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Display information for equation id:math.2573.14 on revision:2573

* Page found: Spezifische Wärme zweiatomiger idealer Gase (eq math.2573.14)

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Spezifische Wärme zweiatomiger idealer Gase Eq: math.2573.14

Hash: ec60dedc79827675a7d344ff68f35bba

TeX (original user input):

\begin{align}

& U=-\frac{\partial }{\partial \beta }\ln Z=-\frac{\partial }{\partial \beta }\left( \frac{1}{N!}{{Z}_{t}}^{N} \right)-N\frac{\partial }{\partial \beta }\left( {{Z}_{r}} \right)-N\frac{\partial }{\partial \beta }\left( {{Z}_{s}} \right) \\

& -\frac{\partial }{\partial \beta }\left( \frac{1}{N!}{{Z}_{t}}^{N} \right)={{U}_{t}} \\

& -N\frac{\partial }{\partial \beta }\left( {{Z}_{r}} \right)={{U}_{r}} \\

& -N\frac{\partial }{\partial \beta }\left( {{Z}_{s}} \right)={{U}_{S}} \\

& \Rightarrow U={{U}_{t}}+{{U}_{r}}+{{U}_{S}} \\

\end{align}

TeX (checked):

{\begin{aligned}&U=-{\frac {\partial }{\partial \beta }}\ln Z=-{\frac {\partial }{\partial \beta }}\left({\frac {1}{N!}}{{Z}_{t}}^{N}\right)-N{\frac {\partial }{\partial \beta }}\left({{Z}_{r}}\right)-N{\frac {\partial }{\partial \beta }}\left({{Z}_{s}}\right)\\&-{\frac {\partial }{\partial \beta }}\left({\frac {1}{N!}}{{Z}_{t}}^{N}\right)={{U}_{t}}\\&-N{\frac {\partial }{\partial \beta }}\left({{Z}_{r}}\right)={{U}_{r}}\\&-N{\frac {\partial }{\partial \beta }}\left({{Z}_{s}}\right)={{U}_{S}}\\&\Rightarrow U={{U}_{t}}+{{U}_{r}}+{{U}_{S}}\\\end{aligned}}

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MathML (4.304 KB / 462 B) :

\begin{aligned} U = - \frac{\partial}{\partial β} \ln Z = - \frac{\partial}{\partial β} (\frac{1}{N!} {Z_{t}}^{N}) - N \frac{\partial}{\partial β} (Z_{r}) - N \frac{\partial}{\partial β} (Z_{s}) \\ - \frac{\partial}{\partial β} (\frac{1}{N!} {Z_{t}}^{N}) = U_{t} \\ - N \frac{\partial}{\partial β} (Z_{r}) = U_{r} \\ - N \frac{\partial}{\partial β} (Z_{s}) = U_{S} \\ \Rightarrow U = U_{t} + U_{r} + U_{S} \end{aligned}

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Identifiers

$U$

$β$

$Z$

$β$

$N$

$Z_{t}$

$N$

$N$

$β$

$Z_{r}$

$N$

$β$

$Z_{s}$

$β$

$N$

$Z_{t}$

$N$

$U_{t}$

$N$

$β$

$Z_{r}$

$U_{r}$

$N$

$β$

$Z_{s}$

$U_{S}$

$U$

$U_{t}$

$U_{r}$

$U_{S}$

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