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Display information for equation id:math.2507.58 on revision:2507

* Page found: Das ideale Gas (eq math.2507.58)

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Das ideale Gas Eq: math.2507.58

Hash: 264559decabd183a48450bd30e915bf1

TeX (original user input):

\begin{align}

& \Rightarrow S=k\left( \beta U-\Psi \left( \beta ,V \right) \right)=k\left( \beta U+N\ln \frac{V}{N}+N\ln \Phi \left( \beta  \right)+N \right) \\

& =kN\left( \frac{3}{2}\ln \frac{U}{N}+\ln \frac{V}{N}+\frac{5}{2}+\frac{3}{2}\ln \frac{4\pi m}{3{{\hbar }^{2}}} \right) \\

\end{align}

TeX (checked):

{\begin{aligned}&\Rightarrow S=k\left(\beta U-\Psi \left(\beta ,V\right)\right)=k\left(\beta U+N\ln {\frac {V}{N}}+N\ln \Phi \left(\beta \right)+N\right)\\&=kN\left({\frac {3}{2}}\ln {\frac {U}{N}}+\ln {\frac {V}{N}}+{\frac {5}{2}}+{\frac {3}{2}}\ln {\frac {4\pi m}{3{{\hbar }^{2}}}}\right)\\\end{aligned}}

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MathML (2.726 KB / 496 B) :

\begin{aligned} \Rightarrow S = k (β U - Ψ (β, V)) = k (β U + N \ln \frac{V}{N} + N \ln Φ (β) + N) \\ = k N (\frac{3}{2} \ln \frac{U}{N} + \ln \frac{V}{N} + \frac{5}{2} + \frac{3}{2} \ln \frac{4 π m}{3 ℏ^{2}}) \end{aligned}

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Identifiers

$S$

$k$

$β$

$U$

$Ψ$

$β$

$V$

$k$

$β$

$U$

$N$

$V$

$N$

$N$

$Φ$

$β$

$N$

$k$

$N$

$U$

$N$

$V$

$N$

$π$

$m$

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