# LaTeX2HTML 2002-2-1 (1.70)
# Associate images original text with physical files.


$key = q/s_{i}^{phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$s_{i}^{\phi}$">|; 

$key = q/N^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$N^{2}$">|; 

$key = q/displaystyleG(T,p)=sum_{i}sum_{phi}n_{i}^{phi}mu_{i}^{phi}(T,p,n_{i}^{phi}),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$\displaystyle G(T, p)
= \sum_{i}\sum_{\phi} n_{i}^{\phi} \mu_{i}^{\phi}(T, p, n_{i}^{\phi}) ,$">|; 

$key = q/p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$p$">|; 

$key = q/delta_{1phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$\delta_{1\phi}$">|; 

$key = q/h_{i}^{phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$h_{i}^{\phi}$">|; 

$key = q/mu_{i}^{phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$\mu_{i}^{\phi}$">|; 

$key = q/{c_{p}}_{i}^{phi}(T);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="${c_{p}}_{i}^{\phi}(T)$">|; 

$key = q/{c_{p}}_{i}^{phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="${c_{p}}_{i}^{\phi}$">|; 

$key = q/i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$i$">|; 

$key = q/displaystyle{{mu_{i}}^{circ}}^{phi}(T);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$\displaystyle {{\mu_{i}}^{\circ}}^{\phi}(T)$">|; 

$key = q/displaystyle+int_{T_{0}}^{T}{c_{p}}_{i}^{phi}(T)dT-Tint_{T_{0}}^{T}frac{{c_{p}}_{i}^{phi}(T)}{T}dT,;;;{{rm{for};phi=1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="379" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$\displaystyle + \int_{T_{0}}^{T}{c_{p}}_{i}^{\phi}(T) dT
- T \int_{T_{0}}^{T} \frac{{c_{p}}_{i}^{\phi}(T)}{T} dT,
\;\;\;{\rm for} \; \phi = 1,$">|; 

$key = q/_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$_3$">|; 

$key = q/T_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$T_{0}$">|; 

$key = q/g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$g$">|; 

$key = q/M;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$M$">|; 

$key = q/h_{i}^{phi}(T_{0});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$h_{i}^{\phi}(T_{0})$">|; 

$key = q/c_{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$c_{p}$">|; 

$key = q/n^{phi}_{i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$n^{\phi}_{i}$">|; 

$key = q/x_{i}^{phi}equivn_{i}^{phi}slashsum_{i}n_{i}^{phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$x_{i}^{\phi} \equiv n_{i}^{\phi}/\sum_{i}n_{i}^{\phi}$">|; 

$key = q/displaystyle{{mu_{i}}^{circ}}^{phi}(T)={{mu_{i}}^{circ}}^{1}(T)+RTln{e_{i}(T)slashp_{0}},;;;{{rm{for};phineq1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="395" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$\displaystyle {{\mu_{i}}^{\circ}}^{\phi}(T)
= {{\mu_{i}}^{\circ}}^{1}(T) + RT \ln{e_{i}(T)/p_{0}},
\;\;\;{\rm for} \; \phi \neq 1,$">|; 

$key = q/{{mu_{i}}^{circ}}^{phi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="${{\mu_{i}}^{\circ}}^{\phi}$">|; 

$key = q/textstyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$\textstyle =$">|; 

$key = q/displaystyleh_{i}^{phi}(T_{0})-Ts_{i}^{phi}(T_{0},p_{0});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$\displaystyle h_{i}^{\phi}(T_{0}) - T s_{i}^{\phi}(T_{0}, p_{0})$">|; 

$key = q/s_{i}^{phi}(T_{0},p_{0});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$s_{i}^{\phi}(T_{0}, p_{0})$">|; 

$key = q/R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$R$">|; 

$key = q/_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$_4$">|; 

$key = q/e_{i}(T);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$e_{i}(T)$">|; 

$key = q/{{mu_{i}}^{circ}}^{phi}(T);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="${{\mu_{i}}^{\circ}}^{\phi}(T)$">|; 

$key = q/phi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$\phi$">|; 

$key = q/p_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$p_{0}$">|; 

$key = q/phi=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$\phi = 1$">|; 

$key = q/G;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$G$">|; 

$key = q/T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$T$">|; 

$key = q/_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$_2$">|; 

$key = q/displaystyleN^{2}=frac{g}{T}left(frac{dT}{dz}+frac{Mg}{c_{p}}right)-frac{g}{M}frac{dM}{dz},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$\displaystyle N^{2}
=
\frac{g}{T}
\left(
\frac{d T}{d z}
+ \frac{M g}{c_{p}}
\right)
-
\frac{g}{M} \frac{dM}{dz},$">|; 

$key = q/displaystylemu_{i}^{phi}(T,p,n_{i}^{phi})={{mu_{i}}^{circ}}^{phi}(T)+RTln{x_{i}^{phi}}+delta_{1phi}RTln{pslashp_{0}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="414" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$\displaystyle \mu_{i}^{\phi}(T, p, n_{i}^{\phi})
= {{\mu_{i}}^{\circ}}^{\phi}(T) + RT \ln{x_{i}^{\phi}} + \delta_{1\phi} RT \ln{p/p_{0}} ,$">|; 

1;

