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Display information for equation id:math.2531.38 on revision:2531

* Page found: Chemische Reaktionen (eq math.2531.38)

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Chemische Reaktionen Eq: math.2532.38

Hash: 61b1f0e8ae2472182fe365d984586604

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\begin{align}

& \Rightarrow {{Q}_{p}}^{\left( \rho  \right)}={{\left( \frac{\partial H}{\partial {{\xi }_{\rho }}} \right)}_{T,p}}=\frac{\partial }{\partial {{\xi }_{\rho }}}\left( G+TS \right)={{\left( \frac{\partial G}{\partial {{\xi }_{\rho }}} \right)}_{T,p}}+T{{\left( \frac{\partial S}{\partial {{\xi }_{\rho }}} \right)}_{T,p}} \\

& {{\left( \frac{\partial G}{\partial {{\xi }_{\rho }}} \right)}_{T,p}}=-{{A}_{\rho }} \\

& {{\left( \frac{\partial S}{\partial {{\xi }_{\rho }}} \right)}_{T,p}}={{\left( \frac{\partial {{A}_{\rho }}}{\partial T} \right)}_{p,{{\xi }_{\rho }}}} \\

& \Rightarrow {{Q}_{p}}^{\left( \rho  \right)}={{\left( \frac{\partial H}{\partial {{\xi }_{\rho }}} \right)}_{T,p}}=-{{A}_{\rho }}+T{{\left( \frac{\partial {{A}_{\rho }}}{\partial T} \right)}_{p,{{\xi }_{\rho }}}} \\

& \Rightarrow {{Q}_{p}}^{\left( \rho  \right)}={{\left( \frac{\partial H}{\partial {{\xi }_{\rho }}} \right)}_{T,p}}={{T}^{2}}\frac{\partial }{\partial T}{{\left( \frac{{{A}_{\rho }}}{T} \right)}_{p,{{\xi }_{\rho }}}} \\

\end{align}

TeX (checked):

{\begin{aligned}&\Rightarrow {{Q}_{p}}^{\left(\rho \right)}={{\left({\frac {\partial H}{\partial {{\xi }_{\rho }}}}\right)}_{T,p}}={\frac {\partial }{\partial {{\xi }_{\rho }}}}\left(G+TS\right)={{\left({\frac {\partial G}{\partial {{\xi }_{\rho }}}}\right)}_{T,p}}+T{{\left({\frac {\partial S}{\partial {{\xi }_{\rho }}}}\right)}_{T,p}}\\&{{\left({\frac {\partial G}{\partial {{\xi }_{\rho }}}}\right)}_{T,p}}=-{{A}_{\rho }}\\&{{\left({\frac {\partial S}{\partial {{\xi }_{\rho }}}}\right)}_{T,p}}={{\left({\frac {\partial {{A}_{\rho }}}{\partial T}}\right)}_{p,{{\xi }_{\rho }}}}\\&\Rightarrow {{Q}_{p}}^{\left(\rho \right)}={{\left({\frac {\partial H}{\partial {{\xi }_{\rho }}}}\right)}_{T,p}}=-{{A}_{\rho }}+T{{\left({\frac {\partial {{A}_{\rho }}}{\partial T}}\right)}_{p,{{\xi }_{\rho }}}}\\&\Rightarrow {{Q}_{p}}^{\left(\rho \right)}={{\left({\frac {\partial H}{\partial {{\xi }_{\rho }}}}\right)}_{T,p}}={{T}^{2}}{\frac {\partial }{\partial T}}{{\left({\frac {{A}_{\rho }}{T}}\right)}_{p,{{\xi }_{\rho }}}}\\\end{aligned}}

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\begin{aligned} \Rightarrow {Q_{p}}^{(ρ)} = {(\frac{\partial H}{\partial ξ_{ρ}})}_{T, p} = \frac{\partial}{\partial ξ_{ρ}} (G + T S) = {(\frac{\partial G}{\partial ξ_{ρ}})}_{T, p} + T {(\frac{\partial S}{\partial ξ_{ρ}})}_{T, p} \\ {(\frac{\partial G}{\partial ξ_{ρ}})}_{T, p} = - A_{ρ} \\ {(\frac{\partial S}{\partial ξ_{ρ}})}_{T, p} = {(\frac{\partial A_{ρ}}{\partial T})}_{p, ξ_{ρ}} \\ \Rightarrow {Q_{p}}^{(ρ)} = {(\frac{\partial H}{\partial ξ_{ρ}})}_{T, p} = - A_{ρ} + T {(\frac{\partial A_{ρ}}{\partial T})}_{p, ξ_{ρ}} \\ \Rightarrow {Q_{p}}^{(ρ)} = {(\frac{\partial H}{\partial ξ_{ρ}})}_{T, p} = T^{2} \frac{\partial}{\partial T} {(\frac{A_{ρ}}{T})}_{p, ξ_{ρ}} \end{aligned}

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Identifiers

$Q_{p}$

$ρ$

$H$

$ξ_{ρ}$

$T$

$p$

$ξ_{ρ}$

$G$

$T$

$S$

$G$

$ξ_{ρ}$

$T$

$p$

$T$

$S$

$ξ_{ρ}$

$T$

$p$

$G$

$ξ_{ρ}$

$T$

$p$

$A_{ρ}$

$S$

$ξ_{ρ}$

$T$

$p$

$A_{ρ}$

$T$

$p$

$ξ_{ρ}$

$Q_{p}$

$ρ$

$H$

$ξ_{ρ}$

$T$

$p$

$A_{ρ}$

$T$

$A_{ρ}$

$T$

$p$

$ξ_{ρ}$

$Q_{p}$

$ρ$

$H$

$ξ_{ρ}$

$T$

$p$

$T$

$T$

$A_{ρ}$

$T$

$p$

$ξ_{ρ}$

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