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author | Karl Berry <karl@freefriends.org> | 2023-11-17 22:02:57 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2023-11-17 22:02:57 +0000 |
commit | d750d4833a1999a7902080b4a55e3e89eead497d (patch) | |
tree | c5670d1d100bd424cfa1854a6713264cd21cf0ca /Master/texmf-dist/doc/latex/thermodynamics/thermodynamics-examples.tex | |
parent | 6719122c781ae5bcef2f225c8f5246f31dacf704 (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.tex | 50 |
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 %% |