% $BI=Bj(B: $B%(%s%H%m%T!<$N$:$l(B
%
% $BMzNr(B: 2004-07-03 $B?y;39L0lO/(B


\chapter{$B%(%s%H%m%T!<$N$:$l(B}

$BK\>O$G$O(B, $B$"$k(B 2 $BAj$,AjJ?9U$N>uBV$K$"$k:]$K(B, $B$=$l$>$l$NAj$N%(%s%H%m%T!<(B
$B$,Ey$7$/$J$k$+H]$+$r8!F$$9$k(B. $BJ?9U>uBV$G$O$=$l$>$l$NAj$N2=3X%]%F%s%7%c%k(B
$B$,Ey$7$$(B. $B%(%s%H%m%T!<$O2=3X%]%F%s%7%c%k$N29EYHyJ,$H$7$FI=8=$G$-$k$N$G(B, 
$B2=3X%]%F%s%7%c%k$,Ey$7$/$F$b79$-$O0[$J$k2DG=@-$,$"$k(B. 

$B<B:]$K?tCM7W;;$7$?7k2L$r(B \Dfigref{entr:entr_gap} $B$K<($9(B. $B$3$N7W;;$K$*$$(B
$B$F7O$K4^$^$l$k2=3X<o$O(B H$_2$(g), He(g), H$_2$O(g), NH$_3$(g), H$_2$O(l),
NH$_3$(l), $B05NO$O(B 1551515.125 Pa, $B85AGNL$O6E=L@-@.J,$K$D$$$FB@M[AH(B
$B@.$N(B 10 $BG\$K$7$F$"$k(B. \Dfigref{entr:entr_gap} $B$K<($7$?29EYNN0h$O$A$g$&$I(B
$B%"%s%b%K%"?eMO1U$N@8$8$k29EYNN0h$G$"$k$,(B, $B%"%s%b%K%"?eMO1U$H:.9g5$BN$N%((B
$B%s%H%m%T!<$K0c$$$,$"$k$?$a$K(B, $B%(%s%H%m%T!<$NCM$,29EY$KBP$7$FITO"B3$H$J$C(B
$B$F$$$k(B. 

\begin{figure}
\begin{center}
 \Depsf[100mm]{./ps/entr_gap.ps}
\end{center}
\caption{}
\Dfiglab{entr:entr_gap}
\end{figure}


\section{$BJ?9U;~$N2=3X%]%F%s%7%c%k(B}

$B$^$:5$Aj$HMO1UAj$NJ?9U>uBV$r9M$($k(B. $B$3$N;~(B, $B5$Aj$N2=3X%]%F%s%7%c%k(B
$\mu^{g}$ $B$HMO1UAj$N2=3X%]%F%s%7%c%k(B $\mu^{l}$ $B$OEy$7$/$J$k(B. $BM}A[5$BN(B,
$BM}A[MO1U$r2>Dj$9$l$P(B, 
%
\begin{eqnarray}
 && \mu_{i}^{g} = \mu_{i}^{l} ,\nonumber \\
 && {\mu_{i}^{\circ}}^{g} + RT \ln x_{i}^{g} + RT \ln{\frac{p}{p_{0}}}
  = {\mu_{i}^{\circ}}^{l} + RT \ln x_{i}^{l} 
\Deqlab{entr:equiv}
\end{eqnarray}
%
$B$H=q$1$k(B. $B$3$3$G@.J,(B $i$ $B$NK0OB>x5$05$r(B $p^{*}(T)$ $B$H$7(B, $B1UAj(B $i$ $B$NI8=`(B
$B2=3X%]%F%s%7%c%k$r5$Aj(B $i$ $B$NI8=`2=3X%]%F%s%7%c%k$HK0OB>x5$05$rMQ$$$F=q(B
$B$1$P(B, 
%
\begin{eqnarray}
 && {\mu_{i}^{\circ}}^{l}  = {\mu_{i}^{\circ}}^{g} + RT \ln{\frac{p^{*}}{p_{0}}}
\Deqlab{entr:mu_std}  
\end{eqnarray}
%
$B$H$J$k(B. \Deqref{entr:equiv} $B<0$K(B \Deqref{entr:mu_std} $B<0$rBeF~$9$k$3$H$G(B, 
%
\begin{eqnarray}
 && {\mu_{i}^{\circ}}^{g} + RT \ln x_{i}^{g} + RT \ln{\frac{p}{p_{0}}}
  = {\mu_{i}^{\circ}}^{l} + RT \ln x_{i}^{l} 
\nonumber \\
 && {\mu_{i}^{\circ}}^{g} + RT \ln{\frac{x_{i}^{g} p}{p_{0}}}
  = \left(
     {\mu_{i}^{\circ}}^{g} + RT \ln{\frac{p^{*}}{p_{0}}}
   \right)
  + RT \ln x_{i}^{l}
  \nonumber \\
 &&  RT \ln{\frac{x_{i}^{g} p}{p_{0}}}
  =  RT \ln{\frac{x_{i}^{l} p^{*}}{p_{0}}}
  \nonumber \\
 &&  x_{i}^{g} p =  x_{i}^{l} p^{*}
\Deqlab{entr:raoult}  
\end{eqnarray}
%
$B$G$"$k(B. \Deqref{entr:raoult} $B<0$OJ?9U;~$N>x5$05(B, $BK0OB>x5$05(B, $B%b%kHf$N4X(B
$B78$r<($9$b$N$G(B, {\bf Raoult $B$NK!B'(B}$B$H8F$P$l$k(B. 


\section{$BJ?9U;~$N%(%s%H%m%T!<(B}

$BJ?9U;~$K$*$1$k(B 1 $B%b%kEv$?$j$NHf%(%s%H%m%T!<$NCM$N:9$r9M$($k(B. 
%
\begin{eqnarray}
 s^{g} - s^{l} 
  = 
  - \DP{{\mu_{i}^{\circ}}^{g}}{T} - R \ln{x_{i}^{g}} - R \ln{\frac{p}{p_{0}}}
  - \left(- \DP{{\mu_{i}^{\circ}}^{l}}{T} - R \ln{x_{i}^{g}} \right).
\Deqlab{entr:entr}
\end{eqnarray}
%
$B$3$3$G(B \Deqref{entr:mu_std} $B<0$rMxMQ$9$k$H(B, 
%
\begin{eqnarray}
 s^{g} - s^{l} 
  &=& 
  - \DP{{\mu_{i}^{\circ}}^{g}}{T} - R \ln{x_{i}^{g}} - R \ln{\frac{p}{p_{0}}}
  + \DP{}{T} \left(
	      {\mu_{i}^{\circ}}^{g} + RT \ln{\frac{p^{*}}{p_{0}}}	      
	    \right)
  + R \ln{x_{i}^{g}},
\nonumber \\
  &=& 
  - \DP{{\mu_{i}^{\circ}}^{g}}{T} - R \ln{x_{i}^{g}} - R \ln{\frac{p}{p_{0}}}
  + \DP{{\mu_{i}^{\circ}}^{g} }{T}
  + R \ln{\frac{p^{*}}{p_{0}}}
  + RT \DP{}{T}\ln{p_{i}^{*}}
  + R \ln{x_{i}^{g}},
\nonumber \\
  &=& 
  - R \ln{\frac{x_{i}^{g} p}{p_{0}}}
  + R \ln{\frac{x_{i}^{l} p^{*}}{p_{0}}}
  + RT \DP{}{T}\ln{p_{i}^{*}}
\Deqlab{entr:entr2}
\end{eqnarray}
%
$B$H$J$k(B. $B$3$3$G(B Raoult $B$NK!B'(B \Deqref{entr:raoult} $B<0$rMxMQ$9$k$H(B, 
\Deqref{entr:entr2} $B<0$N1&JUBh(B 1 $B9`(B, $B1&JUBh(B 2 $B9`$O%-%c%s%;%k%"%&%H$9$k$N(B
$B$G(B, 
%
\begin{eqnarray}
 s^{g} - s^{l} 
  = RT \DP{}{T}\ln{p_{i}^{*}}
\Deqlab{entr:entr3}
\end{eqnarray}
%
$B$H$J$k(B. $B$D$^$jJ?9U;~$K$O2=3X%]%F%s%7%c%k$OEy$7$$$,(B, $BHf%(%s%H%m%T!<$OEy$7(B
$B$/$J$i$J$$$3$H$r<($7$F$$$k(B. 


$B<!$K(B \Deqref{entr:entr3} $B<0$h$j5a$^$kHf%(%s%H%m%T!<$N:9$r8+@Q$j(B,
\Dfigref{entr:entr_gap} $B$K<($5$l$?%(%s%H%m%T!<$N%.%c%C%W$,BEEv$J$b$N$+8!(B
$BF$$9$k(B. $BK0OB>x5$05<0$H$7$FNc$($P(B Antoine $B$N<0$rMxMQ$9$k$H(B, $BK0OB>x5$05$O(B
%
\begin{eqnarray}
 \ln{p^{*}} = A - \frac{B}{C + T}
\Deqlab{entr:antoine}
\end{eqnarray}
%
$B$H=q$1$k(B. $B$?$@$7(B $A, B, C$ $B$O2=3X<o$KBP1~$7$?Dj?t$G$"$k(B. $B$7$?$,$C$F(B
%
\begin{eqnarray}
 s^{g} - s^{l} 
  = \frac{RT B}{(C + T)^{2}}
\Deqlab{entr:ds}
\end{eqnarray}
%
$B$G$"$k(B. H$_2$O(l) $B$K$D$$$F9M$($k$H(B, $R = 8.31, T = 300, B = 1636 \times
\ln(10), C = 224$ $B$J$N$G(B,
%
\begin{eqnarray}
 s^{g} - s^{l} 
  &\approx& \frac{8 \times 3 \times 3 \times 10^{5} }
  {\{224 + (300 - 273)\}^{2}}
\nonumber \\
  &\approx& \frac{72 \times 10^{5}}{9 \times 10^{4}} 
\nonumber \\
  &\approx& 10^{2}
\Deqlab{entr:ds2}
\end{eqnarray}
%
$B$G$"$k(B. $BHf%(%s%H%m%T!<$N:9$O%*!<%@!<$K$7$F(B $10^{2}$ $B$@$1:9$,$"$k$3$H$r<($9(B. 

\Dfigref{entr:entr_gap} $B$N>l9g(B, $B6E7k$K$h$C$F(B $10^{-5}$ $B$@$1(B H$_2$O(l) $B$,(B
$B@8$8$?$N$G(B, $B$=$N@8@.$K$h$C$F7O$NA4%(%s%H%m%T!<$X$N1F6A$O(B, $10^{2} \times
10^{-5} = 10^{-3}$ $B$G$"$k$H8+@Q$b$k$3$H$,$G$-$k(B. \Dfigref{entr:entr_gap}
$B$N%(%s%H%m%T!<$N%.%c%C%W$NBg$-$5$b%*!<%@!<$K$7$F(B $10^{-3}$ $B$J$N$G(B, $B$3$N(B
$B:9$OBEEv$J$b$N$H$_$J$9$3$H$,$G$-$k(B. 