ISITEKS: ENTROPI SISTEM REAL ADALAH FUNGSI

Dari :

$\LARGE \bg_black {\color{Orange} real\rightleftharpoons gas\ ideal}$

$\LARGE \bg_black {\color{Orange} -dn_{real}=dn_{ideal}}$

$\large \bg_black {\color{Orange} \sum _{lksikla}\left [ \left ( \frac{dE+pdV}{T} \right )_{real}+\left ( \frac{dE+pdV}{T} \right )_{gasideal} \right ]=0}$

dengan j adalah real atau gas ideal
i = gas ideal
r = real

$\LARGE \bg_black {\color{Orange} T_{j}=T}$

   $\LARGE \bg_black {\color{Orange} \bar{V}_{j}=\frac{V_{j}}{n_{j}}}$

$\LARGE \bg_black {\color{Orange} \bar{E}_{j}=\frac{E_{j}}{n_{j}}}$

$\large {\color{Orange} V_{j}=\bar{V}_{j}\cdot n_{j}}$

$\large {\color{Orange} E_{j}=\bar{E}_{j}\cdot n_{j}}$

$\large {\color{Orange} dUV=UdV+VdU}$

$\large {\color{Orange} \sum _{lksikla}d\bar{S}_{i}=0}$

$\large {\color{Orange} \bar{H}=\left ( \bar{E}+P\bar{V} \right )}$

$\large {\color{Orange} E_{i}=n_{i}\bar{E}_{i}\left ( T \right )}$

$\LARGE \bg_black {\color{Orange} p_{i}V_{i}=n_{i}RT}$

Jadikan:

$\large {\color{Orange} \sum _{lksikla}\left ( \frac{d\bar{E}+pd\bar{V}}{T} \right )_{real}=0}$

atau

$\large {\color{Orange} \sum _{lksikla}d\bar{S}_{r}=0}$

atau    $\large {\color{Orange} \bar{S}_{r}\ adalah\ fungsi}$

Jawab:

$\large {\color{Orange} \sum _{j}\sum _{lksikla}\left ( \frac{dE+PdV}{T} \right )_{j}=0}$

$\large {\color{Orange} \left ( \frac{dE+PdV}{T} \right )_{j}=\left ( \frac{dn\bar{E}+Pdn\bar{V}}{T} \right )_{j}}$

$\large {\color{Orange} =\left ( \frac{\bar{E}+P\bar{V}}{T} \right )dn+n\left ( \frac{d\bar{E}+Pd\bar{V}}{T} \right )}$

                                      $\large {\color{Orange} =\left ( \frac{\bar{H}}{T} \right )dn+nd\bar{S}}$


$\large {\color{Orange} \sum _{lksikla}\left ( \frac{dE+PdV}{T} \right )_{j}=\left ( K\left ( \frac{\bar{H}}{T} \right ),n+K\left ( n,\bar{S} \right ) \right )_{j}}$

                                                  $\large {\color{Orange} =\left ( d\left ( \frac{\bar{H}}{T} \right )dn-dnd\bar{S} \right )_{j}}$

               $\large {\color{Orange} =\left ( dnd\left ( \frac{\bar{H}}{T}-\bar{S} \right ) \right )_{j}}$

                                                 $\large {\color{Orange} =dn_{j}d\bar{g}_{j}}$

$\large {\color{Orange} \sum _{j}\sum _{lksikla}\left ( \frac{dE+PdV}{T} \right )_{j}=\sum _{j}dn_{j}d\bar{g}_{j}}$

                                     $\large {\color{Orange} =dn_{r}d\bar{g}_{r}+dn_{i}d\bar{g}_{i}}$

         $\large {\color{Orange} =-dn_{i}d\bar{g}_{r}+dn_{i}d\bar{g}_{i}}$

                                                     $\large {\color{Orange} =dn\left ( -d\bar{g}_{r}+d\bar{g}_{i} \right )}$

                                                         $\large {\color{Orange} =0}$

                                            $\large {\color{Orange} d\bar{g}_{r}=d\bar{g}_{i}}$

                                     $\large {\color{Orange} \bar{S}=\frac{\bar{H}}{T}-\bar{g}}$

$\large {\color{Orange} d\bar{S}_{r}=d\left ( \frac{\bar{H}}{T}-\bar{g} \right )_{r}}$

       $\large {\color{Orange} =d\left ( \frac{\bar{H}}{T} \right )_{r}-d\bar{g}_{r}}$

          $\large {\color{Orange} =d\left ( \frac{\bar{H}}{T} \right )_{r}-d\bar{g}_{i}}$


   $\large {\color{Orange} =d\left ( \frac{\bar{H}}{T} \right )_{r}-d\left ( \frac{\bar{H}}{T}-\bar{S} \right )_{i}}$

         $\large {\color{Orange} =d\left ( \frac{\bar{H}}{T} \right )_{r}-d\left ( \frac{\bar{H}}{T} \right )_{i}+d\bar{S}_{i}}$



$\large {\color{Orange} \sum _{lksikla}d\bar{S}_{r}=\sum _{lksikla}d\left ( \frac{\bar{H}}{T} \right )_{r}-\sum _{lksikla}d\left ( \frac{\bar{H}}{T} \right )_{i}+\sum_{lksikla}d\bar{S}_{i}}$

$\large {\color{Orange} =K\left ( 1,\left ( \frac{\bar{H}}{T} \right )_{r} \right )-K\left ( 1,\left ( \frac{\bar{H}}{T} \right )_{i} \right )+0}$

   $\large \bg_black {\color{Orange} =0-0+0}$

                         $\large \bg_black {\color{Orange} =0}$

maka $\LARGE \bg_black {\color{Orange} S_{r}}$ adalah fungsi.

DARI :

$\large {\color{Orange} real\rightleftharpoons gas\ ideal }$     mengalami proses sehingga

$\large {\color{Orange} \left ( \frac{dE+PdV}{T} \right )_{real}+\left ( \frac{dE+PdV}{T} \right )_{gasideal}=dif\ eksak}$ misal $\large {\color{Orange} df\left ( T \right )}$

JADIKAN:

$\large {\color{Orange} \sum _{lksikla}\left [ \left ( \frac{dE+PdV}{T} \right )_{real}+\left ( \frac{dE+PdV}{T} \right )_{gasideal} \right ]=0}$

JAWAB:

$\large {\color{Orange}\left ( \frac{dE+PdV}{T} \right )_{real}+\left ( \frac{dE+PdV}{T} \right )_{gasideal} =diferensial\ eksak}$

$\large {\color{Orange} \sum _{lksikla} \left ( \frac{dE+PdV}{T} \right )_{real}+\left ( \frac{dE+PdV}{T} \right )_{gasideal} =\sum_{lksikla}dif\ eksak}$

$\large {\color{Orange} \sum _{lksikla} \left ( \frac{dE+PdV}{T} \right )_{real}+\left ( \frac{dE+PdV}{T} \right )_{gasideal} =0}$

keterangan:
dif eksak= diferensial eksak
lksikla = langkah sikla

ISITEKS

Minggu, 14 Juli 2013

ENTROPI SISTEM REAL ADALAH FUNGSI

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