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authorKarl Berry <karl@freefriends.org>2022-04-30 20:02:45 +0000
committerKarl Berry <karl@freefriends.org>2022-04-30 20:02:45 +0000
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treece7e4ad794501767b7967f415d6ce5e648dd8e23 /Master/texmf-dist/doc/latex/thermodynamics
parente1738ea0853a78ce457cffe0611bcee5e2062154 (diff)
thermodynamics (30apr22)
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diff --git a/Master/texmf-dist/doc/latex/thermodynamics/README.md b/Master/texmf-dist/doc/latex/thermodynamics/README.md
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+thermodynamics - A package for chemical engineers and others
+=============================================================
+
+Thermodynamics texts (textbooks, articles, and so forth) are typically filled
+with underlined and overlined symbols, partial derivatives surrounded by
+delimiters and containing subscripts, sums over multiple components, and a
+myriad of symbols, including superscript and subscript modifiers. This package
+provides a robust, flexible set of macros to define notation for symbols,
+partial derivatives, sums, and products frequently encountered in mixture
+thermodynamics. Changing one's notes from one textbook to another or from one
+notation style to another can be achieved relatively easily by changing package
+options, without any changes to the user's code (other than perhaps adjusting
+line breaks).
+
+Installation
+------------
+
+The package is suppled in `dtx` format with an accompanying `ins` file to
+install the package. Run `latex thermodynamics.ins` to extract the package;
+instructions for building the documentation are included in the `ins` file.
+
+This package requires the `amstext` package.
+
+Typesetting the documentation requires several other packages:
+ - `geometry`
+ - `fontenc`
+ - `textcomp`
+ - `amsmath`
+ - `pxfonts`
+ - `array`
+ - `booktabs`
+ - `footmisc`
+ - `caption`
diff --git a/Master/texmf-dist/doc/latex/thermodynamics/thermodynamics-examples.tex b/Master/texmf-dist/doc/latex/thermodynamics/thermodynamics-examples.tex
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+%%
+%% This is file `thermodynamics-examples.tex',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% thermodynamics.dtx (with options: `example')
+%%
+%% This is a generated file.
+%%
+%% Copyright (C) 2017-2018 by Karl D. Hammond
+%%
+%% Karl D. Hammond,
+%% Department of Chemical Engineering
+%% University of Missouri
+%% Contact: hammondkd@missouri.edu
+%%
+%% This work may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%% 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.
+\documentclass{article}
+\usepackage[margin=1in]{geometry}
+\usepackage{amsmath,amssymb}
+\usepackage{thermodynamics}
+\title{Examples to Accompany the \textsf{thermodynamics} Package}
+\author{Karl D. Hammond}
+\date{}
+\begin{document}
+\maketitle\noindent
+The combined laws:
+\begin{align*}
+ d\Et &= d\Ut + d\left(\frac12 m v^2\right) - d(m\phi) \\
+ d\Ut &= \dbar\Qt + \dbar\Wt + \Um d\Nt
+ = \dbar\Qt - P d\Vt + \Hm d\Nt
+ \\ &= \Partial*{\Ut}{\St}{\Vt,\allNs} d\St
+ + \Partial*{\Ut}{\Vt}{\St,\allNs} d\Vt
+ + \sumall_i \Partial*{\Ut}{\Nt_i}{\Vt,\St,\allNsbut{i}} d\Nt_i
+ \\ &= T d\St - P d\Vt + \sumall_i \mu_i d\Nt_i
+\end{align*}
+With surfaces present:
+\begin{gather*}
+ d\Ut = T d\St - P d\Vt + \sigma d\At + \sumall_i \mu_i d\Nt_i \\
+ d\Ht = T d\St + \Vt dP + \sigma d\At + \sumall_i \mu_i d\Nt_i \\
+ d\Ft = -\St dT - P d\Vt + \sigma d\At + \sumall_i \mu_i d\Nt_i \\
+ d\Gt = -\St dT + \Vt dP + \sigma d\At + \sumall_i \mu_i d\Nt_i \\
+ d\Lt = -\St dT - P d\Vt + \sigma d\At - \sumall_i \Nt_i d\mu_i \\
+ \Bt = \Ut + P\Vt - T\St - \sigma\At \\
+ d\Bt = -\St dT + \Vt dP - \At d\sigma + \sumall_i \mu_i d\Nt_i \\
+ \mu_i = \Bpm_i = \Gpm_i + \sigma \Apm_i
+\end{gather*}
+Some Maxwell reciprocity relations:
+\begin{gather*}
+ \Partial*{\Vt}{T}{P,\allNs}
+ = \PartialMixSecond*{\Gt}{T}{P}{\allNs}
+ = \PartialMixSecond*{\Gt}{P}{T}{\allNs}
+ = -\Partial{\St}{P}{T,\allNs}
+\\
+ \Partial*{\Gpm_i}{T}{P,\allXs}
+ = \PartialMixSecond*{\Gt}{T}{\Nt_i}{P,\allNsbut{i}}
+ = \PartialMixSecond*{\Gt}{\Nt_i}{T}{P,\allNsbut{i}}
+ = -\Partial*{\St}{\Nt_i}{T,P,\allNsbut{i}}
+ = -\Spm_i
+\end{gather*}
+The heat capacities:
+\begin{gather*}
+ \cV = T \Partial*{\Sm}{T}{\Vm,\allXs} = \Partial*{\Um}{T}{\Vm,\allXs}
+ = -T\PartialSecond{\Fm}{T}{\Vm,\allXs}
+ \\
+ \cP^\IGM = T \Partial*{\Sm^\IGM}{T}{P,\allYs}
+ = \Partial*{\Hm^\IGM}{T}{P,\allYs}
+ \begin{thermobrackets}
+ = -T\PartialSecond{\Gm^\IGM}{T}{P,\allYs}
+ \end{thermobrackets}
+ \\
+ \cVt = T \Partial*{\St}{T}{\Vt,\allNs} = \Partial*{\Ut}{T}{\Vt,\allNs}
+ \begin{thermobraces}
+ = -T\PartialSecond{\Ft}{T}{\Vm,\allNs}
+ \end{thermobraces}
+ \\
+ \begin{thermobar}
+ \cPt = T \Partial*{\St}{T}{P,\allNs} = \Partial*{\Ht}{T}{P,\allNs}
+ = -T\PartialSecond{\Gt}{T}{P,\allNs}
+ \end{thermobar}
+ \\
+ \cVs = T \Partial*{\Ss}{T}{\Vs,\allWs} = \Partial*{\Us}{T}{\Vs,\allWs}
+ \begin{thermoplain}
+ = -T\PartialSecond{\Fs}{T}{\Vs,\allWs}
+ \end{thermoplain}
+ \\
+ \cPs = T \Partialbigg*{\Ss}{T}{P,\allWs} = \Partialbigg*{\Hs}{T}{P,\allWs}
+ = -T\PartialSecondbigg{\Gs}{T}{P,\allWs}
+ \\
+\begin{split}
+ \cPpm_i &= \Partial*{\cPt}{\Nt_i}{T,P,\allNsbut{i}}
+ = T \PartialMixSecond*{\St}{\Nt_i}{T}{P,\allNsbut{i}}
+ = T \PartialMixSecond*{\St}{T}{\Nt_i}{P,\allNsbut{i}}
+ \\ &= T \Partial*{\Spm_i}{T}{P,\allXs}
+ = \Partial*{\Hpm_i}{T}{P,\allXs}
+ = \PartialMixSecond*{\Ht}{T}{\Nt_i}{P,\allNsbut{i}}
+ = \PartialMixSecond*{\Ht}{\Nt_i}{T}{P,\allNsbut{i}}
+ \\ &= -T\PartialSecond*{\Gpm_i}{T}{P,\allXs}
+ = -T\Partial{{}^3 \Gt}{T^2\partial \Nt_i}{P,\allNsbut{i}}
+\end{split}
+\end{gather*}
+Other measurable quantities:
+\begin{align*}
+ \alphaS &= \frac{1}{\Vm} \Partial{\Vm}{T}{\Sm} &
+ \alphaP &= \frac{1}{\Vm} \Partial{\Vm}{T}{P} \\
+ \kappaS &= -\frac{1}{\Vm} \Partial{\Vm}{P}{\Sm} &
+ \kappaT &= -\frac{1}{\Vm} \Partial{\Vm}{P}{T}
+\end{align*}
+The chemical potential, fugacity, and activity:
+\[ \mu_i = \Gpm_i = \Gm_i^\std + RT \ln a_i
+ = \Gm_i^\std + RT\ln\left(\frac{\fmix_i}{\fstd_i}\right) \]
+Equilibrium in a chemical reaction:
+\[ \sumall_i \nu_i \mu_i = 0
+ \Rightarrow
+ \exp\left(\frac{-\Delta\Gm^\std}{RT}\right) = K = \prodall_i a_i^{\nu_i} \]
+Partial molar quantities:
+\begin{align*}
+ \Hpm{i} &= \Partial*{\Ht}{\Nt_i}{T,P,\allNsbut{i}}
+ = \Hm + \Nt \Partial*{\Hm}{\Nt_i}{T,P,\allNsbut{i}}
+ \\ &= \Hm + \Partial*{\Hm}{x_i}{T,P,\allXsbut{i}}
+ - \sumallbutlast_j x_j \Partial*{\Hm}{x_j}{T,P,\allXsbut{j}}
+ = \Partial*{\Hm}{x_i}{T,P,\allXsbut{i}} + \Hpm_\ncomponents
+\end{align*}
+\[ \Vpm_i = \Partial{\Vt}{\Nt_i}{T,P,\allNsbut{i}} \]
+Fugacity and related properties:
+\begin{gather*}
+ \Gpm_i = \mu_i
+ = \Gm_i^\std(T) + RT\ln a_i
+ = \Gm_i^\std(T) + RT\ln\left(\frac{\fmix_i}{\fstd_i}\right)
+ \\
+ 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)
+ \approx x_i \gamma_i
+ \\
+ \begin{split}
+ \fmix_i &= x_i \phimix_i P
+ = x_i \gamma_i \fpure_i = x_i \gamma_i \phipure_i P
+ = 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)
+ \\ &= x_i \gamma_i \Psat_i \phisat_i
+ \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*}
+Chemical Equilibria:
+\begin{gather*}
+ \Deltarxn\Hm^\std = \sumall_i \nu_i \Deltaf\Hm_i^\std \\
+ \Deltarxn\Gm^\std = \sumall_i \nu_i \Deltaf\Gm_i^\std
+ = \sumall_i \nu_i \mu_i^\std \\
+ \Deltarxn\cP^\std = \sumall_i \nu_i \cP_i^\std \\
+ \mu_i = \mu_i^\std + RT\ln a_i \\
+ a_i = \begin{cases}
+\displaystyle
+ \frac{y_i \phimix_i P}{\Pstd} \approx \frac{y_i P}{\Pstd}
+ & \text{(gases)} \\
+\rule{0pt}{5ex}%
+\displaystyle
+ x_i \gamma_i \exp\left(\frac{1}{RT} \int_{\Pstd}^P \Vm_i(T,p)\,dp\right)
+ \approx
+ x_i \gamma_i \exp\left(\frac{\Vm_i(P-\Pstd)}{RT}\right)
+ \approx x_i \gamma_i \approx 1
+ & \text{(solids, solvents)} \\
+\displaystyle
+\rule{0pt}{5ex}%
+ \frac{C_i \gammamol_i}{C_i^\std}
+ \exp\left(\frac{1}{RT}
+ \int_{\Pstd}^P \Vpm_i^\infty(T,p,\allXs)\,dp\right)
+ \approx
+ \frac{C_i \gammamol_i}{C_i^\std} \approx \frac{C_i}{C_i^\std}
+ & \text{(solutes)}
+ \end{cases}
+\end{gather*}
+Phase change properties:
+\begin{gather*}
+ \Deltafus\Sm = \Sm^L - \Sm^S \\
+ \Deltasub\Vm = \Vm^V - \Vm^S \\
+ \Deltavap\Gm = \Gm^V - \Gm^L
+\end{gather*}
+Specific properties:
+\newcommand*{\Btilde}[2][]{\widetilde{B}_{#2}^{#1}}
+\[ \Btilde{j} \equiv \Partial{\Bt}{m_j}{T,\Vs,\allMsbut[i]{j}} \]
+and thus
+\[ \Btilde{i}
+ = \frac{\Bpm{i}}{M_i}
+ + \Biggl(\Vs - \frac{\Vpm_i}{M_i}\Biggr)
+ \Partial*{\Bs}{\Vs}{T,\allMs}
+ = \frac{\Bpm{i}}{M_i}
+ + \Biggl(\Vs - \frac{\Vpm_i}{M_i}\Biggr)
+ \Partial{\Bs}{\Vs}{T,m,\allWs} \]
+and
+\[ \Bs = \sumall_i w_i \Btilde{i}. \]
+Excess and Residual (Departure) Properties:
+\begin{align*}
+ \HR &= \Hm - \Hm^\IG &
+ \FR &= \Fm - \Fm^\IGM \\
+ \SE &= \Sm - \Sm^\IS &
+ \VRpm_k &= \Vpm_k - \Vpm_k^\IGM
+\end{align*}
+\end{document}
+\endinput
+%%
+%% End of file `thermodynamics-examples.tex'.
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