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Display information for equation id:math.2507.23 on revision:2507

* Page found: Das ideale Gas (eq math.2507.23)

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Das ideale Gas Eq: math.2507.23

Hash: ceebb3df34abadc9563e09e479c28a39

TeX (original user input):

\begin{align}

& U=\left\langle H \right\rangle ={{\left( \frac{\partial \Psi }{\partial \beta } \right)}_{\alpha ,V}}=\frac{3}{2\beta }V\Phi \left( \beta  \right){{e}^{-\alpha }} \\

& \bar{N}=\left\langle N \right\rangle ={{\left( \frac{\partial \Psi }{\partial \alpha } \right)}_{\beta ,V}}=V\Phi \left( \beta  \right){{e}^{-\alpha }}=-\Psi  \\

\end{align}

TeX (checked):

{\begin{aligned}&U=\left\langle H\right\rangle ={{\left({\frac {\partial \Psi }{\partial \beta }}\right)}_{\alpha ,V}}={\frac {3}{2\beta }}V\Phi \left(\beta \right){{e}^{-\alpha }}\\&{\bar {N}}=\left\langle N\right\rangle ={{\left({\frac {\partial \Psi }{\partial \alpha }}\right)}_{\beta ,V}}=V\Phi \left(\beta \right){{e}^{-\alpha }}=-\Psi \\\end{aligned}}

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MathML (2.794 KB / 494 B) :

\begin{aligned} U = ⟨ H ⟩ = {(\frac{\partial Ψ}{\partial β})}_{α, V} = \frac{3}{2 β} V Φ (β) e^{- α} \\ \bar{N} = ⟨ N ⟩ = {(\frac{\partial Ψ}{\partial α})}_{β, V} = V Φ (β) e^{- α} = - Ψ \end{aligned}

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Identifiers

$U$

$H$

$Ψ$

$β$

$α$

$V$

$β$

$V$

$Φ$

$β$

$e$

$α$

$\bar{N}$

$N$

$Ψ$

$α$

$β$

$V$

$V$

$Φ$

$β$

$e$

$α$

$Ψ$

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