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Display information for equation id:math.2508.65 on revision:2508

* Page found: Reale Gase (eq math.2508.65)

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Reale Gase Eq: math.2511.65

Hash: 4414fe8e05392f37ebc2f4b6bade515f

TeX (original user input):

\begin{align}

& U={{\left( \frac{\partial \Psi }{\partial \beta } \right)}_{\alpha ,V}}=-\frac{\partial \ln Y}{\partial \beta }\approx -\frac{\partial }{\partial \beta }\left( \xi V+2{{\xi }^{2}}B(T)V \right) \\

& \bar{N}={{\left( \frac{\partial \Psi }{\partial \alpha } \right)}_{\beta ,V}}\Rightarrow \xi ={{e}^{-\alpha }}{{\left( \frac{2\pi mkT}{{{\hbar }^{2}}} \right)}^{\frac{3}{2}}}\approx \frac{{\bar{N}}}{V}-2B(T){{\left( \frac{{\bar{N}}}{V} \right)}^{2}} \\

\end{align}

TeX (checked):

{\begin{aligned}&U={{\left({\frac {\partial \Psi }{\partial \beta }}\right)}_{\alpha ,V}}=-{\frac {\partial \ln Y}{\partial \beta }}\approx -{\frac {\partial }{\partial \beta }}\left(\xi V+2{{\xi }^{2}}B(T)V\right)\\&{\bar {N}}={{\left({\frac {\partial \Psi }{\partial \alpha }}\right)}_{\beta ,V}}\Rightarrow \xi ={{e}^{-\alpha }}{{\left({\frac {2\pi mkT}{{\hbar }^{2}}}\right)}^{\frac {3}{2}}}\approx {\frac {\bar {N}}{V}}-2B(T){{\left({\frac {\bar {N}}{V}}\right)}^{2}}\\\end{aligned}}

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\begin{aligned} U = {(\frac{\partial Ψ}{\partial β})}_{α, V} = - \frac{\partial \ln Y}{\partial β} \approx - \frac{\partial}{\partial β} (ξ V + 2 ξ^{2} B (T) V) \\ \bar{N} = {(\frac{\partial Ψ}{\partial α})}_{β, V} \Rightarrow ξ = e^{- α} {(\frac{2 π m k T}{ℏ^{2}})}^{\frac{3}{2}} \approx \frac{\bar{N}}{V} - 2 B (T) {(\frac{\bar{N}}{V})}^{2} \end{aligned}

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Identifiers

$U$

$Ψ$

$β$

$α$

$V$

$Y$

$β$

$β$

$ξ$

$V$

$ξ$

$B$

$T$

$V$

$\bar{N}$

$Ψ$

$α$

$β$

$V$

$ξ$

$e$

$α$

$π$

$m$

$k$

$T$

$\bar{N}$

$V$

$B$

$T$

$\bar{N}$

$V$

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