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Display information for equation id:math.2473.29 on revision:2473

* Page found: Thermodynamische Potenziale (eq math.2473.29)

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Thermodynamische Potenziale Eq: math.2473.29

Hash: 8bfc4a46ad3a6404d732e190c71b7995

TeX (original user input):

\begin{align}

& dS=\frac{1}{T}dU+\frac{p}{T}dV-\sum\limits_{\alpha }^{{}}{{}}\frac{{{\mu }_{\alpha }}}{T}d{{N}^{\alpha }}\Rightarrow S=\frac{1}{T}U+\frac{pV}{T}-\sum\limits_{\alpha }^{{}}{{}}\frac{{{\mu }_{\alpha }}}{T}{{N}^{\alpha }} \\

& \Rightarrow G=U-TS+pV=\sum\limits_{\alpha }^{{}}{{}}{{\mu }_{\alpha }}{{N}^{\alpha }}=G \\

& G=\sum\limits_{\alpha }^{{}}{{}}{{\mu }_{\alpha }}{{N}^{\alpha }} \\

\end{align}

TeX (checked):

{\begin{aligned}&dS={\frac {1}{T}}dU+{\frac {p}{T}}dV-\sum \limits _{\alpha }^{}{}{\frac {{\mu }_{\alpha }}{T}}d{{N}^{\alpha }}\Rightarrow S={\frac {1}{T}}U+{\frac {pV}{T}}-\sum \limits _{\alpha }^{}{}{\frac {{\mu }_{\alpha }}{T}}{{N}^{\alpha }}\\&\Rightarrow G=U-TS+pV=\sum \limits _{\alpha }^{}{}{{\mu }_{\alpha }}{{N}^{\alpha }}=G\\&G=\sum \limits _{\alpha }^{}{}{{\mu }_{\alpha }}{{N}^{\alpha }}\\\end{aligned}}

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MathML (2.987 KB / 443 B) :

\begin{aligned} d S = \frac{1}{T} d U + \frac{p}{T} d V - \sum_{α}^{} \frac{μ_{α}}{T} d N^{α} \Rightarrow S = \frac{1}{T} U + \frac{p V}{T} - \sum_{α}^{} \frac{μ_{α}}{T} N^{α} \\ \Rightarrow G = U - T S + p V = \sum_{α}^{} μ_{α} N^{α} = G \\ G = \sum_{α}^{} μ_{α} N^{α} \end{aligned}

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Identifiers

$d$

$S$

$T$

$d$

$U$

$p$

$T$

$d$

$V$

$α$

$μ_{α}$

$T$

$d$

$N$

$α$

$S$

$T$

$U$

$p$

$V$

$T$

$α$

$μ_{α}$

$T$

$N$

$α$

$G$

$U$

$T$

$S$

$p$

$V$

$α$

$μ_{α}$

$N$

$α$

$G$

$G$

$α$

$μ_{α}$

$N$

$α$

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