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% Packages
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\usepackage{colortbl}           % For coloured tables
\usepackage{setspace}           % For line height
\usepackage{lastpage}           % Needed for total page number
\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{faabu}
\pdfinfo{
  /Title (kapittel-4-energibalansen.pdf)
  /Creator (Cheatography)
  /Author (faabu)
  /Subject (Kapittel 4 - Energibalansen Cheat Sheet)
}

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% This two commands together give roughly
% the right line height in the tables
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% Commands
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% Header and Footer
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\fancyhead{} % Set header to blank
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\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Kapittel 4 - Energibalansen Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{faabu} via \textcolor{DarkBackground}{\uline{cheatography.com/170836/cs/35843/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}faabu \\
  \uline{cheatography.com/faabu} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 3rd December, 2022.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
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  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{x{1.36 cm} x{6.64 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Energibalansen}}  \tn
% Row 0
\SetRowColor{LightBackground}
\seqsplit{Generelt} & ∆E = ∆U \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
 & ∆𝐸 = 𝐸`𝑓` − 𝐸`0` = 𝐸`𝑖𝑛𝑛` − 𝐸`𝑢𝑡` + 𝑄 + 𝑊 \tn 
% Row Count 5 (+ 3)
% Row 2
\SetRowColor{LightBackground}
 & ∆U = U`𝑓` − U`0` = U`𝑖𝑛𝑛` − U`𝑢𝑡` + 𝑄 + 𝑊 \tn 
% Row Count 8 (+ 3)
% Row 3
\SetRowColor{white}
 & 𝑊 =	𝑊`𝑓𝑙𝑜𝑤` + 𝑊`𝑛` \tn 
% Row Count 10 (+ 2)
% Row 4
\SetRowColor{LightBackground}
 & ∆U = H`inn` - H`ut` + Q + W`n` \tn 
% Row Count 11 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.04 cm} x{4.96 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Arbeid}}  \tn
% Row 0
\SetRowColor{LightBackground}
Generelt & 𝑊 =	𝑊`flow` + 𝑊`∆V` + 𝑊`𝑠` + 𝑊`𝑒𝑙` + \seqsplit{𝑊`𝑎𝑛𝑛𝑒𝑡`} \tn 
% Row Count 4 (+ 4)
% Row 1
\SetRowColor{white}
\seqsplit{Strømningsarbeid} & 𝑊`flow` =  \seqsplit{𝒑`𝒊𝒏𝒏`𝑽`𝒊𝒏𝒏`} − \seqsplit{𝒑`𝒖𝒕`𝑽`𝒖𝒕`} \tn 
% Row Count 8 (+ 4)
% Row 2
\SetRowColor{LightBackground}
Nyttig non-flow arbeid & 𝑊`𝑛` = 𝑊`∆𝑉` + 𝑊`𝑠` + 𝑊`𝑒𝑙`+ \seqsplit{𝑊`𝑎𝑛𝑛𝑒𝑡`} \tn 
% Row Count 12 (+ 4)
% Row 3
\SetRowColor{white}
Mekanisk akselarbeid & 𝑊`𝑠` \tn 
% Row Count 14 (+ 2)
% Row 4
\SetRowColor{LightBackground}
Elektrokjemisk arbeid & 𝑊`𝑒𝑙` \tn 
% Row Count 16 (+ 2)
% Row 5
\SetRowColor{white}
Endring i systemets volum & 𝑊`∆𝑉` \tn 
% Row Count 18 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{1.76 cm} x{6.24 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Strømmens entalpi}}  \tn
% Row 0
\SetRowColor{LightBackground}
\seqsplit{Definisjon} & summen av indre energi (U) og strømningsarbeid (W`flow`) \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\seqsplit{Beregninger} & H`inn` = U`inn` + p`inn`V`inn` \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
 & H`ut` = U`ut` + p`ut`V`ut` \tn 
% Row Count 5 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.72 cm} x{5.28 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Stasjonær adiabatisk prosess uten akselarbeid}}  \tn
% Row 0
\SetRowColor{LightBackground}
Definisjon & Adiabatisk: Q = 0 \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
 & Akselarbeid: W`s` = 0 \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Beregninger & H`inn` = H`ut` \tn 
% Row Count 3 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Spesialtilfelle I: Lukket system}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/faabu_1670014717_111.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Ingen masseutveksling}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.08 cm} x{5.92 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Spesialtilfelle II: Isolert system}}  \tn
% Row 0
\SetRowColor{LightBackground}
Isolert system & ingen utveksling av  arbeid eller varme med omgivelsene \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
 & 𝑄 = 𝑊 = 0 \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
 & 𝑈`𝑓` = 𝑈`0` \tn 
% Row Count 4 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Spesialtilfelle III: Ingen akkumulering}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/faabu_1670015021_Bilde2.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Systemets variable endres ikke med tiden}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Energibalansen med reaksjon}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/faabu_1670023680_Bilde4.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.8 cm} x{5.2 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Entalpiberegninger: blandeprosesser}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Standardmetoden}} & 1. Sett opp massebalanse \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
 & 2. Sett opp den ekvivalente balansen der H`inn`= H`ut` \tn 
% Row Count 5 (+ 3)
% Row 2
\SetRowColor{LightBackground}
 & 3. Utvid med mC`p`(T`i` - T`ref`) \tn 
% Row Count 7 (+ 2)
% Row 3
\SetRowColor{white}
 & 4. Løs for den ukjente \tn 
% Row Count 8 (+ 1)
% Row 4
\SetRowColor{LightBackground}
{\bf{Direkte evaluering}} & 1. Sett opp entalpiendering for delprosesser \tn 
% Row Count 10 (+ 2)
% Row 5
\SetRowColor{white}
 & 2. Sett opp H`inn` - H`ut` = 0 \tn 
% Row Count 12 (+ 2)
% Row 6
\SetRowColor{LightBackground}
 & 3. Løs for den ukjente \tn 
% Row Count 13 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{1.6 cm} x{6.4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Beregninger: blandingsvarme}}  \tn
% Row 0
\SetRowColor{LightBackground}
Formel & ∆T = T`mix` - T`0` \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
 & ∆T= \seqsplit{−∆`𝑚𝑖𝑥`𝐻(𝑇`0`)} / C`p` \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
OBS & Husk at \seqsplit{∆`𝑚𝑖𝑥`𝐻`m`(𝑇`0`)} må multipliseres med antall mol løst toff \tn 
% Row Count 6 (+ 3)
% Row 3
\SetRowColor{white}
 & \seqsplit{∆`𝑚𝑖𝑥`𝐻(𝑇`0`)} = \seqsplit{∆`𝑚𝑖𝑥`𝐻`m`(𝑇`0`)} * n (løst stoff) \tn 
% Row Count 9 (+ 3)
% Row 4
\SetRowColor{LightBackground}
\seqsplit{Antakelser} & 1. Antar varmekapasitet som for vann \tn 
% Row Count 11 (+ 2)
% Row 5
\SetRowColor{white}
 & 2. Antar lik temperatur før blanding \tn 
% Row Count 13 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Beregninger: forbrenningsreaksjoner}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/faabu_1670084148_Bilde7.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{p{1.04 cm} x{6.96 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Beregninger: forbrenning med massebalanse}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{1.}} & Hvis ikke oppgitt, sett antall mol som basis \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
{\bf{2.}} & Sett opp massebalanser \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
{\bf{3.}} & Beregn reaksjonsomfang og sammensetning utstrøm \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
 & 𝑛`𝐴` = 𝑛`𝐴,0` + 𝜈`𝐴` 𝜉 \tn 
% Row Count 8 (+ 2)
% Row 4
\SetRowColor{LightBackground}
4. & Bruk til å beregne ∆𝐻`𝑟𝑥𝑛` (se egen formel) \tn 
% Row Count 10 (+ 2)
% Row 5
\SetRowColor{white}
 & Må i tillegg ha info om C`p` og ∆𝐻\textasciicircum{}0\textasciicircum{} \tn 
% Row Count 12 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.72 cm} x{5.28 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Ventil: Isentalpsik trykkavspenning}}  \tn
% Row 0
\SetRowColor{LightBackground}
Isentalpisk & Prosess uten endringer i entalpi og ingen varmeoverføring \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
 & Q = 0 og H`2` = H`1` \tn 
% Row Count 4 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Ideell gass & T`1` = T`2` \tn 
% Row Count 5 (+ 1)
% Row 3
\SetRowColor{white}
Reell gass & T`1` ≠ T`2` \tn 
% Row Count 6 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\seqsplit{Joule-Thompson-effekt} & Når reell gass ekspanderes i en ventil, fås temperaturfall \tn 
% Row Count 9 (+ 3)
% Row 5
\SetRowColor{white}
Flash-effekt & Når væske ekspanderes i en ventil, fås fordamping og temperaturfall \tn 
% Row Count 12 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}