git a/Master/texmf-dist/doc/latex/thermodynamics/thermodynamics-examples.tex b/Master/texmf-dist/doc/latex/thermodynamics/thermodynamics-examples.tex
index d061ecec6d9..60118041f0f 100644
--- a/Master/texmf-dist/doc/latex/thermodynamics/thermodynamics-examples.tex
+++ b/Master/texmf-dist/doc/latex/thermodynamics/thermodynamics-examples.tex
@@ -8,7 +8,7 @@
%%
%% This is a generated file.
%%
-%% Copyright (C) 2017-2018 by Karl D. Hammond
+%% Copyright (C) 2022-2023 by Karl D. Hammond
%%
%% Karl D. Hammond,
%% Department of Chemical Engineering
@@ -22,6 +22,7 @@
%% http://www.latex-project.org/lppl.txt
%% and version 1.3 or later is part of all distributions of LaTeX
%% version 2005/12/01 or later.
+%%^^A = C_i \gammamol_i \Henrymol_i
\documentclass{article}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath,amssymb}
@@ -30,6 +31,7 @@
\author{Karl D. Hammond}
\date{}
\begin{document}
+\NewThermodynamicProperty{B}{B}
\maketitle\noindent
The combined laws:
\begin{align*}
@@ -65,6 +67,33 @@ Some Maxwell reciprocity relations:
= -\Partial*{\St}{\Nt_i}{T,P,\allNsbut{i}}
= -\Spm_i
\end{gather*}
+Temporary changes of derivative delimiters:
+\begin{gather*}
+ \begin{thermobrackets}
+ \Partial*{\Vt}{T}{P,\allNs}
+ \end{thermobrackets}
+ \begin{thermobar}
+ = \PartialMixSecond*{\Gt}{T}{P}{\allNs}
+ \end{thermobar}
+ \begin{thermomolesrange}
+ = \PartialMixSecond*{\Gt}{P}{T}{\allNs}
+ \end{thermomolesrange}
+ \begin{thermobraces}
+ = -\Partial*{\St}{P}{T,\allNs}
+ \begin{thermoNOsubscripts}
+ \begin{thermomolesrange}
+ = -\Partial{\St}{P}{T,\allNs}
+ \end{thermomolesrange}
+ \end{thermoNOsubscripts}
+ \end{thermobraces}
+\end{gather*}
+Inline derivatives:
+\begin{gather*}
+ \mu_i = \Partialinline{\Gt}{\Nt_i}{T,P,\allNsbut{i}}
+ = \Partialinline{\Ft}{\Nt_i}{T,\Vt,\allNsbut{i}}
+ = \Partialinline{\Ht}{\Nt_i}{\St,P,\allNsbut{i}}
+ = \Partialinline{\Ut}{\Nt_i}{\St,\Vt,\allNsbut{i}}
+\end{gather*}
The heat capacities:
\begin{gather*}
\cV = T \Partial*{\Sm}{T}{\Vm,\allXs} = \Partial*{\Um}{T}{\Vm,\allXs}
@@ -137,7 +166,7 @@ Fugacity and related properties:
\\
a_i = \frac{\fmix_i}{\fstd_i}
= x_i \gamma_i
- \exp\left(\frac{1}{RT} \int_{\Pstd}^P \Vm_i(T,p) dp\right)
+ \exp\left(\frac{1}{RT} \int_{\Pstd}^P \Vm_i(T,p)\,dp\right)
\approx x_i \gamma_i
\\
\begin{split}
@@ -146,9 +175,9 @@ Fugacity and related properties:
= x_i \gammarat_i \Henryrat_i
= C_i \gammamol_i \Henrymol_i
= x_i \gamma_i \fsat_i
- \exp\left(\frac{1}{RT} \int_{\Psat_i}^P \Vm_i(T,p) dp\right)
+ \exp\left(\frac{1}{RT} \int_{\Psat_i}^P \Vm_i(T,p)\,dp\right)
\\ &= x_i \gamma_i \Psat_i \phisat_i
- \exp\left(\frac{1}{RT} \int_{\Psat_i}^P \Vm_i(T,p) dp\right)
+ \exp\left(\frac{1}{RT} \int_{\Psat_i}^P \Vm_i(T,p)\,dp\right)
\approx x_i \gamma_i \Psat_i
\end{split}
\end{gather*}
@@ -206,6 +235,19 @@ Excess and Residual (Departure) Properties:
\SE &= \Sm - \Sm^\IS &
\VRpm_k &= \Vpm_k - \Vpm_k^\IGM
\end{align*}
+Jacobians:
+\begin{gather*}
+ \Jacobian{\St,\Vt}{T,P} = \Jacobiandet{\St,\Vt}{T,P} \\
+ \Jacobian{f,g,h}{x,y,z} = \Jacobiandet[\displaystyle]{f,g,h}{x,y,z} \\
+ \Jacobian{h_1,\dots,h_k}{z_1,\dots,z_k} =
+ \Jacobiandet{h_1,\dots,h_k}{z_1,\dots,z_k} \\
+ \cP = T\Partial{\Sm}{T}{P}
+ = T\Jacobian{\Sm,P}{T,P}
+ = -T\Jacobian{\Sm,P}{T,\Vm} \Jacobian{T,\Vm}{T,P}
+ = -T\Jacobian{P,\Sm}{\Vm,\Sm} \Jacobian{\Vm,\Sm}{T,\Vm}
+ \Jacobian{T,\Vm}{T,P}
+ = \gamma \cV
+\end{gather*}
\end{document}
\endinput
%%