%% Created by Maple V Release 4 (LINUX INTEL UNIX)
%% Source Worksheet: tpd7.mws
%% Generated: Tue Dec 12 13:08:37 2000
\documentclass{article}
\usepackage{maple2e}
\DefineParaStyle{Maple Output}
\DefineCharStyle{2D Math}
\DefineCharStyle{2D Output}
\begin{document}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{eq[1]:= dS = (C[P]/T)*dT -V*alpha[P]*dP:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{eq[2]:= dV =  V*alpha[P]*dT -
V*beta[T]*dP:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{eq[3]:= dU =  T*dS - P*dV:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{eq[4]:= dH =  T*dS + V*dP:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{eq[5]:= dG = -S*dT + V*dP:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{eq[6]:= dA = -S*dT - P*dV:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{eq[7]:= dCC= -dP + m*dT:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{equs:=\{eq[1],eq[2],eq[3],eq[5]\}:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{Variables:=\{dS,dV,dT,dP,dU,dG\};}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\[
{\it Variables} := \{{\it dS}, \,{\it dT}, \,{\it dP}, \,{\it dV}
, \,{\it dU}, \,{\it dG}\}
\]
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{DepVars:=\{dG,dS,dV,dP\};}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\[
{\it DepVars} := \{{\it dS}, \,{\it dP}, \,{\it dV}, \,{\it dG}\}
\]
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{IndepVars:=\{dT,dU\};}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\[
{\it IndepVars} := \{{\it dT}, \,{\it dU}\}
\]
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{n_V:=6: n_D:=4: n_I:=2:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{for i from 1 to n_D do n[i]:=DepVars[i] od:
for j from 1 to n_I do d[j]:=IndepVars[j] od: 
Symb:=matrix(n_D,n_I,(i,j)->n[i]/d[j]):}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{s:=solve(equs,DepVars):}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{assign(s);}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{for i from 1 to n_D do nn[i]:=DepVars[i]
od:}{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{M2:=matrix(n_D,n_I,(i,j)->diff(nn[i],d[j])):}
{%
}
\end{mapleinput}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{evalm(Symb)=evalm(M2);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\begin{eqnarray*}
\lefteqn{ \left[ 
{\begin{array}{cc}
{\displaystyle \frac {{\it dS}}{{\it dT}}}  & {\displaystyle 
\frac {{\it dS}}{{\it dU}}}  \\ [2ex]
{\displaystyle \frac {{\it dP}}{{\it dT}}}  & {\displaystyle 
\frac {{\it dP}}{{\it dU}}}  \\ [2ex]
{\displaystyle \frac {{\it dV}}{{\it dT}}}  & {\displaystyle 
\frac {{\it dV}}{{\it dU}}}  \\ [2ex]
{\displaystyle \frac {{\it dG}}{{\it dT}}}  & {\displaystyle 
\frac {{\it dG}}{{\it dU}}} 
\end{array}}
 \right] = \left[ 
{\begin{array}{cc}
 - {\displaystyle \frac { - {C_{P}}\,P\,{\beta _{T}} + {\alpha _{
P}}^{2}\,T\,P\,V}{{\rm \%1}\,T}}  &  - {\displaystyle \frac {{
\alpha _{P}}}{{\rm \%1}}}  \\ [2ex]
{\displaystyle \frac { - {C_{P}} + P\,V\,{\alpha _{P}}}{V\,{\rm 
\%1}}}  & {\displaystyle \frac {1}{V\,{\rm \%1}}}  \\ [2ex]
 - {\displaystyle \frac {{\alpha _{P}}^{2}\,T\,V - {C_{P}}\,{
\beta _{T}}}{{\rm \%1}}}  &  - {\displaystyle \frac {{\beta _{T}}
}{{\rm \%1}}}  \\ [2ex]
{\displaystyle \frac {S\,{\alpha _{P}}\,T - S\,P\,{\beta _{T}} - 
{C_{P}} + P\,V\,{\alpha _{P}}}{{\rm \%1}}}  & {\displaystyle 
\frac {1}{{\rm \%1}}} 
\end{array}}
 \right] } \\
 & & {\rm \%1} :=  - {\alpha _{P}}\,T + P\,{\beta _{T}}
\mbox{\hspace{87pt}}
\end{eqnarray*}
\end{maplelatex}

\end{maplegroup}
\begin{maplegroup}
\begin{mapleinput}
\mapleinline{active}{1d}{der[U]:=diff(dG,dT);}{%
}
\end{mapleinput}

\mapleresult
\begin{maplelatex}
\[
{{\it der}_{U}} := {\displaystyle \frac {S\,{\alpha _{P}}\,T - S
\,P\,{\beta _{T}} - {C_{P}} + P\,V\,{\alpha _{P}}}{ - {\alpha _{P
}}\,T + P\,{\beta _{T}}}} 
\]
\end{maplelatex}

\end{maplegroup}
\end{document}
%% End of Maple V Output
