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% Document Info
\author{xsgirl99}
\pdfinfo{
  /Title (313-exam-3.pdf)
  /Creator (Cheatography)
  /Author (xsgirl99)
  /Subject (313 Exam 3 Cheat Sheet)
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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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    \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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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{313 Exam 3 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{xsgirl99} via \textcolor{DarkBackground}{\uline{cheatography.com/26903/cs/9256/}}}
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\noindent
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}xsgirl99 \\
  \uline{cheatography.com/xsgirl99} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 25th September, 2016.\\
   Updated 9th December, 2016.\\
   Page {\thepage} of \pageref{LastPage}.
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  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
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\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Laws}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Zeroth Law: If system x = system y \& system y = system z, then system x = system z. (Transitive)} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{First Law: Internal energy(ΔU) of an isolated system is constant. No heat lost, only transferred.} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Second Law: The entropy of any isolated system always increases.} \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Third Law: The entropy of a system approaches a constant value as the temperature approaches absolute zero.} \tn 
% Row Count 9 (+ 3)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Cyclic Rule: ({\emph{d}}P/{\emph{d}}T)`v`({\emph{d}}T/{\emph{d}}V)`p`({\emph{d}}V/{\emph{d}}P)`T`= -1} \tn 
% Row Count 11 (+ 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}{Definitions}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Adiabatic: No transfer of heat or matter} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Diathermal: Heat allowed to transfer, no matter transfer. Can transfer energy in the form of work} \tn 
% Row Count 3 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Enthalpy(ΔH): Amount of heat content used or released in a system at constant pressure} \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Irreversible: A process that cannot return both the system and the surroundings to their original conditions.} \tn 
% Row Count 8 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Exam 2}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{ΔU=m`s`/M`s` ΔU`comb`+m`H2O`/M`H2O` C`v,m`(H2O)ΔT+ΔTC`calorimeter`} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{ΔH\textasciicircum{}o\textasciicircum{}=m`salt`/M`salt` ΔH\textasciicircum{}o\textasciicircum{}`solution`+m`H2O`/M`H2O` C`p,m`(H2O)ΔT+ΔTC`calorimeter`} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{S=k ln(W) W=\#of states} \tn 
% Row Count 5 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Efficiency = 1-|q`cd`|/|q`ab`|  \textless{}1} \tn 
% Row Count 6 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{ΔH\textasciicircum{}o\textasciicircum{}`rt`=ΔH\textasciicircum{}o\textasciicircum{}`298`+∫ΔC`p`(T) dT from 298 to T} \tn 
% Row Count 8 (+ 2)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{ΔH`combustion` = ΔU`combustion`+Δ(PV)} \tn 
% Row Count 9 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{For Solids \& Liquids: ΔH\textasciitilde{}= ΔU} \tn 
% Row Count 10 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\seqsplit{Δs=-nRln(P`f`/P`i`)+∫nC`pm`/T} dT  for P`i` to P`f`} \tn 
% Row Count 12 (+ 2)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\seqsplit{Δs=nRln(V`f`/V`i`)+∫nC`vm`/T} dT  for V`i` to V`f`} \tn 
% Row Count 14 (+ 2)
% Row 9
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Isolated System: ΔS=q`p`(1/T`1` - 1/T`2`)} \tn 
% Row Count 15 (+ 1)
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Isothermal, Ideal: ΔS=nRln(V`f`/V`i`)} \tn 
% Row Count 16 (+ 1)
% Row 11
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\seqsplit{ΔS`total`=ΔS+ΔS`surroundings`}} \tn 
% Row Count 17 (+ 1)
% Row 12
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{ΔG=nRT Σ x`i`ln(x`i`)  x`i` is mole fraction} \tn 
% Row Count 18 (+ 1)
% Row 13
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{ΔG = TΔS`total`} \tn 
% Row Count 19 (+ 1)
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\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}{Internal Energy (ΔU)}}  \tn
% Row 0
\SetRowColor{LightBackground}
General & ΔU=q+w \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Constant Volume & ΔU=C`v`ΔT = q`v` \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Adiabatic, Reversible & ΔU= w = n(C`pm`-R)ΔT = nC`vm`ΔT \tn 
% Row Count 4 (+ 2)
% Row 3
\SetRowColor{white}
Ideal & ΔU=nC`vm`ΔT \tn 
% Row Count 5 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.52 cm} x{4.48 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Enthalpy (ΔH) (State Fxn)}}  \tn
% Row 0
\SetRowColor{LightBackground}
General & ΔH= ΔU+Δ(PV) = ΔU+nRΔT \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Constant Pressure & ΔH= C`p`ΔT \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Ideal & ΔH = q`p` \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
Constant Volume & ΔH= nC`pm`ΔT + VΔP \tn 
% Row Count 5 (+ 1)
% Row 4
\SetRowColor{LightBackground}
Even More General & {\emph{d}}H= ({\emph{d}}H/{\emph{d}}P)`T` dT + ({\emph{d}}H/{\emph{d}}T)`P` dP \tn 
% Row Count 7 (+ 2)
% Row 5
\SetRowColor{white}
Liquids \& Solids & ({\emph{d}}H/{\emph{d}}P)`T` = V(1-Tβ) \tn 
% Row Count 9 (+ 2)
% Row 6
\SetRowColor{LightBackground}
Constant Pressure, closed system & ΔH= \seqsplit{(U`f`+P`f`V`f`)-(U`i`+P`i`V`i`)} \tn 
% Row Count 11 (+ 2)
% Row 7
\SetRowColor{white}
Isobaric & ΔH= n∫C`pm`(T) dT = nC`pm`ΔT \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}{Exam 2 Material}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{S`m`(T)=S`m`(0\textasciicircum{}o\textasciicircum{}k) +∫C`pm`/T dT(solid 0-T`f`) +ΔH`fus`/T`f` + ∫C`pm`/T dT(liquid T`f`-T`b`) +ΔH`vap`/T`b` ∫C`pm`/T dT(gas T`b`-T) `} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{For Ideal Gases: \seqsplit{ΔS`m`=Rln(V`f`/V`i`)=-Rln(P`f`/P`i`)}} \tn 
% Row Count 5 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{ΔG(T`2`)/T`2`= \seqsplit{ΔG(T`1`)/T`1`+ΔH(T`1`)(1/T`2`-1/T`1`)}} \tn 
% Row Count 7 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Max Work: Reversible, adiabatic, isothermal} \tn 
% Row Count 8 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Hess's Law: Total Enthalpy change is independent of \# of steps(path-independent).} \tn 
% Row Count 10 (+ 2)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{ΔA = ΔU-TΔS = ΔH-nRT (Hemholtz)} \tn 
% Row Count 11 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{for ΔG\textasciicircum{}o\textasciicircum{}`r` only include non-pure substances.} \tn 
% Row Count 12 (+ 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}{Exam 3}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{ΔG`R` = ΔG°`R`+RT ln(Q`P`)} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{ln(K`P`) = -ΔG°`R`/RT} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{K`x`=K`P`(P/P°)\textasciicircum{}-ΔV\textasciicircum{}} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{dA = 𝛾 dσ     gamma is surface tension} \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Work = 8pi𝛾r dr} \tn 
% Row Count 5 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Force = 8pi𝛾r} \tn 
% Row Count 6 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{h(capillary rise/depression) = 2𝛾/𝞺gr} \tn 
% Row Count 7 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{𝓾`B`=𝓾°`B`+RTln(𝛾{[}B{]})   gamma is activity coefficient} \tn 
% Row Count 9 (+ 2)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{ΔG`R` = ΔG°`R`-2.303vRT(pH)} \tn 
% Row Count 10 (+ 1)
% Row 9
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{q`x` = kA(T`si`-T`so`)/L} \tn 
% Row Count 11 (+ 1)
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{q''`x`= -k dT/dx = q`x`/A} \tn 
% Row Count 12 (+ 1)
% Row 11
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Ė`in`+Ė`g`-Ė`out` = Ė`internal`} \tn 
% Row Count 13 (+ 1)
% Row 12
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{q`12` = εσA(T`1`\textasciicircum{}4\textasciicircum{}-T`2`\textasciicircum{}4\textasciicircum{}) - Heat xchange via radiation b/t 2 surfaces} \tn 
% Row Count 15 (+ 2)
% Row 13
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{q''`s` = h(T`s`-T`∞`) - Newton's Law of Cooling} \tn 
% Row Count 16 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


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

\end{document}