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Display information for equation id:math.2497.24 on revision:2497

* Page found: Thermodynamische Stabilität (eq math.2497.24)

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Thermodynamische Stabilität Eq: math.2497.24

Hash: c9401ea7a8a553324d3c5b13cf0423d8

TeX (original user input):

\begin{align}

& S=-kI \\

& {{\lambda }_{0}}=\frac{1}{kT} \\

& {{\lambda }_{1}}=\frac{p}{kT} \\

& \Rightarrow {{\left( \frac{\partial S}{\partial T} \right)}_{p}}={{\left( \frac{\partial S}{\partial {{\lambda }_{0}}} \right)}_{p}}{{\left( \frac{\partial {{\lambda }_{0}}}{\partial T} \right)}_{p}}=-\frac{1}{T}{{\left( \frac{\partial S}{\partial {{\lambda }_{0}}} \right)}_{p}}{{\lambda }_{0}}=\frac{k}{T}\left( \frac{\partial I}{\partial {{\lambda }_{0}}} \right){{\lambda }_{0}}\ge 0 \\

\end{align}

TeX (checked):

{\begin{aligned}&S=-kI\\&{{\lambda }_{0}}={\frac {1}{kT}}\\&{{\lambda }_{1}}={\frac {p}{kT}}\\&\Rightarrow {{\left({\frac {\partial S}{\partial T}}\right)}_{p}}={{\left({\frac {\partial S}{\partial {{\lambda }_{0}}}}\right)}_{p}}{{\left({\frac {\partial {{\lambda }_{0}}}{\partial T}}\right)}_{p}}=-{\frac {1}{T}}{{\left({\frac {\partial S}{\partial {{\lambda }_{0}}}}\right)}_{p}}{{\lambda }_{0}}={\frac {k}{T}}\left({\frac {\partial I}{\partial {{\lambda }_{0}}}}\right){{\lambda }_{0}}\geq 0\\\end{aligned}}

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\begin{aligned} S = - k I \\ λ_{0} = \frac{1}{k T} \\ λ_{1} = \frac{p}{k T} \\ \Rightarrow {(\frac{\partial S}{\partial T})}_{p} = {(\frac{\partial S}{\partial λ_{0}})}_{p} {(\frac{\partial λ_{0}}{\partial T})}_{p} = - \frac{1}{T} {(\frac{\partial S}{\partial λ_{0}})}_{p} λ_{0} = \frac{k}{T} (\frac{\partial I}{\partial λ_{0}}) λ_{0} \geq 0 \end{aligned}

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Identifiers

$S$

$k$

$I$

$λ_{0}$

$k$

$T$

$λ_{1}$

$p$

$k$

$T$

$S$

$T$

$p$

$S$

$λ_{0}$

$p$

$λ_{0}$

$T$

$p$

$T$

$S$

$λ_{0}$

$p$

$λ_{0}$

$k$

$T$

$I$

$λ_{0}$

$λ_{0}$

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