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Display information for equation id:math.2555.40 on revision:2555

* Page found: Das ideale Fermigas (eq math.2555.40)

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Das ideale Fermigas Eq: math.2555.40

Hash: e1e24a91ff2c42ce80105f14b03e56a6

TeX (original user input):

\begin{align}

& \frac{{{p}^{2}}}{2mkT}=y \\

& pdp=mkTdy \\

& \frac{\mu }{kT}=\eta =-\alpha  \\

& \bar{N}=\frac{\left( 2s+1 \right)}{2}\left( \frac{V}{{{h}^{3}}} \right)4\pi {{\left( 2mkT \right)}^{\frac{3}{2}}}\int_{0}^{\infty }{{}}dy\frac{{{y}^{\frac{1}{2}}}}{\left( {{e}^{y-\eta }}+1 \right)} \\

& U=\frac{\left( 2s+1 \right)}{2}\left( \frac{V}{{{h}^{3}}} \right)4\pi {{\left( 2mkT \right)}^{\frac{3}{2}}}kT\int_{0}^{\infty }{{}}dy\frac{{{y}^{\frac{3}{2}}}}{\left( {{e}^{y-\eta }}+1 \right)} \\

\end{align}

TeX (checked):

{\begin{aligned}&{\frac {{p}^{2}}{2mkT}}=y\\&pdp=mkTdy\\&{\frac {\mu }{kT}}=\eta =-\alpha \\&{\bar {N}}={\frac {\left(2s+1\right)}{2}}\left({\frac {V}{{h}^{3}}}\right)4\pi {{\left(2mkT\right)}^{\frac {3}{2}}}\int _{0}^{\infty }{}dy{\frac {{y}^{\frac {1}{2}}}{\left({{e}^{y-\eta }}+1\right)}}\\&U={\frac {\left(2s+1\right)}{2}}\left({\frac {V}{{h}^{3}}}\right)4\pi {{\left(2mkT\right)}^{\frac {3}{2}}}kT\int _{0}^{\infty }{}dy{\frac {{y}^{\frac {3}{2}}}{\left({{e}^{y-\eta }}+1\right)}}\\\end{aligned}}

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MathML (4.942 KB / 613 B) :

\begin{aligned} \frac{p^{2}}{2 m k T} = y \\ p d p = m k T d y \\ \frac{μ}{k T} = η = - α \\ \bar{N} = \frac{(2 s + 1)}{2} (\frac{V}{h^{3}}) 4 π {(2 m k T)}^{\frac{3}{2}} \int_{0}^{\infty} d y \frac{y^{\frac{1}{2}}}{(e^{y - η} + 1)} \\ U = \frac{(2 s + 1)}{2} (\frac{V}{h^{3}}) 4 π {(2 m k T)}^{\frac{3}{2}} k T \int_{0}^{\infty} d y \frac{y^{\frac{3}{2}}}{(e^{y - η} + 1)} \end{aligned}

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data-mjx-texclass="ORD"><mi>y</mi><mo>&#x2212;</mo><mi>&#x03B7;</mi></mrow></mrow></msup><mo>+</mo><mn>1</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

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Identifiers

$p$

$m$

$k$

$T$

$y$

$p$

$d$

$p$

$m$

$k$

$T$

$d$

$y$

$μ$

$k$

$T$

$η$

$α$

$\bar{N}$

$s$

$V$

$h$

$π$

$m$

$k$

$T$

$y$

$y$

$e$

$y$

$η$

$U$

$s$

$V$

$h$

$π$

$m$

$k$

$T$

$k$

$T$

$y$

$y$

$e$

$y$

$η$

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