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author | Karl Berry <karl@freefriends.org> | 2022-04-30 20:02:45 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2022-04-30 20:02:45 +0000 |
commit | 3bf07308bf7627c8c23570e03f2bf8ae7058c8c1 (patch) | |
tree | ce7e4ad794501767b7967f415d6ce5e648dd8e23 /Master/texmf-dist/doc/latex | |
parent | e1738ea0853a78ce457cffe0611bcee5e2062154 (diff) |
thermodynamics (30apr22)
git-svn-id: svn://tug.org/texlive/trunk@63188 c570f23f-e606-0410-a88d-b1316a301751
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-rw-r--r-- | Master/texmf-dist/doc/latex/thermodynamics/README.md | 33 | ||||
-rw-r--r-- | Master/texmf-dist/doc/latex/thermodynamics/thermodynamics-examples.tex | 212 | ||||
-rw-r--r-- | Master/texmf-dist/doc/latex/thermodynamics/thermodynamics.pdf | bin | 0 -> 201715 bytes |
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diff --git a/Master/texmf-dist/doc/latex/thermodynamics/README.md b/Master/texmf-dist/doc/latex/thermodynamics/README.md new file mode 100644 index 00000000000..ec0d2d50011 --- /dev/null +++ b/Master/texmf-dist/doc/latex/thermodynamics/README.md @@ -0,0 +1,33 @@ +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 new file mode 100644 index 00000000000..d061ecec6d9 --- /dev/null +++ b/Master/texmf-dist/doc/latex/thermodynamics/thermodynamics-examples.tex @@ -0,0 +1,212 @@ +%% +%% 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'. diff --git a/Master/texmf-dist/doc/latex/thermodynamics/thermodynamics.pdf b/Master/texmf-dist/doc/latex/thermodynamics/thermodynamics.pdf Binary files differnew file mode 100644 index 00000000000..28957964eb7 --- /dev/null +++ b/Master/texmf-dist/doc/latex/thermodynamics/thermodynamics.pdf |